neshaminy school district curriculum map: first grade math€¦ · 1 neshaminy school district...

42
1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math in Focus Curriculum (Teacher Guides, Student Workbook and Textbook, Teacher Resources – Reteach, Extra Practice, Assessments, Enrichment, School-Home Connections) Think Central - Online access to all Math in Focus materials listed above and Virtual Manipulatives Calendar Math, IXL Elementary Math Intervention- Found NSD Intranet Mathematical Practice Standards- Habits of Mind SMP.1 Make sense and persevere in solving problems. Realize that doing mathematics involves solving problems and discussing how they solved them. Explain to themselves the meaning of a problem and look for ways to solve it. Use concrete objects or pictures to help them conceptualize and solve problems. Check their thinking by asking themselves, “Does this make sense?” Willing to try other approaches. SMP.5 Use appropriate tools strategically. Begin to consider the available tools (including estimation) when solving a mathematical problem. Decide when certain tools might be helpful. Decide it might be best to use colored chips to model an addition problem. SMP.2 Reason abstractly and quantitatively. Recognize that a number represents a specific quantity. Connect the quantity to written symbols. Create a representation of a problem while attending to the meanings of the quantities (quantitative reasoning). SMP.6 Attend to precision. Develop their mathematical communication skills. Use clear and precise language in their discussions with others and when they explain their own reasoning. SMP.3 Construct viable arguments and critique the reasoning of others. Construct arguments using concrete referents, such as objects, pictures, drawings, and actions. Practice their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” “Explain your thinking,” and “Why is that true?” Explain their own thinking, but listen to others’ explanations. Decide if the explanations make sense and ask questions. SMP.7 Look for and make use of structure. Begin to discern a pattern or structure. For instance, if students recognize 12 + 3 = 15, then they also know 3 + 12 = 15 (Commutative property of addition). To add 4 + 6 + 4, the first two numbers can be added to make a ten, so 4 + 6 + 4 = 10 + 4 = 14. SMP.4 Model with mathematics. Experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations, etc. Connect the different representations and explain the connections. Use all of these representations as needed. SMP.8 Look for and express regularity in repeated reasoning. Notice repetitive actions in counting and computation, etc. When children have multiple opportunities to add and subtract “ten” and multiples of “ten” they notice the pattern and gain a better understanding of place value. Continually check their work by asking themselves, “Does this make sense?”

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Page 1: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

1

Neshaminy School District Curriculum Map First Grade Math Resources Available to Teachers for Instruction

Math in Focus Curriculum (Teacher Guides Student Workbook and Textbook Teacher Resources ndash Reteach Extra Practice Assessments Enrichment School-Home Connections)

Think Central - Online access to all Math in Focus materials listed above and Virtual Manipulatives

Calendar Math IXL

Elementary Math Intervention- Found NSD Intranet

Mathematical Practice Standards- Habits of Mind

SMP1 Make sense and persevere in solving problems

Realize that doing mathematics involves solving problems and discussing how they solved them

Explain to themselves the meaning of a problem and look for ways to solve it

Use concrete objects or pictures to help them conceptualize and solve problems

Check their thinking by asking themselves ldquoDoes this make senserdquo

Willing to try other approaches

SMP5 Use appropriate tools strategically

Begin to consider the available tools (including estimation) when solving a mathematical problem

Decide when certain tools might be helpful

Decide it might be best to use colored chips to model an addition problem

SMP2 Reason abstractly and quantitatively

Recognize that a number represents a specific quantity

Connect the quantity to written symbols

Create a representation of a problem while attending to the meanings of the quantities (quantitative reasoning)

SMP6 Attend to precision

Develop their mathematical communication skills

Use clear and precise language in their discussions with others and when they explain their own reasoning

SMP3 Construct viable arguments and critique the reasoning of others

Construct arguments using concrete referents such as objects pictures drawings and actions

Practice their mathematical communication skills as they participate in mathematical discussions involving questions like ldquoHow did you get thatrdquo ldquoExplain your thinkingrdquo and ldquoWhy is that truerdquo

Explain their own thinking but listen to othersrsquo explanations

Decide if the explanations make sense and ask questions

SMP7 Look for and make use of structure

Begin to discern a pattern or structure For instance if students recognize 12 + 3 = 15 then they also know 3 + 12 = 15 (Commutative property of addition) To add 4 + 6 + 4 the first two numbers can be added to make a ten so 4 + 6 + 4 = 10 + 4 = 14

SMP4 Model with mathematics

Experiment with representing problem situations in multiple ways including numbers words (mathematical language) drawing pictures using objects acting out making a chart or list creating equations etc

Connect the different representations and explain the connections

Use all of these representations as needed

SMP8 Look for and express regularity in repeated reasoning

Notice repetitive actions in counting and computation etc When children have multiple opportunities to add and subtract ldquotenrdquo and multiples of ldquotenrdquo they notice the pattern and gain a better understanding of place value

Continually check their work by asking themselves ldquoDoes this make senserdquo

2

Mathematical Content Standards

PA Common Core Standard Common Core State Standard

Numbers and Operations

CC211 B1 Extend the counting sequence to read and write numerals to represent objects

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

CC211 B2 Use place value concepts to represent amounts of tens and ones and to compare two digit numbers

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones)

1NBT3 Compare two two-digit numbers based on meanings of the tens and ones digits recording the results of comparisons with the symbols gt = and lt

CC211 B3 Use place value concepts and properties of operations to add and subtract within 100

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten

1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used

1NBT6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used

Operations and Algebraic Thinking

CC221 A1 Represent and solve problems involving addition and subtraction within 20

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem

1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem

1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)

CC221 A2 Understand and apply properties of operations and the relationship between addition and subtraction

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

3

Geometry

CC231 A1 Compose and distinguish between two- and three-dimensional shapes based on their attributes

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes

1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo)

CC231 A2 Use the understanding of fractions to partition shapes into halves and quarters

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

Measurement and Data

CC241 A1 Order lengths and measure them both indirectly and by repeating length units

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object

1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps

CC241 A2 Tell and write time to the nearest half hour using both analog and digital clocks

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

CC241 A4 Represent and interpret data using tablescharts

1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

4

Chapter 1 Numbers to 10

Duration 8 days

Essential Questions How does counting help people Why are numbers important Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting and comparing numbers to 10

Use countable objects to develop the association between the physical representation of the number the number symbol and the number word

Besides counting the objects in a set and creating a set with a given number of objects children also differentiate between numbers of objects in sets a skill that forms a basis for number comparison

Learn to recognize relationships between numbers such as 1 more than and 1 less than

Kindergarten

Count and write numbers 0-20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Zero 0 Six 6

One 1 Seven 7

Two 2 Eight 8

Three 3 Nine 9

Four 4 Ten 10

More Less than

Fewer Pattern

Greater than More than

AugustSeptember Review -Counting and reading numbers and writing numerals Preview -Part and whole relationships for different numbers Practice -Counting and comparing numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

11 Counting to 10 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision

Connecting cubes

Counters

Ten Frame (TR01)

12 Comparing Numbers CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes

Counters

Horizontal Ten Frames (TR02)

Shoes and Socks Cut-Out (TR02)

Scissorsglue

13 Making Number Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Counters

Ten Frame (TR01)

5

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells that the answer is to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer to the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggest that same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Put students into small groups so you have 10 groups Give each group a different number 1-10 Have the group write a sentence and draw a corresponding picture for their number (Ex The octopus has 8 legs) Then put all of the pictures together to make a class counting book Art Discuss the colors on a color wheel (yellow orange red violetpurple blue and green) Have students draw a number pattern with all six colors (Ex One red circle two orange circles three yellow circles etc) The students can choose to use an increasing or decreasing pattern They should write the number that coordinates with that part of the pattern

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 2: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

2

Mathematical Content Standards

PA Common Core Standard Common Core State Standard

Numbers and Operations

CC211 B1 Extend the counting sequence to read and write numerals to represent objects

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

CC211 B2 Use place value concepts to represent amounts of tens and ones and to compare two digit numbers

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones)

1NBT3 Compare two two-digit numbers based on meanings of the tens and ones digits recording the results of comparisons with the symbols gt = and lt

CC211 B3 Use place value concepts and properties of operations to add and subtract within 100

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten

1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used

1NBT6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used

Operations and Algebraic Thinking

CC221 A1 Represent and solve problems involving addition and subtraction within 20

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem

1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem

1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)

CC221 A2 Understand and apply properties of operations and the relationship between addition and subtraction

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

3

Geometry

CC231 A1 Compose and distinguish between two- and three-dimensional shapes based on their attributes

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes

1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo)

CC231 A2 Use the understanding of fractions to partition shapes into halves and quarters

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

Measurement and Data

CC241 A1 Order lengths and measure them both indirectly and by repeating length units

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object

1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps

CC241 A2 Tell and write time to the nearest half hour using both analog and digital clocks

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

CC241 A4 Represent and interpret data using tablescharts

1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

4

Chapter 1 Numbers to 10

Duration 8 days

Essential Questions How does counting help people Why are numbers important Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting and comparing numbers to 10

Use countable objects to develop the association between the physical representation of the number the number symbol and the number word

Besides counting the objects in a set and creating a set with a given number of objects children also differentiate between numbers of objects in sets a skill that forms a basis for number comparison

Learn to recognize relationships between numbers such as 1 more than and 1 less than

Kindergarten

Count and write numbers 0-20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Zero 0 Six 6

One 1 Seven 7

Two 2 Eight 8

Three 3 Nine 9

Four 4 Ten 10

More Less than

Fewer Pattern

Greater than More than

AugustSeptember Review -Counting and reading numbers and writing numerals Preview -Part and whole relationships for different numbers Practice -Counting and comparing numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

11 Counting to 10 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision

Connecting cubes

Counters

Ten Frame (TR01)

12 Comparing Numbers CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes

Counters

Horizontal Ten Frames (TR02)

Shoes and Socks Cut-Out (TR02)

Scissorsglue

13 Making Number Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Counters

Ten Frame (TR01)

5

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells that the answer is to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer to the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggest that same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Put students into small groups so you have 10 groups Give each group a different number 1-10 Have the group write a sentence and draw a corresponding picture for their number (Ex The octopus has 8 legs) Then put all of the pictures together to make a class counting book Art Discuss the colors on a color wheel (yellow orange red violetpurple blue and green) Have students draw a number pattern with all six colors (Ex One red circle two orange circles three yellow circles etc) The students can choose to use an increasing or decreasing pattern They should write the number that coordinates with that part of the pattern

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 3: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

3

Geometry

CC231 A1 Compose and distinguish between two- and three-dimensional shapes based on their attributes

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes

1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo)

CC231 A2 Use the understanding of fractions to partition shapes into halves and quarters

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

Measurement and Data

CC241 A1 Order lengths and measure them both indirectly and by repeating length units

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object

1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps

CC241 A2 Tell and write time to the nearest half hour using both analog and digital clocks

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

CC241 A4 Represent and interpret data using tablescharts

1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

4

Chapter 1 Numbers to 10

Duration 8 days

Essential Questions How does counting help people Why are numbers important Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting and comparing numbers to 10

Use countable objects to develop the association between the physical representation of the number the number symbol and the number word

Besides counting the objects in a set and creating a set with a given number of objects children also differentiate between numbers of objects in sets a skill that forms a basis for number comparison

Learn to recognize relationships between numbers such as 1 more than and 1 less than

Kindergarten

Count and write numbers 0-20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Zero 0 Six 6

One 1 Seven 7

Two 2 Eight 8

Three 3 Nine 9

Four 4 Ten 10

More Less than

Fewer Pattern

Greater than More than

AugustSeptember Review -Counting and reading numbers and writing numerals Preview -Part and whole relationships for different numbers Practice -Counting and comparing numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

11 Counting to 10 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision

Connecting cubes

Counters

Ten Frame (TR01)

12 Comparing Numbers CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes

Counters

Horizontal Ten Frames (TR02)

Shoes and Socks Cut-Out (TR02)

Scissorsglue

13 Making Number Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Counters

Ten Frame (TR01)

5

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells that the answer is to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer to the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggest that same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Put students into small groups so you have 10 groups Give each group a different number 1-10 Have the group write a sentence and draw a corresponding picture for their number (Ex The octopus has 8 legs) Then put all of the pictures together to make a class counting book Art Discuss the colors on a color wheel (yellow orange red violetpurple blue and green) Have students draw a number pattern with all six colors (Ex One red circle two orange circles three yellow circles etc) The students can choose to use an increasing or decreasing pattern They should write the number that coordinates with that part of the pattern

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 4: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

4

Chapter 1 Numbers to 10

Duration 8 days

Essential Questions How does counting help people Why are numbers important Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting and comparing numbers to 10

Use countable objects to develop the association between the physical representation of the number the number symbol and the number word

Besides counting the objects in a set and creating a set with a given number of objects children also differentiate between numbers of objects in sets a skill that forms a basis for number comparison

Learn to recognize relationships between numbers such as 1 more than and 1 less than

Kindergarten

Count and write numbers 0-20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Zero 0 Six 6

One 1 Seven 7

Two 2 Eight 8

Three 3 Nine 9

Four 4 Ten 10

More Less than

Fewer Pattern

Greater than More than

AugustSeptember Review -Counting and reading numbers and writing numerals Preview -Part and whole relationships for different numbers Practice -Counting and comparing numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

11 Counting to 10 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision

Connecting cubes

Counters

Ten Frame (TR01)

12 Comparing Numbers CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes

Counters

Horizontal Ten Frames (TR02)

Shoes and Socks Cut-Out (TR02)

Scissorsglue

13 Making Number Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Counters

Ten Frame (TR01)

5

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells that the answer is to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer to the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggest that same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Put students into small groups so you have 10 groups Give each group a different number 1-10 Have the group write a sentence and draw a corresponding picture for their number (Ex The octopus has 8 legs) Then put all of the pictures together to make a class counting book Art Discuss the colors on a color wheel (yellow orange red violetpurple blue and green) Have students draw a number pattern with all six colors (Ex One red circle two orange circles three yellow circles etc) The students can choose to use an increasing or decreasing pattern They should write the number that coordinates with that part of the pattern

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 5: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

5

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells that the answer is to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer to the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggest that same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Put students into small groups so you have 10 groups Give each group a different number 1-10 Have the group write a sentence and draw a corresponding picture for their number (Ex The octopus has 8 legs) Then put all of the pictures together to make a class counting book Art Discuss the colors on a color wheel (yellow orange red violetpurple blue and green) Have students draw a number pattern with all six colors (Ex One red circle two orange circles three yellow circles etc) The students can choose to use an increasing or decreasing pattern They should write the number that coordinates with that part of the pattern

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 6: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

6

Chapter 2 Number Bonds

Duration 6 days

Essential Questions How can we show the connection between addition and subtraction Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Use number bonds to show the parts and whole for a given number

Using countable objects and a math balance children are led to see how a given number can be made from two smaller numbers

This part-whole analysis forms the basis for the concept of adding two numbers to give another number in Chapter 3

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Show parts and whole numbers using number bonds

Grade 2

Use part-part-whole bar models in addition and subtraction

Part Whole

Number bond

AugustSeptember

Review - Read and write numbers Preview - Addition strategies and number stories Practice - Part and whole relationships for different numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

21 Making Number Bonds CC221 A2 (OA3) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Math balance Weights

Eureka Lessons Eurekam1tal1 EurekaM1TAL2 EurekaM1T1L3 COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA The word bond has multiple meanings Discuss with the class what the meanings of the word could be (joining a close relationship and a material that holds parts together like Velcro) Explain to students that a number bond does the same thing it connects numbers together Science Discuss with students how materials when combined together make a mixture Solids and liquids can be mixed together and sometimes the solid dissolves into the liquid (ex chocolate sauce and milk make chocolate milk) Demonstrate examples of this in class Use a number bond diagram to represent the two parts becoming the whole

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 7: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

7

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 8: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

8

Chapter 3 Addition Facts to 10

Duration 8 days Essential Questions When given a number sentence how do I know what kind of story will match it How does seeing the relationship between a number sentence and a math story help me become a better mathematician

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic addition facts and strategies

Add by counting on and by using number bonds

Learn to construct addition stories from pictures and solve real-world problems by writing addition sentences

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Grade 2

Add 3-digit to 3-digit numbers to 1000

Add Addition sentence

Plus (+) More than

Equal to (=) Addition story

October Activities Review - Part and whole relationships for different numbers Preview - Subtraction concepts and the relationship between addition and subtraction Practice - Addition strategies and number stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

31 Ways to Add 32 Making Addition Stories 33 Real-World Problems Addition

CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Number Cards (TR03)

Eureka Lessons EurekaM1TBL4 EurekaM1TBL5 EurekaM1TBL6 EurekaM1TBL7 ILLUSTRATIVEMATHEMATICS COMMONCORESHEETS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 9: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

9

Cross-Curricular Connections

ReadingELA Review with students that a sentence is a group of words that expresses an idea and makes a statement Explain that sentences include some kind of action Connect these ideas to addition sentences An addition sentence makes a statement but it uses numbers and symbols Point out that the action in an addition sentence is to add Ask children to give examples of sentences and addition sentences Social Studies Apply the part-whole relationship to geography concepts Discuss the relationships below and others that the students may know World (Whole) The 7 Continents (Part) North America (Whole) Canada United States and Mexico (Parts) United States (Whole) The 50 States (Parts)

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 10: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

10

Chapter 4 Subtraction Facts to 10

Duration 11 days

Essential Questions How does seeing the relationship between a number sentence and a math story help me become a better mathematician Explain the relationship between addition and subtraction

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Basic subtraction facts

Use strategies such as the take-away concept Number bonds Counting on and counting back to identify and learn subtraction facts

Write subtraction sentences to represent familiar situations and begin to see the inverse relationship between addition and subtraction by using number bonds

Kindergarten

Represent subtraction stories with small whole numbers

Grade 1

Subtract 2-digit numbers to 100 Grade 2

Subtract 3-digit numbers to 1000

Take away Subtraction sentence

Subtract Subtraction story

Minus (-) Fact family

Less than

October Activities Review - Geometric patterns and attributes of rectangles Preview - Number patterns and length comparisons using longer shorter and the same length as Practice - Sums and differences involving the number 6 and writing addition and subtraction sentences

Content SkillsCompetencies PA Standard Hands on Learning Resources 41 Ways to Subtract CC211 B1 (NBT1)

Extend the counting sequence to read and write numerals to represent objects CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Counting tape Ten Frame(TR01)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

42 Making Subtraction Stories 43 Real- World Problems Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA5 OA6)

Counters Math balance and weights Counting tape Subtraction Action by Loreen Leedy

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 11: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

11

Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP8 Look for and express regularity in repeated reasoning

44 Making Fact Families CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting Cubes NumberSymbol Cards (TR04) Clear plastic container

44a True and False Number Sentences CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Cross-Curricular Connections

ReadingELA Read Aloud Subtraction Action by Loreen Leedy about Miss Prime and her studentsrsquo subtraction adventures at the fair As a class brainstorm subtraction story ideas Choose one of them to be the setting for your class subtraction story book

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 12: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

12

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

End of the 1st Marking Period 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol or the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 13: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

13

Chapter 5 Shapes and Patterns

Duration 14 days

Essential Question Why do you think we are talking about halves and quarters in the chapter about shapes Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Plane and solid shapes in patterns and the real world

Classify and compare plane and solid shapes based on their geometric properties using the appropriate vocabulary for describing shapes

Make composite shapes models and patterns with these shapes

Kindergarten

Identify and name four basic plane shapes

Grade 1

Explore identify and compare plane and solid shapes in patterns and in the real world

Grade 2

Describe extend and create two- and three- dimensional shape patterns

Plane shapes Corner Circle Sort Triangle Color Square Alike Rectangle Size Side Different Solid shapes Pyramid Rectangular prism Stack Cube Slide Sphere Roll Cone Repeating pattern Cylinder

November Activities Review - Comparing and ordering numbers Preview - Measuring of length Practice - Attributes of triangles and finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

51 Exploring Plane Shapes CC231 A1 (G1 G2) Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Attribute blocks 2 Squares to fold (TR06) Shapes to fold (TR07)

COMMONCORESHEETSCOM ILLUSTRATIVEMATHEMATICS

51a Exploring Plane Shapes (Focus Lesson) CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

52 Exploring Solid Shapes CC231 A1 (G1) Compose and distinguish between two- and three-dimensional shapes based on their attributes SMP4 Model with mathematics

Geometric shapes Table of Shapes (TR08)

53 Making Pictures and Models with Shapes CC231 A1 (G2) Attribute blocks

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 14: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

14

Compose and distinguish between two- and three-dimensional shapes based on their attributes CC231 A2 (G3) Use the understanding of fractions to partition shapes into halves and quarters SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision

Geometric solids Shapes to combine for the teacher (TR09) Shapes to cut out(TR10) Table of solids(tR11)

54 Seeing Shapes Around Us SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics

Geometric solids Colored pipe-cleaner Common objects

55 Making Patterns with Plane Shapes SMP5 Use appropriate tools strategically Attribute blocks

56 Making Patterns with Solid Shapes SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Geometric solids

Misconceptions Proper Conceptions

Students may think that a square that has been rotated so that the sides form 45-degree angles with the vertical diagonal is no longer a square but now a diamond

Some students may think that the size of the equal shares is directly related to the number of equal shares (Ex Fourths are larger than halves because there are four fourths in a whole while only two halves in a whole)

Students need to have experiences with shapes in different orientations

Students need to focus on the change in the size of the fractional parts

Cross-Curricular Connections

ReadingELA Discuss with students some of the common meanings of the word shape (noun ndash form or figure has the shape of a rectangle noun ndash condition a car in good shape verb ndash form into a shape to shape dough in a ball) Encourage students to name shapes they see in the classroom PE Clear an area of the room or move to an open area possibly outside Assign a leader and ask children to jog along a route that has the shape of a rectangle Continue by assigning new leaders each time and having students to jog along routes that have the shape of a square triangle circle or any combination of those shapes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G1 Distinguish between defining attributes (eg triangles are closed and three-sided) versus non-defining attributes (eg color orientation overall size) build and draw shapes to possess defining attributes 1G2 Compose two-dimensional shapes (rectangles squares trapezoids triangles half-circles and quarter-circles) or three-dimensional shapes (cubes right rectangular prisms right circular cones and right circular cylinders) to create a composite shape and compose new shapes from the composite shape (Note Students do not need to learn formal names such as ldquoright rectangular prismrdquo) 1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 15: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

15

Chapter 6 Ordinal Numbers and Position Duration 0 (Addressed in Calendar Math)

Essential Question How do ordinal numbers and position words help us in our lives Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Describing order and position using ordinal numbers and words

Use ordinal numbers from first to tenth to describe order and position of objects or persons

Enhance their vocabulary with position words including in front of and other to describe the position of something relative to another

Kindergarten

Know ordinal numbers first to third and some position words

Grade 1

Describe order and position using numbers and words

Grade 2

Describe terms in patterns and steps in games and algorithms

First Tenth

Second Last

Third Before

Fourth After

Fifth Between

Sixth Above

Seventh Below

Eighth Under

Next to Near

In front of Down

Up Right

Ninth Behind

Left

November Activities Review - Place-value concepts Preview - Patterns Practice - Ordinal numbers

Content SkillsCompetencies PA Standard Hands on Learning Resources

61 Ordinal Numbers Connecting cubes

62 Position Words SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Ordinal Position Table (TR12)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Read Aloud Letrsquos Find Rain Forest Animals Up Down Around by Janice Behrens which includes simple questions using positional words along with photos that answer the questions Have students choose a position word from the story create a drawing to illustrate the word and write a sentence to accompany the drawing Science Display in a flow chart this summary of the scientific method (1 Ask a question 2 Do research 3 Make a hypothesis 4 Plan and do a fair test 5 Collect and record data 6 Study the results 7 Make and share your conclusion) Tell students that this is one way to describe the scientific method Ask students to read the information in the flow chart using ordinal words to introduce each step

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 16: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

16

Chapter 7 Numbers to 20

Duration 9 days

Essential Question What are different ways to count Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 20 Count to 20 using pictorial representation of concrete objects

Recognize numbers 10-20 as 1 group of ten and a particular number of ones

Compare numbers and establish number relationships such as greater than and less than

Identify number patterns from these number relationships and extend the patterns

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Eleven Nineteen

Twelve Twenty

Thirteen Place-value chart

Fourteen Greatest

Fifteen Least

Sixteen Order

Seventeen

Eighteen

December Activities Review - Attributes of solid shapes Preview - Comparing numbers to 31 Practice - Finding patterns

Content SkillsCompetencies PA Standard Hands on Learning Resources

71 Counting to 20 72 Place Value

CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Number cube Unit cubes Ten rods Ten Frames (TR01) Craft sticks Place-Value Chart(TR13) Clear containers

73 Comparing Numbers CC211 B2 (NBT2A NBT2B) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Connecting cubes Unit cubes Place-Value Chart (TR13) counters

74 Making Patterns and Ordering Numbers CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2B NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP7 Look for and make use of structure

Connecting cubes Place-Value Chart (TR13)

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 17: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

17

SMP8 Look for and express regularity in repeated reasoning

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

A common misconception is that the commutative property applies to subtraction

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 + 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Cross-Curricular Connections

ReadingELA Review with students that adding a word ending such as ndasher and ndashest changes the meaning of the word Provide examples such as bigger and biggest Tell students that some vocabulary words in this chapter include the word ending ndashteen which means ten more than Use this information to discuss the meanings of the number words thirteen through nineteen Art Remind students that numbers can be shown in terms of place value (ex 15 is 1 ten and 5 ones) Explain that the world value is also used in art Every color has value and the value of a color can be changed by making it darker or lighter When white is mixed with a color it gets lighter When black is mixed with a color it gets darker If possible have students mix different paint colors with black and white paint

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 18: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

18

Chapter 8 Addition and Subtraction Facts to 20

Duration 15 - 17 days

Essential Question How do you know which strategy to use for different types of problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting within 20 using different strategies

Apply strategies such as grouping into a ten and ones number bonds and using doubles facts to add and subtract

Use addition and subtraction sentences to solve real-world problems

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100

Grade 2

Add 3-digit to 3-digit numbers up to 1000

Group Doubles fact

Same Doubles plus one

December Activities Review - Comparing and ordering numbers Preview - Telling time Practice - Addition and subtraction stories

Content SkillsCompetencies PA Standard Hands on Learning Resources

81 Ways to Add 82 Ways to Subtract 83 Real-World Problems Addition and Subtraction Facts

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters Ten Frame (TR01) Spinner base

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means is the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 +7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 19: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

19

A common misconception is that the commutative property applies to subtraction

Cross-Curricular Connections

ReadingELA In this chapter students use doubles and doubles plus one facts to add Tell students that the word double can be used as a noun verb and adjective Present several examples to demonstrate the multiple meanings of the word For example use these sentences A doubles fact is 5 + 5 = 10 The entrance to the school has double doors The baseball player hit a double She doubled the cookie recipe Drama Put students into small groups Have them write either an addition or subtraction story that they can act out Groups should write the problem and also create a script for their act Invite groups to present their acts As a class discuss each act Ask students to describe the problem Write the problem on the board and find the solution with the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA4 understand subtraction as an unknown-addend problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 20: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

20

Chapter 9 Length

Duration 9 days

Essential Question How can measuring length help you in your life Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing the height and length of things and measuring

Compare lengths and heights using terms such as talltallertallest longlongerlongest and shortshortershortest

Use common objects as non-standard units to measure and compare length

Kindergarten

Compare and order lengths and heights using non-standard units

Grade 1

Compare the height and length of more than two things

Measure and compare using non-standard units

Grade 2

Measure and compare length and height in metric and customary units

Tall Long

Taller Longer

Tallest Longest

Short Start line

Shorter About

Shortest Unit

January Activities Review - Using the doubles + 1 addition strategies Preview - Picture of graphs Practice - Comparing quantities

Content SkillsCompetencies PA Standard Hands on Learning Resources

91 Comparing two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes Paper clips

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

92 Comparing more than two things CC241 A1 (MD1) Order lengths and measure them both indirectly and by repeating length units SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Connecting cubes

93 Using a Start Line SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Fish Cut-Outs(TR16) Copy of Strips(TR17)

94 Measuring Things 95 Finding Lengths in Units

CC241 A1 (MD1 MD2) Order lengths and measure them both indirectly and by repeating length units SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Copy of Strip Paper(TR17) Strips for Measuring(TR18) Craft sticks Paper clips Measurement Table(TR19) Long umbrella for demonstration

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 21: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

21

Misconceptions Proper Conceptions

Students may view the measurement process as a procedural and counting task Students need numerous experiences measuring lengths with student-made tapes or rulers with numbers in the center of the spaces They may have gaps or overlaps with the units they are using to measure They may not understand that the units used to measure must be the same size

In order for students to be able to compare objects students need to understand that length is measured from one end point to another end point They determine which of two objects is longer by physically aligning the objects Typical language includes taller shorter longer and higher When students use bigger or smaller as a comparison they should explain what they mean by the word Some objects may have more than one measurement of length so students identify the length they are measuring Both the length and the width of an object are measurements of length

Cross-Curricular Connections

ReadingELA The first three lessons in this chapter focus on comparative and superlative vocabulary Remind students that the ndasher ending means more and the ndash est ending means most Take this opportunity to preview the vocabulary in the chapter (tall short and long with ndasher and ndashest endings) Encourage students to name other comparatives and superlatives that they know Social Studies Point out the locations of mountains and rivers on a map of the United States For example Three tall mountains in the United States are Mt McKinley (Alaska) Mt Whitney (California) and Mt Elbert (Colorado) Three long rivers are the Missouri the Mississippi and the Rio Grande The mountains and rivers are listed in decreasing order Use the terms talltallertallest and longlongerlongest to compare these mountains and rivers

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD1 Order three objects by length compare the lengths of two objects indirectly by using a third object 1MD2 Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps 1MD3 Tell and write time in hours and half-hours using analog and digital clocks

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 22: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

22

Chapter 10 Weight

Duration 9 days

Essential Question Can the weight of items be compared and measured with non-standard units Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Comparing and measuring weights using non-standard units

Compare weights using terms such as lightlighterlightest and heavyheavierheaviestas heavy as

Learn to measure using a balance

Use common objects as non-standard units to measure and compare weight

Kindergarten

Compare and order weights of things Grade 1

Compare the weights of more than 2 things

Measure and compare using non-standard units

Grade 2

Measure and compare mass using

standard metric units

Heavy Lighter

heavier Lightest

Heaviest Weight

Light As heavy as

Unit

January Activities Review - Position words Preview - Mental math strategies Practice - Comparing

Content SkillsCompetencies PA Standard Hands on Learning Resources

101 Comparing Things SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Balance scale calculator Weight table (TR22)

102 Finding the Weight of Things 103 Finding Weight in Units

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Balance scale Connecting cubes Weight table (TR22)

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA This chapter includes questions about comparing weights Review the use of periods and question marks Write the following on the board Which is heavier (lighter) the ______ or the _____ The _______ is heavier (lighter) than the ________ Model how to complete the sentences to compare two classroom objects Have students write a question and answer to complete the weight of two objects Science Tell students that scientists measure things in different ways for example by weighing it Give groups of students a balance scale and different objects that are about the same size such as a rock a Styrofoam ball a plastic bag with rice etc Have students make hypotheses about which objects are heavierlighter than one another Encourage groups to use the balance to test their hypotheses and report the results

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 23: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

23

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 24: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

24

Chapter 11 Picture Graphs and Bar Graphs

Duration 8 days

Essential Question How can you organize and collect data

Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Displaying data using picture graphs tally charts And bar graphs Understand data presented in the form of picture graphs tally charts and bar graphs Interpret and make sense of the data from the diagrams

Kindergarten

Making reading and interpreting picture graphs

Grade 1

Reading and interpreting picture graphs tally charts and bar graphs

Grade 2

Reading and interpreting picture graphs with scales

Data Picture graph

More Most

Fewer Fewest

Tally mark Tally chart

Bar graph

November Activities Review - Place value concepts and counting to 20 Preview - Counting by tens Practice - Interpreting data shown on picture graphs

Content SkillsCompetencies PA Standard Hands on Learning Resources

111 Simple Picture Graphs 112 More Picture Graphs 113 Tally Charts and Bar Graphs

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC241 A4 (MD4) Represent and interpret data using tablescharts SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Cut outs or actual bows 1-6 number cube Picture Graphs(TR23) Connecting cubes Tally Chart (TR24) Tally Chart and Bar Graph (TR24)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

Misconceptions Proper Conceptions

NA NA

Cross-Curricular Connections

ReadingELA Remind students that words can have similar or opposite meanings Write these words on the board more most fewer fewest Ask students to identify the word opposites Then give pairs of children several counters Tell them to make groups with different numbers of counters Ask them to use the word opposites to describe groups of counters Science Display a container with a number of recyclable glass paper metal and plastic items Discuss with students the importance of recycling to protect the environment Take each item out of the container and ask children in which category it belongs After all of the items have been sorted put students in small groups to make a pictograph that shows the number of each kind of recyclable item

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers 1MD4 Organize represent and interpret data with up to three categories ask and answer questions about the total number of data points how many in each category and how many more or less are in one category than in another

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 25: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

25

Chapter 12 Numbers to 40

Duration 7 days

Essential Question How does the position of the digit affect the value of the number

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering numbers to 40

Count as well as read and write numbers to 40

Use place-value charts to show numbers to 40

Learn to compare and order numbers to 40 by classifying them into same tens or different tens categories

Identify number patterns by adding or subtracting

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Twenty-one Twenty-two

Twenty-three Forty

Counting tape

February Activities Review - Collecting and recording data Preview - Telling time to the hour and half hour Practice - Grouping and counting by tens

Content SkillsCompetencies PA Standard Hands on Learning Resources

121 Counting up to 40 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP5 Use appropriate tools strategically

Connecting cubes

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

122 Place Value 123 Comparing Ordering and Patterns

CC221 A2 (OA8) Understand and apply properties of operations and the relationship between addition and subtraction CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP1 Make sense and persevere in solving problems

Connecting Cubes Place-Value Chart (TR13) Blank Counting Tape (TR20)

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 26: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

26

SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically SMP7 Look for and make use of structure

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

A second misconception that many students have is that it is valid to assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Assign each student a number from 20 to 40 pairing some students with the greater numbers if necessary Have each student draw a picture and write a sentence to illustrate their number (Ex Twenty leaves fall from a tree) The page should include the number in standard and word form Display the number pages in order on the wall or put them together to make a class number book PE Review with students how to do some common exercises (ex Sit-ups jumping jacks squats etc) Put students with a partner to perform an exercise of their choice While one student performs a maximum of 40 repetitions the partner counts Partners reverse roles and repeat Finally each student records the number of repetitions and the name of the exercise that he or she performed

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral 1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 27: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

27

Chapter 13 Addition and Subtraction to 40 Duration 17 - 19 days

Essential Questions What are different ways to add and subtract Why is it important to know your basic

facts automatically

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Addition and subtraction of whole numbers with or without regrouping

Add with or without regrouping

Subtract with or without regrouping

Add three 1-digit numbers

Solve real-world problems involving addition and subtraction

Kindergarten

Represent addition stories with small and whole numbers Represent subtraction stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers to 100 Subtract 2-digit numbers from numbers to 100

Grade 2

Add 3-digit to 3-digit numbers to 1000 Subtract 3-digit numbers from numbers to 1000

Count on Place-value chart

Regroup Count back

March Activities Review - Place value concepts Preview - Using a calendar Practice - Real-world addition and subtraction problems

Content SkillsCompetencies PA Standard Hands on Learning Resources

131 Addition Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

COMMONCORESHEETS ILLUSTRATIVEMATHEMATICS Engage NY

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 28: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

28

132 Addition with Regrouping

CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

133 Subtraction Without Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA5 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA4 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

134 Subtraction With Regrouping CC211 B2 (NBT2A) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA4 OA7 OA8)

Counters connecting cubes Base-ten blocks Place-Value Chart(TR13) Blank Counting Tape (TR20)

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 29: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

29

Understand and apply properties of operations and the relationship between addition and subtraction SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

135 Adding Three Numbers CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA3 OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Math balance and weights Connecting cubes or counters Base-ten blocks

136 Real-World Problems Addition and Subtraction

CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA2 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP8 Look for and express regularity in repeated reasoning

Connecting cubes

Misconceptions Proper Conceptions

Many students misunderstand the meaning of the equal sign The equal sign means ndashis the same as but most primary students believe the equal sign tells you that the answer is coming up to the right of the equal sign This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right

First graders need to see equations written multiple ways (Ex 5 + 7 = 12 and 12 = 5 = 7)

Providing problems in which key words (ex Left) are used to represent different operations is essential Students need to analyze word problems and avoid using key words to solve them

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 30: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

30

Many students assume that a key word or phrase in a problem suggests the same operation will be used every time (Ex The word left means to subtract)

Students ignore the need for regrouping when subtracting with numbers 0-20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

step using mathematical drawings ten frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

Cross-Curricular Connections

ReadingELA Remind students that beginnings and endings can be added to base words to make new words Write regrouping on the board Tell students that his word includes a base word a beginning and an ending Challenge them to identify the three word parts Explain that re- means again Group and regroup a set of counters to demonstrate the meanings of grouping and regrouping Social Studies Discuss the necessity of working to make money for food housing etc Tell students that people save money they earn from working Demonstrate the following problem Juan saves ten cents each week How much does he save in three weeks 10 + 10 + 10 = 30 Have students work in groups to create their own problems about saving or spending money Have groups exchange and solve each otherrsquos problems

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2) 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 31: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

31

Chapter 14 Mental Math Strategies

Duration 7 days

Essential Question When should you use mental math Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Number Bonds are helpful when adding and subtracting mentally

Add mentally by using double facts and the strategies of add the ones or add the tens

Subtract mentally by recalling number bonds and using the strategies of subtract the ones or subtract the tens

Kindergarten

Find parts and wholes in addition and subtraction stories

Grade 1

Use number bonds to develop basic facts and mental math strategies to add and subtract 1- and 2-digit numbers

Grade 2

Use number bonds and bar models to develop mental-math strategies to add and subtract 3-digit numbers

Mentally Doubles fact

March Activities Review - Place value concepts and comparing and ordering numbers Preview - Using a calendar Practice - Addition and subtraction concepts and mental math

Content SkillsCompetencies PA Standard Hands on Learning Resources 141 Mental Addition 142 Mental Subtraction

CC211 B3 (NBT4 NBT5) Use place value concepts and properties of operations to add and subtract within 100 CC221 A1 (OA1 OA6) Represent and solve problems involving addition and subtraction within 20 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Counters Number Cards(TR26) and (TR27) Number Bonds (TR21) Transparency Spinner Spinner Base (TR28) Number Cards(TR29)

Misconceptions Proper Conceptions

Students ignore the need for regrouping when subtracting with numbers 0- 20 and think that they should always subtract a smaller number from a larger number (Ex 15-7 is 7-5=2 and 1-0=1 thus 15-7=12)

Students need to relate their understanding of place-value concepts and grouping in tens and ones to their steps for subtraction They need to show these relationships for each step using mathematical drawings ten-frames or base-ten blocks so they can understand an efficient strategy for multi-digit subtraction

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 32: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

32

Cross-Curricular Connections

ReadingELA Read Aloud One Nation America by the Numbers by Devlin Scillian and illustrator Pam Carroll The story presents numbers in the context of American symbols As you read use the numbers and examples to present addition and subtraction problems that children can solve using mental math Social Studies Share with students these facts about the United States flag It has 7 red stripes and 6 white stripes There are 50 stars to represent the 50 states Have students use mental math to answer these questions How many stripes are there in all How many more stars are there than red stripes How many more stars are there than white stripes

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1NBT5 Given a two-digit number mentally find 10 more or 10 less than the number without having to count explain the reasoning used 1OA1 Use Addition and subtraction within 20 to solve word problems involving situations of adding to taking from putting together taking apart and comparing with unknowns in all positions eg by using objects drawings and equations with a symbol for the unknown number to represent the problem 1OA6 Add and subtract within 20 demonstrating fluency for addition and subtraction within 10 Use strategies such as counting on making ten (eg 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (eg 13 ndash 4 = 13 ndash 3 ndash 1 = 10 ndash 1 = 9) using the relationship between addition and subtraction (eg knowing that 8 + 4 = 12 one knows 12 ndash 8 = 4) and creating equivalent but easier or known sums (eg adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 33: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

33

Chapter 15 Calendar and Time

Duration 7 days

Essential Question Why is telling time important Big IdeasEnduring Understandings Skills Trace (Vertical Alignment) Vocabulary Calendar Math Measuring the passage of time using calendars and clocks

Learn to read a calendar in terms of the days of the week and the months in a year

Learn to write the date

Learn to read an show time to the hour and half hour

Kindergarten

Know the days of the week and months of the year in a calendar

Grade 1

Read a calendar and tell time to the hour and half hour

Grade 2

Tell time in hours and minutes Use AM and PM to show morning afternoon and evening Tell how much time has elapsed

Calendar Days

Weeks Months

Year Date

Warmer Colder

Seasons Orsquoclock

Minute hand Hour hand

Half past Half hour

April Activities Review - comparing weights Preview - Place-value concepts Practice - Using a calendar

Content SkillsCompetencies PA Standard Hands on Learning Resources

151 Using a Calendar Calendar(TR30) ILLUSTRATIVEMATHEMATICS

152 Telling Time to the Hour 152a Telling Time to the Hour (Focus Lesson) 153 Telling Time to the Half Hour 153a Telling Time to the Half Hour (Focus Lesson)

CC241 A2 (MD3) Tell and write time to the nearest half hour using both analog and digital clocks SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively

Demonstration clock with movable hands Clock faces(TR31) Paper plate fastener Childrenrsquos Clock from Hands on Activity page 164

Misconceptions Proper Conceptions

Students have difficulty distinguishing the hour and minute hand on the clock Students need many opportunities to work with a clock manipulating the hands and telling the time

Cross-Curricular Connections

ReadingELA Ask students to name some types of words that always begin with capital letters They might mention names places and the first word in a sentence Tell students that the days of the week and the months of the year all begin with a capital letter You may want to display a calendar and invite students to browse through it to find the capital letters Point out that the names of the seasons are not capitalized You may also want to have students research the origin of the names of the days of the weeks and the months of the year Social Studies Explain to students that most workers follow time schedules Give partners this schedule and have them draw clock faces to show each time on the schedule Start Work-- 800 Break-- 1030 Lunch-- 100 End Work-- 400

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1MD3 Tell and write time in hours and half-hours using analog and digital clocks

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 34: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

34

Chapter 16 Numbers to 100

Duration 9 days

Essential Questions What are different ways to count Are some ways better than others when counting larger numbers

Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Counting comparing and ordering of numbers 1-100

Learn to count on read and write numbers beyond 40

Learn to represent numbers to 100 using place-value charts

Learn strategies to compare numbers to 100

Learn to identify number patterns with numbers to 100

Kindergarten

Count and write numbers 0 to 20 Grade 1

Count and compare numbers to 100 Grade 2

Count and compare numbers to 1000

Fifty Sixty

Seventy Eighty

Ninety One hundred

Estimate Number line

April Activities Review - Using a calendar Preview - Counting coins Practice - Using place-value models

Content SkillsCompetencies PA Standard Hands on Learning Resources

161 Counting to 100 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

Ten-rods and unit cubes Craft sticks

ILLUSTRATIVEMATHEMATICS

161a Counting to 120 CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects SMP2 Reason abstractly and quantitatively SMP5 Use appropriate tools strategically

162 Place Value CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP5 Use appropriate tools strategically

Craft sticks

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 35: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

35

163 Comparing Ordering and Patterns CC211 B1 (NBT1) Extend the counting sequence to read and write numerals to represent objects CC211 B2 (NBT2A NBT2C NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC221 A1 (OA5) Represent and solve problems involving addition and subtraction within 20 SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP7 Look for and make use of structure

Base-ten blocks and Number lines(TR33) Blank number lines(TR34) Transparent spinners Spinner bases(TR35) and (TR36) Place-Value Charts(TR13) Hundreds Chart(TR32)

163a Comparing Ordering and Patterns (Focus Lesson)

CC211 B2 (NBT3) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

ReadingELA Review with students endings that can be added to words to change the meaning Use ndashs and ndashes as examples of endings that make words plural Write the number words twenty through ninety on the board Challenge students to find the ending that all of these words have in common (ty) Then help them to see how the base words relate to the numbers two through nine PE Discuss the scoring in the game of bowling Explain that in each frame a bowler gets two changes to know down the pins If the player knocks all ten pins down in one turn (strike) or two turns (spare) then he or she gets to add pins knocked down on the next turn to the ten in the previous frame Pose situations and ask students to find the total for the frame

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT1 Count to 120 starting at any number less than 120 In this range read and write numerals and represent a number of objects with a written numeral

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 36: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

36

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT3 Compare two two-digit numbers based on meanings of the tens and onesrsquo digits recording the results of comparisons with the symbols gt = and lt 1OA5 Relate counting to addition and subtraction (eg by counting on 2 to add 2)

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 37: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

37

Chapter 17 Addition and Subtraction to 100

Duration 8 days

Essential Question How are adding and subtracting groups of ten the same as adding and subtracting ones Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Adding and subtracting numbers to 100 with and without regrouping

Learn to add with and without regrouping

Learn to subtract with and without regrouping

Kindergarten

Represent addition stories with small whole numbers

Grade 1

Add 2-digit to 2-digit numbers up to 100 Grade 2

Add 3-digit to 3-digit numbers up to 1000 Subtract 3-digit numbers from numbers within 1000

May Activities Review - solid shapes Preview - counting money Practice - addition with numbers to 100

Content SkillsCompetencies PA Standard Hands on Learning Resources

171 Addition without Regrouping 172 Addition with Regrouping 173 Subtraction without Regrouping 174 Subtraction with Regrouping

CC211 B2 (NBT2A NBT2C) Use place value concepts to represent amounts of tens and ones and to compare two digit numbers CC211 B3 (NBT4) Use place value concepts and properties of operations to add and subtract within 100 CC221 A2 (OA7 OA8) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP4 Model with mathematics SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Hundreds Chart (TR32) Transparent spinner Base-ten blocks Spinner base(TR37) Counters Number cube

ILLUSTRATIVEMATHEMATICS

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

Cross-Curricular Connections

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 38: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

38

ReadingELA Put students in pairs to write story problems with 1- and 2-digit numbers Supply partners with numbers and create a theme such as the zoo Tell students to use the given numbers to create addition or subtraction word problems about the theme Partners can exchange problems and solve You can then collect the problems to create a class book of addition and subtraction word problems Drama Collect studentrsquos story problems from the readingELA activity Work with them to create a dramatization of their problems Encourage students to draw pictures or create other visuals to use as props Invite partners to dramatize their problems in front of the class

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1NBT2 Understand that the two digits of a two-digit number represent amounts of tens and ones Understand the following as special cases a 10 can be thought of as a bundle of ten ones mdash called a ldquotenrdquo The numbers from 11 to 19 are composed of a ten and one two three four five six seven eight or nine ones The numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones) 1NBT4 Add within 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value properties of operations andor the relationship between addition and subtraction relate the strategy to a written method and explain the reasoning used Understand that in adding two-digit numbers one adds tens and tens ones and ones and sometimes it is necessary to compose a ten 1OA8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 + = 11 5 = 1048781 ndash 3 6 + 6 = 1048781 1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 39: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

39

Chapter 18 Multiplication and Division

Duration 7 days

Essential Question How can we use addition and subtraction to solve multiplication and division problems Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Multiplying by adding equal groups and dividing by sharing equally

Add the same numbers to understand the concept of multiplication

Distribute items equally to understand the concept of sharing equally Children distribute items into equal groups to understand the concept of dividing into equal groups

Kindergarten

Count by 2s and 5s to make pairs and groups

Grade 1

Multiply by adding equal groups and divide by sharing equally or putting things into equal groups

Grade 2

Learn the multiplication tables of 2 3 4 5 and 10 Divide using related multiplication facts

Same Groups

Each Share

MayJune Activities Review - Attributes of solid shapes Preview - Counting money Practice - Counting equal groups

Content SkillsCompetencies PA Standard Hands on Learning Resources

181 Adding the Same Number SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP5 Use appropriate tools strategically SMP6 Attend to precision SMP8 Look for and express regularity in repeated reasoning

Connecting cubes Counters String or yarn

182 Sharing Equally SMP5 Use appropriate tools strategically Counters

183 Finding the Number of Groups SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Counters Connecting cubes

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 40: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

40

Cross-Curricular Connections

ReadingELA Brainstorm with studentsrsquo items that are often found in groups (Insects have 3 pairs of legs a package has 6 juice boxes a hand has five fingers) Ask students to draw an example of groups of objects and write a sentence (Ex The insect has 3 pairs of legs It has 6 legs in all) You may decide to have students complete this task in their math journal Science Tell students that objects weigh more on Earth than on the Moon in facts about six times more Show students how to determine the weight of a 24-pound object on the moon Use 24 counters and make equal groups of 6 Explain that something that weighs 24 pounds on Earth only weighs 4 pounds on the Moon Give groups of students counters and ask them to find these weights on the Moon 12lbs 18lbs 30lbs and 36lbs

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1G3 Partition circles and rectangles into two and four equal shares describe the shares using the words halves fourths and quarters and use the phrases half of fourth of and quarter of Describe the whole as two of or four of the shares Understand for these examples that decomposing into more equal shares creates smaller shares

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 41: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

41

Chapter 19 Money

Duration 5 days

Essential Questions Why is it important to have money Why do we need to know the value of coins Big IdeasEnduring Understandings

Skills Trace (Vertical Alignment)

Vocabulary Calendar Math

Knowing that penny nickel dime and quarter can be used in different combinations to buy things and that they can be added and subtracted

Learn about penny nickel dime and quarter

Count the value of coins

Add and subtract money in real-world problems

Kindergarten

Identify the penny nickel dime and quarter and count pennies to buy items

Grade 1

Show and count coins (penny nickels dimes and quarters) Add subtract and solve real-world problems using money

Grade 2

Show and count money amounts in bills and coins and solve real-world problems involving addition and subtraction of money amounts

Cents Nickel Value Penny Dime Exchange Quarter Change

June Activities Review - Addition with numbers to 100 Preview - 3-digit numbers Practice - Counting money

Content SkillsCompetencies PA Standard Hands on Learning Resources

191 Penny Nickel and Dime 192 Quarter 193 Counting Money

SMP5 Use appropriate tools strategically SMP6 Attend to precision

Plastic money Coins (TR38) Exchanging Quarters Table (TR39) Hundreds Chart (TR32)

194 Adding and Subtracting Money CC221 A2 (OA7) Understand and apply properties of operations and the relationship between addition and subtraction SMP1 Make sense and persevere in solving problems SMP2 Reason abstractly and quantitatively SMP3 Construct viable arguments and critique the reasoning of others SMP6 Attend to precision

Misconceptions Proper Conceptions

A common misconception is that the commutative property applies to subtraction

First graders might have informally encountered negative numbers in their lives so they think they can take away more than the number of items in a given set resulting in a negative number below zero

After students have discovered and applied the commutative property for addition ask them to investigate whether this property works for subtraction Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction

Provide many problems where students take away all objects from a set (ex 19-19=0) and focus on the meaning of 0 objects and 0 as a number Ask students whether they can take away more objects than what they have

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2

Page 42: Neshaminy School District Curriculum Map: First Grade Math€¦ · 1 Neshaminy School District Curriculum Map: First Grade Math Resources Available to Teachers for Instruction: Math

42

Cross-Curricular Connections

ReadingELA Read Aloud The Coin Counting Book by Rozanne Lanczak William If possible give students real or play coins to count as you read Students can group the coins to show the different equivalencies that are featured in the book Reread the book asking students to join in Social Studies Tell students that long ago before there was money people used to trade items Native Americans used beads and trinkets to trade for other goods Put price tags on several objects such as books markers and other classroom supplies Assign the values of 1 cent 5 cents 10 cents and 25 cents to other objects such as paper clips counters counting cubes etc Invite students to offer equivalent amounts of these items to trade for the objects with price tags

Assessments

Calendar Math Assessments

Math in Focus Assessments

End-of-Year Common Assessments

Ongoing Formative Assessments

1OA7 Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false For example which of the following equations are true and which are false 6 = 6 7 = 8 ndash 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2