First Grade

MATHEMATICS Curriculum Map

2017 – 2018

Volusia County Schools

Mathematics Florida Standards

1 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

2 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

Elementary Instructional Math Block

Time Components Description

5-15 minutes

Number Talks

Short, daily fluency routine that engages students in meaningful conversations around purposefully crafted computation problems that are solved using number relationships and the structure of numbers. Students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally while the teacher records their ideas with mathematical precision. These exchanges lead to the development of more accurate, efficient, and flexible strategies.

5 minutes

Opening: Hook/Coherence Connection

The teacher will engage students to create interest for the whole group lesson or review prerequisite standards to prepare students to make explicit connections that will allow students to apply and extend previous learning when interacting with the lesson’s grade-level content.

15 minutes

Whole Group: Mini Lesson/Guided Practice

Used prior to small group to introduce/practice new knowledge and skills or after small group to refine/practice strategies discovered by students.

The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s), or part(s) thereof, intentionally targeting the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.

During this time, the teacher makes the mathematics of the lesson explicit using clear and correct explanations, representations, tasks, and/or examples. The teacher provides opportunities for all students to work with and practice grade-level problems and exercises, deliberately checking for understanding throughout the lesson and adapting the lesson according to student understanding. The teacher poses high-quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Class created anchor charts are constructed by strategically adding key concepts throughout the topic’s lessons.

30-40 minutes

Small Collaborative Groups/ Independent Practice

The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for student choice of appropriate tools and promote productive struggle. Students work in small, flexible collaborative groups to engage in mathematical tasks while the teacher circulates and asks questions to elicit thinking, providing support or extensions as needed. The teacher asks students to explain and justify work, connecting and developing students’ informal language to precise mathematical language appropriate to their grade, and provides feedback that helps students revise initial work. The teacher makes observations to select and sequence appropriate strategies for students to share during the class discussion.

5 minutes

Closure: Summarize

The teacher strengthens all students’ understanding of the content by strategically sharing a variety of students’ representations and solution methods. The teacher facilitates the summary of the mathematics with references to student work and by creating the conditions for student conversations where students are encouraged to talk about each other’s thinking in order to reinforce the purpose of the lesson.

Formative techniques occur throughout the framework to drive instruction, guide collaborative grouping, and evaluate which students will need intervention/enrichment.

Grade 1 Math Curriculum Map July 2017

3 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Year At A Glance

Unit 1: August 14 – October 10 Topic 1: Understanding ten ones make a ten Topic 2: Using data to add and subtract within 20 Topic 3: Ordering and comparing lengths Topic 4: Exploring quantities to 99 Topic 5: Telling and writing time to the hour

Unit 2: October 11 – December 20 Topic 6: Developing addition and subtraction strategies Topic 7: Distinguishing attributes of shapes Topic 8: Using place value to read, write, represent, and compare numbers Topic 9: Extending strategies for solving addition and subtraction problems

Unit 3: January 8 – March 8 Topic 10: Telling and writing time to the half hour Topic 11: Adding multiples of ten Topic 12: Identify and combine values of money Topic 13: Composing and drawing shapes Topic 14: Interpreting and using symbols in numeric expressions and comparisons

Unit 4: March 19 – May 30 Topic 15: Using understanding of place value to add and subtract Topic 16: Applying properties of operations to solve problems Topic 17: Measuring lengths using a ruler Topic 18: Finding equal shares of shapes Topic 19: Demonstrating proficiency in addition and subtraction situations

4 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Unit 1 PACING: August 14 – October 10

Topic 1: Understanding ten ones make a ten Pacing: August 14 – 25 In Kindergarten, students have gained familiarity with making groups of ten ones. This topic develops a more abstract understanding of place value, viewing 2-digit numbers as tens and ones. This understanding of place value supports counting on and making ten strategies that students use to become more efficient in addition and subtraction situations.

Standards Academic Language

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

MAFS.1.OA.3.6

bundle compose counting on decompose difference digit equivalent making 10 ones represent strategies sum tens value

Students will:

• use counting on and making ten strategies to add within 20.

• use mathematical tools such as ten frames, part-part whole, and number lines to represent addition within 20.

• explain strategies used to add within 20.

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 — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or

nine ones.

MAFS.1.NBT.2.2

Students will:

• understand that the two digits of a two-­‐digit number represent amounts of tens and ones.

• bundle objects in groups of ten and explain that ten ones can be called a “ten”.

• represent the numbers 11 to 19 as a ten and some ones.

2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.

MAFS.K12.MP.2.1 MAFS.K12.MP.3.1

Topic Comments:

In this topic the focus in 1.OA.3.6 is on counting on and making ten.

1.OA.3.6 is repeated in topics 6, 9, and 19 to provide multiple opportunities to learn and practice all of the different strategies.

In each of these topics, new strategies will be introduced to expand students’ proficiency in addition and subtraction to work

towards fluency.

1.NBT.2.2 will be extended in topic 8 to include place value understanding of multiples of ten from 10-90, as well as the process of decomposing two-digit numbers in multiple ways (e.g., 64 can be decomposed into 6 tens and 4 ones or into 5 tens and 14 ones).

Students will progress from concrete to pictorial to more abstract reasoning (MP.2). This includes the habit of listening to others and responding (MP.3).

5 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 1 Clowning Around With the Facts

Seek and Hide

Teacher Guide, pp. 10 - 11

Daily Math Practice Journal, pp. 2, 4

Discovery Can: Addition and Subtraction

Addition & Subtraction Stamps Operations Activity Stations

Addition Fluency Puzzles

No aligned resources www.cpalms.org Using the "Make a Ten" strategy to Add

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 6 Lesson 9: Fluently add numbers within 20 by making a ten

http://achievethecore.org/ Fluency Resources

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Topic 1 Following the Rules

Tens to Ones

Teacher Guide, pp. 16 - 17

Daily Math Practice Journal, pp. 26, 27, 30, 31, 36, 40, 44

Discovery Can: Place Value

Magnetic Ten Frames

Operations Activity Stations

Put Objects into Bundles of Ten

https://www.illustrativemathematics.org/ No aligned resources

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 1 Lesson 1: Bundle of ten Lesson 2: Ten cars make one trailer Lesson 3: A ten and some ones Lesson 4: How many more than ten

6 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 2: Using data to add and subtract within 20 Pacing: August 28 - September 14 In this topic, students build on the strategies and problem types with which they are familiar with from Kindergarten, extending the number range to 20. The data work in this topic provides a context for students to make important connections to addition and subtraction.

Standards Academic Language

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, e.g., by

using objects, drawings, and equations with a symbol for the unknown number to represent the

problem (Students are not required to independently read the word problems.).

NOTE: This standard has been amended in Florida to include “Students are not required to independently

read the word problems”.

MAFS.1.OA.1.1

adding to addend count all count back count on category data points decrease difference equation (9 = 4 + 5) increase interpret organize patterns putting together represent sequence

sort sum taking apart taking from total

Students will:

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, and taking apart using tools (manipulatives, number lines, 120 chart, balance, ten-frame, part-part-whole).

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, and taking apart using drawings.

NOTE: See Common Addition and Subtraction Situations Table on page 43.

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). MAFS.1.OA.3.5

Students will:

• add by counting all and counting on.

• subtract by counting back and counting up from.

• identify, describe and use mathematical patterns to relate the counting sequence to addition and subtraction.

NOTE: Instructional tools such as number lines and number charts will help students begin to recognize patterns relating to the counting sequence.

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.

MAFS.1.MD.3.4

Students will:

• sort and represent up to three categories of data.

• answer questions about the total number of data points and how many data points are in each category.

NOTE: Students will begin using graphs in grade 2.

1. Make sense of problems and persevere in solving them. 4. Model with mathematics.

MAFS.K12.MP.1.1 MAFS.K12.MP.4.1

Topic Comments:

1.OA.1.1 is addressed in full in topic 9 to include all problem types. 1.MD.3.4 is used as a context for students to make sense of numbers and as an application in everyday life. It can also be used as a context throughout the year. This standard will be addressed in full in topic 9 to include compare problems.

Working with data gives students an opportunity to model with mathematics (MP.4) Students use the context of data to reason through rich problem situations that encourage them to persevere when problem solving (MP.1).

7 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 2 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 2 Telling Tales

Through the Window Numbers

Teacher Guide, pp. 3-5

Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 23

Fish in a Pond

Trains and Jump ropes

https://www.illustrativemathematics.org/ Link Cube Addition

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 1 Lesson 7: Subtraction using counting on and counting back

http://achievethecore.org/ Solving Addition Math Stories

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Topic 2 No aligned resources

Teacher Guide, pp. 8 - 10

Discovery Can: Addition & Subtraction

Magnetic Ten Frames

Addition and Subtraction Equations

Beads on a Necklace

Skyler’s Dog Biscuits

Using Counting on Strategies

www.cpalms.org One More Up on Top

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 2 Lesson 5: Organize data into a set by counting on Lesson 6: Count on to add Lesson 9: Relate counting on to subtraction

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Topic 2 Buttons, Buttons, Who Is Wearing Buttons? (avoid comparison problems-starts at number 10.

Daily Math Practice Journal, pp. 61, 63

No aligned resources www.cpalms.org Favorite Ice Cream Flavor

https://www.illustrativemathematics.org/ Favorite Ice Cream Flavor

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 2 Lesson 1: Organize and represent data into categories Lesson 2: Collect, organize and represent data Lesson 3: Our favorite pets. Interpret a visual representation

8 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 3: Ordering and comparing lengths Pacing: September 15 – 21 In this topic, students explore length comparisons both directly and indirectly. They build and expand upon the direct comparison that they learned in

Kindergarten to compare and order three objects directly, and then extend this to indirect comparisons through the use of a third object. This concrete

experience with length comparisons supports students’ understanding of number comparisons and comparison problem solving.

Standards Academic Language

Order three objects by length; compare the lengths of two objects indirectly by using a third object. MAFS.1.MD.1.1 compare length longer longest order shorter shortest taller tallest

Students will:

• compare and order three objects by length.

• compare the length of two objects, indirectly, by using a third object.

E.g., Ms. Smith shows her students two pencils. She asks, “Which is longer, the unsharpened pencil or the sharpened pencil?” Ms. Smith then says, “I saw a pencil in Rylie’s desk that was shorter than this sharpened pencil. Which do you think would

be longer, this unsharpened pencil or the pencil in Rylie’s desk?”

3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically.

MAFS.K12.MP.3.1 MAFS.K12.MP.5.1

Topic Comments:

1.MD.1.1 involves measuring non-­‐standard units. Comparison is the focus of this topic, whereas iterating length units (1.MD.1.a), is

addressed in topic 17.

Students need to use the tools appropriately (MP.5), but this topic should also provide an opportunity for students to explain their reasoning.

Topic 3 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 3 Measuring Mice

Reproducibles, p. 11

Daily Math Practice Journal, pp. 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 58, 60, 62

Discovery Can: Measurement

Comparing Widths and Heights of Books

Line Lengths

Longest to Shortest Cubes

The Missing Pencil

What’s the Length of the third set

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 3 Lesson 1: Compare length directly. Understand importance of aligning endpoint. Lesson 3: Understand indirect comparison of object attributes Lesson 4: Compare length using indirect comparison

9 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 4: Exploring quantities to 99 Pacing: September 22 – October 3 This topic is focused on counting and writing two-­‐digit numbers. This topic provides students opportunities to practice making groups of ten to efficiently represent and count objects.

Standards Academic Language

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. MAFS.1.NBT.1.1

pattern sequence two-digit Students will:

• count to 99 starting at any number less than 99.

• read 2-digit numerals up to 99.

• write 2-digit numerals up to 99.

• label a set of objects with a written numeral up to 99.

6. Attend to precision. 7. Look for and make use of structure.

MAFS.K12.MP.6.1 MAFS.K12.MP.7.1

Topic Comments: The focus of this topic is numbers within 99. 1.NBT.1.1 will be repeated in topic 8, in which the number range will be extended

to 120. In this topic, students can focus on the uniformity of how tens and ones change as you count greater quantities.

1.NBT.1.1 is developed throughout the year. The target for topic 4 is counting to 99 by ones from any given number, but this

should not be a limit. Students who are proficient at counting to 100 (a Kindergarten skill) may proceed to 120.

In this topic students recognize and apply number patterns (MP.7) and communicate this understanding precisely in reading,

writing, and representing numbers (MP.6).

Topic 4 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 4 No aligned resources

Daily Math Practice Journal, pp. 26, 29, 30, 33

Discovery Can: Place Value

Magnetic Ten Frames

Baskets of Apples

How many Fish

https://www.illustrativemathematics.org/ Hundred Chart Digit Game Number of the Day

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 4 Lesson 1: Count, write and explore quantities through 99 by ones Lesson 2: Count within 99 by ones Lesson 3: Represent and write numbers through 99

10 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 5: Telling and writing time to the hour Pacing: October 4 – 10 This is students’ first experience in the classroom telling and writing time. In this topic, students are not performing any operations with time. Students identify the different parts of the clock, making connections between these parts and the time in hours.

Standards Academic Language

Tell and write time in hours and half-­‐hours using analog and digital clocks. MAFS.1.MD.2.3 analog clock colon digital clock hour hand hour minute hand o’clock time

Students will:

• identify a digital and an analog clock.

• identify the components of a digital and an analog clock.

• tell and write time in hours using analog and digital clocks.

5. Use appropriate tools strategically. 6. Attend to precision.

MAFS.K12.MP.5.1 MAFS.K12.MP.6.1

Topic Comments: The focus of 1.MD.2.3 in this topic is telling time in hours. Students will extend this skill to telling time to the half hour in topic 10.

Precisely communicating the roles of the different components of the clock is the focus of this topic (MP.5, MP.6).

Topic 5 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 5 Flipping Over Time (be sure to only focus on Time to the Hour)

Hands on the Hour

Hour by Hour

Teacher Guide, pp. 21 - 22

Reproducibles, p. 13

No aligned resources www.cpalms.org What time is it? Part One (complete part one only)

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 5 Lesson 3: Tell time to the hour using both hands on the clock Lesson 4: Practice telling time to the hour with analog and digital clocks

11 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Unit 2 PACING: October 11 – December 20

Topic 6: Developing addition and subtraction strategies Pacing: October 11 – 27 In this topic, the focus is on “Put Together/Take Apart” problems with unknown addends. These problem types give students the opportunity to see subtraction as the opposite of addition in a different way than as reversing the action. Counting on strategies reinforce that subtraction is an unknown addend problem, which help students view subtraction as being just as easy as addition and emphasizes the relation between subtraction and addition.

Standards Academic Language

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is

known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the

second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative

property of addition.)

MAFS.1.OA.2.3

equation relationship same value as strategies unknown-addend

Students will:

• understand that when adding numbers in any order, the sum does not change.

E.g., 4 + 8 = 12; 8 + 4 = 12; *This is the Commutative Property of addition.

• use the commutative property as a strategy to add.

E.g., When adding 2 + 9 the student would use the commutative property to form the equivalent, but easier expression 9 + 2 in order to start with 9 and count on 2.

NOTE: Students do not need to use formal terms (Commutative) for these properties.

Understand subtraction as an unknown-­‐addend problem. For example, subtract 10 – 8 by finding

the number that makes 10 when added to 8. MAFS.1.OA.2.4

Students will:

• demonstrate the relationship between addition and subtraction using a variety of strategies and tools as a foundation for missing addends.

• show and explain how a subtraction equation can be rewritten as a related addition equation with an unknown addend.

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

MAFS.1.OA.3.6

Students will:

• use mathematical tools such as ten frames, part-part whole, and number lines to represent addition and subtraction within 20.

• use counting on and making 10 strategies to add within 20.

• use the relationship between addition and subtraction to solve within 20.

• explain strategies used to add and subtract within 20.

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

12 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic Comments:

1.OA.2.3 is repeated in topic 16 to add the Associative property to students’ repertoire.

In this topic, the focus in 1.OA.3.6 is on the relationship between addition and subtraction. This standard is repeated in topics 9

and 19 to provide multiple opportunities to learn and practice all of the different strategies. In each of these topics, new strategies

will be introduced to expand students’ proficiency in addition and subtraction to work towards fluency.

It is important for students to construct viable arguments (MP.3) because in order for students to develop this conceptual

understanding, they need to be given the opportunity to explain how they know a strategy works. Exploring structure of problem

types facilitate the development of more sophisticated strategies (MP.7).

Topic 6 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 6 I See, You See Turn Around Taxi Tic Tac and Twenty (game)

Teacher Guide, pp. 5 - 7 Daily Math Practice Journal, pp. 3, 5, 7, 9 Discovery Can: Addition and Subtraction Monkey Math Balance Addition & Subtraction Stamps Operations Activity Stations

Justifying the Commutative Property of Addition Turtles in a Pond

https://www.illustrativemathematics.org/ Domino Addition

www.IXL.com/signin/volusia https://learnzillion.com/ Unit 6 Lesson 1: Understand the commutative property of addition Lesson 3: Solve problems using the commutative property of addition

13 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 6 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 6 No aligned resources

Teacher Guide, pp. 5 - 7

Daily Math Practice Journal, pp. 2, 4, 6, 8, 18, 20, 22, 24

Discovery Can: Addition and Subtraction Addition & Subtraction Stamps

Operations Activity Stations

Two Students’ Strategies Use Addition to Solve Subtraction Using Addition to Solve Subtraction Problems Using Inverse Operations

https://www.illustrativemathematics.org/ Cave Game Subtraction

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 6 Lesson 4: Understand that subtraction can be thought of as an unknown addend problem Lesson 5: Explore related addition and subtraction equations Lesson 6: Use addition strategies to solve word problems

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Topic 6 Clowning Around With the Facts Rally with Differences Seek and Hide Tic Tac and Twenty (game)

Teacher Guide, pp. 10 - 11

Daily Math Practice Journal, pp. 2, 4, 6, 8, 12, 14, 16

Discovery Can: Addition and Subtraction

Addition & Subtraction Stamps Operations Activity Stations

Addition Fluency Puzzles

More than One Way to Solve a Problem Use Strategies to Add and Subtract

www.cpalms.org Make a Ten to Subtract

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 6 Lesson 9: Fluently add numbers within 20 by making a ten

http://achievethecore.org/ Fluency Resources

14 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 7: Distinguishing attributes of shapes Pacing: October 30 – November 3 In this topic, students extend their understanding of attributes—e.g. orientation, size, and number of sides—they learned in Kindergarten to distinguish

between defining attributes and non-­‐defining attributes. Students need to explore various examples in different ways so that their experiences with shapes

are not limited to single examples (e.g. if a student has only worked with equilateral triangles, it may be difficult for them to develop more general

understandings of triangles).

Standards Academic Language

Distinguish between defining attributes (e.g., triangles are closed and three-­‐sided) versus non-­‐ defining

attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. MAFS.1.G.1.1

closed figure compare defining attributes non-defining attributes open figure sides vertex/vertices

Students will:

• explain that defining attributes are features that are always true for categories of shapes.

E.g. Defining attributes include closed sides, number of sides and vertices.

• explain that non-defining attributes are features that may be present but are not used to classify shapes.

E.g. Non-defining attributes include color, size, texture and orientation.

• identify defining and non-defining attributes when shown a shape.

NOTE: Students need to be exposed to half-circles, quarter-circles, rectangles, squares, trapezoids, triangles, cubes, rectangular prisms, cones, and cylinders.

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

Topic Comments:

Although building and drawing shapes can support students’ understanding of defining attributes, this part of 1.G.1.1 is not

required until topic 13.

This topic gives students opportunities to construct arguments and justify their conclusions based on defining attributes and the structure of geometric figures (MP.3, MP.7).

Topic 7 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

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Topic 7 Meaty Math (do not focus on hexagons) Shape Takers

Teacher Guide, p. 23

Reproducibles, p. 15

Daily Math Practice Journal, pp. 65, 67, 69, 71

Discovery Can: Geometry

Turning a Square Is it Still a Rectangle

https://www.illustrativemathematics.org/ All vs. Only Some

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 7 Lesson 2: Defining and non-defining attributes

15 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 8: Using place value to read, write, represent, and compare numbers Pacing: November 6 – 28 In this topic, students extend their understanding from topic 1, to a larger number range. Students apply the structure of teen numbers to reason about greater quantities and their relative magnitude.

Standards Academic Language

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. MAFS.1.NBT.1.1

compare compose decompose equal to greater than less than ones digit place value represent tens digit two-digit value

Students will:

• count to 120 starting at any number less than 120.

• read numerals to 120.

• write numerals to 120.

• label a set of objects with a written numeral to 120.

Understand that the two digits of a two-­‐digit number represent amounts of tens and ones.

Understand the following as special cases:

c. 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).

d. Decompose two-digit numbers in multiple ways (e.g., 64 can be decomposed into 6 tens and 4 ones

or into 5 tens and 14 ones).

NOTE: This standard has been amended in Florida to include part d.

MAFS.1.NBT.2.2

Students will:

• understand that the two digits of a two-­‐digit number represent amounts of tens and ones

• identify a digit’s value based on its place in a two-digit numeral.

E.g., For the number 53, the 5 has a value of 50 and the 3 has a value of 3.

• represent multiples of 10 up to 90 as bundles of 10, using appropriate tools.

E.g., unifix cubes, ten frames, base-ten blocks, etc.

• explain that the numbers 10, 20, 30, 40, 50, 60, 70, 80 and 90 are one, two, three, four, five, six, seven, eight, or nine tens and 0 ones.

E.g., 70 is the same as 7 tens and 0 ones.

• decompose numbers in multiple ways. E.g., 63 is:

63 ones 6 tens and 3 ones 4 tens and 23 ones

16 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Compare two two-­‐digit numbers based on meanings of the tens and ones digits, recording the results of

comparisons with the symbols >, =, and <. MAFS.1.NBT.2.3

Students will:

• compare numbers from 10-99 by understanding the value of the tens digit and the ones digit to determine when a 2-digit number is greater than, less than, or equal to another 2-digit number.

• explain why a 2-digit number is greater than, less than, or equal to another 2-digit number.

2. Reason abstractly and quantitatively. 7. Look for and make use of structure.

MAFS.K12.MP.2.1 MAFS.K12.MP.7.1

Topic Comments: 1.NBT.1.1 involves relating the structure of numbers 0-­‐20 to the numbers 100-­‐120.

1.NBT.2.2 is finalized in this topic to include place value understanding of multiples of ten from 10-90, as well as the process of decomposing two-digit numbers in multiple ways.

In this topic, 1.NBT.2.3 focuses on students using comparative language to describe numerical comparisons. Mathematical

comparison symbols (< and >) will be introduced in topic 14.

Students continue to explore the structure of place value (MP.7); namely that the two digits of a two-­‐digit number represent amounts of tens and ones and that to compare numbers relies on their relative magnitudes. Students make sense of the relationships between the numerals and the quantities (MP.2).

17 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.N

BT

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Topic 8 No aligned resources

Daily Math Practice Journal, pp. 26, 29, 30, 33, 34, 38 Discovery Can: Place Value Magnetic Ten Frames

Baskets of Apples Counting to 120 How many Fish Reading and Writing Numerals

www.cpalms.org Over 100 Hungry Ants: Counting to 120

https://www.illustrativemathematics.org/ Hundred Chart Digit Game Number of the Day

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 8 Lesson 1: Counting to 120 using tens and ones Lesson 2: Filling in missing numbers in 120 chart

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Topic 8 Following the Rules Tens to Ones

Teacher Guide, pp. 16 - 17

Daily Math Practice Journal, pp. 26, 27, 28, 30, 31, 32, 34, 36, 38, 40, 42, 44

Discovery Can: Place Value

Magnetic Ten Frames

Operations Activity Stations

How Many Tens and Ones are There How Many Tens and Ones Making Tens Put Objects into Bundles of Ten Tens and Ones

www.cpalms.org How Many in Your Cup? Musical Place Value

https://www.illustrativemathematics.org/ Roll and Build

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 8 Lesson 3: Identify how many tens and ones are in a two-digit number

http://achievethecore.org/ Building Tens at the Lego Factory

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Topic 8 No aligned resources

Teacher Guide, p. 17

Discovery Can: Place Value

Magnetic Ten Frames

Operations Activity Stations

No aligned resources https://www.illustrativemathematics.org/ Ordering Numbers

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 8 Lesson 7: Compare the values of two-digit numbers Lesson 8: Compare two-digit numbers using place value Lesson 9: Practice comparing two-digit numbers using place value

18 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 9: Extending strategies for solving addition and subtraction problems Pacing: November 29 – December 20 In this topic, data provides an authentic context for students to develop appropriate strategies to reason about and solve addition and subtraction problems. In particular, this topic introduces “compare” problems and because compare problems are relatively difficult for students to master, this topic should provide students time to grapple with the misleading language and difficult contexts involved in these problem types.

Standards Academic Language

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, e.g., by

using objects, drawings, and equations with a symbol for the unknown number to represent the

problem (Students are not required to independently read the word problems.).

NOTE: This standard has been amended in Florida to include “Students are not required to independently

read the word problems”.

MAFS.1.OA.1.1

Balanced category compare data points decompose equation (4 + 5 = 9) related facts interpret inverse operation represent same value as sort symbol unknown value

Students will:

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, taking apart and comparing using tools (manipulatives, number lines, 120 chart, balance, ten-frame, part-part-whole).

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, and taking apart and comparing using drawings or equations with a symbol for the unknown number to represent the problem.

E.g., Symbols of unknown numbers may be, but are not limited to the following:

3 + = 7 ? – 6 = 3 9 = 5 + ____ 4 + 2 = ____

• solve word problems with unknown numbers in different positions. E.g., Start unknown: Change unknown: Result unknown: NOTE: See Common Addition and Subtraction Situations Table on page 43.

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

MAFS.1.OA.3.6

Students will:

• use mathematical tools such as ten frames, part-part whole, and number lines to represent addition and subtraction within 20.

• use counting on and making 10 strategies to add within 20.

• decompose a number leading to a ten to subtract within 20.

NOTE: When decomposing to lead to a ten, students will subtract in two steps: E.g Step 1: decompose the subtrahend and subtract to get to 10 Step 2: subtract the remainder of the subtrahend

• use the relationship between addition and subtraction to solve within 20.

_ + 9 = 18 _ - 9 = 9

9 + _ = 18 18 - _ = 9

9 + 9 = __ 18 - 9 = __

14 – 7 = 14 – 4 = 10 10 – 3 = 7

19 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

• explain strategies used to add and subtract within 20.

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 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

MAFS.1.OA.4.7

Students will:

• explain that the equal sign means “is the same value as” or “balances”.

NOTE: Many students confuse the equal sign with “the answer is.” It should be taught that the equal sign means there are equal quantities on both sides of the equal sign.

E.g., 5 is the same value as 2 plus 3 (5 = 2 + 3) 4 plus 6 is the same value as 10 (4 + 6 = 10) 2 plus 4 balances 3 plus 3 (2 + 4 = 3 + 3) 7 balances 7 (7 = 7)

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.

MAFS.1.MD.3.4

Students will:

• sort and represent up to three categories of data.

• answer questions about the total number of data points and how many data points are in each category.

• determine when a category has more, or less than another category.

• determine how many more, or less are in one category than in another.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.

MAFS.K12.MP.1.1 MAFS.K12.MP.2.1 MAFS.K12.MP.3.1

Topic Comments: 1.OA.1.1 is addressed in its entirety in this topic to include “compare” problems (the most difficult problem type). The other problem types should also be revisited during this topic. Students will have the opportunity to discuss how this problem type relates to the previous ones they have encountered. 1.OA.3.6 will be addressed in its entirety in topic 19 in which students are expected to demonstrate fluency. 1.OA.4.7 is repeated in full in topic 14 to provide the opportunity for students to reason about equality and expressions. 1.MD.3.4 is a useful context for practicing compare problem types and Level 3 strategies (e.g., make a ten, decomposing a number leading to a ten, and thinking of subtraction as finding an unknown addend) and provides opportunity for students to construct arguments about the context and strategies involved.

Reasoning about strategies and selecting appropriate strategies is critical to developing conceptual understanding of addition and subtraction in all situations (MP.1, MP.2, MP.3).

2 + 2 3 + 1

20 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 9 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

A.1

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Topic 9 Safari Sums and Differences Telling Tales Through the Window Numbers

Teacher Guide, pp. 3-5 Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 23 Reproducibles, p. 3 Addition & Subtraction Stamps Discovery Can: Addition and Subtraction Operations Activity Stations Problem Solving Center

Add to (Change Unknown) Word Problems

Add to (Result Unknown) Word Problems

Add to (Start Unknown) Word Problems

Birds on a Branch

Compare (Bigger Unknown) Word Problems

Compare (Differences Unknown) Word Problems

Compare (Smaller Unknown) Word Problems

Fish in a Pond

How Many More Stickers

More Add to (Change Unknown) Problems

Put Together/Take Apart (Addend Unknown) Word Problem

Put Together/Take Apart (Both Addends Unknown) Word Problems

Put Together/Take Apart (Total Unknown) Word Problem

Red Birds and Blue Birds

Take From (Change Unknown) Word Problems

Take From (Result Unknown)

Take From Start Unknown

The Cupcake Problem

Trains and Jump ropes

How Many M&M’s

www.cpalms.org Cookie Subtraction Word Problem Lesson Addition Stories at the Food Store

https://www.illustrativemathematics.org/ At the Park Boys and Girls - 1 Maria’s Marbles Sharing Markers Finding a Chair Peyton’s Books

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 1 Lesson 6: Strategies for adding numbers within 20 Lesson 9: Counting up and counting back on a number path Lesson 10: Solving candy store problems Unit 9 Lesson 1: Understand how to solve compare problems Lesson 2: Practice solving compare problems

21 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 9 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

A.3

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Topic 9 Clowning Around With the Facts Rally with Differences Seek and Hide Tic Tac and Twenty (game)

Teacher Guide, pp. 10 - 11

Daily Math Practice Journal, pp. 2, 4, 6, 8, 12, 14, 16

Discovery Can: Addition and Subtraction

Addition & Subtraction Stamps Operations Activity Stations

Addition Fluency Puzzles

More than One Way to Solve a Problem Use Strategies to Add and Subtract

No aligned resources

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 6 Lesson 9: Solve problems with related facts

http://achievethecore.org/ Fluency Resources

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Topic 9 Pound Pooches Teacher Guide, pp. 12 - 13 Discovery Can: Addition and Subtraction Monkey Math Balance Operations Activity Stations

No aligned resources https://www.illustrativemathematics.org/ Equality Number Sentences

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 9 Lesson 7: Understand the equal sign

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Topic 9 Buttons, Buttons, Who Is Wearing Buttons?

Daily Math Practice Journal, pp. 47, 49, 51, 53, 55, 57, 59, 61, 63

Flavors of Ice Cream

Pocket Data

Sort it Out

What’s for Lunch

www.cpalms.org Favorite Ice Cream Flavor

https://www.illustrativemathematics.org/ Favorite Ice Cream Flavor

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 9 Lesson 11: Organize and represent data and compare the values in three categories

22 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Unit 3 PACING: January 8 – March 8

Topic 10: Telling and writing time to the half hour Pacing: January 8 – 12

In this topic, students extend their understanding of telling and writing time from topic 5 to include situations that deal with telling time to the half hour.

Standards Academic Language

Tell and write time in hours and half-­‐hours using analog and digital clocks. MAFS.1.MD.2.3 analog digital hour hand minute hand o’clock time

Students will:

• identify a digital and an analog clock.

• identify the components of a digital and an analog clock.

• understand that there are 60 minutes in one whole hour, so there are 30 minutes in half an hour.

• tell and write time in hours and half-hours using analog and digital clocks.

5. Use appropriate tools strategically. 6. Attend to precision.

MAFS.K12.MP.5.1 MAFS.K12.MP.6.1

Topic Comments: As in topic 5, precisely communicating the roles of the different components of the clock is the focus of this topic (MP.5, MP.6).

Topic 10 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.M

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Topic 10 Flipping Over Time Hands on the Hour Hour by Hour

Teacher Guide, pp. 21 - 22 Reproducibles, p. 13 Daily Math Practice Journal, pp. 46, 48, 50, 52, 54, 56, 58, 60, 62 Discovery Can: Time

After school Digital Clocks Match the Times What Time is Lunch

www.cpalms.org What Time is it? What Time is it? The Grouchy Ladybug

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 10 Lesson 2: Practice telling time to the half hour using analog clocks Lesson 4: Practice telling time to the half hour on digital and analog clocks

23 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 11: Adding multiples of ten Pacing: January 16 – 26 In this topic, students build on their understanding of adding and subtracting within 20 to develop strategies for adding greater numbers. Students are also introduced to mentally adding 10. These standards are grouped together because the ability to compose a ten and the ability to add and subtract ten is a crucial understanding that can help students develop number sense and proficiency with numbers and operations. Concrete objects or drawings afford connections with written numerical work and discussions in terms of tens and ones by using activities that build number sense.

Standards Academic Language

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, and/or 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.

MAFS.1.NBT.3.4

decompose increase place value

Students will:

• add a two-digit number and a one-digit number, within 100, using appropriate tools (e.g., concrete models and drawings) and strategies based on place value.

E.g.,

• add a two-digit number and a multiple of ten, within 100, using appropriate tools (e.g., concrete models and drawings) and strategies based on place value. E.g.,

• use properties of operations and/or the relationship between addition and subtraction to show adding a two-digit number and a one-digit number and a two-digit number and a multiple of ten.

E.g.,

NOTE: Students should NOT be taught the standard algorithm in grade 1. This standard focuses on developing a conceptual understanding of addition- the intent is not to introduce traditional algorithms or rules. The standard algorithm for addition will be taught in grade 4.

25 + 7

25 + 5 + 2

30 + 2 = 32

32 + 40

30 + 2

30 + 40 + 2

70 + 2 = 72

24 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Given a two-­‐digit number, mentally find 10 more or 10 less than the number, without having to count;

explain the reasoning used. MAFS.1.NBT.3.5

Students will:

• count forward by tens starting at any number within 100 on a hundred chart.

E.g., 3, 13, 23, 33, 43, 53…

• identify the pattern that occurs when counting by tens.

• use mental math to find ten more than a given two-digit number.

1. Make sense of problems and persevere in solving them. 5. Use appropriate tools strategically.

MAFS.K12.MP.1.1 MAFS.K12.MP.5.1

Topic Comments: While 1.NBT.3.4 calls for first graders to add two two-­‐digit numbers (adding the tens to tens and ones to ones, which may involve

composing tens), they are not expected to compute differences of two-­‐digit numbers other than multiples of ten.

1.NBT.3.4 and 1.NBT.3.5 are repeated in topic 15 to provide the opportunity for students to explain their reasoning.

Students should have ample time to make sense of concrete models with a focus on composing tens (MP.1, MP.5).

Topic 11 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.N

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Topic 11 Following the Rules

Teacher Guide, p. 18

Reproducibles, pp. 8 - 10

Daily Math Practice Journal, pp. 32, 34, 35, 37, 39, 43

Magnetic Ten Frames Addition & Subtraction Stamps Discovery Can: Place Value Operations Activity Stations Addition Fluency Puzzles

Jumping Rope

www.cpalms.org Adding and Subtracting Ten with Justen (Just Ten) Frog

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 11 Lesson 6: Using place value to add a two-digit number to a multiple of ten https://learnzillion.com/ Lesson 8: Composing a ten while adding ones onto a two-digit number Lesson 9: Fluently adding a two-digit number with a one-digit number

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Topic 11 Puzzling Number Patterns (avoid 10 less questions)

Teacher Guide, p. 19

Reproducibles, p. 10

Daily Math Practice Journal, pp. 27, 29

First Graders Present on Tuesday

Keisha’s Shells

No aligned resources

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 11 Lesson 3: Using place value to add a two-digit number to a multiple of ten

25 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 12: Identify and combine values of money Pacing: January 29 – February 9 In this topic, students identify the value of pennies, nickels, dimes, and quarters, relating the value of pennies, dimes, and quarters to the dollar. Students also compute the whole number value of combinations of pennies and/or dimes (Decimal numbers are first addressed in Grade 4). The standard addressed in topic 12 allows students to use money and its relationship to number as a context throughout the remainder of the year.

Standards Academic Language

Identify and combine values of money in cents up to one dollar working with a single unit of currency. a. Identify the value of coins (pennies, nickels, dimes, quarters). b. Compute the value of combinations of coins (pennies and/or dimes). c. Relate the value of pennies, dimes, and quarters to the dollar (e.g., There are 100 pennies or ten dimes

or four quarters in one dollar.) (Students are not expected to understand the decimal notation for combinations of dollars and cents.) NOTE: This standard has been added in Florida.

MAFS.1.MD.2.a

cents coins combination dimes dollar nickels pennies quarters value

Students will:

• identify both sides of coins (pennies, nickels, dimes, and quarters).

• identify the value of pennies, nickels, dimes, and quarters.

• know how many pennies equal $1.

• know how many dimes equal $1.

• know how many quarters equal $1.

• calculate the value of a combination of pennies and/or dimes up to $1 (e.g. If you have 2 dimes and 3 pennies, how many cents do you have?).

2. Reason abstractly and quantitatively. 6. Attend to precision.

MAFS.K12.MP.2.1 MAFS.K12.MP.6.1

Topic Comments:

1.MD.2.a introduces the concept of money, which is new to this grade level.

Students make sense of quantities and their relationships to coin and dollar values (MP.2) and use precise language to indicate whether quantities refer to cents or dollars (MP.6)

Topic 12 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.M

D.2

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Topic 12 No aligned resources

Teacher Guide, pp. 21 - 22

Reproducibles, p. 14

Determining Values of Coins

How Much Money?

Relating Coins to a Dollar- 1

Relating Coins to a Dollar- 2

www.cpalms.org Mystery Coins Counting Coins How Many Ways Can you Make Combinations of Pennies and Dimes

www.IXL.com/signin/volusia

26 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 13: Composing and drawing shapes Pacing: February 12 – 22 In this topic, students transition from using trial and error to applying their understanding of different attributes in order to draw and compose shapes.

Composing and decomposing figures supports students’ understanding of part-­‐whole relationships.

Standards Academic Language

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non- defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

MAFS.1.G.1.1 circle closed figure compose cone cube cylinder defining attributes half-circle non-defining attributes quarter-circle rectangle rectangular prism sides square three-dimensional (solid) trapezoid triangle two-dimensional (flat) vertex/vertices

Students will:

• explain that defining attributes are features that are always true for categories of shapes.

• explain that non-defining attributes are features that may be present but are not used to classify shapes.

• identify defining and non-defining attributes when shown a shape.

• build and draw a shape when given specific defining attributes.

E.g. Model a closed figure with 4 sides and 4 vertices. NOTE: Students need to be exposed to half-circles, quarter-circles, rectangles, squares, trapezoids, triangles, cubes,

rectangular prisms, cones, and cylinders.

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.

MAFS.1.G.1.2

Students will:

• combine two-dimensional shapes to create a composite shape (e.g., two triangles to make a square).

• compose a new shape by adding a two-dimensional shape to the composite shape (e.g., a square and a trapezoid to make a hexagon).

• combine three-dimensional solids to create a composite solid.

• compose a new solid by adding a three dimensional solid to the composite solid.

• choose the shapes needed to model a given composite figure.

NOTE: A composite shape is a figure made from two or more geometric figures. Students do not have to learn this term.

Students do not need to learn formal names such as “right circular cone.”

2. Reason abstractly and quantitatively. MAFS.K12.MP.2.1

Topic Comments:

Rectangular prisms, trapezoids, half-circles, and quarter circles are introduced to students in grade 1.

Students model these geometric figures in meaningful ways that highlight defining attributes in an abstract way (MP.2). For

example, students understand that a new shape can be composed from two other shapes and can simultaneously see both the

composite shape and the component shapes.

27 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 13 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.G

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Topic 13 Meaty Math (do not focus on hexagons)

Shape Takers

Teacher Guide, p. 23

Reproducibles, p. 15

Daily Math Practice Journal, pp. 65, 67, 69, 71

Discovery Can: Geometry

Draw Triangles

Turning a Square

Is it Still a Rectangle

www.cpalms.org Shape Sorting and Building Being Shapely

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 7 Lesson 2: Defining and non-defining attributes Lesson 3: Creating equations from a pictorial solution

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Topic 13 Cube Combos

Teacher Guide, pp. 23 - 24

Reproducibles, pp. 16 - 17

Daily Math Practice Journal, pp. 64, 66, 68, 70

Discovery Can: Geometry

Building with 3 Dimensional Shapes

Compose Shapes with Triangles

Compose Shapes with Triangles and Trapezoid

Composing a Trapezoid

https://www.illustrativemathematics.org/ Make Your Own Puzzle Grandfather Tang’s Story

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 12 Lesson 3: Understand composite shapes Lesson 4: Compose shapes

28 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 14: Interpreting and using symbols in numeric expressions and comparisons Pacing: February 23 – March 8 In this topic, students apply their conceptual understanding of addition, subtraction, and comparison to interpret and write expressions and equations. It is important for students to make sense of the symbols involved, as well as knowing when to use them. A new concept to this topic is reasoning about whether equations are true or false. This topic also provides an opportunity for students to apply their understanding of the symbols while practicing their addition and subtraction strategies in different problem situations.

Standards Academic Language

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 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. MAFS.1.OA.4.7

Balanced compare equation (4 + 5 = 9) greater than (>) less than (<) same value as symbol

Students will:

• explain that the equal sign means “is the same value as” or “balances”.

• compare the quantities of both sides of an equation and determine whether the equation is true or false. Determine the unknown whole number in an addition or subtraction equation relating three whole

numbers. For example, determine the unknown number that makes the equation true in each of the

equations 8 + ? = 11, 5 = – 3, 6 + 6 = . MAFS.1.OA.4.8

Students will:

• solve addition and subtraction equations where the unknown number is represented by a symbol.

E.g., 10 + = 19, − 6 = 11

Compare two two-­‐digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

MAFS.1.NBT.2.3

Students will:

• compare numbers from 10-99 by understanding the value of the tens digit and the ones digit to determine when a 2-digit number is greater than, less than, or equal to another 2-digit number.

• explain why a 2-digit number is greater than, less than, or equal to another 2-digit number.

• record using the symbols (=, <, >) to compare two 2-digit numbers.

NOTE: Students need to associate the comparative meaning of the symbols (i.e., <, >, =) with the names less than, greater than and equal to.

2. Reason abstractly and quantitatively. MAFS.K12.MP.2.1

Topic Comments: 1.OA.4.7 was addressed in topic 9. Students now use their understanding of the equal sign to determine whether equations are true or false.

1.OA.4.8 introduces the use of symbols to represent unknown quantities. Teachers may have been using some sort of symbol

to represent unknown quantities in earlier topics, but students do so during this topic. Students will not see unknowns

represented by letters until grade 3.

1.NBT.2.3 is repeated in this topic to now include the use of mathematical symbols in expressing numeric comparisons.

Correctly placing the < and > symbols is a challenge for early learners.

Students will use models to justify their reasoning throughout this unit (MP.4) and will represent these concrete models with

abstract symbols and expressions (MP.2).

29 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 14 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

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Topic 14 Pound Pooches Teacher Guide, pp. 12 - 13 Daily Math Practice Journal, pp. 10, 12, 14, 16, 18, 20, 22, 24

Discovery Can: Addition and Subtraction

Monkey Math Balance

Operations Activity Stations

Equal or Not Equal

Equality

Is the Equation True or False?

More True and False Equations

www.cpalms.org True or False? Understanding the Equal Sign

https://www.illustrativemathematics.org/ Valid Equalities

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 13 Lesson 1: Birthday party / Distinguish between true and false equations Lesson 2: Determine whether equations are true or false using multiple strategies Lesson 3: True or false sort equation cards

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Topic 14 Space Probe Teacher Guide, pp. 13 - 14

Daily Math Practice Journal, pp. 10, 12, 14, 16, 18, 20, 22, 24

Discovery Can: Addition and Subtraction

Addition & Subtraction Stamps

Operations Activity Stations

Unknown In Equations

https://www.illustrativemathematics.org/ Find the Missing Number

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 9 Lesson 4: Understand how addition and subtraction are related Unit 13 Lesson 6: Practice finding unknown numbers in equations Lesson 7: Cookie detective / Find missing values in equations

1N

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Topic 14 Dealing with Digits (2nd grade)

Comparing Catches (Kindergarten)

Teacher Guide, p. 17

Daily Math Practice Journal, pp. 26, 28, 30, 36, 40, 42, 44

Discovery Can: Place Value

Magnetic Ten Frames

Operations Activity Stations

Greater, Less, Or Equal

Inequalities with Base Ten Blocks

Laps Around the Track

Tens and Ones with Base Tens Blocks

Using Symbols to Compare Numbers

www.cpalms.org Greater Than, Less Than Shuffle

https://www.illustrativemathematics.org/

Comparing Numbers

www.IXL.com/signin/volusia

30 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Unit 4 PACING: March 19 – May 20

Topic 15: Using understanding of place value to add and subtract Pacing: March 19 – 30 In this topic, students extend their understanding from topic 11 to include subtraction. They are also expected to relate their strategies for addition and subtraction to written methods and explain their reasoning.

Standards Academic Language

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, and/or 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.

MAFS.1.NBT.3.4

Compose decrease increase ones place value relationship tens

Students will:

• add a two-digit number and a one-digit number, within 100, using appropriate tools (e.g., concrete models and drawings) and strategies based on place value.

• add a two-digit number and a multiple of ten, within 100, using appropriate tools (e.g., concrete models and drawings) and strategies based on place value.

• use properties of operations and/or the relationship between addition and subtraction to show adding a two-digit number and a one-digit number and a two-digit number and a multiple of ten.

• explain and record the steps that were followed when using these strategies.

NOTE: Students should NOT be taught the standard algorithm in grade 1. This standard focuses on developing a conceptual understanding of addition- the intent is not to introduce traditional algorithms or rules. The standard algorithm for addition will be taught in grade 4.

Given a two-­‐digit number, mentally find 10 more or 10 less than the number, without having to count;

explain the reasoning used. MAFS.1.NBT.3.5

Students will:

• count forward and backward by tens starting at any number from 10 to 100 on a hundred chart.

• identify the pattern that occurs when counting forward or backward by tens.

• use mental math to find ten more or ten less than a given two-digit number.

• explain mental math strategies used to find 10 more or 10 less than any two-digit number.

31 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

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, and/or the relationship between addition and subtraction; relate the strategy to a written method

and explain the reasoning used.

MAFS.1.NBT.3.6

Students will:

• subtract a multiple of ten from a multiple of ten in the range 10-90, using concrete models or drawings.

• subtract a multiple of ten from a multiple of ten in the range 10-90, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• explain and record the steps that were followed when subtracting a multiple of ten from a multiple of ten.

6. Attend to precision. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.6.1 MAFS.K12.MP.8.1

Topic Comments: While 1.NBT.3.4 calls for first graders to add two two-­‐digit numbers (adding the tens to tens and ones to ones, which may involve

composing tens), they are not expected to compute differences of two-­‐digit numbers other than multiples of ten. 1.NBT.3.5 is repeated here to include mentally subtracting 10 from a number. 1.NBT.3.6 calls for students to extend on their work with adding and subtracting 10 to subtracting multiples of ten.

In doing the mental calculation without counting, students give carefully formulated explanations for their reasoning by saying that they have one more or one less ten than before (MP.6). This relies on the students’ attention to the regularity in the structure of two-­‐digit numbers (MP.8).

32 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 15 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.N

BT

.3.4

Topic 15 Following the Rules

Teacher Guide, p. 18

Reproducibles, pp. 8 - 10

Daily Math Practice Journal, pp. 32, 34, 35, 36, 37, 39, 43

Magnetic Ten Frames Addition & Subtraction Stamps Discovery Can: Place Value Operations Activity Stations Addition Fluency Puzzles

Adding Tens to Numbers

Adding Within 100

Muffins

www.cpalms.org Make a Ten to Make Adding Easy!

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 11 Lesson 6: Using place value to add a two-digit number to a multiple of ten Lesson 8: Composing a ten while adding ones on to a two-digit number Lesson 9: Fluently adding a two-digit number with a one-digit number

1.N

BT

.3.5

Topic 15 Puzzling Number Patterns

Teacher Guide, p. 19

Reproducibles, p. 10

Daily Math Practice Journal, pp. 27, 29, 31, 38, 40, 42, 44

First Graders Present on Tuesday

Keisha’s Shells

Pages in a Book

Subtract ten

www.cpalms.org Mentally Add and Subtract Tens Let's Have Fun With 10 More and 10 Less

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 14 Lesson 5: Finding ten less than a number Lesson 6: Subtracting ten with a hundred chart

1.N

BT

.3.6

Topic 15 No aligned resources

Teacher Guide, p. 19

Reproducibles, p. 10

Daily Math Practice Journal, pp. 33, 39, 41, 45

Subtracting 40

Subtracting Multiples of Ten

www.cpalms.org Disappearing Tens!

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 14 Lesson 8: Subtracting multiples of ten Lesson 9: Strategies for subtracting multiples of ten

33 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 16: Applying properties of operations to solve problems Pacing: April 2 – 13 Throughout other topics, students have been building understandings of properties of operations through repeated experience with addition and subtraction. In this topic, students apply these understandings to solve real-­‐world and mathematical word problems.

Standards Academic Language

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

MAFS.1.OA.1.2

addends equation symbol unknown number

Students will:

• solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, using tools (manipulatives, number lines, 120 chart, balance, ten-frame, part-part-whole).

• solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20, using drawings or equations with a symbol for the unknown number to represent the problem.

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

MAFS.1.OA.2.3

Students will:

• understand that when adding numbers in any order, the sum does not change.

E.g., 4 + 8 = 12; 8 + 4 = 12; *This is the Commutative Property of addition.

• use the commutative property as a strategy to add.

• understand that when adding three addends, two addends can be grouped to create a friendly number making addition easier.

E.g., To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10, therefore the sum is 12. *This is the Associative Property of addition.

• use the associative property as a strategy to add.

NOTE: Students do not need to use formal terms (Commutative or Associative) for these properties.

7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.7.1 MAFS.K12.MP.8.1

Topic Comments:

1.OA.2.3 is repeated here to include the Associative property of addition.

This topic focuses on students’ understanding of the structure of addition and subtraction and use of properties in problem solving (MP.7) and applying it to their calculations (MP.8).

34 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 16 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

A.1

.2

Topic 16 Safari Sums and Differences

Space Probe

Through the Window Numbers

Teacher Guide, pp. 3 - 5

Daily Math Practice Journal, pp. 15, 17, 19, 21, 25

Reproducibles, p. 3 Addition & Subtraction Stamps

Discovery Can: Addition and Subtraction

Operations Activity Stations

Adding Three Whole Numbers

Bean Bag Toss

Canned Food Drive

Tickets to the School Carnival

www.cpalms.org Mission Addition- Adding Three Numbers

Three's A Charm (Students do not need to record vertically as mentioned in lesson)

https://www.illustrativemathematics.org/content-standards

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 15 Lesson 1 Understand that we can add more than two numbers Lesson 3 Addition with three addends Solve word problems with three addends Lesson 6 Solve word problems with three addends Lesson 8 Using known facts to add three addends

1.O

A.2

.3

Topic 16 I See, You See

Turn Around Taxi

Teacher Guide, pp. 5 - 7 Daily Math Practice Journal, pp. 3, 5, 7, 9, 13, 17 Discovery Can: Addition and Subtraction Monkey Math Balance Addition & Subtraction Stamps Operations Activity Stations

Justifying the Commutative Property of Addition

Lemons and Oranges

Turtles in a Pond

Does it Work for Subtraction

https://www.illustrativemathematics.org/content-standards Domino Addition

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 15 Lesson 9 Using the associative property to solve word problems with three addends

35 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 17: Measuring lengths using a ruler Pacing: April 16 – 27 In this topic, students apply their understanding of measuring length with non-standard units (from Kindergarten) to develop proficiency in using a ruler to measure length to the nearest inch.

Standards Academic Language

Understand how to use a ruler to measure length to the nearest inch. a. Recognize that the ruler is a tool that can be used to measure the attribute of length. b. Understand the importance of the zero point and end point and that the length measure is the span between two

points. c. Recognize that the units marked on a ruler have equal length intervals and fit together with no gaps or overlaps.

These equal interval distances can be counted to determine the overall length of an object. NOTE: This standard has been added in Florida.

MAFS.1.MD.1.a

attribute end point distance height inch intervals length measurement units width zero point

Students will:

• understand and recognize that the ruler is a tool used to measure the attribute of length.

• understand the importance of the zero point and end point and that the length measure is the interval between two points.

• recognize and explain that a ruler has equal length intervals with no gaps or overlaps which can be counted to determine the length of an object.

• use a ruler to measure to the nearest inch by counting the units to determine the overall length of an object.

NOTE:

3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically.

MAFS.K12.MP.3.1 MAFS.K12.MP.5.1

Topic Comments: 1.MD.1.a introduces the inch as a standard unit of measurement for length, which is new to this grade level. Using the ruler as a tool that measures standard units is new for students. Students become familiar with using the ruler as a tool and recognize the strengths and weaknesses of this tool in order to make their own decisions about when and why this tool would be useful (MP.5). Giving students opportunities to justify and critique strategies for measurement (MP.3) supports conceptual understanding of measurement rather than just procedural skills.

Topic 17 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.M

D.1

.a

Topic 17 No aligned resources

Teacher Guide, pp. 20 - 21

Reproducibles, p. 12

Discovery Can: Measurement

Measuring Michael’s Toy Car- 2

www.cpalms.org Measuring With Inches Inch By Inch

www.IXL.com/signin/volusia

https://learnzillion.com/ No aligned resources

Student will count: 1 inch, 2 inches, 3 inches. The length of the crayon is 3 inches.

36 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 18: Finding equal shares of shapes Pacing: April 30 – May 4 In this topic, students partition shapes into equal shares. The focus is fair shares and equal area to support initial understandings of properties such as congruence and symmetry in area—not to discuss fractions. The terms “halves, fourths, and quarters” name the amount of area that is represented to describe the part-­‐whole relationship. Fraction notation is first used in Grade 3.

Standards Academic Language

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.

MAFS.1.G.1.3

area decompose equal shares fourths half halves partition quarters whole

Students will:

• partition circles and rectangles into two and four equal shares. o describe the area of the shape using the words halves, fourths, and quarters. o describe the area of the shape using the phrases half of, fourth of, and quarter of. o describe the whole area as two of two equal shares or four of four equal shares.

• explain that decomposing a shape (i.e., breaking it into smaller shapes/pieces) into more equal shares creates smaller shares.

E.g., one of two shares is larger than one of four shares because the whole has been decomposed into less shares.

3. Construct viable arguments and critique the reasoning of others. MAFS.K12.MP.3.1

Topic Comments:

Students construct arguments to support their own partitioning, but also distinguish correct reasoning from that which is flawed (MP.3).

Topic 18 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.G

.1.3

Topic 18 No aligned resources

Teacher Guide, pp. 23 - 24 Reproducibles, pp. 16 - 17 Daily Math Practice Journal, pp. 67, 69, 70, 71 Discovery Can: Geometry

Half of a Rectangle

Partition a Rectangle

Which is Less

www.cpalms.org Pizza Anyone? Exploring Halves and Fourths/Quarters

Fair Share Picnic

https://www.illustrativemathematics.org/content-standards Equal Shares

https://learnzillion.com/ Unit 17 Lesson 1 Partition shapes into halves Lesson 3 Partition shapes into fourths Lesson 4 Partition shapes into fourths Lesson 5 Partition shapes into halves and quarters

37 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 19: Demonstrating proficiency in addition and subtraction situations Pacing: May 7 – 30 In this topic, students apply their understanding from the entire year to demonstrate fluency in addition and subtraction. They should have experienced ample opportunities to practice the various problem types using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

Standards Academic Language

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, e.g., by

using objects, drawings, and equations with a symbol for the unknown number to represent the

problem (Students are not required to independently read the word problems.).

NOTE: This standard has been amended in Florida to include “Students are not required to independently

read the word problems”.

MAFS.1.OA.1.1

doubles (+/-) equivalent fluent known sums

Students will:

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, taking apart and comparing using tools (manipulatives, number lines, 120 chart, balance, ten-frame, part-part-whole).

• model and solve addition and subtraction word problems within 20 involving situations of adding to, taking from, putting together, and taking apart and comparing using drawings or equations with a symbol for the unknown number to represent the problem.

• solve word problems with unknown numbers in different positions.

NOTE: See Common Addition and Subtraction Situations Table on page 43.

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

MAFS.1.OA.3.6

Students will:

• use counting on and making 10 strategies to add within 20.

• decompose a number leading to a ten to subtract within 20.

• use the relationship between addition and subtraction to solve within 20.

• use strategies to add and subtract within 20 (creating equal but easier or known sums, doubles, doubles +/- 1).

• add and subtract within 10 with fluency.

NOTE: Computational fluency is defined as accuracy, efficiency, and flexibility.

3. Construct viable arguments and critique the reasoning of others. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.3.1 MAFS.K12.MP.8.1

Topic Comments:

1.OA.3.6 is finalized in this topic to include creating equivalent but easier or known sums (e.g., doubles plus or minus 1) as a

strategy for solving addition and subtraction problems.

Students will select, justify, and explain their strategies in addition and subtraction situations (MP.3). Students find shortcuts by using numerical reasoning to effectively add and subtract (MP.8).

38 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 19 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

A.1

.1

Topic 19 Safari Sums and Differences

Telling Tales

Through the Window Numbers

Teacher Guide, pp. 3-5

Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 23

Reproducibles, p. 3 Addition & Subtraction Stamps

Discovery Can: Addition and Subtraction

Operations Activity Stations

Problem Solving Center

Add to (Change Unknown) Word Problems

Add to (Result Unknown) Word Problems

Add to (Start Unknown) Word Problems

Birds on a Branch

Compare (Bigger Unknown) Word Problems

Compare (Differences Unknown) Word Problems

Compare (Smaller Unknown) Word Problems

Fish in a Pond

How Many More Stickers

More Add to (Change Unknown) Problems

Put Together/Take Apart (Addend Unknown) Word Problem

Put Together/Take Apart (Both Addends Unknown) Word Problems

Put Together/Take Apart (Total Unknown) Word Problem

Red Birds and Blue Birds

Take From (Change Unknown) Word Problems

Take From (Result Unknown)

Take From Start Unknown

The Cupcake Problem

Trains and Jump ropes

How Many M&M’s

https://www.illustrativemathematics.org/content-standards At the Park Boys and Girls - 1 Maria’s Marbles Sharing Markers Finding a Chair Peyton’s Books

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 1 Lesson 6: Strategies for adding numbers within 20 Lesson 9: Counting up and counting back on a number path Lesson 10: Solving candy store problems

Unit 9 Lesson 1: Understand how to solve compare problems Lesson 2: Practice solving compare problems

39 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Topic 19 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

1.O

A.3

.6

Topic 19 Clowning Around With the Facts

Rally with Differences

Seek and Hide

Tic Tac and Twenty (game)

Teacher Guide, pp. 10 - 11

Daily Math Practice Journal, pp. 2, 4, 6, 8, 10, 12, 14, 16

Discovery Can: Addition and Subtraction

Addition & Subtraction Stamps Operations Activity Stations

Addition Fluency Puzzles

More than One Way to Solve a Problem

Use Strategies to Add and Subtract

Using Addition and Subtraction Strategies

Ways to Solve a Problem

www.cpalms.org Dangerous Doubles

www.IXL.com/signin/volusia

https://learnzillion.com/ Unit 6 Lesson 9: Solve problems with related facts Unit 18 Lesson 4 Solving many kinds of problems using addition and subtraction Lesson 8 Using known facts to solve new addition and subtraction problems Lesson 9 Creating easier but equivalent problems

http://achievethecore.org Fluency Resources

40 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Critical Areas for Mathematics in Grade 1

In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

(1) Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They

use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.

(2) Students develop, discuss and use efficient, accurate, and generalizable methods to add and subtract multiples of 10 within 100. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.

(3) Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal sized units) and the transitivity principle for indirect measurement.1

(4) Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build

understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.

1 Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use this technical term.

41 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Grade 1 Major, Supporting, and Additional Work

Topic Title Major Work Supporting Work Additional Work

1 Understanding ten ones make a ten

1.OA.3.6, 1.NBT.2.2

2 Using data to add and subtract within 20

1.OA.1.1, 1.OA.3.5 1.MD.3.4

3 Ordering and comparing lengths

1.MD.1.1

4 Exploring Quantities to 99

1.NBT.1.1

5 Telling and writing time to the hour

1.MD.2.3

6 Developing addition and subtraction strategies 1.OA.2.3, 1.OA.2.4,

1.OA.3.6

7 Distinguishing attributes of shapes

1.G.1.1

8 Using place value to read, write, represent, and compare numbers

1.NBT.1.1, 1.NBT.2.2, 1.NBT.2.3

9 Extending strategies for solving addition and subtraction problems 1.OA.1.1, 1.OA.3.6,

1.OA.4.7 1.MD.3.4

10 Telling and writing time to the half hour

1.MD.2.3

11 Adding multiples of ten

1.NBT.3.4, 1.NBT.3.5

12 Identify and combine values of money

1.MD.2.a

13 Composing and drawing shapes

1.G.1.1, 1.G.1.2

14 Interpreting and using symbols in numeric expressions and comparisons

1.OA.4.7, 1.OA.4.8, 1.NBT.2.3

15 Using understanding of place value to add and subtract 1.NBT.3.4, 1.NBT.3.5,

1.NBT.3.6

16 Applying properties of operations to solve problems

1.OA.1.2, 1.OA.2.3

17 Measuring lengths using a ruler

1.MD.1.a

18 Finding equal shares of shapes

1.G.1.3

19 Demonstrating proficiency in addition and subtraction situations

1.OA.1.1, 1.OA.3.6

42 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Standards for Mathematical Practice

Grade 1 students will:

1. Make sense of problems and persevere in solving them. (SMP.1) Mathematically proficient students in Grade 1 examine problems (tasks), can make sense of the meaning of the task and find an entry point or a way to start the task. Grade 1 students also develop

a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Grade 1, students’ work builds from Kindergarten and still heavily

relies on concrete manipulatives and pictorial representations. The exception is when the CCSS uses the word fluently, which denotes mental mathematics. Grade 1 students also are expected to

persevere while solving tasks; that is, if students reach a point in which they are stuck, they can reexamine the task in a different way and continue to solve the task. Lastly, at the end of a task

mathematically proficient students in Grade 1 ask themselves the question, “Does my answer make sense?”

2. Reason abstractly and quantitatively. (SMP.2) Mathematically proficient students in Grade 1 make sense of quantities and the relationships while solving tasks. This involves two processes- decontextualizing and contextualizing. In Grade 1,

students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 60 children on the playground and some children go line up. If there are 20

children still playing, how many children line up?” Grade 1 students are expected to translate that situation into the equation: 60 – 20 = ___ and then solve the task. Students also contextualize

situations during the problem solving process. For example, while solving the task above, students refer to the context of the task to determine that they need to subtract 20 since the number of

children on the playground is the total number except for 20 that are still playing. The processes of reasoning also applies to Grade 1, as they look at ways to partition 2-dimensional geometric

figures into halves, and fourths.

3. Construct viable arguments and critique the reasoning of others. (SMP.3) Mathematically proficient students in Grade 1 accurately use definitions and previously established answers to construct viable arguments about mathematics. For example, while solving the task,

“There are 15 books on the shelf. If you take some books off the shelf and there are now 7 left, how many books did you take off the shelf?” students will use a variety of strategies to solve the task.

After solving the task, Grade 1 students are expected to share problem solving strategies and discuss the reasonableness of their classmates’ strategies.

4. Model with mathematics. (SMP.4) Mathematically proficient students in Grade 1 model real-life mathematical situations with a number sentence or an equation, and check to make sure that their equation accurately matches the

problem context. Grade 1 students rely on concrete manipulatives and pictorial representations while solving tasks, but the exception is that they will also write an equation to model problem

situations. For example, while solving the task “There are 11 bananas on the counter. If you eat 4 bananas, how many are left?” Grade 1 students are expected to write the equation 11 – 4 = 7.

Likewise, Grade 1 students are expected to create an appropriate problem situation from an equation. For example, students are expected to create a story problem for the equation, 13 – 7 = 6. 5. Use appropriate tools strategically. (SMP.5)

Mathematically proficient students in Grade 1 have access to and use tools appropriately. These tools may include counters, base ten blocks, hundred charts, number lines, and concrete geometric

shapes. Students should also have experiences with educational technologies, such as calculators and virtual manipulatives that support conceptual understanding and higher-order thinking skills.

During classroom instruction, students should have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use. For example, while solving 12

+ 8 = __, students explain why base ten blocks are more appropriate than counters.

6. Attend to precision. (SMP.6) Mathematically proficient students in Grade 1 are precise in their communication, calculations, and measurements. In all mathematical tasks, students in Grade 1 describe their actions and strategies

clearly, using Grade-level appropriate vocabulary accurately as well as giving precise explanations and reasoning regarding their process of finding solutions. For example, while measuring objects

students check to make sure there are no gaps or overlaps. During tasks involving number sense, students check their work to ensure the accuracy and reasonableness of solutions.

7. Look for and make use of structure. (SMP.7) Mathematically proficient students in Grade 1 carefully look for patterns and structures in the number system and other areas of mathematics. While solving addition problems, students begin to

recognize the commutative property. While decomposing two-digit numbers, students realize that any two-digit number can be broken into tens and ones. Further, Grade 1 students make use of

structure when they work with subtraction as missing addend problems.

8. Look for and express regularity in repeated reasoning. (SMP.8) Mathematically proficient students in Grade 1 begin to look for regularity in problem structures when solving mathematical tasks. For example students look for opportunities to use strategies they are

familiar with. Further, students use repeated reasoning while solving a task with multiple correct answers. For example when looking for combinations of numbers which make 10.

43 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department July 2017

Common Addition and Subtraction Situations Table

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Both Addends Unknown1 Addend Unknown2

Put Together/

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = ? + ? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5 5 – 3 = ?

Difference Unknown Bigger Unknown Smaller Unknown

Compare

“How many more?” version:

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

“How many fewer?” version:

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5 5 – 2 = ?

“More” version suggests operation:

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

“Fewer” version suggests operation:

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

“Fewer” version suggests wrong operation:

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ? 3 + 2 = ?

“More” version suggests wrong operation: Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ? ? + 3 = 5

Darker shading indicates the four Kindergarten problem subtypes. Grade 1 and 2 students work with all subtypes and variants. Unshaded (white) problems are the four difficult subtypes or variants that students should work with in Grade 1 but need not master until Grade 2. Adapted from CCSS, p. 88, which is based on Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity, National Research Council, 2009, pp. 32–33.

1 This can be used to show all decompositions of a given number, especially important for numbers within 10. Equations with totals on the left help children understand that = does not always mean “makes” or “results in” but always means “is the same number as.” Such problems are not a problem subtype with one unknown, as is the Addend Unknown subtype to the right. These problems are a productive variation with two unknowns that give experience with finding all the decompositions of a number and reflecting on the patterns involved.

2 Either addend can be unknown; both variations should be included.