web viewthe common core state standards for mathematical practice are expected to be integrated into...

Striving toward greater focus and coherence throughContent Standards and Practice Standards

Waterloo Community Unit School District

Third Grade Mathematics Curriculum Map

Waterloo School District

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How to Read the Grade Level Content Standards

Standards define what students should understand and be able to do.

Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.

Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

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Standards for Mathematical PracticeThe Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all students Grades K-12. Below are a few examples of how these Practices may be integrated into tasks students complete.

1. Make sense of problems and persevere in solving them.

In third grade, mathematically proficient students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.

2. Reason abstractly and quantitatively.

Mathematically proficient third graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.

3. Construct viable arguments and critique the reasoning of others.

In third grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.

4. Model with mathematics.

Mathematically proficient students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Third graders should evaluate their results in the context of the situation and reflect on whether the results make sense.

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5. Use appropriate tools strategically.

Mathematically proficient third graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles.

6. Attend to precision.

Mathematically proficient third graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square units.

7. Look for and make use of structure.

In third grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and distributive properties).

8. Look for and express regularity in repeated reasoning.

Mathematically proficient students in third grade should notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”

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Third Grade Mathematics Curriculum Map

Waterloo School District Scope and Sequence Overview

Unit of StudyEveryday

Math Alignment

Domain and Standards

1 Section 1

Domain:Standards:

2

3

4

5

6

7

8

9

10

11

12

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Third GradeInstruction and Assessment Schedule

2013-2014

It is expected that the units will be taught consecutively. The table below reflects which units are assessed on each benchmark. It is possible to begin a new unit prior to the quarter in which it is being assessed.

Approx. Number of

Days of Instruction

B

ench

mar

k 1

?? ?? ??

Com

mon

Ass

essm

ent A

?? ?? ??

C

omm

on A

sses

smen

t B

Ben

chm

ark

2

?? ?? ??

C

omm

on A

sses

smen

t C

?? ?? ??

C

omm

on A

sses

smen

t D

Ben

chm

ark

3

End ofYear

InstructionalContent

Unit ofStudy

1

Unit ofStudy

2

Unit ofStudy

3

Unit ofStudy

4

Unit ofStudy

5

Unit ofStudy

6

Unit ofStudy

7

Unit ofStudy

8

Unit ofStudy

9

Unit ofStudy

10

Unit ofStudy

11

Unit ofStudy

12

Getting Ready for Gr.1 Unit

Assessment Ch. 1Test

Ch. 2Test

Ch. 3Test

Ch. 4Test

Ch. 5Test

Ch. 6Test

Ch. 7 Test

Ch. 8Test

Ch. 9Test

Ch. 10Test

Ch. 11Test

Ch. 12Test

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Third Grade Mathematics Curriculum Map - Overview Waterloo School District policy requires elementary mathematics instruction to be 60 minutes per day.

Unit of Study The mathematical content is sequenced in Units of Study that will take approximately 2-3 weeks each to teach.The sequence of Units of Study provides a coherent flow to mathematics instruction throughout the year.

Everyday Math The primary textbook adopted in Waterloo School District for Grades K-6

Teacher’sResources and Notes

Teachers are encouraged to make notes of their own lesson ideas and resources that align with each Unit ofStudy.

AdditionalResources

Assessment

There are many formative and summative assessment options:

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Unit of Study 1 & 5: Place Value

Third Grade Quarter 1 Approx. ?? days

Domain: NBTCluster(s): 3.NBT.1, 3.NBT.2

Domain: MDCluster(s): 3.MD.1

Domain: OACluster(s): 3.OA.9

Math Content Objectives Vocabulary Teacher’s Resources and Notes

I can:3.NBT.1

Round whole numbers to the nearest 10 or 100

3.NBT.2 Fluently add and subtract within the thousands

using strategies

3.MD.1 Tell and write time to the nearest minute Solve word problems involving addition and

subtraction of time intervals in minutes

3.OA.9 Find arithmetic (number) patterns in the addition

and multiplication tables. Explain these patterns.

Data Decompose Units Number grid Arrow Rule Difference Equivalent Elapsed time Decimal point Bar graph Frames-and Arrows Diagram Picture graph Line plot Pattern Tally Chart

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Unit of Study 1 (continued)Math Content Objectives Vocabulary Teacher’s Resources and Notes

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Everyday MathCommon Core Alignment

Unit of Study 1 – Additional Resources

Telling Time Lesson 1-4:

3.NBT.23.MD.1

MoneyLesson 1-10:

3.NBT.2

Lesson 1-11:3.NBT.13.NBT.2

Number Grid/PatternsLesson 1-1: Number and Number Sequences

Lesson 1-2: Number Grids

Lesson 1-8: Finding Differences

3.NBT.23.OA.9

Lesson 1-12: Patterns

Beginning of Year Assessment

Super Teacher Telling Time – Nearest 5 minute, exact minute, and elapsed time

Skip Lesson 1-5 during Unit 1. Use the bar graph part later during Unit 10.

Super Teacher Money Worksheets and Game

Super Teacher Number pattern Worksheets

After completing Unit 1, go to Unit 5.

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Place ValueLesson 5-1: Place Value through Ten-Thousands

Lesson 5-2: Reading, Writing, and ordering Numbers

Lesson 5-4: Place Value through Hundred-Thousands

Use Homelink 5-5 for Lesson 5-1.

Play Number Top-It during Lessson 5-2.

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Unit of Study 2 Third Grade Quarter ?? Approx. ?? days

Domain: NBTCluster(s): 3.NBT.1, 3.NBT.2

Domain: MDCluster(s):

Domain: OACluster(s): 3.OA.8, 3.OA.9


I can:3.NBT.1



using strategies

3.OA.8 Use mental math, estimation and rounding to

decide if my answer is reasonable Represent the problem using an equation/number

model with a letter for the unknown Use addition, subtraction, multiplication and

division to solve two step word problems3.OA.9

Identify and explain arithmetic patterns in addition and multiplication

Units Difference Change Diagram Comparison Diagram Parts-and-total diagram Addend Ball-park estimate Deposit Turn-around rule Rule Output Input Fact family/number family Number model Function machine Partial-sums algorithm Partial-sums method Trade-first algorithm Number story

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Lesson 2-1: Fact Families3.OA.9, 3.NBT.2

Lesson 2-2: Extensions of Addition and Subtraction Facts3.OA.9, 3.NBT.2

Lesson 2-3: “What’s My Rule?”3.NBT.2

Lesson 2-4: Parts-and-Total Stories3.NBT.2

Lesson 2-5: Change Number Stories3.NBT.2

Lesson 2-6: Comparison Number Stories3.NBT.2

Lesson 2-7: The Partial-Sums Algorithm3.NBT.1, 3.NBT.2

Lesson 2-8: Subtraction Algorithms3.NBT.2, 3.NBT.1

Lesson 2-9: Addition with Three or More Addends3.OA.8, 3.NBT.2

Lesson 2-10: Assessment

Start addition and subtraction timed tests.

Play Roll to 100, Name That Number, Beat the Calculator, Subtraction Top-It, Number Grid Difference, Target 50, and Base Ten Trading Game for fluency practice. (See page 92 in the Teacher’s Edition.)

More possible practice Student Journal p. 56-57. (3 digit subtraction and addition)

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Domain: NFCluster(s): 3.NF.2a, 3.NF.2b, 3.NF.3a

Domain: MDCluster(s): 3.MD.4, 3.MD.5a, 3.MD5b, 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.8

Domain:Cluster(s):


I can:

3.NF.2a Divide a number line into equal intervals (0arts) to

represent fractions

3.NF.2b Place fractions on a number line that is divided into

intervals

3.NF.3a Show two fractions as equivalent (equal) if they are

the same size Show two fractions as equivalent (equal) if they are

on the same point on a number line

3.MD.4 Measure and record lengths to the nearest half and

fourth of an inch Use measurement data to make a horizontal line

plot marked off in appropriate units

Area Centi- Centimeter (cm) Deci- Decimeter (dm) Foot Inch (in.) Length Line segment Meter Metric system Milli- Millimeter (mm) Parallelogram Perimeter Polygon Rectangle Rhombus Square Square feet Square yards

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3.MD.5a Use square units to measure area

3.MD.5b Label area with square units

3.MD.6 Measure area by counting square units (sq.

centimeters and sq. inches)

3.MD.7a Find the area of a rectangle with tiles and show

the area can be found by multiplying the side lengths

3.MD.7b Solve real-world math problems that involve area

3.MD.8 Solve real-world problems involving perimeter and

area

Standard unit Tiling Trapezoid Triangle U.S. customary system Yard

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Lesson 3-2: Measuring with a Ruler3.NF.2a, 3.NF.2b, 3.NF.3a3.MD.4

Lesson 3-3: Standard Linear Measure3.MD.4

Lesson 3-4: Perimeter3.MD.8

Lesson 3-5:3.MD.4

Lesson 3-6: Exploring Perimeter and Area3.MD.5a, 3.MD.5b, 3.MD.6

Lesson 3-7: Area3.MD.5a, 3.MD.5b, 3.MD.63.MD.7a

Lesson 3-8: Number Models for Area3.MD.5a, 3.MD.5b, 3.MD.63.MD.7a, 3.MD.7b

For Lesson 3-5, do not teach part 1 of Teaching the Lesson

Do not teach Lesson 3-9. Just do Math boxes on p. 77.

Do Math Journal p. 99 (Do this page any time during Unit 3. It is measuring to the nearest half and fourth inch.

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19


Domain: NBTCluster(s): 3.NBT.2

Domain: MDCluster(s): 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.8

Domain: OACluster(s): 3.OA.1, 3.OA.2, 3. OA.3, 3.OA.4, 3. OA.5, 3.OA.6, 3.OA.7, 3.OA.9


I can:

3.NBT.2 Fluently add and subtract within the thousands using

strategies

3.MD.6 Measure area by counting square units

3.MD.7a Find the area of a rectangle with tiles and show the

area can be found by multiplying the side lengths

Array As the crow flies Dividend Divisor Factor Multiples of equal groups Multiplication Multiplication/division diagram Multiplication/division fact table Product Quotient Remainder Square numbers Turn-around shortcut

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3.MD.7b Solve real-world math problems that involve area

3.MD.8 Solve real-world problems involving perimeter

3.OA.1 Explain the meaning of the product

3.OA.2 Explain the meaning of the quotient

3.OA.3 Solve multiplication/word problems within 100

involving equal groups, arrays and/or measurement quantities

3.OA.4 Find the unknown whole number (variable) in a

multiplication/division equation

3.OA.5 Use the properties to multiply and divide

(commutative property)

3.OA.6 Use multiplication to find the answer to a division

problem3.OA.7

Fluently multiply and divide within 100 using strategies and properties

3.OA.9 Identify and explain arithmetic patterns in addition

and multiplication

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Lesson 4-1: Multiples of Equal Groups3. OA.1, 3.OA.3, 3.OA.43.OA.5, 3.OA.7

Lesson 4-2: Multiplication Arrays3. OA.1, 3.OA.3, 3.OA.43.OA.5, 3.OA.7, 3.MD.7a3.MD.7b, 3.MD.8

Lesson 4-3: Equal Shares and Equal Groups3.OA.1, 3.OA.2, 3.OA.33.OA.4, 3.OA.6, 3.OA.7

Lesson 4-4: Division Ties to Multiplication3.OA.2, 3.OA.3, 3.OA.43.OA.6, 3.OA.7

Lesson 4-5: Multiplication Fact Power and Shortcuts3.OA.5, 3.OA.7, 3.OA.93.NBT.2

Lesson 4-6: Multiplication and Division Fact Families3.OA.2, 3.OA.4, 3.OA.53.OA.6, 3.OA.7, 3.OA.9

Begin multiplication timed tests to begin establishing fluency.

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Lesson 4-7: Baseball Multiplication3.OA.5, 3.OA.7

Lesson 4-8: Exploring Arrays and Facts3.OA.1, 3.OA.7, 3.OA.9,3.MD.6

Lesson 4-9:3.MD.6, 3.MD.7b

Do not complete Lesson 4-9. Only do Math Journal pages 96A and 96B.

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Domain: NBTCluster(s):


Domain: OACluster(s):


I can:

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25



26



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Domain: GCluster(s): 3.G.1


Domain: OACluster(s):


I can:3.MD.8

Solve real-world problems involving perimeter and area.

3.G.1

Classify shapes by their attributes and draw a shape that does not belong to a group according to the attributes.

2-dimenisional Equilateral triangle kite Line segment Parallel Parallelogram Plane figures Polygon Quadrangle Rectangle Regular polygon Rhombus Right angle (used for describing shape) Right triangle Side Square Trapezoid Triangle Vertex/Vertices

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Lesson 6-4: Triangles3.MD.8Lesson 6-5: Quadrangles3.MD.8, 3.G.1

Lesson 6-6: Polygons3.MD.8, 3.G.1

Lesson 6-8: Area and Perimeter

3.MD.8

Skip Homelink 6-4.

Skip part 1 in Lesson 6-8. Teach part 2 using Math Master p. 205A.

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Domain: NBTCluster(s): 3.NBT.1, 3.NBT.2, 3.NBT.3


Domain: OACluster(s): 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.9


I can:3.OA.1

Explain the meaning of the product.

3.OA.4 Find the unknown whole number in a multiplication

and division equation.

3.OA.5 Use the properties to multiply and divide. Use multiplication to find the answer to a division

problem.

3.OA.7 Fluently multiply and divide within 100 using

strategies and properties Fluently recall my multiplication facts 0-9.

Estimate Extended facts Factor Parentheses Product Square number Square product

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3.OA.9 Identify and explain arithmetic patterns in addition

and multiplication.3.NBT.1

Round whole numbers to the nearest 10 or 100.3.NBT.2

Add and subtract within 100.

3.NBT.3 Multiply one-digit whole numbers by multiples of

10

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Lesson 7-1: Patterns in Products3.OA.1, 3.OA.4, 3.OA.7, 3.OA.9

Lesson 7-2: Multiplication Facts Survey3.OA.4, 3.OA.5, 3.OA.7, 3.OA.9

Lesson 7-3: Fact Power3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.6, 3.OA.7

Lesson 7-4: Number Models with Parentheses3.OA.8, 3.NBT.2

Lesson 7-5: Scoring in Basketball3.OA.7, 3.OA.8

Lesson 7-6: Extended Facts: Multiplication and Division3.OA.6, 3.OA.7, 3.NBT.3

Lesson 7-7: Estimating Costs3.OA.3, 3.OA.8, 3.NBT.1, 3.NBT.3

Lesson 7-8: Extended Facts: Products of Tens3.OA.3, 3.NBT.3

Skip lesson 7-9

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Lesson 7-10:Assessment

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Domain: NFCluster(s): 3.NF.1, 3.NF.2, 3.NF.2a, 3.NF.2b, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.NF.3d

Domain: GCluster(s): 3.G.1, 3.G.2



I can:3.NF.1

Explain and show that a fraction is a part of a whole Explain and show the meaning of the numerator

and denominator.

3.NF.2 Explain how a fraction is a number on a number

line and represent fractions on a number line.3.NF.2a

Divide a number line into equal parts to represent fractions.

3.NF.2b Place fractions on a number line that is divided into

parts.3.NF.3

Explain why fractions are equivalent.

Denominator Equal Equivalent fractions Mixed number Numerator Unit fraction Whole(the one)

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3.NF.3a Show two fractions as equal if they are on the same

point on a number line.

3.NF.3b Recognize and show simple equal fractions.

3.NF.3c Write whole numbers as fractions and recognize

that they are equal.3.NF.3d

Compare two fractions with the same numerator or the same denominator.

3.G.1 Classify shapes by their attributes and draw a

shape that does not belong to a group according to the attributes.

3.G.2 Divide shapes into equal areas and write the area

of each part as a fraction.

3.MD.4 Measure and record lengths to the nearest half and

fourth of an inch

Measurement data to make a horizontal line plot marked off in appropriate units.

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Lesson 8-1: Naming Parts with Fractions3.NF.1

Lesson 8-3: Exploring Fractions, Re-Forming Squares, and Combinations3.G.2

Lesson 8-4: Number-Line Posters for Fractions3.NF.1, 3.NF.2, 3.NF.2a, 3.NF.2b, 3.NF.3, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.NF.3d, 3.G.1

Lesson 8-5: Equivalent Fractions3.NF.1, 3.NF.2, 3.NF.2a, 3.NF.2b, 3.NF.3, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.NF.3d, 3.G.2

Lesson 8-6: Comparing Fractions3.NF.3a, 3.NF.3b, 3.NF.3d

Lesson 8-7: Fractions Greater than One3.NF.1, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.G.2

Lesson 8-8: Fractions in Number Stories

3.NF.2, 3.NF.2a, 3.NF.2b, 3.NF.3, 3.NF.3a, 3.NF.3c, 3.NF.3d, 3.MD.4

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Lesson 8-9: Assessment

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Domain: NBTCluster(s): 3.NBT.1, 3.NBT.2, 3.NBT.3

Domain: MDCluster(s): 3.MD.5b, 3.MD.7a, 3.MD.7c, 3.MD.7d

Domain: OACluster(s): 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8


I can:3.NBT.1



using strategies

3.NBT.3 Use strategies to multiply one-digit whole numbers

by multiples of 10

3.MD.5b Label area with square units

3.MD.7a Find the area of a rectangle with tiles and show the

area can be found by multiplying the side lengths

degrees Celsius degrees Fahrenheit lattice multiplication partial-products algorithm

Make sure to play Fraction Top-It. (9-5)

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3.MD.7c

Use tiles to make the area of a rectangle and represent the distributive property using this model

3.MD.7d Find the area of rectilinear figures by separating

the figure and adding the area of the separated figures together

3.OA.1 Explain the meaning of the product

3.OA.2 Explain the meaning of the quotient

3.OA.3 Solve multiplication/division word problems within

100 involving equal groups, arrays, and measurement quantities.

3.OA.5 Use the properties to multiply and divide

(Commutative, Associative, Distributive Property)

3.OA.6 Use multiplication to find the answer to a division

problem

3.OA.7 Fluently multiply and divide within 100 using

strategies and properties

3.OA.8 Use any of the four operations to solve two-step

word problems Represent the problem using an equation with a

letter for the unknown Use mental math, estimation, and rounding to

decide if my answer makes sense

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Lesson 9-1: Multiply and Divide with Multiples of 10, 100, and 1,0003.OA.3, 3.OA.6, 3.OA.83.NBT.3

Lesson 9-2: Using Mental Math to Multiply

3.OA.1, 3.OA.3, 3.OA.53.OA.8, 3.NBT.3

Lesson 9-3: Exploring Arrays, Areas, and Fractions

3.NBT.3, 3.MD.5b, 3.MD.7a3.MD.7c, 3.MD.7d

Lesson 9-4: A Multiplication Algorithm

3.OA.3,3.OA.5, 3.NBT.23.MD.7a, 3.MD.7c,3.MD.7d

Lesson 9-5: Buying at the Stock-Up Sale3.OA.3, 3.OA.8, 3.NBT.13.NBT.2

Lesson 9-6: Factors of a Whole Number

3.OA.2, 3.OA.5, 3.OA.7 Make sure to play Fraction Top-It before Unit test.

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Lesson 9-7: Sharing Money3.OA.2, 3.OA.3, 3.OA.7

Lesson 9-8: Broken-Calculator Division3.OA.3

Assessment

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44


Domain: NFCluster(s): 3.NF.3, 3.NF.3d

Domain: MDCluster(s): 3.MD.2, 3.MD.3, 3.MD.4

Domain:Cluster(s):


45

I can:3.NF.3

Recognize when two fractions are equivalent when they are the same size or the same point on a number line

3.NF.3d Compare two fractions with the same numerator or

the same denominator using <, >, or =

capacity of a container capacity of a scale cubic centimeter frequency table plotting the point precision volume weight

46


3.MD.2 Estimate and measure liquid volumes using liters Solve one-step word problems involving volume Estimate and measure masses of objects using

grams and kilograms Solve one-step word problems involving mass

3.MD.3 Draw a scaled picture graph or bar graph Solve one and two-step problems using the

picture or bar graph

3.MD.4 Measure and record lengths to the nearest half

and fourth of an inch Use measurement data to make a horizontal line

plot marked off in appropriate units

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Lesson 10-1: Review: Length3.NF.33.NF.3d

Lesson 10-2: Volume

Lesson 10-3: Weight3.MD.2

Lesson 10-4: Exploring Weight and Volume

Lesson 10-5: Capacity3.MD.2

Lesson 10-6: Bar & Picture Graphs3.MD.3

Lesson 10-9: Frequency Distributions

Assessment

Play Fraction-Top it

Use scales and graduated cylinders.

Do not do Mean and Median. Super Teacher Worksheets for Bar Graphs and Picture Graphs

Use Math Master 345 with Lesson 10-6.

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