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312NASE

Did you know that tigers can leap horizontally up to 10 meters? Thats almost 33 feet! You may not be able to jump that far, but Performance Coach will help you do your best on your tests this year!

E n g l i s h L a n g u a g e A r t sMathematicsMathematics

312NASE_G5_MATH_SE_cvr.indd 1 2/14/14 10:41 AM

CONTENTS

Standards

Letter to the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Domain 1: oPERaTionS anD aLGEBRaiC THinKinG . . . . 5Lesson 1 Writing Numerical Expressions . . . . . . . . . . . . . . . . . 6 5.OA.2

Lesson 2 Evaluating Numerical Expressions . . . . . . . . . . . . . . 13 5.OA.1

Lesson 3 Relating Numerical Expressions . . . . . . . . . . . . . . . . 21 5.OA.3

Domain 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Domain 2: nUmBER anD oPERaTionS in BaSE TEn . . . 37Lesson 4 Comparing the Values of the Digits of a Number. . . 38 5.NBT.1

Lesson 5 Multiplying and Dividing by Powers of 10. . . . . . . . 45 5.NBT.2

Lesson 6 Reading and Writing Decimals . . . . . . . . . . . . . . . . . 52 5.NBT.3.a

Lesson 7 Comparing Decimals. . . . . . . . . . . . . . . . . . . . . . . . . 59 5.NBT.3.b

Lesson 8 Rounding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.NBT.4

Lesson 9 Multiplying Whole Numbers . . . . . . . . . . . . . . . . . . 74 5.NBT.5

Lesson 10 Dividing Whole Numbers . . . . . . . . . . . . . . . . . . . . . 83 5.NBT.6

Lesson 11 Adding and Subtracting Decimals . . . . . . . . . . . . . . 93 5.NBT.7

Lesson 12 Multiplying Decimals. . . . . . . . . . . . . . . . . . . . . . . . 103 5.NBT.7

Lesson 13 Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.NBT.7

Domain 2 Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Domain 3: nUmBER anD oPERaTionS FRaCTionS . . . . 129Lesson 14 Adding and Subtracting Fractions and

Mixed Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.NF.1

Lesson 15 Solving Problems with Addition and Subtraction of Fractions . . . . . . . . . . . . . . . . . . . . . 140 5.NF.2

Lesson 16 Interpreting Fractions as Division. . . . . . . . . . . . . . 148 5.NF.3

Lesson 17 Multiplying Fractions. . . . . . . . . . . . . . . . . . . . . . . . 155 5.NF.4.a

Lesson 18 Area of Rectangles. . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.NF.4.b

Lesson 19 Comparing Products to Factors . . . . . . . . . . . . . . . 173 5.NF.5.a, 5.NF.5.b

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iii

Standards

Lesson 20 Solving Problems with Multiplying Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . 180 5.NF.6

Lesson 21 Dividing Unit Fractions with Whole Numbers. . . . 188 5.NF.7.a, 5.NF.7.b

Lesson 22 Solving Problems with Division of Unit Fractions and Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . 197 5.NF.7.c

Domain 3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Domain 4: mEaSUREmEnT anD DaTa . . . . . . . . . . . . . . 211Lesson 23 Converting Measurement Units . . . . . . . . . . . . . . . 212 5.MD.1

Lesson 24 Line Plots with Fractions . . . . . . . . . . . . . . . . . . . . . 220 5.MD.2

Lesson 25 Understanding Volume . . . . . . . . . . . . . . . . . . . . . . 229 5.MD.3.a, 5.MD.3.b, 5.MD.4

Lesson 26 Volume of Rectangular Prisms . . . . . . . . . . . . . . . . 237 5.MD.5.a, 5.MD.5.b

Lesson 27 Adding Volumes of Rectangular Prisms. . . . . . . . . 245 5.MD.5.c

Domain 4 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

Domain 5: GEomETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Lesson 28 Graphing on Coordinate Planes. . . . . . . . . . . . . . . 260 5.G.1

Lesson 29 Solving Problems with Coordinate Planes . . . . . . 268 5.G.2

Lesson 30 Classifying Two-Dimensional Figures . . . . . . . . . . 276 5.G.3, 5.G.4

Domain 5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

Performance Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

math Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

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1 GETTING ThE IDEA

A pattern is a sequence of numbers in an ordered list. Each number in the pattern is called a term. The first 5 terms of a pattern are shown below.

8, 16, 24, 32, 40,

You can generate numerical patterns using given rules, identify relationships of the corresponding terms between two patterns, and graph the patterns on a coordinate plane.

Example 1Write a rule for each pattern. Then identify the relationship between the two patterns.

4, 8, 12, 16, 20,

12, 24, 36, 48, 60,

Strategy Compare terms to identify rules and relationships in the patterns.

Step 1 Identify a rule in each pattern.

Determine what you can do to the first term to get the second term.

Check that the rule applies to every term in the pattern.

4, 8, 12, 16, 20,

444 4

You can add 4 to a term to get the next term. The rule is add 4.

12, 24, 36, 48, 60,

121212 12

You can add 12 to a term to get the next term. The rule is add 12.

Lesson 3: Relating Numerical Expressions 21

5.OA.3

Relating Numerical Expressions

LESSON 3

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Step 2 Identify corresponding terms in each pattern.

You can list the sets of corresponding terms.

4

12

8

24

12

36

16

48

20

604, 12 8, 24 12, 36 16, 48 20, 60

Step 3 Compare corresponding terms.

Compare the terms in the second pattern to the corresponding terms in the first pattern.

12 and 4: 12 is 3 times 4 or 8 more than 4.

24 and 8: 24 is 3 times 8, but not 8 more than 8.

Step 4 Check the remaining terms and identify a relationship.

Terms in the second pattern are 3 times the corresponding terms in the first pattern.

Solution The rule is add 4 for the first pattern and add 12 for the second pattern. The terms in the second pattern are 3 times the corresponding terms in the first pattern.

Example 2Use the given rules and the starting numbers to generate the first 5 terms in two different numerical patterns. Then identify the relationship between corresponding terms in the patterns.

First pattern: Add 2, starting with 2.

Second pattern: Add 8, starting with 8.

Strategy Use counting by multiples to generate the patterns. Then compare the corresponding terms.

Step 1 Generate the numerical patterns.

Count by multiples of 2 for the first pattern: 2, 4, 6, 8, 10

Count by multiples of 8 for the second pattern: 8, 16, 24, 32, 40

Step 2 List the corresponding terms in the two patterns.

2, 8 4, 16 6, 24 8, 32 10, 40

22 Domain 1: Operations and Algebraic Thinking

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Step 3 Identify the relationship between corresponding terms.

In the first two corresponding terms, 8 is 4 3 2 and 16 is 4 3 4.

Check each of the corresponding terms to make sure the relationship applies to all of the terms.

The terms