EM2 Tennessee Learn | Grade 4 Module 4 by Great Minds

A Story of Units®

Fractional Units LEARN ▸ Module 4 ▸ Foundations for Fraction Operations

Student

Talking Tool Share Your Thinking

I know . . . . I did it this way because . . . . The answer is

because . . . .

My drawing shows . . . . Agree or Disagree

I agree because . . . . That is true because . . . . I disagree because . . . . That is not true because . . . . Do you agree or disagree with

Ask for Reasoning

Why did you . . . ? Can you explain . . . ? What can we do first? How is

Say It Again

related to

I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?

Content Terms

Place a sticky note here and add content terms.

? Why?

What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

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Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2022 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-511-2

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A Story of Units®

Fractional Units ▸ 4 LEARN

Module

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1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

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EUREKA MATH2 Tennessee Edition

4 ▸ M4

Contents Foundations for Fraction Operations Topic A Fraction Decomposition and Equivalence Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Decompose whole numbers into a sum of unit fractions.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Decompose fractions into a sum of unit fractions. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Decompose fractions into a sum of fractions.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Represent fractions by using various fraction models.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Rename fractions greater than 1 as mixed numbers. Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Rename mixed numbers as fractions greater than 1.

Topic B Equivalent Fractions Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Rename fractions as a sum of equivalent smaller unit fractions. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Generate equivalent fractions with smaller units for unit fractions.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Generate equivalent fractions with smaller units for non-unit fractions.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Generate equivalent fractions with larger units. 2

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Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Represent equivalent fractions by using tape diagrams, number lines, and multiplication or division. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Generate equivalent fractions for fractions greater than 1 and generate equivalent mixed numbers.

Topic C Compare Fractions Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Compare fractions by using the benchmarks 1 0, _2 , and 1. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Compare fractions with related denominators.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Compare fractions with related numerators.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Generate a common numerator or denominator to compare fractions.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Apply fraction comparison strategies to compare fractions greater than 1.

Topic D Add and Subtract Fractions Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Estimate sums and differences of fractions by using benchmarks.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Add and subtract fractions with like units.

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Subtract a fraction from a whole number. © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

4 ▸ M4

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Lesson 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Solve addition and subtraction word problems and estimate the reasonableness of the answers.

Represent data on a line plot.

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Add two fractions with related units. (Optional)

Repeated Addition of Fractions as Multiplication

Topic E Add and Subtract Mixed Numbers Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Add a fraction to a mixed number. Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Add a mixed number to a mixed number.

Topic F

Lesson 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Decompose non–unit fractions into a product of a whole number and a unit fraction. Lesson 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Multiply a whole number by a fraction by using the associative property.

Subtract a fraction from a mixed number, part 1.

Lesson 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Solve word problems involving multiplication of a whole number by a fraction.

Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Lesson 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Subtract a fraction from a mixed number, part 2.

Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Subtract a mixed number from a mixed number. Lesson 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 Represent and solve word problems with mixed numbers by using drawings and equations.

Multiply a whole number by a mixed number by using the distributive property.

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 296

Lesson 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Solve problems by using data from a line plot.

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4 ▸ M4 ▸ TA ▸ Lesson 1 ▸ Blank Tape Diagram

EUREKA MATH2 Tennessee Edition

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 1 ▸ Number Line 0 to 2

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TA ▸ Lesson 1

Date

Complete the equations to match each partitioned polygon. Each polygon represents 1.

2 halves =

half +

half

_ _____ + _____ 2 = 2

3 thirds = 1

1 1 1 _ _____ + _____ + _____ 3 = 3

4 fourths =

fourth + fourth +

fourth fourth

_ _____ + _____ + _____ + _____ 4 = 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 1

Complete the number bonds and equations to match each tape diagram. Tape Diagram

Number Bond and Equation

1 = _____ + _____ 2

2 = (_____ + _____) + (_____ + _____) 2

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 1

Tape Diagram

Number Bond and Equation

2=( +(

+ +

)

+ +

)

Draw and label a tape diagram to represent each equation. Equation

Tape Diagram

1 _ 8. 1 = _ + 1 + 1_ + 1_ + 1_ 5 5 5 5 5

9. 3_ = 1_ + 1_ + 1_ 3 3 3 3

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 1

Equation

Tape Diagram

1 _ 10. 2 = (_ + 1 + _1 + 1_ + _1 + 1_ 3 3 3) (3 3 3)

1 11. 3 = (1_ + _ + 1_ + _1 + 1_ + _1 2 2) (2 2) (2 2)

12. Deepa eats half of a chocolate chip cookie. Gabe eats half of an oatmeal cookie. The actual size of each cookie is shown. Did they eat the same amount of cookie? Explain. Chocolate Chip Cookie

Oatmeal Cookie

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 1

Name

Date

Complete the table to represent different ways to decompose each number into the given unit fraction. Tape Diagram

Number Bond

Equation

2 = (1_ + _1 + 1_) + (1_ + _1 + _1) 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 2 ▸ Blank Tape Diagram

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EUREKA MATH2 Tennessee Edition

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4 ▸ M4 ▸ TA ▸ Lesson 2 ▸ Blank Number Line

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 2

Name

Date

Draw a tape diagram to represent the fraction. Then write an equation to express the fraction as a sum of unit fractions. The first one has been done for you. Tape Diagram

4 1. _ 6

Equation

_ _ _ _ _

4 1 1 1 1 = + + + 6 6 6 6 6

2 2. _ 3

3 3. _ 4

5 4. _ 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 2

Draw a tape diagram to represent the fraction. Locate the fraction on the number line. Then write an equation to express the fraction as a sum of unit fractions. The first one has been done for you. Tape Diagram and Number Line

Equation

8 6

5. 8_ 6

_8 = _1 + _1 + _1 + _1 + _1 + 1_ 6 0

8 6

+ _1 + _1 6

3 6. _ 2

4 7. _ 3

7 8. _ 5

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 2

Tape Diagram and Number Line

Equation

9. 6_ 4

12 . Did Eva make a mistake? Explain. 10. Eva drew a tape diagram and number line to show __ 10

12 10

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12 10

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 2

Name

Date

1. Draw a tape diagram to represent the fraction. Then write an equation to express the fraction as a sum of unit fractions. Fraction

Tape Diagram

Equation

_ 3 6

2. Draw a tape diagram to represent the fraction. Locate the fraction on the number line. Then write an equation to express the fraction as a sum of unit fractions. Fraction

Tape Diagram and Number Line

Equation

_ 5 4

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4 ▸ M4 ▸ TA ▸ Lesson 3 ▸ Blank Tape Diagram

EUREKA MATH2 Tennessee Edition

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

Name

Date

1. Shade and label the tape diagram to match the number bond. Then complete the equation. 4 3

4 3

2 3

_4 = 3

2 3

2. Complete the number bond, the tape diagram, and the equation to decompose 3 in a different way from problem 1.

4 3

_4 = 3

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4 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

3. Shade the number line to match the equation.

_3 = 2_ + 1_ 5 5 5

4. Shade the number line to decompose the fraction and complete the equation. 6_ = 4

LESSON

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TA ▸ Lesson 3

Date

Each fraction is decomposed two different ways. Show how the fraction is decomposed by using a tape diagram, a number bond, and an equation. 1.

4 6

Tape Diagram

Number Bond

4 6

Equation

_ _____ + _____

1 6

4= 6

3 6

4 6

4= 6 2 6

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2 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

5 3

Tape Diagram

Number Bond

Equation

a. 5 3

5 3

5 = 3 3 3

b. 5 3

5 3

5 = 3

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

Each fraction is decomposed two different ways. Show how the fraction is decomposed by using a number line, a number bond, and an equation. 3.

7 8

Number Line

Number Bond

Equation

a. 7 8 0

2 8

7 8

_ _____ + _____

7 = 8

b. 7 8 0

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4 8

7 8

7= 8

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

_8 4. 5 Number Line

Number Bond

Equation

a. 8 5 0

8 = 5

5 5

b. 8 5 0

8 = 5

6 5

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

Write two different equations to show the fraction decomposed into a sum of fractions. 5.

9 10

a. b.

7 4

a. b.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

Name

Date

Show how each fraction is decomposed by completing the models. 1. 5_ 6

Fraction

Tape Diagram

Number Bond

Equation

5 6

5 = 6

5 6

5 = 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 3

2. 7_ 5 Fraction

Number Line

Number Bond

Equation

a. 7 5

5 5

7 5

7 = 5

b. 7 5

EXIT TICKET

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6 7 5 5

7 = 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Identify Fractional Parts of Tape Diagrams

Sprint Each tape diagram represents 1 whole. Write the fraction that the shaded amount represents. 1. 2.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Identify Fractional Parts of Tape Diagrams

Number Correct:

Each tape diagram represents 1 whole. Write the fraction that the shaded amount represents. 1.

19.

20.

21.

22.

23.

24.

25.

26.

27.

10.

28.

11.

29.

12.

30.

13.

31.

14.

32.

15.

33.

16.

34.

17.

35.

18.

36.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Identify Fractional Parts of Tape Diagrams

Number Correct: Improvement:

Each tape diagram represents 1 whole. Write the fraction that the shaded amount represents. 1.

19.

20.

21.

22.

23.

24.

25.

26.

27.

10.

28.

11.

29.

12.

30.

13.

31.

14.

32.

15.

33.

16.

34.

17.

35.

18.

36.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 4

Name

Date

Draw a number line to represent each fractional amount. Write an equation to show one way to decompose the fraction. Number Line

Equation

1. _3 cups of juice 4

1 cup 1 cup 2

__7 of the students 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 4

Draw an area model to represent each fractional amount. Write an equation to show one way to decompose the fraction. Area Model

Equation

3. _2 of a pizza 3

4. _3 hours 5

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 4

9 meters. 5. Draw two different models to represent __ 10

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 4

Name

Date

Draw two different models to represent _5 yards. 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

Name

Date

1. Write an equation to represent each number bond. Rename fractions equivalent to whole numbers. 10 3

10 3

3 3

1 3 3 3

3 3

9 3

1 3

Rename each fraction as a mixed number. Show the decomposition on a number line and write an equation. 14 2. __ = 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

15 __ = 6

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

Name

Date

Complete each number bond and equation. Rename the fractions that are equivalent to whole numbers. 1.

5 2

17 5

2 5

4 2

_5 = _4 + _____

17 _____ _ __ = +2

_5 =

17 __ =

_5 = 2

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+ ___

___

17 __ = 5

+ _____

___

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

Rename the given fraction as a mixed number. Show the decomposition on a number line and write the equations. The first one has been done for you. 13 = 3. __ 6

2 _1 6

12 6

13 6

13 = 12 __ + 1_ __ 6

13 __ = 2 + 1_ 6 6 1 13 = 2 _ __ 6

4. 7_ = 2

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

8= 5. _ 3

13 = 6. __ 4

Rename each fraction greater than 1 as a mixed number. Use a model to show the decomposition. 29 = 7. __ 6

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__ = 8. 47 8

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 5

__ = 9. 77 10

__ = 10. 53 12

15 pizzas. Who eats 11. David and Oka order mini pizzas to share. David eats 3__3 pizzas. Oka eats __ 4 4 more pizza? Explain.

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TA ▸ Lesson 5

Date

Rename each fraction greater than 1 as a mixed number. Use a model to show the decomposition. 1.

7_ = 3

15 __ = 4

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TA ▸ Lesson 6

Date

1. Ray needs 3 cups of flour to make bread. He only has a _1 -cup measuring scoop. How can he use the _1 -cup scoop to measure 3 cups of flour?

Rename each mixed number as a fraction greater than 1. Show the decomposition on a number line and write the equations. 2. 2 _3 = 4

3. 3 _1 = 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 6

4. Rename the mixed number as a fraction greater than 1. Use a model to show the decomposition.

3 _2 = 6

5. Rename the mixed number as a fraction greater than 1.

4 8_6 =

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 6

Name

Date

Rename each mixed number as a fraction greater than 1. Show the decomposition on the number line and write the equations. The first one has been done for you. 1. 2 _5 =

17 __ 6

1 12 5_ 2 5_ = __ +

2. 2 _1 =

6 6 __ 2 5_ = 17 6 6

12 6

17 6

26 3

3. 3 _2 = 3

EM2_0404SE_A_L06_problem_set.indd 57

11/24/2021 12:28:50 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TA ▸ Lesson 6

3 4. 3 _ = 4

Rename each mixed number as a fraction greater than 1. Use a model to show the decomposition. 5. 4 _1 =

6. 5 _5 =

3 7. 6 __ =

7 8. 4 __ =

11 slices of bread. 9. Mr. Davis slices some bread. Adam takes 5 _1 slices of bread. Jayla takes __ 2

Did they take the same amount of bread? Explain.

PROBLEM SET

EM2_0404SE_A_L06_problem_set.indd 58

11/24/2021 12:28:51 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TA ▸ Lesson 6

Date

Rename each mixed number as a fraction greater than 1. Use a model to show the decomposition. 1. 2 _1 = 4

2. 3 _3 = 5

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11/24/2021 12:27:57 PM

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11/24/2021 12:27:57 PM

EUREKA MATH2 Tennessee Edition

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4 ▸ M4 ▸ TB ▸ Lesson 7 ▸ Three Number Lines

11/24/2021 12:40:20 PM

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11/24/2021 12:40:20 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 7

Date

Rename each fraction by decomposing it into smaller unit fractions. Label the number line to show the decomposition and write an equation to express the equivalence as a sum. Fraction

Number Line and Equation

1 2

4 5

EM2_0404SE_B_L07_classwork.indd 63

11/24/2021 12:31:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

The area model represents 1. Rename each fraction by decomposing it into smaller unit fractions. Use the area model to show the decomposition and write an equation to express the equivalence as a sum. Fraction

Area Model and Equation

1 4

2 3

LESSON

EM2_0404SE_B_L07_classwork.indd 64

11/24/2021 12:31:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

5. Label the number line with equivalent fractions. Then write an addition equation to show equivalence.

6. Label the area model with equivalent fractions. Then write an equation.

EM2_0404SE_B_L07_classwork.indd 65

LESSON

11/24/2021 12:31:23 PM

EM2_0404SE_B_L07_classwork.indd 66

11/24/2021 12:31:23 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

Name

Date

Rename each fraction by decomposing it into smaller unit fractions. Label the number line to show the decomposition. Then complete the equations. Number Line and Equations 1 1. _ 4

1 4

1 = 4

1 1 _____ + _____

(

)

_ _____

1 = 4 2 2. _ 3

2 3

2 = 3 (

)+(

)

2 = 3

EM2_0404SE_B_L07_problem_set.indd 67

11/24/2021 12:35:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

Number Line and Equations 3 3. _ 5

3 = 5 (

)+(

)

3 = 5

Each large square represents 1. Rename each fraction by decomposing it into smaller unit fractions. Label the area model to show the decomposition. Then complete the equations. Area Model and Equations 1 4. _ 2

1 2

1 = 2

1 1 _____ + _____

(

)

_ _____

1 = 2

PROBLEM SET

EM2_0404SE_B_L07_problem_set.indd 68

11/24/2021 12:35:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

Area Model and Equations 1 5. _ 3

1 3

1 = 3 (

)

1 = 3

3 6. _ 4

3 = 4 (

)

3 = 4

EM2_0404SE_B_L07_problem_set.indd 69

PROBLEM SET

11/24/2021 12:35:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

Show that the fractions are equivalent by drawing a model. Then write an equation to express the equivalence as a sum. 2 7. _1 and __ 5

10 8. _5 and __ 6

PROBLEM SET

EM2_0404SE_B_L07_problem_set.indd 70

11/24/2021 12:35:05 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

9. Explain why _1 + _1 + _1 + _1 + _1 + _1 is the same as _2 . 9

2 3

6 9

EM2_0404SE_B_L07_problem_set.indd 71

PROBLEM SET

11/24/2021 12:35:05 PM

EM2_0404SE_B_L07_problem_set.indd 72

11/24/2021 12:35:05 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 7

Name

Date

3 Show that the fractions _1 and __ are equivalent by drawing a model. Then write an equation to express 4

the equivalence as a sum.

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11/24/2021 12:39:05 PM

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11/24/2021 12:39:05 PM

EUREKA MATH2 Tennessee Edition

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4 ▸ M4 ▸ TB ▸ Lesson 8 ▸ Three Number Lines

11/24/2021 12:44:00 PM

EM2_0404SE_B_L08_removable_fluency_three_number_lines.indd 76

11/24/2021 12:44:00 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 8

Name

1 2

1 = 2

Date

1 2

1 = 2

1 2

1 = 2

1 = 5

EM2_0404SE_B_L08_classwork.indd 77

11/24/2021 12:41:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 8

1_ = 4

LESSON

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11/24/2021 12:41:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 8

Name

Date

Each large square represents 1. Label each area model to show the equivalent fraction. Express each equivalence by using multiplication. 1.

1 2

×1

2 × 1 _____ _1 = ____ = 2

EM2_0404SE_B_L08_problem_set.indd 79

×3

1 = 4

_1 = ________ = _____

2×2

1 3

1 = 5

11/24/2021 12:43:34 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 8

Partition each area model to show smaller fractional units. Then label the equivalent fraction. Express each equivalence by using multiplication. 5. Decompose into sixths.

6. Decompose into twelfths.

1 2

×1

_1 = _______ = _____ 2

1 = 3

×2

Show that each pair of fractions is equivalent by drawing an area model. Then express each equivalence by using multiplication. 7. _1 and _3 3

PROBLEM SET

EM2_0404SE_B_L08_problem_set.indd 80

8. _1 and _2 4

11/24/2021 12:43:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 8

9. Find two equivalent fractions for _1 . 6

10. Mr. Lopez bakes a pan of brownies. He gives Robin _2 of the brownies. He gives Ivan 6

_1 of the brownies. 3

Do they both get the same amount? Explain.

EM2_0404SE_B_L08_problem_set.indd 81

PROBLEM SET

11/24/2021 12:43:37 PM

EM2_0404SE_B_L08_problem_set.indd 82

11/24/2021 12:43:37 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 8

Date

Partition the area model to show smaller fractional units. Then label the equivalent fraction. Express the equivalence by using multiplication. 1 3

1 = 3

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11/24/2021 12:43:00 PM

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11/24/2021 12:43:00 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 9

Date

1. Decompose _4 into tenths.

_4 = 5

2. Decompose _2 into twelfths.

_2 =

EM2_0404SE_B_L09_classwork.indd 85

11/24/2021 12:50:54 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 9

Decide whether each equation is true or false. Show your work. 3. _2 = _4 3 6

9 4. _3 = __ 6 12

LESSON

EM2_0404SE_B_L09_classwork.indd 86

11/24/2021 12:50:55 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 9

Name

Date

Each square represents 1. Label each area model to show the equivalent fraction. Express each equivalence by using multiplication. 1.

2 3

×3 3_ _______ _____ = = 4 ×4

2_ ____ = 2 × 2 = _____ 3 2×3

_2 = 5

EM2_0404SE_B_L09_problem_set.indd 87

3 4

_4 = 6

11/24/2021 12:53:34 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 9

Partition each area model to show smaller units. Then label the equivalent fraction. Express each equivalence by using multiplication. 5. Decompose into ninths.

6. Decompose into twelfths.

2 3

×2

_2 = _______ = _____ 3

5_ = 6

×3

Show that each pair of fractions is equivalent by drawing an area model. Then express each equivalence by using multiplication. 8 7. _2 and __ 3

PROBLEM SET

EM2_0404SE_B_L09_problem_set.indd 88

6 8. _3 and __ 5

11/24/2021 12:53:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 9

Complete each equation to show an equivalent fraction. 2 = _____ 9. _ 8 4

8 4 = _____ 10. _ 5

11. Ray needs _3 cups of flour. He only has two measuring cups, a _1 -cup and a _1 -cup. 4

a. Which cup should Ray use? Explain.

b. How many of the cups you chose in part (a) will it take to measure _3 cups of flour? 4

EM2_0404SE_B_L09_problem_set.indd 89

PROBLEM SET

11/24/2021 12:53:35 PM

EM2_0404SE_B_L09_problem_set.indd 90

11/24/2021 12:53:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 9

Name

Date

Partition the area model to show smaller units. Then label the equivalent fraction. Express the equivalence by using multiplication. 3 4

_3 = 4

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11/24/2021 12:52:39 PM

EM2_0404SE_B_L09_exit_ticket.indd 92

11/24/2021 12:52:39 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Compare Fractions

Sprint Write >, =, or <. 1.

1 third

1 4

5 6

__2

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11/25/2021 4:43:57 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Compare Fractions

Number Correct:

Write >, =, or <.

2 thirds

1 third

23.

1 2

2 2

2 3

1 3

24.

2 2

1 fourth

2 fourths

25.

1 3

0 3

1 4

2 4

26.

2 3

3 sixths

1 sixth

27.

0 4

2 4

3 6

1 6

28.

3 4

1 eighth

29.

4 6

0 6

1 8

30.

6 6

4 eighths

1 eighth

31.

6 8

5 8

10.

4 8

1 8

32.

7 8

11.

1 2

33.

1 4

2 4

12.

1 2

2 2

34.

3 6

1 6

13.

1 3

2 3

35.

2 2

3 2

14.

3 3

2 3

36.

3 3

4 3

15.

2 4

3 4

37.

7 4

5 4

16.

4 4

38.

17.

4 6

2 6

39.

7 6

9 8

18.

6 6

3 6

40.

19.

5 6

41.

4 2

5 3

20.

3 8

4 8

42.

21.

4 8

6 8

43.

9 4

18 6

22.

8 8

5 8

44.

31 8

_ _

_ _ _ _

_ _

_ _ _

EM2_0404SE_B_L10_fluency_removable_sprint_compare_fractions.indd 94

_ _

_ _ _ _ _ _

_ _ _ _

_ _ _ _ _

_ _ _

_ _

_ _ _

11/24/2021 2:08:22 PM

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11/24/2021 2:08:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Compare Fractions

Number Correct: Improvement:

Write >, =, or <.

1 third

2 thirds

23.

2 2

1 2

1 3

2 3

24.

2 2

2 fourths

1 fourth

25.

0 3

2 3

2 4

1 4

26.

1 3

1 sixth

4 sixths

27.

3 4

0 4

1 6

4 6

28.

2 4

1 eighth

29.

0 6

5 6

1 8

30.

6 6

1 eighth

5 eighths

31.

5 8

7 8

10.

1 8

5 8

32.

6 8

11.

1 2

33.

1 3

2 3

12.

2 2

1 2

34.

3 4

1 4

13.

2 3

1 3

35.

3 2

2 2

14.

2 3

3 3

36.

4 3

3 3

15.

3 4

1 4

37.

5 4

16.

4 4

38.

7 4

8 6

17.

1 6

4 6

39.

10 8

18.

2 6

6 6

40.

4 2

19.

5 6

41.

20.

4 8

2 8

42.

4 3

10 4

21.

6 8

3 8

43.

18 6

22.

4 8

8 8

44.

30 8

_ _

_ _ _

_ _ _ _

_ _

EM2_0404SE_B_L10_fluency_removable_sprint_compare_fractions.indd 96

_ _

_ _ _

_ _ _ _ _

_ _ _

_ _

_ _ _ _ _ _

__ _

11/24/2021 2:08:23 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 10

Name

Date

Represent an equivalent fraction by using an area model. Then express the equivalence by using division. 2.

4 8

_4 = 8

2 6

_2 = 6

4 6

_4 = 6

9 and compose an equivalent fraction. Then use division to express the composition. Shade __ 12

9 = __ 12

EM2_0404SE_B_L10_classwork.indd 97

11/24/2021 2:02:49 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 10

Draw an area model and use division to demonstrate the equivalence. 5.

3 6 =_ __ 10 5

Use division to compose twelfths into halves. 6.

6 = _____ __ 2 12

LESSON

EM2_0404SE_B_L10_classwork.indd 98

11/24/2021 2:02:50 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 10

Name

Date

Each large square represents 1. Trace the area model to show how the larger unit is composed. Then label the equivalent fractions. Express each equivalence by using division. 2.

2÷

2 ÷ 2 _____ _2 = ____ = 4

_2 = _______ = _____

4÷2

2 4

2 6

3 __ = 12

EM2_0404SE_B_L10_problem_set.indd 99

6÷

2 __ = 10

11/24/2021 2:09:34 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 10

5. Show how _ and _4 can be renamed as the same unit fraction. Shade and label the area model 3 6

to show the fractions. Then express each equivalence by using division. a. 3_ 6

b. 4_ 8

6. Draw an area model to represent the equivalent fractions. ÷ 2 3_ _6 = 6____ = 8 8÷2 4

100

PROBLEM SET

EM2_0404SE_B_L10_problem_set.indd 100

11/24/2021 2:09:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 10

Complete each equation to show an equivalent fraction. You may draw an area model to help you. 7.

1 _3 = _____ 9

8 = _____ 8. __ 5 10

9. Mr. Endo needs 8 cups of sugar to bake muffins. Liz says that is the same amount as 4 cups of sugar. Is Liz correct? Explain.

10. Show an equivalent fraction for 8 by using multiplication. Then show an equivalent fraction for 8 by using division.

EM2_0404SE_B_L10_problem_set.indd 101

PROBLEM SET

101

11/24/2021 2:09:36 PM

EM2_0404SE_B_L10_problem_set.indd 102

11/24/2021 2:09:36 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 10

Date

The large square represents 1. Trace the area model to show how the larger unit is composed. Then label the equivalent fractions. Express the equivalence by using division.

EM2_0404SE_B_L10_exit_ticket.indd 103

103

11/24/2021 2:05:55 PM

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11/24/2021 2:05:55 PM

EUREKA MATH2 Tennessee Edition

EM2_0404SE_B_L11_removable_fluency_three_number_lines.indd 105

4 ▸ M4 ▸ TB ▸ Lesson 11 ▸ Three Number Lines

105

11/24/2021 2:10:57 PM

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11/24/2021 2:10:57 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 11

Name

Date

1. Partition, shade, and label the tape diagram to represent 3 . Then use the tape diagram and multiplication to partition and label the number line to represent the equivalent fraction. a. 2_ ____ = 3 × 2 = 6_ 3 3×3 9

b. 8 2_ ____ = 4 × 2 = __ 3 4 × 3 12

c. How are the fractions in parts (a) and (b), 3 , _ , and __ , related?

EM2_0404SE_B_L11_problem_set.indd 107

6 9

8 12

107

11/24/2021 2:10:31 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 11

2. Partition and label the number line to represent the fraction _ . Then use the number line and 6 8

division to partition, shade, and label the tape diagram to represent the equivalent fraction. Number Line and Tape Diagram

Division 6 a. _ 8 6_ ____ = 6 ÷ 2 = 3_ 8 8÷2 4

9 b. __ 12 9÷3 9 __ = _____ = 3_ 12

12 ÷ 3

c. How are the fractions in parts (a) and (b), _ , _ , and __ , related? 3 6 4 8

108

PROBLEM SET

EM2_0404SE_B_L11_problem_set.indd 108

9 12

11/24/2021 2:10:32 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 11

3. Use the tape diagram and number line.

a. Partition and shade the tape diagram to show _ . 3 5

b. Locate _ on the number line. Decompose _ into 9 equal lengths. 3 5

3 5

c. Use multiplication to show how the tape diagram and the number line represent equivalent fractions.

4. Use the tape diagram and number line. a. Locate __ on the number line. 4 10

b. Partition the tape diagram into fifths. Shade to show a fraction equivalent to __ . 4 10

c. Use division to show how the tape diagram and the number line represent equivalent fractions.

EM2_0404SE_B_L11_problem_set.indd 109

PROBLEM SET

109

11/24/2021 2:10:33 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 11

8 4 2 4 5. Luke says _ is equivalent to _ . Zara says _ is equivalent to __ . 3 12 6 6

a. Do you agree with Luke, Zara, or both? Explain.

4 b. Write another fraction equivalent to _ . 6

110

PROBLEM SET

EM2_0404SE_B_L11_problem_set.indd 110

11/24/2021 2:10:33 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 11

Name

Date

1. Partition, shade, and label the tape diagram to represent 6 . Then use the tape diagram and multiplication to partition and label the number line to represent the equivalent fraction.

8 4_ ____ = 2 × 4 = __ 6 2 × 6 12

2. Partition and label the number line to represent 6 . Then use the number line and division to partition, shade, and label the tape diagram to represent the equivalent fraction.

4÷2 _ _4 = ____ =2 6 6÷2 3

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111

11/24/2021 2:10:03 PM

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11/24/2021 2:10:03 PM

EUREKA MATH2 Tennessee Edition

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4 ▸ M4 ▸ TB ▸ Lesson 12 ▸ Three Number Lines

113

11/24/2021 2:13:45 PM

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11/24/2021 2:13:45 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 12

Date

1. Use the picture of the crackers to complete parts (a)–(d). Each cracker is 1 whole.

a. Draw lines to show how each cracker can be partitioned into halves.

b. Write a fraction to represent the total number of halves.

c. Draw more lines to show how each cracker can be partitioned into fourths.

d. Write a fraction to represent the total number of fourths.

EM2_0404SE_B_L12_classwork.indd 115

115

11/24/2021 2:11:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Partition the number line and label the given fraction. Decompose fractional units to find an equivalent fraction. Then use multiplication to express the equivalence. 2.

116

_7 4

_4 3

LESSON

EM2_0404SE_B_L12_classwork.indd 116

11/24/2021 2:11:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Partition the number line and label the given mixed number. Decompose fractional units to find an equivalent mixed number. Then use multiplication to express the equivalent mixed numbers. 2 4. 1 _5

2 5. 2 _ 3

EM2_0404SE_B_L12_classwork.indd 117

LESSON

117

11/24/2021 2:11:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Circle True or False for the statement. Use a model to explain your choice.

Statement

True or False

11 13 __ __ is equivalent to . 6

__3

7. 3 4 is equivalent to 3 12 .

118

LESSON

EM2_0404SE_B_L12_classwork.indd 118

Model

True

False

True

False

11/24/2021 2:11:23 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Name

Date

Label the number line to show fractions greater than 1. Then use multiplication to express the equivalence. 1.

3_ 2

3 2

×3

_3 = _______ = ____ 2

×2

5_ 3

×5

_5 = _______ = ____ 3

EM2_0404SE_B_L12_problem_set.indd 119

×3

119

11/24/2021 2:13:19 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Label the number line to show mixed numbers. Then use multiplication to express the equivalence. 1 3. 1 _ 3

13 0

×1 1_ = + _______ = ____ � 1 6 13 1 � ×3

3 4. 2 _ 4

2_4 = 2 + � _______ � = 2 ____ 3

×3

×4

120

PROBLEM SET

EM2_0404SE_B_L12_problem_set.indd 120

11/24/2021 2:13:20 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TB ▸ Lesson 12

Complete each equation to show equivalent fractions. You may draw a number line to help you. 5.

9_ ____ = 12 4

8 ____ 16 = 6. _ 5

4 1 7. 2_ = 2 ____ 2

5 8. 3_ = 3 ____ 12 6

9. Mrs. Smith asks students to write an equivalent fraction for 2 3 . Pablo

Carla

James

Amy

14 __ 6

2 _6

2 _9

a. Which two students made a mistake? b. Correct the mistakes the two students made.

c. Write another fraction equivalent to 2 3 .

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PROBLEM SET

121

11/24/2021 2:13:20 PM

EM2_0404SE_B_L12_problem_set.indd 122

11/24/2021 2:13:20 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TB ▸ Lesson 12

Date

Complete each equation to show an equivalent fraction. You may draw a number line to help you. 1.

_7 = _____ 3 6

3 6 2. 1 _ = 1 _____ 4

EM2_0404SE_B_L12_exit_ticket.indd 123

123

11/24/2021 2:12:50 PM

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EUREKA MATH2 Tennessee Edition

1 2

4 ▸ M4 ▸ TC ▸ Lesson 13 ▸ Number Line 0 to 1

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 13

Name

Date

Plot the fractions on the number line. Use >, =, or < to compare the fractions. 1.

9 5_ _1 , __ , 4 10 8

1 2

_1 2

a. 4

b. c.

9 __ 10

d. 1

1 2 7_ _ 2. _ , , 5 8 3

a. b.

_0 3

_1 2

2 c. _ 5 2 d. _ 5

_5 8

10 __ 10

0 1_ 3

_1 2

_7 8

1 Explain how you can use the benchmarks 0, _ , and 1 to compare the fractions. Then write >, =, or < 2 to compare the fractions.

3. 2

4. 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 13

5_ 6

_7 8

Check True or False for each number sentence. Then correct the false number sentences by changing one of the numbers in the number sentences. 1 2 <_ 6. __ 10 2

True

False

_3 > 2_ 8 3

True

False

9 11 __ __ < 12 10

True

False

128

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 13

5 _1 __5 _1 9. Casey says __ is greater than 2 . Deepa says 12 is less than 2 . Is Casey or Deepa correct? Explain. 12

3 _1 hours reading. She spends 4 hour drawing. Does Eva spend less time reading 10. Eva spends __ 10

or less time drawing? Explain.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 13

Name

Date

1. Plot the fractions on the number line. Use >, =, or < to compare the fractions. 9 _ __ , 1 , _4

10 4 6

1 2

9 __

_1 2

1 b. _ 4

_1 2

1 c. _ 4

9 __ 10

d. _4 6

_1 2

2. Explain how you can use the benchmark 0, _1 , or 1 to compare the fractions. Then write >, =, 2 or < to compare the fractions. _2 _4 3 5

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4 ▸ M4 ▸ TC ▸ Lesson 14 ▸ Models to Compare

EUREKA MATH2 Tennessee Edition

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 14

Name

Date

Use >, =, or < to compare the fractions. 1. 1 third

2 thirds

2. 4 fifths

2 fifths

3. 5 tenths

7 tenths

Represent each pair of fractions with the tape diagrams. Use >, =, or < to compare the fractions. 5 5. 6_

3_ 4

1 4. _ 2

2 __ 3

1 = 2

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 14

Represent each pair of fractions on the number line. Use >, =, or < to compare the fractions. 1 6. _ 3

2_ 9 1 3

7 7. __ 10

3 _ 5

Compare each pair of fractions by using >, =, or <. Show your thinking by using pictures, numbers, or words. 2 8. __ 10

1 _ 5

3 9. _ 4

5_ 8

7 10. __ 12

2 _ 3

5 11. _ 6

11 __ 12

136

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 14

12. David eats 3 of a chocolate bar. Oka eats 6 of a different, but same-size, chocolate bar. Do David and Oka eat the same amount? Explain.

__7

13. Jayla’s tomato plant is 12 feet tall. Her bean plant is 4 feet tall. Which plant is taller? Explain.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TC ▸ Lesson 14

Date

Compare each pair of fractions by using >, =, or <. Show your thinking by using pictures, numbers, or words. 1.

_1 4

3 __

5_ 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Round to the Nearest Ten Thousand

Sprint Round to the nearest ten thousand. 1. 2.

43,000 ≈

271,905 ≈

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Round to the Nearest Ten Thousand

Number Correct:

Round to the nearest ten thousand. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

31,000 ≈ 34,000 ≈

23.

46,300 ≈

26.

77,250 ≈

29.

85,284 ≈

32.

214,000 ≈

35.

623,700 ≈

38.

836,910 ≈

41.

37,000 ≈

24.

49,400 ≈

27.

71,960 ≈

30.

84,563 ≈

33.

219,000 ≈

36.

625,600 ≈

39.

834,750 ≈

42.

42,900 ≈

25.

73,810 ≈

28.

83,713 ≈

31.

212,000 ≈

34.

628,100 ≈

37.

832,840 ≈

40.

831,560 ≈

43.

142

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44.

341,725 ≈ 348,291 ≈ 345,366 ≈ 562,004 ≈ 580,089 ≈ 509,107 ≈ 750,062 ≈ 775,009 ≈ 706,083 ≈ 940,740 ≈ 902,081 ≈ 905,305 ≈ 38,100 ≈ 34,900 ≈ 55,555 ≈ 75,955 ≈ 95,599 ≈ 99,595 ≈

555,555 ≈ 595,955 ≈ 959,595 ≈ 995,599 ≈

11/24/2021 2:21:39 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Round to the Nearest Ten Thousand

Number Correct: Improvement:

Round to the nearest ten thousand. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

21,000 ≈ 24,000 ≈

23.

36,300 ≈

26.

67,250 ≈

29.

75,284 ≈

32.

114,000 ≈

35.

523,700 ≈

38.

736,910 ≈

41.

27,000 ≈

24.

39,400 ≈

27.

61,960 ≈

30.

74,563 ≈

33.

119,000 ≈

36.

525,600 ≈

39.

734,750 ≈

42.

32,900 ≈

25.

63,810 ≈

28.

73,713 ≈

31.

112,000 ≈

34.

528,100 ≈

37.

732,840 ≈

40.

731,560 ≈

43.

144

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44.

241,725 ≈ 248,291 ≈ 245,366 ≈ 462,004 ≈ 480,089 ≈ 409,107 ≈ 650,062 ≈ 675,009 ≈ 606,083 ≈ 840,740 ≈ 802,081 ≈ 805,305 ≈ 28,100 ≈ 24,900 ≈ 55,555 ≈ 75,855 ≈ 95,588 ≈ 99,585 ≈

555,555 ≈ 595,855 ≈ 958,585 ≈ 995,588 ≈

11/24/2021 2:21:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 15

Name

Date

Use >, =, or < to compare the fractions. 1. 1 half

1 third

2. 2 eighths

2 fifths

3. 5 sixths

5 twelfths

Represent each pair of fractions with the tape diagrams. Use >, =, or < to compare the fractions. 4. 2_ 3

4 _ 5

9 5. __ 10

3 _ 4

2 = 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 15

Represent each pair of fractions on the number line. Use >, =, or < to compare the fractions. 6. 3_ 4

6 _ 8 3 4

2 7. _ 3

10 __ 12

Compare each pair of fractions by using >, =, or <. Show your thinking by using pictures, numbers, or words. 6 8. _ 8

2 _ 3

9. 2_ 5

10. 3_ 4

9 __ 12

10 11. __ 12

146

PROBLEM SET

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5_ 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 15

9 12. Gabe walks __ miles. Liz walks _3 miles. Do they walk the same distance? Explain. 10

7 7 is greater than __ 14 . Who is correct? Explain. 14 . Mia says __ 13. Robin says __ is less than __ 10

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TC ▸ Lesson 15

Date

Compare each pair of fractions by using >, =, or <. Show your thinking by using pictures, numbers, or words. 1. 2_ 3

8 __

2. 3_ 5

6_ 9

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149

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 16

Name

Date

Rename each pair of fractions by using common denominators. Use >, =, or < to compare the fractions. 1.

2_ 3

_1 2

2 2×2 = = 3 2×3

1_ 3

2_ 4

1 = 3

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1 3×1 = = 2 3×2

×1

×3

2 = 4

×2

×4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 16

3 3. _ 5

_2 3

3_ 8

_1 3

Rename each pair of fractions by using common numerators. Use >, =, or < to compare the fractions. 1_ 4

2_ 9

2 6. _ 5

3_ 7

152

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 16

Compare each pair of fractions by using >, =, or <. Explain your thinking by using pictures, numbers, or words. 7.

1_ 3

2_ 5

5_ 6

7_ 8

_2 3

3 10. _ 5

__7

_3 4

7 __ 12

11. Ray and Zara run around a track. Ray runs 10 miles. Zara runs 6 miles. Did Ray or Zara run the least number of miles? Explain.

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TC ▸ Lesson 16

Date

Compare the fractions by using >, =, or <. Explain your strategy by using pictures, numbers, or words. 1.

_2 9

_1 4

2_ 3

3_ 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 17 ▸ Comparison Strategy Sort

Common Numerator

7 __ 10

4_ 5

6 __ 11

Common Denominator

3_ 7

_3 8

7 __ 12

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2 5_ 8

Compare to a Benchmark

2 3_ 4

_9 2

15 __ 6

_5 6

_2 3

157

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TC ▸ Lesson 17

Date

Compare the fractions by using >, =, or <. Explain your strategy by using pictures, numbers, or words. 1.

3_ 2

4_ 3

5 2. 3 __ 12

12 __ 10

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3 24_

_6 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TC ▸ Lesson 17

9 4. 7 __ 10

10 __ 3

13 __ 6

2 6. 8 _ 3

160

7 35_

8 43_

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TC ▸ Lesson 17

Date

Compare the fractions by using >, =, or <. Explain your strategy by using pictures, numbers, or words. 1. 8_ 5

2. 2 2_ 6

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_ 4 3

2 5_ 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18 ▸ Expression Cards

Estimates of Sums and Differences Sort

_1 + _1

3 4_ _ − 5 5

2 1 __ + __

_4 − _3

_1 + _6

9 1 __ − __

3 5 1 __ + __ + __

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_6 − _5 2

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18 ▸ Expression Cards

Estimates of Sums and Differences Sort

_1 + _2 + _2

15 __ − _3 8 8

9 1 2 __ + __ + __

13 _ __ −7

_1 + _5

_4 − _1

_1 + 1_ 3

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10 __ __ − 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18

Name

Date

Use the Read–Draw–Write process to solve the problem. 1. Carla makes food for a bake sale. Each recipe lists vanilla as an ingredient. The cake recipe 23 teaspoons. The pie recipe uses _ 9 teaspoons. The cookie recipe uses _ 3 teaspoons. uses __ 8

11 teaspoons. About how many teaspoons of vanilla does Carla use? The cupcake recipe uses __ 8

Use the Read–Draw–Write process to solve the problem.

9 miles in the morning and __ 3 miles in the evening. About how many more miles 2. Deepa runs __ 10

does Deepa run in the morning than in the evening?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18

Name

Date

2 _ +5≈ 1. _ 6 6

Estimate the sum or difference. 2.

7 _ 3. _ −3≈ 8 8

11 __ __6 + __ +4 ≈ 10

12 5_ 4. __ −4≈ 4

Use the Read–Draw–Write process to solve each problem.

5. James drinks _3 liters of water in the morning. He drinks _4 liters of water in the afternoon. About 5

how many liters of water does James drink altogether?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18

9 meters. If one ribbon is __ 4 meters long, about how long 6. The total length of two ribbons is __

is the length of the other ribbon?

7. Mr. Lopez plans to spend _7 hours cooking a meal. He finishes cooking in _4 hours instead. About 6

how much earlier does Mr. Lopez finish cooking the meal?

170

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18

16 pounds of rice, and _ 7 pounds of oats. About how many 8. Miss Wong buys _3 pounds of wheat, __ 8

pounds of grains does Miss Wong buy altogether?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 18

Name

Date

Use the Read–Draw–Write process to solve each problem.

1. David spends _2 hours studying history and _5 hours studying math. About how long does David 6

spend studying altogether?

14 inches tall. Last 2. Liz measures the height of her plant every Sunday. This Sunday it measures __ 12

7 inches tall. About how much has Liz’s plant grown since last Sunday? Sunday her plant was __ 12

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 19

Name

Date

Add or subtract. Write the sum or difference in unit form. 1. 2 fifths + 1 fifth =

2. 5 eighths + 4 eighths =

3. 3 fourths − 1 fourth =

4. 7 tenths − 4 tenths =

Add or subtract. Write the sum or difference in fraction form. 1 _ 5. _ +2= 4 4

2 _ 6. _ +3= 6 6

2 _ −1= 7. _ 3 3

4 _ −2= 8. _ 5 5

3 _ +2= 9. _ 3 3

5 __ = + 11 10. __ 12 12

5 _ −3= 11. _ 6 6

10 __ − 7 = 12. __ 10 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 19

Add or subtract. Write the sum or difference in fraction form. Use the number line to represent the addition or subtraction. 2 _ +2= 13. _ 5 5 +

2 5

5 14. 3_ + _ = 8 8

4 3_ 15. _ + = 4 4

176

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 19

5 7 16. __ + __ = 10 10

3 = 17. 3_ − _ 4 4 3

˜4

3 4

2 18. 4_ − _ = 6 6

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 19

7 _ 19. _ −4= 8 8

12 __ 20. __ − 5 = 12 12

178

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TD ▸ Lesson 19

Date

Add or subtract. Write the sum or difference in fraction form. You may use a number line to help you. 6 1. 7_ − _ = 8 8

3 _ 2. _ +2= 4 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 20

Name

Date

Use the three numbers to write two subtraction and two addition equations. 3 , 4_ , 7_ 1. _ 8 8 8

6 , __ 4 2. 1, __ 10 10

Subtract. Use a number line to represent the subtraction. 3. 1 − _2 = 3 ˜2 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 20

4. 1 − _2 = 5

5. 2 − _3 = 4

6. 2 − _5 = 8

182

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Rename or decompose the total to subtract. 7. 1 − _1 = 4

_4 − _1 = 4 4

4 ▸ M4 ▸ TD ▸ Lesson 20

8. 1 − 5_ = 6

_____

3 = 9. 2 − __ 10

10.

11. 3 − _7 = 8

2˜

7 = 12

12. 5 − _1 = 6

13. Miss Wong had 2 gallons of lemonade. After a party, she has _1 gallon left. How many fewer gallons does Miss Wong have now?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 20

14. Mr. Davis asks students to find the difference between 2 and _3 . Ivan says the answer is 1 _3 . Pablo 6

says the answer is 1 _1 . Amy says the answer is _9 . Is each person correct? Explain. 2

15. Adam has 1 yard of cloth. He uses _1 yard for a project. 3

a. How many yards of cloth does Adam have left?

b. How many feet of cloth does Adam have left?

184

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TD ▸ Lesson 20

Date

Subtract. Explain your strategy by using pictures, numbers, or words. 1. 1 − 3_ 4

2. 2 − _2 5

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185

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 21

Name

Date

Use the Read–Draw–Write process to solve each problem.

1. Shen walks 5 mile in the morning and 5 miles in the afternoon. How many total miles does Shen walk?

__9

__2

2. A container has 10 liters of water. Casey pours out 10 liters. How many liters of water are left in the container?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 21

3. Luke bakes a loaf of banana bread. After giving some away to a friend,

he has 6 of a loaf left. How much of a loaf does Luke give away?

__5

__7

4. Eva uses 12 feet of pink ribbon. She uses 12 feet more blue ribbon than pink ribbon. a. How many feet of blue ribbon does Eva use?

b. Is your answer from part (a) reasonable? Explain.

188

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 21

5. Carla has 2 pounds of oatmeal. She uses 4 pounds. a. How many pounds of oatmeal does Carla have left?

b. Is your answer from part (a) reasonable? Explain.

6. Miss Diaz buys 8 pounds of strawberries. She also buys 8 pounds of blueberries and 8 pounds of raspberries.

a. How many pounds of berries does Miss Diaz buy?

b. Is your answer from part (a) reasonable? Explain.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 21

Name

Date

James hikes _7 miles. The next day he hikes _5 miles.

Use the Read–Draw–Write process to solve the problem. 8

a. How far does James hike altogether?

b. Is your answer from part (a) reasonable? Explain.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 22

Name

Date

Represent the addition by using a number line. Then complete the statements. 1.

_1 + 1_ = 1_ + _____ = _____ 4 2 4 4

1 4

3_ 1_ 3_ _____ _____ + = + = 4 2 4

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3 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 22

_1 + _1 = _____ + _____ = _____ 6

_5 + _1 = 6

194

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 22

Rename to find the sum. Show your work.

_1 + 1_ = _____ + _____ = _____ 2 6

3 + 2_ __ 6. 10 5

3_ 5_ + 4 8

7 __ + 2_ 12

__5

9. James spends 4 of the year in Florida. He spends 12 of the year in Vermont. What fraction of the year does James spend in Florida or Vermont?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TD ▸ Lesson 22

__7

10. Liz drinks 5 liters of water. Gabe drinks 10 liters of water. How many liters of water do they drink altogether?

a. Write the answer as a fraction greater than 1.

b. Write the answer as a mixed number.

c. Should Liz and Gabe describe the total as a fraction greater than 1 or as a mixed number? Explain.

196

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TD ▸ Lesson 22

Date

Find the sum. Show your work. 1.

_1 + 3_ 2 8

_3 + 2_ 6 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 23

Name

Date

Add.

1 1_ 1. 3 _ + = 5 5

2 + 4 3_ = 2. _ 8 8

3. 5 1_ + 1_ = 2 2

Add. Show your thinking. 1 _ 4. 2 _ +1= 4 4

5. 2_ + 7 3_ = 6 6

4 _ 6. 3 _ +1= 5 5

7. 5_ + 5 3_ = 8 8

2 _ 8. 4 _ +2= 3 3

9 7 9. 8 __ + __ = 10 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 23

11 5 . Explain why both David and Oka are correct. 10. David and Oka find the sum of 10 __ and __ 12

Oka’s Way

David’s Way 1

10 12 + 12 = 11 4

11 + 12 = 11 12

200

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10 12 + 12 = 10 12 16

1012 = 10 + 12 + 12 = 1112

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 23

Date

Add. Show your thinking. 2 = 1. 3 1_ + _ 3 3

2. 1 4_ + 3_ = 5 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 24

Name

Date

Add. 1. 1 _1 + 2 _1 = 3 3

2. 3 _2 + 1 _2 = 5 5

3. 2 _1 + 1 _1 = 2 2

Add. Show your thinking. 4. 1 _2 + 1 _2 = 3 3

2 5. 1 _ + 3 _3 = 4 4

6. 2 _5 + 3 _3 = 6 6

7. 2 _4 + 2 _4 = 5 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 24

8. 3 _5 + 3 _6 = 8 8

6 8 9. 2 __ + 3 __ = 10 10

5 10 10. 4 __ + 3 __ = 12 12

9 8 11. 4 __ + 5__ = 12 12

7 9 minutes. Adam runs the next part in 4 __ minutes. 12. Deepa runs the first part of a relay race in 5 __ 10 10 What is their total time?

204

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 24

Date

Add. Show your thinking. 1. 1 1_ + 1 1_ = 3 3

2. 2 3_ + 1 2_ = 5 5

3. 3 5_ + 2 6_ = 8 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 25

Name

Date

Subtract. 1. 1 _3 − _2 = 4 4

4 __ − __ 3. 7 11 = 12 12

3 6 − __ = 2. 5 __ 10 10

Subtract by counting on. Use the arrow way or a number line to help you. Then complete the equations. 4. 1 1_ − 2_ = 4 4

_2 + 4

= 1 _1 4

2 4

1 4

2 4_ 5. 1 _ − = 5 5 4_ + 5

= 1 _2 5

1 _ 6. 2 _ −4= 6 6 4_ + 6

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= 2 1_ 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 25

Subtract by using compensation. Use the arrow way or a number line to help you. Then complete the equation. 3 8 − __ = 7. 1 __ 10 10

110

°1

3 10

2 10

8. 1 2_ − 7_ = 8 8

9. 2 1_ − 3_ = 5 5

208

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 25

Rename the mixed number to subtract. Then complete the equation. 1

16 ° 6 =

10. 6 6

7 5 ° = 6 6

2 _ 11. 1 _ −3= 4 4

1 _ 12. 2 _ −2= 3 3

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 25

Subtract. Show your thinking. 13. 1 1_ − 7_ = 8 8

5 __ = 14. 1 __ − 10 12 12

1 _ −2= 15. 4 _ 3 3

2 _ 16. 5 _ −4= 5 5

210

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 25

10 7 17. Jayla and Pablo use the arrow way to find 7 __ − __ . Is their work correct? Explain. 12

Jayla’s Work

Pablo’s Work

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10 12

2 12

7 12

1 −

7 12

7 −

3 12

7 12

9 12

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 25

Date

Subtract. Show your thinking. 1 3 1. 1 _ − _ = 5 5

5 7 2. 2 __ − _ = 8 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 26

Name

Date

Decompose the part to subtract. Use the arrow way to help. Then complete each equation. 2 5 1. 1 ˜ = 8 8 2 8 8

2 8

–

2 8

–

3 8

3 _ 2. 1 _ −4= 5 5

3 1−_ 3. 2 _ = 4 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 26

Decompose the total to subtract from 1. Then complete each equation. 4.

110 ˜ 10 = 1 10

7 = _____ 1 − __ 10

__3 + _____ = _____ 10

5. 1 2_ − 5_ = 6 6

1 _ 6. 2 _ −2= 3 3

216

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 26

Rename the total to subtract. Then complete each equation. 7.

26 ˜ 6 = 7 6

_ _ _____

7−4= 6 6

1 + _____ = 1 _____ 6

1 _ 8. 2 _ −5= 8 8

2 _ 9. 3 _ −4= 5 5

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 26

Subtract. Show your thinking. 5 = 10. 1 1_ − _ 6 6

7 2 11. 2 __ − __ = 10 10

3 _ −7= 12. 3 _ 8 8

5 9 13. 5 __ − __ = 12 12

218

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 26

5 10 14. Ray and Amy find 7 __ − __ . Is their work correct? Explain. 12 12

Ray’s Work 5 10 7 12 – 12 =

Amy’s Work 7

1 12

7 10 = 6 __ __ − __ 6 17 12

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5 10 7 12 – 12 =

6 12

7 12 17 12

6 12

7 6 + 7 = 6 12 12

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 26

Date

Subtract. Show your thinking. 3 = 1. 2 1_ − _ 5 5

2 2. 3 1_ − _ = 3 3

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 27

Name

Date

Subtract. 2 1. 3 _ − 1 _1 = 3 3

3 2. 4 5_ − 2 _ = 6 6

3 8 3. 7 __ − 3 __ = 12 12

Subtract by counting on. Use the arrow way or a number line to help you. Then complete the equations. 1 − 1 _2 = 4. 4 _ 3 3

1 _2 +

= 4 _1

+ 13

5. 5 2_ − 2 4__ = 5 5

2 4_ +

= 5 _2

6. 6 3_ − 1 6_ = 8 8

1 6_ + 8

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= 6 _3 8

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 27

Subtract by using compensation. Use the arrow way or a number line to help you. Then complete the equation. 4 = 7. 5 1_ − 1__ 6 6

+ 26

˜2

1 8. 6 _ − 1 3_ = 4 4

2 9. 7 _ − 2 _3 = 5 5

224

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 27

Decompose the total to subtract from a whole number. Then complete the equation. 1

4 10 ˜ 110 =

10.

2 2 10

8 2 − 1 __ = _____ 10

1 2 __ + _____ = 2 _____ 10

1 11. 5 _ − 1 _2 = 3 3

2 − 3 _5 = 12. 7 _ 6 6

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 27

Subtract. Show your thinking. 3 13. 4 2_ − 2 _ = 4 4

1 14. 6 _ − 1 6_ = 8 8

9 2 15. 6 __ − 3 __ = 10 10

5 __ = 16. 8 __ − 5 10 12 12

226

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 27

3 6 17. Mia rides her bike 15 __ kilometers on Saturday and Sunday combined. She rides 7 __ kilometers 10

on Sunday. How many kilometers does Mia ride on Saturday?

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 27

Date

Subtract. Show your thinking. 1. 3 1_ − 12_ = 6 6

2 − 3 _3 = 2. 5 _ 4 4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 28

Name

Date

Use the Read–Draw–Write process to solve the problem.

1. There were 6 _ pizzas on a table when lunch started. 3 8

At the end of lunch, there were 2 _ pizzas left. 6 8

How many pizzas were eaten during lunch?

Use the Read–Draw–Write process to solve the problem. 2. Ray bikes 4 __ km. Zara bikes 2 __ km . 4 10

7 10

a. How many more kilometers does Ray bike than Zara?

b. How many kilometers do Ray and Zara bike together?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 28

Name

Date

Use the Read–Draw–Write process to solve each problem.

1. Casey went to camp for 3 _ days in June and 6 _ days in July. How many days was Casey at camp altogether?

1 2

2. Mia uses 4 _ meters of wire to make some flowerpot hangers. She has 1 _ meters left. How much 4 5

wire did Mia have to begin with?

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3 5

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 28

3. A bucket can hold 5 _ gallons. Luke pours 2 _ gallons of water in the bucket. How much more 3 8

water is needed to fill the bucket?

5 8

4. Pablo reads 9 _ pages in his science book. He reads 6 _ pages in his social studies book. 1 3

2 3

a. How many more pages does Pablo read in his science book than in his social studies book?

b. How many pages does Pablo read altogether?

234

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 28

5. Mr. Endo donates 4 __ kilograms of pet food to the animal shelter in May. He donates 7 10

9 2 __ kilograms more pet food in June than in May. 10

a. How many kilograms of pet food does Mr. Endo donate in June?

b. How many total kilograms of pet food does Mr. Endo donate in May and June?

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TE ▸ Lesson 28

Date

Use the Read–Draw–Write process to solve each problem.

A watermelon weighs 8 _1 kilograms. A pumpkin weighs 4 _2 kilograms. 3

a. How much more does the watermelon weigh than the pumpkin?

b. How much do the watermelon and the pumpkin weigh altogether?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29 ▸ Line Plot Questions

a. What does each X indicate?

b. How many bags of apples does the fruit stand sell on Monday?

c. How many bags of apples will the fruit stand sell on Tuesday?

d. What is the weight of the lightest bag of apples?

e. How many apples are in the heaviest bag of apples? f.

Use >, =, or < to compare the weight of the lightest bag of apples to the weight of the heaviest bag of apples.

g. Which weight occurs most frequently? How do you know? h. How many bags of apples does the fruit stand have left to sell?

How many bags of apples weigh at least 3 _1 pounds?

Estimate the total weight of all the bags of apples that weigh 2 _ pounds.

7 8

Find the actual weight. k. Who buys the bag of apples that weighs 3 _ pounds? 5 8

Where would a bag of apples that weighs _ pounds be plotted on the line plot? How do you know?

6 2

m. How much money does the fruit stand make from selling apples on Monday?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29

Name

Date

1. Zara measures the distance her paper airplane travels each time she throws it. She records the data on a line plot. Distances the Paper Airplane Travels

× 0

× × ×

× ×

× 17

Distance (feet)

a. How many times does Zara throw her paper airplane?

b. What is the longest distance her paper airplane travels?

c. Use >, =, or < to compare the longest distance to the shortest distance.

d. Which distance occurs most frequently? How do you know?

e. How many times does the airplane travel at least 15 _ feet? 2 4

Estimate the difference between the longest and shortest distances.

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4 ▸ M4 ▸ TE ▸ Lesson 29

g. What is the difference between the longest and shortest distances?

h. Zara throws her airplane one more time. She records the distance it travels as __ feet. 59 4

Where should the distance be plotted on the line plot? How do you know?

2. A fruit stand measures the weight of each bag of apples it sells on Monday. They make a line plot from the data. Weights of Bags of Apples Sold on Monday

× 0

× × ×

× ×

× × × ×

× ×

× 4

Weight (pounds)

242

LESSON

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EUREKA MATH2 Tennessee Edition

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4 ▸ M4 ▸ TE ▸ Lesson 29

LESSON

243

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29

Name

Date

1. The students in Mrs. Smith’s class measure the lengths of ribbons. They make a line plot from the data. Lengths of Ribbons in Mrs. Smith’s Classroom

× 0

× ×

× 1

× 2

× × ×

× 3

Length (feet)

a. How many ribbons does the class measure?

b. What is the length of the longest ribbon?

c. Use >, =, or < to compare the length of the longest ribbon to the length of the shortest ribbon.

d. How many ribbons are at least 1 _ feet long? 1 4

e. Which length occurs most frequently? How do you know?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29

Estimate the total length of all the ribbons that are 2 _ feet long. Show your work. 1 4

g. What is the total length of all the ribbons that are 2 _ feet long? 1 4

h. Mrs. Smith finds one more ribbon in her desk. The length of the ribbon is _ feet. 5 2

Where should the length of this ribbon be plotted on the line plot? How do you know?

2. The Animal Rescue Center measures the weights of 10 kittens. The weights of the kittens, in pounds, are shown on the line plot. Weights of Kittens at the Animal Rescue Center

× × × × ×

× × 0

× × × 2

Weight (pounds)

a. What is the weight of the lightest kitten?

b. Use >, =, or < to compare the weight of the lightest kitten to the weight of the heaviest kitten.

246

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29

c. How many kittens weigh less than or equal to 1 _ pounds? 5 8

d. Which weight occurs most frequently? How do you know?

e. Two kittens each weigh 2 _ pounds. What is the total weight of the two kittens? 5 8

How many more pounds does the heaviest kitten weigh than the lightest kitten?

g. Estimate the total weight of all the kittens who weigh between 2 and 3 pounds. Show your work.

h. Ivan says, “More kittens are heavier than 1 _ pounds than kittens who are lighter than 1 _ pounds.” Do you agree with Ivan? Why?

7 8

A worker brings in a new kitten who weighs __ pounds. How would the line plot need 30 8

to change to be able to plot the weight of the new kitten?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 29

Name

Date

1. Mr. Endo records the amount of time each of his students reads this week. The times, in hours, are shown on the line plot. Time Spent Reading

× 0

× ×

× × × 2

× 3

Time (hours)

a. What is the longest amount of time that a student spent reading?

b. How many students are in Mr. Endo’s class?

c. How many students read for 2 hours or less?

d. What is the difference between the greatest amount of time a student read and the least amount of time a student read?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Add and Subtract Fractions with Like Units

Sprint Add or subtract. Write the sum or difference in fraction form.

_ _

1 1 + = 6 6

2 4 + = 6 6

3 1 − = 6 6

7 2 − = 6 6

_ _ _ _ _ _

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ Sprint ▸ Add and Subtract Fractions with Like Units

Number Correct:

Add or subtract. Write the sum or difference in fraction form.

_ _

1 1 + = 4 4

23.

1 7 + = 8 8

1 2 + = 4 4

24.

3 6 + = 8 8

2 1 − = 4 4

25.

8 3 − = 8 8

3 1 − = 4 4

26.

1 1 + = 5 5

27.

__1 + __9 =

1 3 + = 5 5

28.

6 6 + = 10 10

3 1 − = 5 5

29.

10 − 2 = 10 10

4 2 − = 5 5

30.

13 6 − = 10 10

1 2 + = 6 6

31.

__1 + 11 __ = 12

10.

32.

__5 + __9 = 12

11.

4 2 − = 6 6

33.

12 − 4 = 12 12

12.

5 3 − = 6 6

34.

8 17 __ __ − =

13.

1 3 + = 4 4

35.

1 1 + = 3 3

14.

2 3 + = 4 4

36.

3 1 − = 3 3

15.

4 2 − = 4 4

37.

16.

5 2 − = 4 4

38.

15 7 − = 6 6

17.

1 4 + = 5 5

39.

8 8 + = 8 8

18.

3 4 + = 5 5

40.

19.

5 2 − = 5 5

41.

11 23 + = 10 10

20.

8 4 − = 5 5

42.

37 15 − = 10 10

43.

14 38 + = 12 12

_ _ _ _

_ _

_ _ _ _

_ _

_2 + 3_ = 6

_ _

_ _ _ _

_ _

_ _ _ _ _ _

21.

_1 + _5 =

22.

4 5 + = 6 6

_ _

252

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44.

_ _

__ _

10 3 − = 8 8

__ __

_ _

6 6 + = 6 6

__ _ _ _

__ _

17 8 − = 8 8

__ __ __ __

__ __

55 26 − = 12 12

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4 ▸ M4 ▸ Sprint ▸ Add and Subtract Fractions with Like Units

Number Correct: Improvement:

Add or subtract. Write the sum or difference in fraction form.

_ _

1 1 + = 4 4

23.

2 1 + = 4 4

24.

2 1 − = 4 4

25.

_ _ _ _

_ _

_7 + 1_ = 8

_6 + 3_ = _8 − _5 =

__ _

3 2 − = 4 4

26.

1 1 + = 5 5

27.

__9 + __1 =

3 1 + = 5 5

28.

6 6 + = 10 10

29.

8 10 − = 10 10

_ _

10 7 − = 8 8

__ __

_3 − _2 =

4 2 − = 5 5

30.

13 − 7 = 10 10

31.

11 + 1 = 12 12

32.

_ _

_2 + 1_ =

__ __ __ __ __ __

10.

_3 + _2 =

11.

4 2 − = 6 6

33.

8 12 __ __ − =

34.

9 17 − = 12 12 1 1 + = 3 3

_ _

__9 + __5 = 12

12.

_5 − 4_ =

13.

3 1 + = 4 4

35.

36.

_3 − _2 =

6 6 + = 6 6

_ _

__ __ _ _

14.

_3 + _2 =

15.

4 2 − = 4 4

37.

16.

5 3 − = 4 4

38.

15 8 − = 6 6

17.

4 1 + = 5 5

39.

8 8 + = 8 8

18.

4 3 + = 5 5

40.

19.

5 3 − = 5 5

41.

23 __ __ + 11 =

20.

8 4 − = 5 5

42.

37 16 − = 10 10

21.

5 1 + = 6 6

43.

38 14 + = 12 12

22.

5 4 + = 6 6

44.

_ _ _ _

_ _

_ _ _ _ _ _

_ _

254

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_ _

__ _ _ _

__ _

17 9 − = 8 8

__ __

55 29 − = 12 12

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TE ▸ Lesson 30

Name

Date

1. Miss Diaz records how far she walks each day for 14 days.

Day

Walking Distance (miles)

1 6_8

2 1_8

1 3_8

5 6 7 8

1 6_8

2 7_8 2 1_8 1 5_8

2 3_8

7 8

11 12 13 14

1 5_8 2 1_8 2 5_8 2 3_8

a. How many miles does Miss Diaz walk on day 10?

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4 ▸ M4 ▸ TE ▸ Lesson 30

1 b. How many days does Miss Diaz walk more than 2 _ miles? 8

c. What is the longest distance Miss Diaz walks?

3 miles? d. On which days does Miss Diaz walk 2 _ 8

e. Use the data in the table to make a line plot.

What is the most frequent distance Miss Diaz walks?

g. How many miles does Miss Diaz walk on day 8?

h. Use >, =, or < to compare the distances Miss Diaz walks on day 6 and day 13.

256

What is the difference, in miles, between the longest and the shortest distances?

LESSON

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4 ▸ M4 ▸ TE ▸ Lesson 30

2. Use the data cards to complete the table.

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LESSON

257

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4 ▸ M4 ▸ TE ▸ Lesson 30

a. Use the data in the table to make a line plot.

b. Write a question that can be answered more efficiently by using the line plot.

258

LESSON

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4 ▸ M4 ▸ TE ▸ Lesson 30

Name

Date

1. Mr. Lopez is researching blueberry muffin recipes. He finds 10 different blueberry muffin recipes. He lists the amount of flour needed for each recipe in the table. a. Use the data in the table to make a line plot. Title:

2 Amount of Flour (cups)

b. Which recipe needs the least amount of flour?

c. Which recipes need 1 4 cups of flour?

d. How many recipes need at least 1 4 cups of flour?

Blueberry Muffin Recipe

Amount of Flour (cups)

1 _4

2 _4

1 _4

3 2 3

e. What is the difference, in cups, between the greatest and least amount of flour?

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4 ▸ M4 ▸ TE ▸ Lesson 30

Use >, =, or < to compare the amounts of flour in recipes G and H.

g. What is the most frequent amount of flour in a recipe? How do you know?

h. Mr. Lopez wants to bake 2 batches of blueberry muffins by using recipe C. How many cups of flour does he need?

260

13 __

Mr. Lopez finds that recipe K needs 8 cups of flour. Where would he plot the amount of flour for recipe K on the line plot? Why?

Mr. Lopez has 7 cups of flour. He wants to bake 3 batches of blueberry muffins by using the recipe that needs the largest amount of flour. Does Mr. Lopez have enough flour to bake 3 batches?

PROBLEM SET

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4 ▸ M4 ▸ TE ▸ Lesson 30

2. 10 students measure the snow depth at different locations around their school. They list the data in a table. a. Use the data in the table to create a line plot.

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Student

Snow Depth (inches)

Zara

3 _8

Shen

3 _8

Casey

Ray

4 _8

James

2 _8

Luke

4 _8

Robin

3 _8

Amy

3 _8

Carla

2 _8

Eva

4 _8

3 6 3

3 7

PROBLEM SET

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4 ▸ M4 ▸ TE ▸ Lesson 30

b. Use >, =, or < to compare the least and greatest snow depths.

c. How many more students measured the greatest amount of snow than the least amount of snow?

d. What is the difference between the largest and smallest measurements?

e. Miss Wong’s snow depth measurement is twice Carla’s measurement. Estimate Miss Wong’s snow depth measurement. Show your work.

262

What is Miss Wong’s snow depth measurement?

PROBLEM SET

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4 ▸ M4 ▸ TE ▸ Lesson 30

Name

Date

A weatherperson measures the rainfall amounts each month and records the data in the table shown. Use the data to make a line plot. Month

Jan

Feb

Mar

Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

Rainfall (inches)

1 _4

2 _4

1 _4

1 _2

1 _4

2 _4

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 31

Name

Date

7_ = 7 × 1_8 8

7 eighths = 7 × 1 eighth a. Draw a tape diagram to represent the fraction decomposition.

b. Draw a number line to represent the fraction decomposition.

c. 8 is the

multiple of 8 .

9 1 __ = 9 × __ 12

a. Draw a tape diagram to represent the fraction decomposition.

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4 ▸ M4 ▸ TF ▸ Lesson 31

b. Draw a number line to represent the fraction decomposition.

__9

c. 12 is the

multiple of

12 1 __ __ = 12 × 10 10

a. Draw a tape diagram to represent the fraction decomposition.

b. Draw a number line to represent the fraction decomposition.

12 __

c. 10 is the

266

LESSON

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multiple of

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 31

Name

Date

Complete the equation and statement. Then represent the equation with a tape diagram. The first tape diagram has been done for you. 2 = 1_ + 1_ 1. _ 3 3 3 2_ = 3

2 3

× _____

1 3

_2 is the second multiple of 3

1 3

2. _3 = _1 + _1 + _1 3 3 3 3 3_ = 3

× _____ 3

_3 is the 3

multiple of

3. 4_ = 1_ + 1_ + 1_ + 1_ 3 3 3 3 3 4_ = 3

_4 is the 3

EM2_0404SE_F_L31_problem_set.indd 267

× _____

267

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 31

Complete each equation and statement. Then represent the equation with a number line. 4. 3_ = 1_ + 1_ + 1_ 4 4 4 4 3_ = 4

× ____ 4

_3 is the third multiple of 4

1 1_ _ 5. 4_ = _ + + 1 + _1 4 4 4 4 4 4_ = 4

× _____

_4 is the

multiple of

1 1_ _ 6=_ + + 1 + _1 + 1_ + 1_ 6. _ 4 4 4 4 4 4 4

_6 = 4

× _____

_6 is the 4

268

multiple of

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 31

Write an equation to express each fraction as a whole number times a unit fraction. 7.

7 __

9 __ 10

2 9. _ 2

8 10. _ 8

7 11. _ 5

__ 12. 10 6

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PROBLEM SET

269

11/24/2021 4:37:26 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 31

Name

Date

Complete the equation to express each fraction as a whole number times a unit fraction. 1.

_3 = 8

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× ____

6_ = 6

× _____

_7 = 4

× _____

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 32

Name

Date

Label the number line. Then use unit form and the associative property to find the product. 1 5

1 5

3 × (1 fifth) = (3 × =

EM2_0404SE_F_L32_problem_set.indd 273

fifths

2 5

) fifth

2 5

5 × (2 fifths) = ( =

× 2) fifths fifths

273

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 32

Complete the expression to represent the tape diagram. Then complete the statements to find the product.

3. 3 4

2 × 4_3 = 2 × (3 × _____ ) 4

3 4

= (2 × 3) × _____ 4

2 × ____ 4

= 6 × _____

= _____

4 × 6_ = 4 × �2 × _____� 2

2 6

) × _____

4 × _____ =

× _____

= _____

274

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 32

×�

4 × 8_ = 5

5 8

× _____� ) × _____

× _____ × _____

= _____

Complete the statements to find the product. 2× 3 6. 2 × 5_ = _______ 5

× 3 7. 5 × _ = __________ 8

= _____ 5

= _____

9 3 × __ = __________ 10

= _____

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4 7 × __ = __________ 12

= _____

PROBLEM SET

275

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 32

Choose a method and find the product. 4 10. 3 × _ 5

3 11. 6 × __ 10

8 12. 4 × __ 12

4 13. 5 × _ 3

276

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TF ▸ Lesson 32

Date

Choose a method and find the product. 3 1. 4 × __ 10

6 2. 5 × _ 8

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TF ▸ Lesson 33

Date

Use the Read–Draw–Write process to solve the problem.

1. Deepa makes 5 pitchers of lemonade to sell at her stand. She uses 4 cups of sugar in each

pitcher. She only has a 4 -cup measuring scoop. How many times does Deepa fill the measuring scoop to make the 5 pitchers of lemonade?

Use the Read–Draw–Write process to solve the problem.

2. A kitten weighs 5 kilograms. A puppy is 6 times as heavy as the kitten. How many kilograms does the puppy weigh?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 33

Name

Date

Use the Read–Draw–Write process to solve each problem.

1. Carla walks 5 miles each day on Tuesday, Thursday, and Saturday. How many miles does Carla walk in all?

2. A rectangular garden measures 9 feet by 4 feet. What is the area of the garden?

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 33

3. A bag of cherries weighs 8 pounds. Before any cherries were eaten, the bag of cherries weighed

8 times this amount. What was the weight of the original bag of cherries?

__7

4. Mr. Davis puts 10 kilograms of soil into each of his flowerpots. He fills 1 dozen flowerpots.

__1

He uses a measuring container that holds 10 kilogram of soil. How many times does Mr. Davis fill the measuring container for all the flowerpots? (Hint: 1 dozen flowerpots = 12 flowerpots)

282

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 33

5. There are 15 players on Mrs. Smith’s soccer team. They are having a pizza party. If each player _3 eats 8 of a pizza, how many pizzas does Mrs. Smith need to buy?

6. A piece of blue ribbon is 6 yards long. A piece of red ribbon is 11 times as long as the piece of blue ribbon. What is the total length of the two pieces of ribbon?

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PROBLEM SET

283

11/24/2021 4:41:00 PM

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TF ▸ Lesson 33

Date

Use the Read–Draw–Write process to solve each problem.

1. David walks _3 miles a day for 8 days. How many miles does David walk altogether? 4

2. A rectangular piece of paper measures 6 inches by _7 inches. What is the area of the 8 piece of paper?

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285

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 34

Name

Date

Multiply by using the distributive property. 1. 2 × 4 1_ 3

1 3

2 × 4 1_ = 2 × (4 + _3) 3

= (2 × 4) + (2 × _3) 1

+ _____ 3

2. 3 × 5 2_ 8

2 8

3 × 5 2_ = 3 × (5 + _8) 2

= (3 ×

) + 3 × _____

+ _____

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 34

3. 4 × 4 3_ 4

3 4

4. 5 × 7 5_ 6

288

5 6

PROBLEM SET

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4 × 4 _3 = 4 × �

+ _____�

× 4) + (

__ + 12

× _3) 4

= 16 + =

5 × 7 5_ 6

11/24/2021 4:41:55 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 34

Multiply by using the distributive property. You may draw a model to help you. 5. 2 × 3 1_ = 4

2 6. 4 × 4 __ = 10

2 7. 5 × 4 _ = 5

EM2_0404SE_F_L34_problem_set.indd 289

PROBLEM SET

289

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 34

5 8. 8 × 9 __ = 12

Use the Read–Draw–Write process to solve each problem.

9. Mr. Endo’s new puppy weighed 6 _5 pounds when he brought the puppy home. Now, the puppy 8

weighs 8 times as much. How much does the puppy weigh now?

290

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M4 ▸ TF ▸ Lesson 34

3 10. Mia runs 5 __ miles each day. How many miles does Mia run in 2 weeks? (Hint: 1 week = 7 days) 10

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PROBLEM SET

291

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M4 ▸ TF ▸ Lesson 34

Date

Multiply by using the distributive property. You may draw a model to help you. 3 1. 2 × 3 __ = 8

1 2. 4 × 5 _ = 3

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293

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4 ▸ M4

Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. Cover, Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York; page 12, venski/Shutterstock.com; page 52, Av ONYXprj/Shutterstock.com; page 81, eurobanks/Shutterstock.com; page 188, Rob Marmion/Shutterstock.com; All other images are the property of Great Minds. For a complete list of credits, visit http://eurmath.link/media-credits.

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EUREKA MATH2 Tennessee Edition

4 ▸ M4

Acknowledgments Kelly Alsup, Leslie S. Arceneaux, Lisa Babcock, Adam Baker, Christine Bell, Reshma P. Bell, Joseph T. Brennan, Dawn Burns, Leah Childers, Mary Christensen-Cooper, Nicole Conforti, Jill Diniz, Christina Ducoing, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Marlene Pineda, Elizabeth Re, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Tara Stewart, Mary Swanson, James Tanton, Julia Tessler, Jillian Utley, Saffron VanGalder, Rafael Velez, Jackie Wolford, Jim Wright, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

296

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Talking Tool Share Your Thinking

I know . . . . I did it this way because . . . . The answer is

because . . . .

My drawing shows . . . . I agree because . . . .

Agree or Disagree

That is true because . . . . I disagree because . . . . That is not true because . . . . Do you agree or disagree with

Ask for Reasoning

? Why?

Why did you . . . ? Can you explain . . . ? What can we do first? How is

Say It Again

related to

I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?

EM2_0404SE_acknowledgements.indd 297

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Thinking Tool When I solve a problem or work on a task, I ask myself Before

Have I done something like this before? What strategy will I use? Do I need any tools?

During

Is my strategy working? Should I try something else? Does this make sense?

After

What worked well? What will I do differently next time?

At the end of each class, I ask myself

What did I learn? What do I have a question about?

EM2_0404SE_acknowledgements.indd 298

11/24/2021 12:03:16 PM

MATH IS EVERYWHERE Do you want to compare how fast you and your friends can run? Or estimate how many bees are in a hive? Or calculate your batting average? Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars. Fueled by your curiosity to understand the world, math will propel you down any path you choose. Ready to get started?

Module 1 Place Value Concepts for Addition and Subtraction Module 2 Place Value Concepts for Multiplication and Division Module 3 Multiplication and Division of Multi-Digit Numbers Module 4 Foundations for Fraction Operations Module 5 Place Value Concepts for Decimal Fractions Module 6 Angle Measurements and Plane Figures

What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

ISBN 978-1-63898-511-2

781638 985112