3

A Story of Units®

Units of Any Number LEARN ▸ Module 5 ▸ Fractions as Numbers

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? Swiss-born artist Paul Klee was interested in using color to express emotion. Here he created a grid, or array, of 35 colorful squares arranged in 5 rows and 7 columns. We will learn how an array helps us understand a larger shape by looking at the smaller shapes inside. Learning more about arrays will help us notice patterns and structure— an important skill for multiplication and division. On the cover Farbtafel “qu 1,” 1930 Paul Klee, Swiss, 1879–1940 Pastel on paste paint on paper, mounted on cardboard Kunstmuseum Basel, Basel, Switzerland Paul Klee (1879–1940), Farbtafel “qu 1” (Colour Table “Qu 1” ), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der Klee-Gesellschaft, Bern. © 2020 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 978-1-63898-506-8

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A Story of Units®

Units of Any Number ▸ 3 LEARN

Module

EM2_0305SE_title_page.indd 1

1

Multiplication and Division with Units of 2, 3, 4, 5, and 10

2

Place Value Concepts Through Metric Measurement

3

Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

4

Multiplication and Area

5

Fractions as Numbers

6

Geometry, Measurement, and Data

11/2/2021 5:24:46 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5

Contents Fractions as Numbers Topic A Partition a Whole into Equal Parts Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Partition a whole into equal parts and name the fractional unit.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Partition different wholes into fractional units concretely.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Partition a whole into fractional units by folding fraction strips. Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Partition a whole into fractional units pictorially and identify the unit fraction.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Partition a whole into fractional units and write fractions in fraction form.

Topic B Unit Fractions and Their Relationship to the Whole

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Compare non-unit fractions less than 1 with

the same numerator by using tape diagrams.

Topic C Fractions on the Number Line Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Locate fractions from 0 to 1 on a number line by using fraction tiles. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Represent fractions from 0 to 1 on a number

line.

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Identify equivalent fractions from 0 to 1 with tape diagrams and on number lines. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Recognize that equivalent fractions share the same location on a number line.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Identify fractions on a ruler as numbers on a number line. Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Build non-unit fractions less than 1 from unit

Measure lengths and record data on a line plot.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Topic D

fractions concretely.

Identify and represent a whole as two parts: a unit fraction and a non-unit fraction.

Comparing Fractions Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Represent fractions greater than 1 on a

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Identify and represent a whole as two non-unit fractions.

number line and identify fractions equivalent to whole numbers.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Compare unit fractions by reasoning about their size concretely.

Compare fractions with like units by using a number line.

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This document is the confidential information of Great Minds PBC provided solely for review purposes which may not be reproduced or distributed. All rights reserved.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Compare fractions with unlike units but the same numerator by using number lines.

Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Generate equivalent fractions greater than 1 by using a number line.

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Compare fractions with related units by using a number line.

Express whole numbers as fractions with a denominator of 1.

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Compare various fractions by representing them on number lines.

Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Create a ruler with 1-inch, half-inch, and quarter-inch intervals. Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Topic E Equivalent Fractions

Apply fraction concepts to complete a multi-part task. (Optional)

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

Identify fractions equivalent to whole numbers by using number lines.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 282

Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Reason to find fractions equivalent to whole numbers by using patterns and number lines.

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3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 1

1

Name

Use the shapes for problems 1–5. Shape A

Shape B

Shape D

Shape E

Shape C

Shape F

1. Circle the shapes that are partitioned into equal parts.

2. Did you circle shape B? Why?

© Great Minds PBC •

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This document is the confidential information of Great Minds PBC provided solely for review purposes which may not be reproduced or distributed. All rights reserved.

5

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 1

3. Do any of the shapes show fourths? How do you know?

4. Zara says that shape D is partitioned into halves. Do you agree with her? Why?

5. Shen draws another line in shape A. He says that shape A is now partitioned into sixths. Do you agree with Shen? Why? Shape A

6

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 1

Write the name of the fractional unit for each rectangle. Word Bank halves

thirds

fourths

6.

7.

8.

9.

sixths

eighths

Partition each rectangle into the given fractional units. 11.

10.

halves

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12.

fourths

eighths

PROBLEM SET

7

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 1

13.

14.

thirds

sixths

15. James cuts a sandwich into 2 equal parts. Draw a rectangle to represent the sandwich and show the equal parts. What fractional unit does James cut his sandwich into?

16. Amy draws lines on a rectangular piece of wood. Her lines show how to cut it into 4 equal parts. Draw the piece of wood and show the equal parts. What fractional unit does Amy use?

8

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 1

1

Name

1. Circle the shapes that are partitioned into equal parts.

2. Luke cuts a rectangular sheet of paper into 6 equal parts. a. Draw the paper and show the 6 equal parts.

b. What fractional unit does Luke cut the paper into?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

2

Name

My Station

Fractional Unit:

Station

Fractional Unit:

Square

Rectangle

Paper Strip

Fractional Unit:

Station

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11

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

My Station

Fractional Unit:

Station

Fractional Unit:

Clay

Cups

Wax Craft Stick

Fractional Unit:

Station

12

LESSON

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

2

Name

1. Ivan partitions his 1 ball of clay into equal parts.

Ivan’s ball of clay

a. Complete the table to show how Ivan can equally share the ball of clay with his friends. Number of People Equally Sharing the Clay

2

Clay

Fractional Unit

halves

3

fifths

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

b. Ivan says, “When I partition the clay into thirds, the parts are bigger than when I partition the clay into fifths.” Do you agree with Ivan? Why?

c. When 8 people equally share the clay, what fractional unit is the clay partitioned into? How do you know?

d. Ivan partitions his clay into 10 pieces. Do these pieces represent tenths? Explain your answer.

14

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

Partition each rectangle into the given fractional units. 2. Thirds

3. Fourths

4. Fifths

5. Sixths

6. Eighths

7. Tenths

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

8. Casey, Eva, and Robin cut their pizzas into equal pieces.

’s pizza

’s pizza

’s pizza

a. Use the statements to label each pizza with the correct person’s name. •

Eva cuts her pizza into fourths.

•

Robin cuts her pizza into eighths.

•

Casey cuts her pizza into halves.

b. Whose pizza has the most pieces?

c. Whose pizza is cut into the smallest pieces? How do you know?

d. What do you notice about your answers to parts (b) and (c)?

16

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 2

2

Name

1. Partition each shape into fourths.

2. Partition each shape into sixths.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 7

Sprint

by Twos and Fours

Complete each equation. 1.

2×7=

2.

14 ÷ 7 =

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 7

A

Number Correct:

Complete each equation. 1.

1×7=

23.

7×

= 21

2.

2×7=

24.

7×

= 35

3.

3×7=

25.

21 ÷ 7 =

4.

7÷7=

26.

35 ÷ 7 =

5.

14 ÷ 7 =

27.

7×

= 49

6.

21 ÷ 7 =

28.

7×

= 63

7.

4×7=

29.

49 ÷ 7 =

8.

5×7=

30.

63 ÷ 7 =

9.

6×7=

31.

7×

=7

10.

28 ÷ 7 =

32.

7×

=0

11.

35 ÷ 7 =

33.

7÷7=

12.

42 ÷ 7 =

34.

21 ÷ 7 =

13.

7×7=

35.

7×

14.

8×7=

36.

15.

9×7=

37.

16.

49 ÷ 7 =

38.

17.

56 ÷ 7 =

39.

18.

63 ÷ 7 =

40.

19.

10 × 7 =

41.

20.

1×7=

42.

21.

70 ÷ 7 =

43.

22.

7÷7=

44.

20

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= 14 × 7 = 28

7×

= 42 × 7 = 56

7×

= 70 ÷7=2

28 ÷

=7 ÷7=6

56 ÷

© Great Minds PBC •

=7 ÷ 7 = 10

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 7

B

Number Correct: Improvement:

Complete each equation. 1.

1×7=

23.

7×

= 14

2.

2×7=

24.

7×

= 28

3.

3×7=

25.

14 ÷ 7 =

4.

7÷7=

26.

28 ÷ 7 =

5.

14 ÷ 7 =

27.

7×

= 42

6.

21 ÷ 7 =

28.

7×

= 56

7.

3×7=

29.

42 ÷ 7 =

8.

4×7=

30.

56 ÷ 7 =

9.

5×7=

31.

7×

=7

10.

21 ÷ 7 =

32.

7×

=0

11.

28 ÷ 7 =

33.

7÷7=

12.

35 ÷ 7 =

34.

14 ÷ 7 =

13.

6×7=

35.

7×

14.

7×7=

36.

15.

8×7=

37.

16.

42 ÷ 7 =

38.

17.

49 ÷ 7 =

39.

18.

56 ÷ 7 =

40.

19.

9×7=

41.

20.

10 × 7 =

42.

21.

63 ÷ 7 =

43.

22.

70 ÷ 7 =

44.

22

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= 21 × 7 = 35

7×

= 49 × 7 = 63

7×

= 70 ÷7=3

35 ÷

=7 ÷7=7

63 ÷

© Great Minds PBC •

=7 ÷ 7 = 10

10/29/2021 5:36:46 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 3

3

Name

1. Circle the paper strips that are folded into equal parts.

Complete the sentences to describe each fraction strip. Then label each equal part. The first one is done for you. 2. There are parts in all.

2

The fractional unit is One unit is called

3. There are parts in all.

equal

1 half

halves

1 half

. .

equal .

The fractional unit is One unit is called

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1 half

.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 3

4. There are parts in all.

equal .

The fractional unit is .

One unit is called

5. There are parts in all.

equal .

The fractional unit is .

One unit is called

6. Luke folds a piece of paper into equal parts and labels each part. 1 sixth

1 sixth

1 sixth

1 sixth

1 sixth

1 sixth

1 sixth

1 sixth

What mistake does Luke make?

24

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 3

7. Use the fraction strips to answer parts (a)–(d).

1 half

1 half

1 third

1 third

1 fourth 1 fifth 1 sixth

1 fourth 1 fifth 1 sixth

1 third 1 fourth

1 fifth 1 sixth

1 sixth

1 fourth

1 fifth

1 fifth

1 sixth

1 sixth

a. How many units are in the whole when one unit is called 1 fourth?

b. Which fractional strip shows how 5 people can equally share a candy bar?

c. Eva folds a strip of paper into thirds. Then she folds each third in half. Which fraction strip matches Eva’s strip of paper? How do you know?

d. Ray says, “The fraction strips show that 1 sixth is smaller than 1 fourth.” Do you agree with Ray? Why?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 3

3

Name

Use your fraction strips to answer parts (a)–(c). a. How many units are in the whole when one unit is called 1 sixth?

b. Which fraction strip shows how 3 people can equally share a granola bar?

c. Amy folds a strip of paper into halves. Then she folds each half in half. Which fraction strip matches Amy’s strip of paper? How do you know?

© Great Minds PBC •

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3 ▸ M5 ▸ TA ▸ Lesson 4 ▸ Horizontal Input–Output Table

Output

Input

Pattern:

EUREKA MATH2 Tennessee Edition

29

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 4 ▸ Partitioning Shapes

B

A

C

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 4

4

Name

1. For each shape, name the fractional unit and the fraction of the shape that is shaded. The first one is done for you. b.

a.

Fractional unit: Fraction shaded:

Fractional unit:

halves

Fraction shaded:

1 half

c.

d.

Fractional unit:

Fractional unit:

Fraction shaded:

Fraction shaded:

e. David says that the fraction shaded for each shape is a unit fraction. Do you agree with David? Why?

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 4

2. Partition each image into fourths. Then shade the image to show 1 fourth.

3. Robin partitions and shades a shape. She says, “My shape shows 1 fourth shaded.” Do you agree with Robin? Why?

4. Draw a rectangle.

a. Partition the rectangle into sixths. b. Shade a unit fraction. c. Name the fraction of the shape that is shaded.

34

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 4

5. Two friends want to equally share a pizza. Show how to partition the pizza into 2 equal pieces.

a. What fractional unit is the pizza partitioned into?

b. Two more friends come and want to share the pizza. Partition the pizza to show how it can be equally shared among all the friends.

c. What fractional unit is the pizza partitioned into now?

d. Shade to show how much of the pizza 1 friend gets. What fraction of the pizza does each friend get?

© Great Minds PBC •

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PROBLEM SET

35

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 4

4

Name

1. Name the fractional unit and the fraction of the rectangle that is shaded.

Fractional unit: Fraction shaded:

2. Partition the rectangle into thirds. Then shade the rectangle to show 1 third.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5 ▸ Vertical Input–Output Table

Pattern: Input

© Great Minds PBC •

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Output

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

5

Name

1.

2.

3.

© Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

4.

5.

6.

42

LESSON

EM2_0305SE_A_L05_Classwork.indd 42

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

5

Name

1. Complete the table.

Shape

© Great Minds PBC •

EM2_0305SE_A_L05_problem_set.indd 43

Number of Shaded Units

Total Number of Units

Shaded Fraction in Unit Form

Shaded Fraction in Fraction Form

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

Shape

Number of Shaded Units

Total Number of Units

Shaded Fraction in Unit Form

Shaded Fraction in Fraction Form

2. Miss Wong wants to cut a piece of paper into 6 equal parts. Which rectangle shows how Miss Wong should cut the paper? How do you know?

Rectangle A

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PROBLEM SET

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Rectangle B

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

3. Jayla partitions two rectangles that are the same size into equal units. Rectangle A is partitioned into thirds, and rectangle B is partitioned into fourths. a. Draw lines on rectangle A to change the fractional unit from thirds to sixths.

Rectangle A

b. Draw lines on rectangle B to change the fractional unit from fourths to eighths.

Rectangle B

c. Shade 1 unit in each rectangle. Write the fraction you shaded for each rectangle in fraction form. Rectangle A: _____

Rectangle B: _____

d. Jayla says that 8 is a bigger number than 6, but the units in rectangle B are smaller than the units in rectangle A. Explain why the units in rectangle B are smaller than the units in rectangle A.

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PROBLEM SET

45

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TA ▸ Lesson 5

5

Name

1. Complete the table.

Shape

Number of Shaded Units

Total Number of Units

Shaded Fraction in Unit Form

Shaded Fraction in Fraction Form

2. Each shape represents 1 whole. Write the fraction that is shaded in fraction form.

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47

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 6

6

Name

1. Complete the table. Write all fractions in fraction form.

Shape

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Total Number of Units

Unit Fraction

Total Number of Units Shaded

Shaded Fraction

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 6

2. Deepa partitions a rectangle into fractional units.

a. Write the unit fraction on each unit. b. Shade units to show _ . 5 8

c. Complete the counting sequence to show how to count by eighths to _ . 5 8

_ _____ , _____ , _____ , _____ 1, 8

8

8

d. Deepa says, “If 2 more units are shaded, the whole rectangle will be shaded.” Do you agree with Deepa? Why?

50

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 6

3. Partition each rectangle and label each part with the unit fraction it represents. Then shade to show the given fraction and write the shaded fraction in fraction form. The first one has been started for you. a. Unit form: 3 fourths Fraction form:

1 4

1 4

1 4

1 4

b. Unit form: 7 eighths Fraction form:

c. Unit form: 2 thirds Fraction form:

d. Unit form: 3 sixths Fraction form:

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 6

4. James partitions a rectangular piece of wood into 10 equal parts. Draw to show what the piece of wood might look like.

a. James paints 4 of the equal parts red. Shade your rectangle to show the parts that James paints red.

b. What fraction of the wood is painted red?

c. James needs to paint __ of the wood blue. How many equal parts should James paint blue? 10 How do you know? 3

52

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 6

6

Name

The rectangle is partitioned into fractional units.

a. Write the unit fraction on each unit.

b. Shade four units.

c. How much of the rectangle is shaded? Write your answer in fraction form.

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53

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 7

7

Name

Complete the number bond to represent the shaded and unshaded parts of each shape. 1.

2.

2 2

3.

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4.

55

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 7

Complete each statement. 5. There are

thirds in 1.

6. There are

sixths in 1.

7. There are

tenths in 1.

Each tape diagram represents 1 whole. Write fractions to label the shaded and unshaded units. 8.

9.

56

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 7

10.

Draw to represent each problem. Then write a solution statement. 11. Mia reads 1 sixth of her book. What fraction of her book does she have left to read?

12. Shen bakes a cake and cuts it into 8 equal pieces. He eats 1 piece. What fraction of the cake is left?

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PROBLEM SET

57

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 7

7

Name

1. Complete the number bond to represent the shaded and unshaded parts of the rectangle.

2. The tape diagram represents 1. Write fractions to label the shaded and unshaded units.

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59

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8 ▸ Finding Area Cards, Set A

1 unit

2 units

1 unit

1 unit 2 units

1 unit

2 units

2 units

3 units 2 units

2 units

2 units

4 units

3 units

2 units

4 units

5 units 2 units

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61

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8 ▸ Finding Area Cards, Set A

5 units 2 units

3 units

4 units

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14 units

1 unit

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11/2/2021 7:26:08 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8 ▸ Finding Area Cards, Set A

3 units 1 unit 5 units 1 unit

3 units

3 units

5 units

3 units

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2 units 8 units

65

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11/2/2021 7:26:09 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8

8

Name

Complete the number bond to represent the shaded and unshaded parts of each shape. Shape

Number Bond

1.

2.

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67

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8

Partition and shade the tape diagram to represent each number bond. Tape Diagram

Number Bond

3.

1 5 6

4.

1 6

1 2 8

6 8

5. Complete the number bond. Draw a tape diagram with shaded and unshaded parts to represent the number bond.

1

3 8

68

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8

6. David and Zara draw number bonds to represent the shaded and unshaded parts of a shape. David’s Number Bond 10 10

4 10

6 10

Zara’s Number Bond

1

4 10

6 10

Whose number bond correctly represents the shaded and unshaded parts of the shape? How do you know?

© Great Minds PBC •

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8

_1

7. Amy uses 4 of a package of clay for a project. She saves the rest of the clay to use later. a. Draw a tape diagram to represent Amy’s clay. Partition and shade the tape diagram to represent the clay that Amy saves.

b. Draw a number bond to represent the clay that Amy saves and the clay that she uses.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 8

8

Name

1. Complete the number bond to represent the shaded and unshaded parts of the rectangle.

2. Complete the number bond. Draw, partition, and shade a tape diagram to represent the number bond.

2 6

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1

71

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9 ▸ Finding Area Cards, Set B

3 units

7 units

2 units 5 units 2 units 4 units

11 units

4 units

4 units

6 units

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73

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9 ▸ Finding Area Cards, Set B

1 unit

9 units 2 units

3 units

6 units

2 units

5 units

5 units 2 units

3 units

2 units 1 unit

2 units

2 units

4 units

4 units

1 unit

1 unit

3 units

2 units

3 units

1 unit

2 units

1 unit

3 units

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75

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9 ▸ Finding Area Cards, Set B

3 units

6 units

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77

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9 ▸ Comparing Unit Fractions

1 2

1 2

1 4

1 4

1 8

1 8

1 4

1 8

1 8

1 3 1 6

is greater than

1 6

1 8

.

1 8 1 3

1 6

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1 8

1 3 1 6

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1 8

1 4

1 6

is less than

1 6

.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9

9

Name

1. Shade the first fractional unit in each tape diagram. 1 2 1 4

1 8

1 3

1 6

Use the tape diagrams to help you answer parts (a)–(f). Circle less than or greater than to make true comparison statements. Whisper-read the complete statements. a. 1_ is 2

1 is c. _ 6

1 is e. _ 2

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less than greater than

less than greater than

less than greater than

1_ . 4

b. 1_ is 8

1_ . 3

1 is d. _ 3

1_ . 6

f.

1_ is 8

less than greater than

less than greater than

less than greater than

1_ . 4

1_ . 8

1_ . 6

81

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9

2. Shen uses _1 cup of oil and _1 cup of water to make muffins. Does he use more oil or water? 3

4

Explain how you know.

Each tape diagram represents 1. Partition and shade to show each comparison statement. 3. 1 half is greater than 1 eighth.

4. 1 sixth is less than 1 third.

Write less than or greater than to make true comparison statements. 5. 1 fourth is

7.

__1 is 10

9. _1 is 2

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PROBLEM SET

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1 third.

_1 . 5

_1 . 3

6. 1 eighth is

8. _1 is 4

10.

__1 is 10

© Great Minds PBC •

1 sixth.

_1 . 5

_1 . 6

10/29/2021 7:18:42 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9

11. Oka eats _1 of a small pizza. Luke eats _1 of a large pizza. 2

4

a. Shade the circles to represent the amount of pizza that Oka eats and the amount of pizza that Luke eats. Luke’s Pizza

Oka’s Pizza

b. Luke says, “My piece of pizza is bigger than yours, so that means _1 is always greater than _1 .” 2 4 Do you agree with Luke? Why?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 9

9

Name

Use the tape diagrams to help you answer parts (a) and (b). a. Shade the first fractional unit in each tape diagram. 1 4 1 3

1 2

b. Circle less than or greater than to make true comparison statements. Use the tape diagrams to help you. 1_ is 4

1_ is 3

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less than greater than

less than greater than

1. _ 3

1 is _ 2

1. _ 4

1 is _ 4

less than greater than

less than greater than

1. _ 3

1. _ 2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 9

Sprint

Dividing Fractions

Complete the equations. 1.

2×9=

2.

18 ÷ 9 =

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 9

A

Number Correct:

Complete each equation. 1.

1×9=

23.

9×

= 27

2.

2×9=

24.

9×

= 45

3.

3×9=

25.

27 ÷ 9 =

4.

9÷9=

26.

45 ÷ 9 =

5.

18 ÷ 9 =

27.

9×

= 63

6.

27 ÷ 9 =

28.

9×

= 81

7.

4×9=

29.

63 ÷ 9 =

8.

5×9=

30.

81 ÷ 9 =

9.

6×9=

31.

9×

=9

10.

36 ÷ 9 =

32.

9×

=0

11.

45 ÷ 9 =

33.

9÷9=

12.

54 ÷ 9 =

34.

27 ÷ 9 =

13.

7×9=

35.

9×

14.

8×9=

36.

15.

9×9=

37.

16.

63 ÷ 9 =

38.

17.

72 ÷ 9 =

39.

18.

81 ÷ 9 =

40.

19.

10 × 9 =

41.

20.

1×9=

42.

21.

90 ÷ 9 =

43.

22.

9÷9=

44.

88

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= 18 × 9 = 36

9×

= 54 × 9 = 72

9×

= 90 ÷9=2

36 ÷

=9 ÷9=6

72 ÷

© Great Minds PBC •

=9 ÷ 9 = 10

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Multiply and Divide by 9

B

Number Correct: Improvement:

Complete each equation. 1.

1×9=

23.

9×

= 18

2.

2×9=

24.

9×

= 36

3.

3×9=

25.

18 ÷ 9 =

4.

9÷9=

26.

36 ÷ 9 =

5.

18 ÷ 9 =

27.

9×

= 54

6.

27 ÷ 9 =

28.

9×

= 72

7.

3×9=

29.

54 ÷ 9 =

8.

4×9=

30.

72 ÷ 9 =

9.

5×9=

31.

9×

=9

10.

27 ÷ 9 =

32.

9×

=0

11.

36 ÷ 9 =

33.

9÷9=

12.

45 ÷ 9 =

34.

18 ÷ 9 =

13.

6×9=

35.

9×

14.

7×9=

36.

15.

8×9=

37.

16.

54 ÷ 9 =

38.

17.

63 ÷ 9 =

39.

18.

72 ÷ 9 =

40.

19.

9×9=

41.

20.

10 × 9 =

42.

21.

81 ÷ 9 =

43.

22.

90 ÷ 9 =

44.

90

EM2_0305SE_B_L10_removable_fluency_sprint_multiply_and_divide_by_9.indd 90

= 27 × 9 = 45

9×

= 63 × 9 = 81

9×

= 90 ÷9=3

45 ÷

=9 ÷9=7

81 ÷

© Great Minds PBC •

=9 ÷ 9 = 10

10/29/2021 7:27:47 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10 ▸ Blank Tape Diagrams

is greater than

© Great Minds PBC •

is less than

.

is equal to

.

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.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10

10

Name

Shade each tape diagram to represent the fraction. Then use the fractions to make true comparison statements. 1. 2 fourths is greater than

.

is greater than

.

2 eighths

2. 2 sixths

2 thirds

3. 4 tenths is less than

.

is less than

.

4 fifths

4. 5 eighths

5 tenths

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93

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10

Partition and shade the tape diagrams to show each comparison statement. 5. 3 fourths is greater than 3 eighths.

6. 3 sixths is less than 3 thirds.

7. Ivan runs _3 of a mile. Deepa runs _3 of a mile. 6

4

a. Partition and shade the tape diagrams to represent how far Ivan and Deepa run.

b. Who runs farther? How do you know?

8. Casey and James read the same book. Casey reads _4 of the book and James reads _4 of the book. 8

6

a. Draw two tape diagrams to represent how much of the book Casey and James each read.

b. Who reads less of the book?

94

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10

4 and _ 4. 9. Pablo draws, partitions, and shades tape diagrams to compare __ 10

5

4 10 4 5

Pablo uses his tape diagrams to write a comparison statement.

_4 is less than __4 . 5

10

What mistake does Pablo make?

Write greater than or less than to make true comparison statements. 10. 2 thirds is

12.

__5 is 10

14. _4 is 5

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EM2_0305SE_B_L10_problem_set.indd 95

2 fourths.

_5 . 8

_4 . 6

11. 3 eighths is

13. _3 is 4

15.

__6 is 10

3 sixths.

_3 . 5

_6 . 6

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10

16. Gabe and Liz draw models to represent different fractions of the same whole. Gabe draws a model to represent _3 . Liz draws a model to represent _3 .

8

4

a. Label each model with the student’s name and write the fraction of the model that is shaded. ’s model

Shaded fraction:

’s model

Shaded fraction:

b. Use the models to write a comparison statement for _3 and _3 . 8

96

PROBLEM SET

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© Great Minds PBC •

4

10/29/2021 7:23:22 PM

EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TB ▸ Lesson 10

10

Name

Shade each tape diagram to represent the fraction. Then use the fractions to make true comparison statements. 1. 2 thirds is greater than

.

2 eighths

2. 3 sixths is less than

.

3 fourths

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97

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11 ▸ Equal Parts

1

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99

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EUREKA MATH2 Tennessee Edition

© Great Minds PBC •

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3 ▸ M5 ▸ TC ▸ Lesson 11 ▸ Number Lines

101

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11

11

Name

Use the fraction strip to mark and label the fractions on the number line. Include the fractions at 0 and 1. Then complete the number bond to show how the unit fractions make 1. 1. Halves

1

0

1

2. Thirds

1

0

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1

103

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11

3. Fourths

1

0

1

4. Mia uses a fraction strip to partition the interval from 0 to 1 into fractional units. a. What fractional unit does Mia partition the interval into?

b. Label the fractions on the number line. Include the fractions at 0 and 1.

0

104

PROBLEM SET

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1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11

5. Ray cuts a piece of ribbon into 8 equal pieces. a. Partition the fraction strip into 8 equal parts to show how Ray cuts the ribbon. b. Use the fraction strip to help you mark and label the fractions on the number line. Include the fractions at 0 and 1.

0

1

6. Robin runs 1 mile. She checks her watch every quarter mile. a. Partition the interval from 0 to 1 into quarters to represent when Robin checks her watch. b. Label each quarter on the number line. Include the fractions at 0 and 1.

0

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1

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11

7. Carla uses unit fraction tiles to partition and label the interval from 0 to 1 into fifths. 1 5

1 5

1 5

1 5

1 5

0 1 5

1 2 5

3 5

4 5

5 5

6 5

What mistake does Carla make?

106

PROBLEM SET

EM2_0305SE_C_L11_problem_set.indd 106

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 11

11

Name

Partition the fraction strip into sixths. Then mark and label the fractions on the number line. Include the fractions at 0 and 1.

0

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1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set C

Equal Groups Cards Set C

7 sixes

6

6

6

6

6

6

6

8×6 6

6

6

6

6

6

6

6 5×6

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3×6

109

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set C

Equal Groups Cards Set C

7

7

7

7

7

7

7

7

8 sevens

(5 × 7) + (3 × 7)

(5 × 7) + (4 × 7)

9 sevens

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111

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set C

Equal Groups Cards Set C

8 eights

8

8

8

8

8

8

8

8

9×9 9

9

9

9

9

9

9

9

9 5×9

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4×9

113

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set D

Equal Groups Cards Set D

6 sixes

6

6

6

6

6

6

7×7 7

7

7

7

7

7

7 5×7

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2×7

115

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set D

Equal Groups Cards Set D

8

8

8

8

8

8

6 eights

(5 × 8) + (1 × 8)

(5 × 8) + (2 × 8)

7 eights

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117

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Groups Cards Set D

Equal Groups Cards Set D

6 nines

9

9

9

9

9

9

8×9 9

9

9

9

9

9

9

9 5×9

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3×9

119

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12 ▸ Equal Parts

1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

12

Name

1.

0

1

0

1

2.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

3. Partition the number line into sixths.

_2

Plot 6 on the number line.

_2

_2

Highlight from 0 to 6 in one color and from 6 to 1 in another color. Draw a number bond to match the number line.

0

1

_1

4. Deepa cleans her room for 1 hour. After each 4 hour, Deepa starts to clean a different part of her room. a. How many different parts of her room does Deepa clean during her 1-hour cleaning time?

b. What fraction of the whole cleaning time has Deepa completed when she gets to the point on the number line shown by the star?

_3

c. At 4 hours, Deepa starts to clean her closet. Label the number line to show when Deepa starts to clean her closet.

0

1

hours

124

LESSON

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hour

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

12

Name

Partition the interval into equal parts. Label the fractions at 0 and 1. Plot the given fraction on the number line. Then complete the number bond to match. 1 1. _ 3 0 3

3 3

0

1

5 2. _ 6

1

0

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1

1

125

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

6 3. _ 8

1

0

1

4. Complete the equations to show fractions that are equivalent to 0 and 1.

_____ = 0

_____ = 0

_____ = 0

_____ = 1

_____ = 1

_____ = 1

3

3

126

PROBLEM SET

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6

6

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8

8

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

Draw a number line that shows the interval from 0 to 1. Partition the interval into equal parts. Label the fractions at 0 and 1. Then plot the given fraction on the number line. Box the fractions that are equivalent to whole numbers. 1 5. _ 2

6. 3_ 4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

7. Mr. Davis works out at the gym for 1 hour. After each _1 hour, Mr. Davis starts doing 5 a different exercise. a. How many different exercises does Mr. Davis do during his 1-hour workout?

b. At _2 hours, Mr. Davis starts using the treadmill. Label the number line to show when 5

Mr. Davis starts using the treadmill.

0

1

hours

hour

c. The star on the number line represents what fraction of Mr. Davis’s workout?

8. Jayla says the point on the number line represents _5 of the distance from 0 to 1. Do you agree 7 with Jayla? Why?

0

128

PROBLEM SET

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1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 12

12

Name

Partition the interval into equal parts. Label the fractions at 0 and 1. Plot the given fraction on the number line. Then complete the number bond to match. 1. 2_ 3

1

0

1

3 2. _ 4

1

0

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1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

13

Name

1.

1 2

1 2

1 4

1 4

_ _____ 0 = 2

2.

4

_ _____ 1 = 2

_ _____ 2 = 2

4

1 2

1 8

1 8

_ _____

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4

1 2

1 8

0 = 2

EM2_0305SE_C_L13_classwork.indd 131

1 4

1 4

8

1 8

1 8

_ _____ 1 = 2

8

1 8

1 8

1 8

_ _____ 2 = 2

8

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

3.

1 2

1 6

1 2

1 6

1 6

1 6

_ _____ 0 = 2

4.

1 8

_ _____ 0 = 4

132

8

LESSON

EM2_0305SE_C_L13_classwork.indd 132

_ _____ 1 = 2

6

1 4

1 8

_ _____

1 = 4

8

1 6

_ _____ 2 = 2

6

1 4

1 8

1 6

6

1 4

1 8

1 8

_ _____

2 = 4

8

1 4

1 8

1 8

_ _____ 3 = 4

© Great Minds PBC •

8

1 8

_ _____ 4 = 4

8

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EUREKA MATH2 Tennessee Edition

5.

3 ▸ M5 ▸ TC ▸ Lesson 13

1 3

1 3

1 6

1 6

_ _____ 0 = 3

6

1 6

_ _____ 1 = 3

6

1 3

1 6

1 6

_ _____ 2 = 3

6

1 6

_ _____ 3 = 3

6

6.

0

1

0

1

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LESSON

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

7. Partition one number line into halves. Partition the other number line into sixths. Label the fractions. Box equivalent fractions.

0

1

0

1

8. Partition one number line into thirds. Partition the other number line into sixths. Label the fractions. Box equivalent fractions.

134

LESSON

EM2_0305SE_C_L13_classwork.indd 134

0

1

0

1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

13

Name

Use the number lines to find equivalent fractions. Color the equivalent fractions on the number lines. The first one has been colored for you. 1.

0 2

1 2

2 2

0

1

0

1

0 4

1 4

2 4

3 4

_

_____

_

_____

_

_____

__0

= _____

_

_____

_

_____

0 = 2

1 = 2

0 2

1 2

2 2

0

1

0

1

0 8

1 8

2 8

3 8

4 8

5 8

6 8

7 8

8 8

2

1 = 2

2 = 2

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4

4 4 2 = 2

2.

4

4

8

8

8

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

3.

0 4

1 4

0

1 1 8

2 8

_____ _1

_

4

8

=

3 8

4 8

_____ _2 8

4

0 2

=

5 8

_____ _3 4

8

6 8

7 8

=

_____ _4 8

1 2

8 8

4

=

1

0

1

_____

1 6

= 0_ 6

PROBLEM SET

EM2_0305SE_C_L13_problem_set.indd 136

2 6

3 6

_

1 = 2

_____ 8

2 2

0

0 6

136

4 4

1

0 = 4

2

3 4

0

0 8

4.

2 4

4 6

_____ 6

5 6

6 6

_____ 2

= 6_

© Great Minds PBC •

6

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EUREKA MATH2 Tennessee Edition

5.

0 3

1 3

2 3

3 3

0

1

0

1

0 6

_____ 3

3 ▸ M5 ▸ TC ▸ Lesson 13

1 6

= 0_ 6

2 6

_

1 = 3

3 6

_____ 6

4 6

_____ 3

5 6

= 4_

6 6

_

0 = 4

6

_____ 8

6. Amy draws two number lines to try to show that _1 = _2 . 4

2

0 2

1 2

2 2

0

1

0 0 4

1 1 4

2 4

3 4

4 4

What mistake does Amy make?

© Great Minds PBC •

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 13

13

Name

Draw a model to show that _1 = _3 . 2

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6

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EUREKA MATH2 Tennessee Edition

×

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Hidden Factor Mat

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Multiples of 10

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Multiples of 10

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Multiples of 10

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Multiples of 10

70 70 80 80 © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14 ▸ Multiples of 10

90 90 © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

14

Name

1.

0

1

0

1

0

1

2.

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153

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

3.

0

1

4.

154

LESSON

EM2_0305SE_C_L14_classwork.indd 154

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

14

Name

1. Complete the number line. Draw a box around the pairs of equivalent fractions. Part (a) is started for you. a. 0 1 4

4

fourths

0 0 8

eighths

1 8

2 4

3 8

4 4

5 8

7 8

1

b.

0 3

thirds

0

sixths

3 3

1 6

1

3 6

c. Choose 4 different pairs of equivalent fractions from parts (a) and (b). Use the pairs to complete the equations.

_____ = _____ 4

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8

2 1 _____ = _____

_____ = _____

_____ = _____

155

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

2. The interval from 0 to 1 is partitioned into halves. Use the number line to complete parts (a)–(d). a. Label all the halves from 0 to 1. b. Partition the interval from 0 to 1 into eighths. c. Label all the eighths from 0 to 1. d. Draw a box around each pair of equivalent fractions.

0

1

3. Use the number line to complete parts (a)–(c). a. Partition the interval into halves. Label all the halves from 0 to 1. b. Partition the interval into sixths. Label all the sixths from 0 to 1. c. Draw a box around each pair of equivalent fractions.

0

156

PROBLEM SET

EM2_0305SE_C_L14_problem_set.indd 156

1

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

4. A recipe for slime asks for _1 cup of water. Casey’s measuring cup is marked in fourths. 2

How many fourths does Casey need to make _1 ? 2

Draw, partition, and label a number line to help explain your thinking.

5. Adam uses the same recipe to make some slime. His measuring cup is marked in eighths. He says, “I need _5 cups of water to make the slime.” 8

Do you agree with Adam? Why? Draw a number line to help explain your thinking.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 14

14

Name

The interval from 0 to 1 is partitioned into fourths. Use the number line to complete parts (a)–(d).

0

1

a. Label all the fourths from 0 to 1. b. Partition the interval from 0 to 1 into eighths. c. Label all the eighths from 0 to 1. d. Draw a box around each pair of equivalent fractions.

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159

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Write the Fraction

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

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Write the Fraction

A

Number Correct:

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

19.

2.

20.

3.

21.

4.

22.

5.

23.

6.

24.

7.

25.

8.

26.

9.

27.

10.

28.

11.

29.

12.

30.

13.

31.

14.

32.

15.

33.

16.

34.

17.

35.

18.

36.

162

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Write the Fraction

B

Number Correct: Improvement:

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

19.

2.

20.

3.

21.

4.

22.

5.

23.

6.

24.

7.

25.

8.

26.

9.

27.

10.

28.

11.

29.

12.

30.

13.

31.

14.

32.

15.

33.

16.

34.

17.

35.

18.

36.

164

EM2_0305SE_C_L15_removable_sprint_write_the_fraction.indd 164

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 15

15

Name

Use the ruler to measure the length of each object. inches

1. Length:

1

2. Length: 4 and

EM2_0305SE_C_L15_problem_set.indd 165

3

4

5

6

2

3

4

5

6

inches

1

© Great Minds PBC •

2

165

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 15

3. Length: 5 and

inches

1

4. Length: 1 and

PROBLEM SET

EM2_0305SE_C_L15_problem_set.indd 166

3

4

5

6

2

3

4

5

6

inches

1

166

2

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EUREKA MATH2 Tennessee Edition

5. Length:

inches

1

6. Length:

and

1

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3 ▸ M5 ▸ TC ▸ Lesson 15

2

3

4

5

6

3

4

5

6

inches

2

PROBLEM SET

167

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 15

7. Length:

and

inches

1

2

3

4

5

6

3

4

5

6

8. Oka says the string is 3 and _1 inches long. 2

Ivan says the string is 7 half inches long. Who is correct? Explain your answer.

1

168

PROBLEM SET

EM2_0305SE_C_L15_problem_set.indd 168

2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 15

15

Name

Use the ruler to measure the length of each object. 1. Length: 1 and

inches

1

2. Length:

and

1

3. Length:

and

1

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3

4

5

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3

4

5

6

3

4

5

6

inches

2

inches

2

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EUREKA MATH2 Tennessee Edition

×

3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Hidden Factor Mat

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Multiples of 10

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Multiples of 10

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Multiples of 10

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Multiples of 10

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Multiples of 10

90 90

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3 ▸ M5 ▸ TC ▸ Lesson 16 ▸ Grid for Line Plot

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 16

16

Name

1. A six-inch paper strip is partitioned into equal parts. a. Label the missing whole numbers. b. Label the halves. c. Label the fourths.

1 4

1 2

3 4

1

2

5

d. Complete each statement.

1 inch is equal to

half inches.

1 inch is equal to

quarter inches.

1 half inch is equal to

quarter inches.

2. Partition 1 inch into eighths. Label the eighths from 0 to 1.

1 4

1 2

1 4

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1 2

1

3 4

1

2

3

4

5

6

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 16

3. The students in Mr. Lopez’s class measure the lengths of pencils. They record the data on a line plot. Pencils in Mr. Lopez’s Classroom

0

×

× ×

4

44

1

× × × ×

× × × 1

3

42

44

× × × × ×

× × ×

5

54

1

× × 1

52

3

54

× ×

×

6

64

1

Length (inches)

a. How many pencils did the class measure?

b. Which length occurs most frequently? How do you know? c. How many pencils are at least 4 _ inches long? 3 4

d. Luke says, “There are more pencils longer than 5 inches than there are pencils shorter than 5 inches.” Do you agree with Luke? Why?

e. Mr. Lopez finds one more pencil in his desk. He says the length of the pencil is 11 half inches. Where should the length of this pencil be plotted on the line plot? How do you know?

186

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TC ▸ Lesson 16

16

Name

A four-inch paper strip is partitioned into equal parts.

a. Label the whole numbers. b. Label the halves. c. Label the quarters. d. Complete each statement.

3 inches is equal to

half inches.

4 inches is equal to

quarter inches.

2 half inches is equal to

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quarter inches.

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3 ▸ M5 ▸ TD ▸ Lesson 17 ▸ Blank Number Line

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 17

17

Name

Complete parts (a)–(d) for problems 1–4. Problem 1 has been started for you. a. Partition and label the number line to show each whole number. b. Partition each whole number interval into the given fractional units. c. Label each fraction. d. Draw a box around each fraction that is equivalent to a whole number. 1. Halves

0 2

1 2

0

2 2 1

2

2. Thirds

0

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2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 17

3. Halves

2

3

4

4. Fourths

2

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4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 17

5. Partition each whole number interval into sixths. a. Label all the sixths. b. Draw a box around each sixth that is equivalent to a whole number.

1

2

3

6. Label the first tick mark 0 and the last tick mark 3. a. Partition and label the number line to show the whole numbers from 0 to 3. b. Partition each whole number interval into thirds. c. Label all the thirds. d. Draw a box around each third that is equivalent to a whole number.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 17

7. Miss Diaz buys 4 gallons of juice for a class party. The point on the number line shows how many gallons of juice the class drinks at the party. 12 gallons of juice.’’ James says, ‘‘We drank 3 gallons of juice.’’ Carla says, ‘‘We drank __ 4

Use the number line to show that Carla and James are both correct.

0

194

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4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 17

17

Name

Use the number line for parts (a)–(c).

1

2

3

a. Partition each whole number interval into fourths. b. Label all the fourths. c. Draw a box around each fourth that is equivalent to a whole number.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 18 ▸ Fraction Cards

12 ― 6

13 ― 6

14 ― 6

15 ― 6

16 ― 6

17 ― 6

18 ― 6

19 ― 6

20 ― 6

21 ― 6

22 ― 6

23 ― 6

24 ― 6

25 ― 6

26 ― 6

27 ― 6

28 ― 6

29 ― 6

30 ― 6

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 18

18

Name

1. Use the number line to complete parts (a)–(e). 3 3

1

4 3

5 3

6 3

7 3

2

8 3

9 3

10 3

3

11 3

12 3

4

a. Write a fraction that is less than _8 . 3

b. Write a fraction that is greater than _8 . 3

c. Pablo says that zero is not on the number line. What can you tell Pablo about the location of 0?

d. Which of the fractions shown on the number line is closest to 0?

e. Which whole number shown on the number line is greater than _9 ? How do you know? 3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 18

2. Partition each whole number interval into sixths. 3 12 , _ , and _9 on the number line. a. Label _1 , _6 , __ 6 6

6

6

6

b. Draw a box around the fractions that are equivalent to whole numbers.

0

1

2

3

3. Partition each whole number interval on the number line into fourths. 16 12 , __ , and _4 on the number line. a. Label _8 , _6 , __ 4 4

4

4

4

b. Draw a box around the fractions that are equivalent to whole numbers.

1

200

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2

3

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4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 18

4. Mrs. Smith’s class measures the lengths of caterpillars for a science project. Gabe’s caterpillar 15 is 2 inches long. Robin’s caterpillar is __ inches long. 8

a. Draw a number line. Partition each whole number interval. Label each tick mark with a fraction. Plot a point to represent the length of each caterpillar. Label the length of Robin’s caterpillar, R. Label the length of Gabe’s caterpillar, G.

b. Whose caterpillar is shorter? How do you know?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 18

18

Name

Use the number line for parts (a) and (b).

0

1

2

3

a. Partition each whole number interval into thirds. b. Label _7 , _2 , and _4 on the number line. 3 3

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3

203

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 19

19

Name

1. Use the number lines to complete parts (a) and (b).

0

0

2 6

1

1

2 8

a. Write greater than, equal to, or less than to complete the statement. 2 is _ 6

2. _ 8

b. Write >, =, or < to complete the comparison statement. 2_ 6

2_ 8

2. Partition the intervals and label each fraction.

3 5

3 8

0

1

0

1

Write >, =, or < to complete the comparison statement. 3_ 8

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3_ 5

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 19

3. Amy and David read the same book. Amy reads _4 of the book. David reads _4 of the book. 6

8

a. Draw two number lines to represent how much of the book Amy reads and how much of the book David reads.

b. Write >, =, or < to complete the comparison statement. 4_ 8

4_ 6

c. Who reads more of the book?

4. Zara walks _2 miles, from her home to school. Shen walks _2 miles, from his home to school. 8

5

a. Draw two number lines to represent the distance Zara walks to school and the distance Shen walks to school.

b. Whose home is closer to the school?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 19

5. Mr. Endo buys _2 kilograms of peaches, _2 kilograms of berries, and _2 kilograms of plums. Draw 3

6

4

to represent the weights of the peaches, berries, and plums Mr. Endo buys. Which amount of fruit weighs the most?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 19

6. Mia and Ray have the same homework assignment. Mia completes _3 of the homework before she 4

goes outside to play. Ray completes _3 of the homework before his piano lesson. 6

a. Draw to represent the amount of homework each student completes.

b. Who has less homework left to complete? How do you know?

208

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 19

19

Name

Partition the intervals and label each fraction. Then write >, =, or < to complete the comparison statement. 2_ 3

2_ 6

0

1

0

1

2_ 3

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2_ 6

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 20

20

Name

1.

_7 3

_8 6

2.

_4 3

_4 6

3.

4.

_5 3

13 __ 6

5. 2 = _____

6.

_7 < _____ 3 6

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_8 3

16 __ 6

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 20

20

Name

1. The number line shows fourths and eighths from 0 to 3. 0 4

0 0 8

1 4

1 8

2 8

2 4

3 8

4 8

3 4

5 8

6 8

4 4

7 8

1 8 8

5 4

9 8

6 4

7 4

8 4

9 4

10 4

11 4

12 4

2

3

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

a. Write >, =, or < to compare the numbers. Use the number line to help you.

_8 4

3_ 4

_7 8

15 __ 8

24 __

_8

_1 4

_1 8

_6 8

_6 4

12 __ 8

12 __ 4

_4 8

_8 4

_7 4

_9 8

_6 4

8

8

1

b. Use the number line to help you complete each comparison statement.

_7 > _____ 4 4

18 _____ __ < 8 8

10 _____ __ = 4 8

_____ < 13 __

24 _____ __ = 4 8

_____ > 5_

4

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8

8

4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 20

2. Adam spends _8 hours each week at soccer practice. He spends _8 hours each week at cooking 3

6

class. Does Adam spend more time at soccer practice or at cooking class?

Draw, partition, and label a number line to represent Adam’s time at each activity. Write a solution statement.

3. Write a word problem that compares the fractions _9 and _9 . 8

214

PROBLEM SET

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4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 20

4. Amy and Pablo draw, partition, and label a number line to compare _5 and _9 . 2

6

5 2

0

1

2

9 6

3

Amy says, “I know _5 is greater than _9 because _5 is farther from 0 than _9 .” 2

2

6

6

Pablo says, “I know _5 is greater than _9 because _5 is to the right of _9 on the number line.” 2

6

2

6

Who is correct? How do you know?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 20

20

Name

The number line shows thirds and sixths from 0 to 2. 0 3

0 0 6

1 3

1 6

2 6

2 3

3 6

4 6

3 3

5 6

1 6 6

4 3

7 6

8 6

5 3

9 6

10 6

6 3

11 6

2

12 6

1. Write >, =, or < to compare the numbers. Use the number line to help you.

_4 3

_2 3

_5 3

_5 6

_4 6

1

2. Use the number line to help you complete each comparison statement.

_2 < _____ 3 3

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6 _6 < _____ 6

_3 = _____ 3 6

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ One Fractional Unit More

Sprint Write the fraction that is one fractional unit more. Write your answer as a whole number when possible. 1.

1 fourth

2.

3 4

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3 ▸ M5 ▸ Sprint ▸ One Fractional Unit More

A

Number Correct:

Write the fraction that is one fractional unit more. Write your answer as a whole number when possible. 1.

1 third

2.

_1 3

24.

3.

1 fourth

4.

_1

25.

4

26.

5.

1 sixth

27.

6.

1 6

28.

7.

2 eighths

29.

8.

2 8

30.

9.

3 eighths

31.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

_ _ _

3 8 0 3 2 3 0 4 2 4 3 4 0 6 3 6 5 6 0 8 3 8 5 8 7 8

_

_ _ _

_ _

_

_ _

_

_

_

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23.

32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44.

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_

2 3 5 3 7 3 3 4 7 4 9 4 5 6 7 6 9 6 11 6 1 6 1 8 13 8 15 8 11 4 14 4 17 6 29 6 19 8 31 8 34 6 47 8

_ _

_ _

_

_ _

_

__ _ _

__

__ __ __ __ __ __

__ __ __

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ One Fractional Unit More

B

Number Correct: Improvement:

Write the fraction that is one fractional unit more. Write your answer as a whole number when possible. 1.

1 third

2.

1 3

24.

3.

1 fourth

25.

4.

1 4

26.

5.

1 sixth

27.

6.

1 6

28.

7.

1 eighth

29.

8.

1 8

30.

9.

2 eighths

31.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

_ _ _ _ _

23.

2 8 0 2 1 2 0 3 2 3 0 4 3 4 0 6 2 6 5 6 0 8 4 8

32.

7

44.

_ _ _ _ _ _ _ _ _ _ _

_ 8

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33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.

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_

1 2 3 2 4 2 2 3 5 3 7 3 3 4 4 4 5 4 7 4 1 4 1 6 9 6 11 6 11 4 13 4 17 6 23 6 17 8 31 8 33 6 39 8

_

_ _ _ _

_ _

_ _ _ _ _

__

__ __

__

__ __ __

__ __

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 21

21

Name

Partition each number line and label both fractions. Circle the fraction that is closer to 0. Use >, =, or < to compare the fractions. 5 1. _ 4

6 2. _ 3

4 3. _ 2

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_7 4

0

3

0

3

0

3

_5 3

_5 4

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 21

Partition each interval from 0 to 3 and label one fraction on each number line. Circle the fraction that is farther from 0. Use >, =, or < to compare the fractions. 7 4. _ 6

_7 8

0

3

0

3

5. Luke cuts two pieces of ribbon for a project. The blue ribbon is _5 meters long. The yellow ribbon 6

is _2 meters long. 6

a. Draw, partition, and label a number line to represent the lengths of the ribbons.

b. Which ribbon is longer? How do you know?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 21

6. Jayla reads for _6 hours on Monday. She reads for _6 hours on Tuesday. 5

4

a. Draw number lines to represent how long Jayla reads on Monday and Tuesday.

b. On which day does Jayla read for a shorter amount of time? How do you know?

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 21

7. David draws number lines to compare _3 , _7 , and _5 . 4 8

0

6

1

3 4

7 8

0

0

5 6

1

1

David says that _3 is farther from 0 than _5 and _7 , so it’s the largest fraction. Do you agree with 4 6 8 David? Why?

226

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TD ▸ Lesson 21

21

Name

Partition the number line and label both fractions. Circle the fraction that is closer to 0. Use >, =, or < to compare the fractions. 8 1. _ 6

7 2. _ 3

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12 __ 6

0

3

0

3

_4 3

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EUREKA MATH2 Tennessee Edition

© Great Minds PBC •

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3 ▸ M5 ▸ TE ▸ Lesson 22 ▸ Three Number Lines

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 22

22

Name

1. Use the number line to help you answer each question. 0 2

1 2

2 2

0

3 2

4 2

1

2

How many halves make 0? How many halves make 1? How many halves make 2? 2. Complete the equations. Use the number line to help you. a.

0 4

1 4

2 4

3 4

4 4

0

6 4

7 4

8 4

1

0 = _____ 0 2

2

_____ = 1

4

b.

5 4

1 2

2 2

0

3 2

1

0 = _____ 2

2 = _____

4

_____ = 1 2

4 2

5 2

6 2

2 2 = _____ 2

3

_____ = 3

7 2

8 2

4 = _8 2

c. What fraction, in halves, is equivalent to 5? How do you know?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 22

3. Partition each whole number interval into the given fractional units.

thirds

1

2

3

1

2

3

sixths

a. Label the fractions from 1 to 3 on each number line. b. Complete each equation.

1 = _____

2 = _____

3 = _____

1 = _____

2 = _____

3 = _____

_5 = _____ 3 6

14 _____ __ = 3 6

_____ = 16 __

3

6

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3

6

3

6

3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 22

4. Miss Diaz and Mr. Lopez each have 3 meters of string.

10 meters long. Miss Diaz cuts her string to make a piece that is __ 4

20 meters long. Mr. Lopez cuts his string to make a piece that is __ 8

Use the number lines to show that the cut pieces of string are the same length.

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0

3

0

3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 22

22

Name

Complete the equations. Use the number line to help you. 0 3

1 3

2 3

3 3

0 1. 0 = _____ 3

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2.

4 3

5 3

6 3

1

2

_____ = 2

3. 3 = _____

3

7 3

8 3

9 3

3 4.

= 3_ 3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 23

23

Name

1. The number line shows halves and fourths from 0 to 2. 0 2

1 2

0 0 4

1 4

2 2

2 4

3 2

1

3 4

4 4

5 4

6 4

4 2

7 4

2 8 4

a. Complete the equations. Use the number line to help you.

1 = _____

2 = _____

1 = _____

2 = _____

_2 = _____ 2 4

_____ = 8_

_1 = _____ 2 4

_3 = _____ 2 4

2

2

2

4

4

4

b. Carla uses the number line to write a statement.

2 = 4_ = 8_ 2

4

Is Carla’s statement true or false? How do you know?

2. Count by 2 halves to find a fraction that is equivalent to 4. Then complete the equation.

2 halves,

halves,

halves,

halves

4 = _____ 2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 23

3. Use the number line to complete parts (a)–(c).

1

2

3

a. Partition each whole number interval into thirds, and then label all the thirds from 1 to 3. b. Partition each whole number interval into sixths, and then label all the sixths from 1 to 3. c. Write 3 different equations that show equivalent fractions from the number line.

_____ = _____

_____ = _____

_____ = _____

12 . 4. Draw, partition, and label a number line to show that _3 is equivalent to __ 2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 23

5. Mr. Davis asks his class to write the number that is represented by the point on the number line.

2

4

a. Oka writes 3. Label the number line to show that Oka is correct.

b. Ray writes _6 . Partition each whole number interval and label the number line to show that 2

Ray is correct.

12 . Partition each whole number interval and label the number line to show that c. Casey writes __ 4

Casey is correct.

d. Explain how all 3 students are correct.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 23

23

Name

The number line shows thirds and sixths from 0 to 3. Use the number line to help you complete the equations. 0 3

0 0 6

2 3

1 3

1 6

2 6

3 6

4 6

4 3

3 3

1

5 6

6 6

7 6

8 6

1. 2 = _____ 6

2. 2 = _____ 3

5 _____ 4. _ = 3 6

5.

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_____ = 14 __ 3

6

6 3

5 3

9 6

10 6

11 6

2

12 6

8 3

7 3

13 6

14 6

15 6

16 6

9 3

3

17 18 6 6

12 _____ 3. __ = 3 6

6.

_____ = 8_ 6

3

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EUREKA MATH2 Tennessee Edition

0

1

3 ▸ M5 ▸ TE ▸ Lesson 24 ▸ Single Number Line

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2 3

4

______ = ______

_____ = _____

6

3

______ = ______

6

_____ = _____

3

______ = ______

______ = ______

______ = ______

______ = ______

c. Write 8 different equations that represent equivalent fractions on the number line. The first one is done for you.

b. Use a blue colored pencil to partition each whole number interval into sixths. Label each sixth below the number line.

a. Use a red colored pencil to partition each whole number interval into thirds. Label each third above the number line.

1

1. Use the number line to complete parts (a)–(c).

EUREKA MATH2 Tennessee Edition 3 ▸ M5 ▸ TE ▸ Lesson 24

Name

24

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 24

Write an equivalent fraction for the given point on each number line. Use halves, fourths, sixths, or eighths. 2.

8 4

1

3.

2

7 3

2

_ ______ 8 = 4

_ ______ 3

7 = 3

4.

______ = ______ 3

4

5.

______ = ______ 2

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 24

6. Liz draws a number line from 1 to 3 that shows fourths and eighths. 4 4

5 4

1

8 8

9 8

6 4

10 8

11 8

12 8

7 4

13 8

14 8

8 4

15 8

2

16 8

9 4

17 8

18 8

10 4

19 8

20 8

11 4

21 8

12 4

22 8

23 8

3

24 8

a. Liz wants to find how many fourths and how many eighths are equivalent to _ . Use the 2 number line to help you complete Liz’s statement. 4

_ _____ = _____ 4 = 2

4

8

b. Can Liz use her number line to find how many fourths and how many eighths are equivalent to _ ? Why? 8 2

7. Eva studies for _ hours. Gabe studies for _ hours. 6 4

3 2

a. Draw a number line to represent how many hours Eva studied and how many hours Gabe studied.

b. Who spends more time studying? How do you know?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 24

24

Name

Write two different fractions for the given point on each number line. Use halves, fourths, or eighths. 1.

0

1

_____ = _____

2.

1

2

_____ = _____

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

25

Name

1. James bakes 3 loaves of bread. He cuts the first loaf of bread into thirds. He cuts the second loaf of bread into halves. He leaves the third loaf of bread whole.

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

2. James bakes 3 kinds of bread: rye, wheat, and white. He bakes 2 loaves of each kind of bread. He cuts the loaves of rye bread into thirds. He cuts the loaves of wheat bread into halves. He leaves the loaves of white bread whole.

_____ =

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_____ =

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_____ =

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

25

Name

Write a fraction to represent the amount of pizza shown. Each pizza represents 1 whole. 1.

2.

_____

3.

_____

_____

Write a fraction to represent the amount of pie shown. Each pie represents 1 whole. 4.

6.

5.

_____

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_____

_____

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

7. Use the number line to complete parts (a) and (b).

0 1

1

0

1

2

4

3

6

5

a. Complete the number line by renaming the whole numbers as fractions. b. Write 3 equations that represent equivalent whole numbers and fractions shown on the number line. The first one is started for you.

1

254

PROBLEM SET

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= _____ 1

= _____

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= _____

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

8. Use the number line to complete parts (a) and (b).

10

11

14

1

1

1

12

13

16

15

a. Complete the number line. b. Write 3 equations that represent equivalent whole numbers and fractions shown on the number line.

= _____

= _____

= _____

9. How are _3 and _3 different? Draw a model to help explain your answer. 3

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 25

25

Name

Use the number line for parts (a) and (b).

3 1

1

3

4

5

6

7

a. Complete the number line by renaming the whole numbers as fractions. b. Write 3 equations that represent equivalent whole numbers and fractions shown on the number line.

= _____

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= _____

= _____

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Compare Fractions

Sprint Write >, =, or <. 1.

1 third

2.

2 4

1 4

3.

5 6

1

_

_

_

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1 third

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Compare Fractions

A

Number Correct:

Write >, =, or <. 1.

2 thirds

2.

2 3

3.

1 fourth

4.

1 4

5.

3 sixths

6.

3 6

7.

1 eighth

8.

1 8

9.

4 eighths

_ _

_ _ _

_

1 2

_

2 2

1 third

23.

1 3

_

24.

_2

2 fourths

25.

_

1 3

0 3

2 4

26.

1

2 3

1 sixth

27.

_

0 4

1 6

28.

_

2 4

3 4

1

1 eighth

29.

_

_0

_

4 6

1 8

30.

1

_6

1 eighth

31.

6 8

2

_

_

_

1

_ _ _

6

6

_

5 8

10.

4 8

1 8

_

32.

_7

11.

1 2

1 2

_

33.

1 4

2 4

_

8

_

1

_

12.

_1 2

2 2

_

34.

1 6

13.

1 3

_

3 6

2 3

35.

2 2

3 2 4 3

_

_ _

_ _

14.

_3

_2

36.

2 4

_3

3 3

15.

_

3

4

37.

5 4

16.

4 4

_

7 4

4 4

38.

1

17.

4 6

_

2 6

39.

_9

7 6

1

18.

6 6

3 6

_

40.

2

_4

19.

5 6

5 6

_

41.

_5

2

20.

3 8

4 8

_

42.

2

21.

4 8

6 8

_

43.

22.

8 8

_

18 6

5 8

44.

4

3

_

_ _ _

_ _ _

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_

_

8

3

__

_

_ _

2

_

9 4

3

__

31 8

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ Sprint ▸ Compare Fractions

B

Number Correct: Improvement:

Write >, =, or <. 1.

1 third

2.

1 3

3.

2 fourths

4.

2 4

5.

1 sixth

6.

1 6

7.

1 eighth

8.

1 8

9.

1 eighth

_ _

_ _ _

_

_

2 thirds

23.

_

2 2

1 2

2 3

24.

1

2 2

1 fourth

25.

_

0 3

2 3

1 4

26.

1 3

1

4 sixths

27.

_

3 4

0 4

4 6

28.

1

2 4

1 eighth

29.

_

0 6

5 6

1 8

30.

6 6

1

5 eighths

31.

_5

_

_ _

_ _ 8

_ _ _ _ _ _

7 8

10.

1 8

5 8

_

32.

1

11.

1 2

1 2

_

33.

2 3

12.

2 2

_1

1 3

2

34.

1 4

13.

2 3

_

3 4

1 3

35.

2 2

14.

2 3

_

3 2

3 3

36.

3 3

15.

3 4

_

4 3

1 4

37.

7 4

16.

4 4

_

5 4

4 4

38.

1

17.

1 6

_

8 6

4 6

39.

1

18.

2 6

6 6

_

40.

2

19.

5 6

_

4 2

5 6

41.

2

20.

4 8

_

4 3

2 8

42.

21.

6 8

_

10 4

3 8

43.

3

22.

4 8

8 8

_

44.

30 8

_

_ _ _ _ _ _ _

_ _ _ _

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_ _ _ _ _ _

_ __ __

_

6 8

_ _

_ _

_ __

10 8

_

2

__

18 6

4

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3 ▸ M5 ▸ TE ▸ Lesson 26 ▸ Lined Paper

0

1

2

3

4

5

6

EUREKA MATH2 Tennessee Edition

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 26

26

Name

1. Plot and label 1 on the number line. Use the relationship between 0 and _1 to help you. 4

0

1 4

2. Plot and label 2 on the number line. Use the relationship between 1 and _7 to help you. 3

7 3

1

3. Luke says, “When the minute hand points to the 6, that represents _1 hour.”

2 Robin says, “When the minute hand points to the 6, that represents 2 hours.” 4

_

Who is correct? How do you know?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 26

18 4. Mia and Ivan play a number game. Ivan says, “Pick a number between 2 and 5.” Mia picks __ . 4

Did Mia pick a number between 2 and 5? How do you know? Draw, partition, and label a number line to help explain your answer.

3 24 pans of brownies. Zara makes _ 5. David and Zara make brownies for a party. David makes __ pans 1 8 of brownies.

Who makes more pans of brownies? How do you know?

266

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 26

6. James partitions a paper strip into thirds. a. Draw a model to represent the paper strip.

b. James uses a ruler to measure the length of each third. Each third is 2 inches long. What is the total length of the paper strip?

c. James partitions each third in half. What new fractional unit did James make?

d. How can James find the length of each new fractional unit without using his ruler?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 26

26

Name

Use the ruler shown for parts (a)–(d). 1 4

1 2

3 4

1

1 4

1 2

3 4

2

1 4

1 2

3 4

3

1 4

1 2

3 4

4

a. How many half inches are in 2 inches? half inches b. What is _1 inch less than 3 inches? 4

inches c. What is _1 inch more than 2 inches? 2

inches d. How many quarter inches are in 4 inches? quarter inches

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

27

Name

Robin and David both make pizzas that are the same size. The charts show information about their pizzas. Robin’s Pizza

David’s Pizza

Total Number of Equal Slices

8

Total Number of Equal Slices

6

Number of Slices with Peppers

1

Number of Slices with Peppers

3

Number of Slices with Olives

2

Number of Slices with Olives

2

Number of Slices with Mushrooms

5

Number of Slices with Mushrooms

1

4

Number of People Equally Sharing the Pizza

3

Number of People Equally Sharing the Pizza

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

1. Whose pizza has a larger part with olives? Use pictures, words, or numbers to explain your answer.

2. Whose friends each get a larger part of the whole pizza? Use pictures, words, or numbers to explain your answer.

272

LESSON

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

_1

3. David says, “More than 2 of my pizza has peppers.” Do you agree? Why?

_7

4. Robin and David each take their pizza to a friend’s home. Robin’s friend lives 4 miles away. 10 __

David’s friend lives 8 miles away. Who travels farther to get to their friend’s home?

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LESSON

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

27

Name

Amy and Luke plant square gardens that are the same size. 1. Amy partitions her garden into 4 equal parts. She plants corn in 2 parts. a. Show how Amy partitions her garden.

b. Shade to show the part of the garden where Amy plants corn.

c. What fraction of the garden does Amy plant with corn?

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

2. Luke partitions his garden into 3 equal parts. He plants corn in 2 parts. a. Show how Luke partitions his garden.

b. Shade to show the part of the garden where Luke plants corn.

c. What fraction of the garden does Luke plant with corn?

3. Whose garden has a larger part for corn? How do you know?

276

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

4. Whose garden has more space left for other plants? Use the number lines to show your thinking.

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0

1

0

1

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

3 ▸ M5 ▸ TE ▸ Lesson 27

27

Name

Mia and Ivan have rectangular bookmarks that are the same size. 1. Mia partitions her bookmark into 3 equal parts. She colors 2 parts green.

a. Show how Mia partitions her bookmark. b. Shade to show the part of the bookmark that is green. c. What fraction of the bookmark is green?

2. Ivan partitions his bookmark into 4 equal parts. He colors 2 parts green.

a. Show how Ivan partitions his bookmark. b. Shade to show the part of the bookmark that is green. c. What fraction of the bookmark is green?

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3. Whose bookmark has more space left to color? Use the number lines to show your thinking.

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0

1

0

1

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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, Paul Klee, 1879–1940, Farbtafel “qu 1” (Colour table “Qu 1”), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der Klee-Gesellschaft, Bern. © 2020 Artists Rights Society (ARS), New York; pages 13, 14, sergua/ Shutterstock.com; pages 16, 253, ONYXprj/Shutterstock.com; page 165, Peter Hermes Furian/ Shutterstock.com; page 168, Picsfive/Shutterstock; 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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Acknowledgments Kelly Alsup, Leslie S. Arceneaux, Lisa Babcock, Christine Bell, Dawn Burns, Cathy Caldwell, Karla Childs, Mary Christensen-Cooper, Cheri DeBusk, Jill Diniz, Christina Ducoing, Melissa Elias, Janice Fan, Scott Farrar, Gail Fiddyment, Krysta Gibbs, Julie Grove, Jodi Hale, Karen Hall, Eddie Hampton, Tiffany Hill, Robert Hollister, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Marlene Pineda, DesLey V. Plaisance, Elizabeth Re, Meri Robie-Craven, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Theresa Streeter, Mary Swanson, James Tanton, Julia Tessler, Saffron VanGalder, Rachael Waltke, 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, Patricia Mickelberry, Ivonne Mercado, Sandra Mercado, Brian Methe, 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

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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?

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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?

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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 Multiplication and Division with Units of 2, 3, 4, 5, and 10 Module 2 Place Value Concepts Through Metric Measurement Module 3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9 Module 4 Multiplication and Area Module 5 Fractions as Numbers Module 6 Geometry, Measurement, and Data

What does this painting have to do with math? Swiss-born artist Paul Klee was interested in using color to express emotion. Here he created a grid, or array, of 35 colorful squares arranged in 5 rows and 7 columns. We will learn how an array helps us understand a larger shape by looking at the smaller shapes inside. Learning more about arrays will help us notice patterns and structure—an important skill for multiplication and division. On the cover Farbtafel “qu 1,” 1930 Paul Klee, Swiss, 1879–1940 Pastel on paste paint on paper, mounted on cardboard Kunstmuseum Basel, Basel, Switzerland Paul Klee (1879–1940), Farbtafel “qu 1” (Colour Table “Qu 1” ), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der KleeGesellschaft, Bern. © 2020 Artists Rights Society (ARS), New York.

ISBN 978-1-63898-506-8

9

781638 985068