4

A Story of Units®

Fractional Units LEARN ▸ Module 2 ▸ Place Value Concepts for Multiplication and Division

Student

Talking Tool Share Your Thinking

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

because . . . .

My drawing shows . . . . Agree or Disagree

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

Ask for Reasoning

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

Say It Again

related to

?

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

Content Terms

Place a sticky note here and add content terms.

? Why?

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

EM2_NA_E_G04_SE_coverpage.indd 1

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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 978-1-63898-509-9

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A Story of Units®

Fractional Units ▸ 4 LEARN

Module

EM2_0402SE_title_page.indd 1

1 2 3 4 5 6

Place Value Concepts for Addition and Subtraction

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

Foundations for Fraction Operations

Place Value Concepts for Decimal Fractions

Angle Measurements and Plane Figures

29-Nov-21 2:50:19 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2

Contents Place Value Concepts for Multiplication and Division Topic A

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Compose and Decompose Units of Ten

Multiply by applying simplifying strategies. (Optional)

Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Multiply multiples of 10 by one-digit numbers by using the associative property of multiplication. Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Divide two- and three-digit multiples of 10 by

one-digit numbers.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Investigate and use a formula for the area of a rectangle.

Topic B

Topic C Division of Tens and Ones by One-Digit Numbers Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Divide by using familiar strategies.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Divide two-digit numbers by one-digit numbers by using an area model.

Multiplication of Tens and Ones by One-Digit Numbers

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Divide three-digit numbers by one-digit numbers by using an area model.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Multiply by using familiar strategies.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Multiply by using place value strategies and the distributive property. Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Multiply with regrouping by using place value strategies and the distributive property.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Multiply by using an area model and the distributive property. Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Multiply by applying the distributive property and write equations.

Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Solve multiplication word problems.

2

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Divide two-digit numbers by one-digit numbers by using place value strategies.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Divide three-digit numbers by one-digit numbers by using place value strategies. Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Divide by using the break apart and distribute strategy.

Topic D Problem Solving with Measurement Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Determine relative sizes of customary length units.

© Great Minds PBC •

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.

01-Dec-21 11:22:38 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Investigate and use formulas for the perimeter of a rectangle.

Recognize that a number is a multiple of each of its factors.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Apply area and perimeter formulas to solve problems.

Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Explore properties of prime and composite numbers up to 100 by using multiples.

Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Solve word problems involving additive and multiplicative comparisons.

Use relationships within a pattern to find an unknown term in the sequence.

Topic E

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Factors and Multiples

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 204

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Find factor pairs for numbers up to 100 and use factors to identify numbers as prime or composite. Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Use division and the associative property of multiplication to find factors. Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Determine whether a whole number is a multiple of another number.

© 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.

3

01-Dec-21 9:02:56 AM

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29-Nov-21 2:22:30 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 1

Name

1

Date

Complete the equations. 1.

tens

ones

2.

2 × 4 = 2 × 4 ones =

tens

2 × 40 = 2 × 4 tens

ones

=

=

3.

=

ones

tens tens

= © Great Minds PBC •

EM2_0402SE_A_L01_problem_set.indd 5

tens

=

tens

3 × 20 = 3 ×

ones

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.

4.

tens

2 × 50 = =

ones

×

tens

tens

= 5

29-Nov-21 11:57:58 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 1

Multiply. Use the place value chart to check your work. 5. 3 × 40 =

=

×

tens

tens

tens

ones

=

Decompose and then multiply. 6. 4 × 60 = 4 × 6 ×

7. 7 × 30 =

×

= 24 ×

=

×

=

=

8. 5 × 80 =

×

=

×

×

=

9. 9 × 90 =

×

=

×

×

×

=

Multiply. 10. 4 × 20 =

11. 6 × 30 =

12. 5 × 40 =

13. 40 × 8 =

14. 7 × 80 =

15. 70 × 9 =

6

PROBLEM SET

EM2_0402SE_A_L01_problem_set.indd 6

© Great Minds PBC •

29-Nov-21 11:57:58 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 1

16. Carla and Shen use the associative property to find 8 times as much as 60. Does Carla or Shen think about 8 × 60 as 48 tens? How do you know? Carla’s Way

8 × 60 = 8 × 6 × 10 = 48 × 10

© Great Minds PBC •

EM2_0402SE_A_L01_problem_set.indd 7

Shen’s Way

8 × 60 = 8 × 10 × 6 = 80 × 6

PROBLEM SET

7

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29-Nov-21 11:57:58 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 1

Name

1

Date

Decompose and then multiply. a. 3 × 40 = 3 ×

=

× ×

=

© Great Minds PBC •

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b. 6 × 50 = 6 ×

=

× ×

=

9

29-Nov-21 11:57:26 AM

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29-Nov-21 11:57:26 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 2

Name

2

Date

Divide. Use the place value disks to help you. 1.

2.

8 ÷ 4 = 8 ones ÷ 4 =

80 ÷ 4 = 8 tens ÷ 4

ones

=

=

tens

=

Divide. Draw place value disks to help you. 3.

4.

150 ÷ 5 = =

tens ÷ tens

=

© Great Minds PBC •

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120 ÷ 3 = =

tens ÷ tens

=

11

29-Nov-21 11:58:49 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 2

Divide. Use unit form to help you. 5. 60 ÷ 2 = 6 tens ÷

=

6. 90 ÷ 3 = 9 tens ÷

tens

=

=

tens

=

7. 180 ÷ 6 =

tens ÷

=

8. 240 ÷ 4 =

tens

=

=

tens ÷ tens

=

Divide. Use multiplication with an unknown factor to help you. 9. 140 ÷ 2 =

2×

12

10. 350 ÷ 5 =

× 10 = 140

PROBLEM SET

EM2_0402SE_A_L02_problem_set.indd 12

5×

11. 270 ÷ 3 =

× 10 = 350

© Great Minds PBC •

3×

× 10 = 270

29-Nov-21 11:58:50 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 2

Divide. 12. 250 ÷ 5 =

13. 280 ÷ 4 =

14. 400 ÷ 8 =

Use Read–Draw–Write to solve the problem. 15. Deepa reads 9 times as many pages as James. Deepa reads 450 pages. How many pages does James read?

© Great Minds PBC •

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PROBLEM SET

13

29-Nov-21 11:58:50 AM

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29-Nov-21 11:58:50 AM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TA ▸ Lesson 2

2

Date

Divide. Use unit form to help you. a. 80 ÷ 2 = 8 tens ÷

=

tens

=

© Great Minds PBC •

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b. 60 ÷ 3 = 6 tens ÷

=

tens

=

15

29-Nov-21 11:58:22 AM

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29-Nov-21 11:58:22 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Multiply and Divide Within 100

Sprint Complete each equation. 1.

3×5=

2.

15 ÷ 3 =

© Great Minds PBC •

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17

30-Nov-21 12:26:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Multiply and Divide Within 100

A

Number Correct:

Complete each equation. 1.

2×3=

23.

5×7=

2.

6÷2=

24.

45 ÷ 5 =

3.

2×4=

25.

6×7=

4.

8÷2=

26.

54 ÷ 6 =

5.

2×5=

27.

7×7=

6.

10 ÷ 2 =

28.

63 ÷ 7 =

7.

2×6=

29.

8×7=

8.

14 ÷ 2 =

30.

72 ÷ 8 =

9.

2×8=

31.

9×7=

10.

18 ÷ 2 =

32.

81 ÷ 9 =

11.

3×3=

33.

4×4=

12.

15 ÷ 3 =

34.

10 × 8 =

13.

3×6=

35.

100 ÷ 10 =

14.

21 ÷ 3 =

36.

11 × 4 =

15.

3×8=

37.

66 ÷ 11 =

16.

27 ÷ 3 =

38.

12 × 3 =

17.

4×6=

39.

60 ÷ 12 =

18.

28 ÷ 4 =

40.

11 × 8 =

19.

4×8=

41.

110 ÷ 11 =

20.

36 ÷ 4 =

42.

12 × 7 =

21.

5×4=

43.

108 ÷ 12 =

22.

25 ÷ 5 =

44.

12 × 12 =

18

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© Great Minds PBC •

30-Nov-21 12:28:33 PM

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29-Nov-21 12:01:46 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Multiply and Divide Within 100

B

Number Correct: Improvement:

Complete each equation. 1.

2×2=

23.

5×6=

2.

4÷2=

24.

40 ÷ 5 =

3.

2×3=

25.

6×6=

4.

6÷2=

26.

48 ÷ 6 =

5.

2×4=

27.

7×6=

6.

8÷2=

28.

56 ÷ 7 =

7.

2×5=

29.

8×6=

8.

12 ÷ 2 =

30.

64 ÷ 8 =

9.

2×7=

31.

9×6=

10.

16 ÷ 2 =

32.

72 ÷ 9 =

11.

3×3=

33.

3×3=

12.

12 ÷ 3 =

34.

10 × 7 =

13.

3×5=

35.

90 ÷ 10 =

14.

18 ÷ 3 =

36.

11 × 3 =

15.

3×7=

37.

55 ÷ 11 =

16.

24 ÷ 3 =

38.

12 × 2 =

17.

4×5=

39.

48 ÷ 12 =

18.

24 ÷ 4 =

40.

11 × 7 =

19.

4×7=

41.

99 ÷ 11 =

20.

32 ÷ 4 =

42.

12 × 6 =

21.

5×3=

43.

96 ÷ 12 =

22.

20 ÷ 5 =

44.

12 × 11 =

20

EM2_0402SE_A_L03_removable_fluency_sprint_multiply_divide_within_100.indd 20

© Great Minds PBC •

30-Nov-21 12:28:43 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 3

Name

3

Date

Complete each multiplication equation to find the area of each rectangle. 2.

1.

4 cm 2 cm

2m

A=l×w

A=l×w

A=

A=

The area is

sq cm.

The area is

40 m

sq m.

4.

3.

30 cm

50 m

5 cm

6m

A=l×w

A=l×w

A=

A=

The area is

© Great Minds PBC •

EM2_0402SE_A_L03_problem_set.indd 21

sq cm.

The area is

sq m.

21

29-Nov-21 11:59:45 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 3

Write an equation to find each unknown side length. Then fill in the blanks. 5. The area is 70 sq cm.

6. The area is 450 sq m.

p cm

dm 9m Equation:

7 cm

d= The unknown side length is

m.

Equation:

p= The unknown side length is

cm.

7. Jayla draws a rectangle that has a width of 4 centimeters and a length of 9 centimeters. a. What is the area of Jayla’s rectangle?

b. David draws a rectangle that has the same length but is 2 times as wide as Jayla’s rectangle. What is the width of David’s rectangle?

c. What is the area of David’s rectangle?

22

PROBLEM SET

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© Great Minds PBC •

29-Nov-21 11:59:46 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 3

8. Casey finds the unknown length of a rectangle. Explain his strategy.

r cm 5 cm The area is 200 sq cm.

l×w=A r × 5 = 200 r = 40

9. A rectangular garden has an area of 360 square meters. The width is 9 meters. What is the length of the garden?

10. Rectangle A has a length of 8 centimeters and a width of 3 centimeters. Rectangle B is 5 times as long and 2 times as wide as rectangle A. a. What is the length and width of rectangle B?

b. What is the area of rectangle B?

© Great Minds PBC •

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PROBLEM SET

23

29-Nov-21 11:59:46 AM

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29-Nov-21 11:59:46 AM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TA ▸ Lesson 3

Name

Date

3

1. Complete the equation and find the area of the rectangle.

60 m 3m A=l×w A= The area is

sq m.

2. Write an equation and find the unknown side length. The area is 280 sq cm.

n cm

7 cm Equation:

n= The unknown side length is

© Great Minds PBC •

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cm.

25

29-Nov-21 11:59:09 AM

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29-Nov-21 11:59:09 AM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 4

Date

4

Multiply. Show or explain your strategy. 1. 3 × 82

2. 6 times as much as 37

© Great Minds PBC •

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27

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29-Nov-21 12:02:24 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 4

Date

4

Multiply. Show or explain your strategy. 1. 3 times as much as 47

2. 4 times as long as 64 meters

© Great Minds PBC •

EM2_0402SE_B_L04_problem_set.indd 29

29

29-Nov-21 12:03:13 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 4

3. Find 67 × 6 by using two different strategies. Put a star next to the strategy that is more efficient for you.

Use the Read–Draw–Write process to solve the problem. 4. Pablo has 35 times as many marbles as his brother. His brother has 8 marbles. How many marbles does Pablo have?

30

PROBLEM SET

EM2_0402SE_B_L04_problem_set.indd 30

© Great Minds PBC •

29-Nov-21 12:03:13 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 4

Date

4

Multiply. Show or explain your strategy.

4 × 32

© Great Minds PBC •

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31

29-Nov-21 12:02:47 PM

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29-Nov-21 12:02:47 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 5

Name

Date

5

Draw on the place value chart to help you multiply. Then complete the equation. Problem 1 has been started for you. 1. 3 × 32 tens

ones

+

=

2. 4 × 32 tens

ones

+

© Great Minds PBC •

EM2_0402SE_B_L05_problem_set.indd 33

=

33

29-Nov-21 12:05:07 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 5

Draw on the place value chart to represent the expression. Complete the equations. 3. 4 × 21 tens

ones

4 × 21 = 4 × (2 tens + 1 one) = (4 × =( =

tens) + (4 × tens) + (

one) ones)

+

=

4. 5 × 41 tens

ones

5 × 41 = 5 × (

+

=(

×

=(

tens) + (

=

) tens) + (

×

one)

ones)

+

=

34

PROBLEM SET

EM2_0402SE_B_L05_problem_set.indd 34

© Great Minds PBC •

29-Nov-21 12:05:08 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 5

Use the distributive property to multiply. 5. 2 × 22 = 2 × (20 + 2)

6. 4 × 22 = 4 × (

= (2 × 20) + (2 × 2)

= (4 ×

=

=

+

=

+

)

) + (4 ×

)

+

)

+

=

7. 4 × 62 = 4 × (

+

)

8. 5 × 81 =

×(

Use the Read–Draw–Write process to solve the problem. 9. Miss Wong buys 8 recess games. Each game costs $41. What is the total cost of the games?

© Great Minds PBC •

EM2_0402SE_B_L05_problem_set.indd 35

PROBLEM SET

35

29-Nov-21 12:05:08 PM

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29-Nov-21 12:05:08 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 5

Name

5

Date

Draw on the place value chart to represent the expression 3 × 41. Complete the equations. tens

ones

3 × 41 = 3 × (

tens +

= (3 × =( =

one)

tens) + (3 × tens) + (

one) ones)

+

=

© Great Minds PBC •

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37

29-Nov-21 12:04:34 PM

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29-Nov-21 12:04:34 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 6

Name

6

Date

Draw on the place value chart to represent the expression. Complete the equations. 1. 3 times as much as 42 tens

ones

3 × 42 = (3 × 4 tens) + (3 × 2 ones) =(

tens) + (

ones)

= 120 + =

2. 3 times as much as 24 tens

ones

3 × 24 = (3 × =( =

tens) + (3 × tens) + (

ones) ones)

+

=

© Great Minds PBC •

EM2_0402SE_B_L06_problem_set.indd 39

39

29-Nov-21 12:06:07 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 6

3. 4 × 24 tens

(

ones

× 2 tens) + ( (

× 4 ones) = 4 × 24

tens) + (

ones) = +

= =

4. 4 × 35 tens

(

×

tens) + ( (

ones

×

ones) = 4 × 35

tens) + (

ones) = +

= =

40

PROBLEM SET

EM2_0402SE_B_L06_problem_set.indd 40

© Great Minds PBC •

29-Nov-21 12:06:08 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 6

Use the distributive property to multiply. 5. 3 × 51 = 3 × (50 + 1)

6. 4 × 23 = 4 × (

= (3 × 50) + (3 × 1)

= (4 ×

=

=

+

=

+

)

) + (4 ×

)

+

=

7. 19 × 5 = (

+

= (10 × =

)×5 ) + (9 ×

8. 56 × 6 = (

+

)×

=(

×

)+(

)

+

=

=

×

)

+

=

9. A multiplicative expression is represented in the place value chart. Three students use the distributive property to find the product. Who made mistakes? Explain their mistakes.

tens

ones

Eva’s work:

Gabe’s work:

Ray’s work:

53 × 3 = (3 × 30) + (3 × 5) = 90 + 15 = 105

53 × 3 = (5 × 50) + (5 × 3) = 250 + 15 = 265

53 × 3 = (3 × 3) + (3 × 50) = 9 + 150 = 159

© Great Minds PBC •

EM2_0402SE_B_L06_problem_set.indd 41

PROBLEM SET

41

29-Nov-21 12:06:09 PM

EM2_0402SE_B_L06_problem_set.indd 42

29-Nov-21 12:06:09 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 6

Name

6

Date

Draw on the place value chart to represent the expression 4 × 43. Complete the equations. tens

ones

4 × 43 = 4 × (

tens +

= (4 × =( =

ones)

tens) + (4 × tens) + (

ones) ones)

+

=

© Great Minds PBC •

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43

29-Nov-21 12:05:31 PM

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29-Nov-21 12:05:31 PM

EUREKA MATH2 Tennessee Edition

© Great Minds PBC •

EM2_0402SE_B_L07_removable_centimeter_grid.indd 45

4 ▸ M2 ▸ TB ▸ Lesson 7 ▸ Centimeter Grid

45

30-Nov-21 12:29:26 PM

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29-Nov-21 12:13:50 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 7

Name

7

Date

Fill in the area model. 1.

2.

3

20 2 tens

3 3 ones

3 × 2 tens =

3 × 3 ones =

tens

ones

2

2 × 4 tens =

40

4 tens

6

6 ones

tens

2 × 6 ones = ones

Fill in the area model and complete the equations. 3. 2 × 34

30

4

2

2 × 34 = 2 × (3 tens + 4 ones) = (2 × 3 tens) + (2 × =

ones)

+

=

© Great Minds PBC •

EM2_0402SE_B_L07_problem_set.indd 47

47

29-Nov-21 12:10:50 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 7

4. 3 × 21

20 3

3

3 × 21 = 3 × (2 tens + = (3 × =

) ) + (3 ×

)

+3

=

5. 3 × 26

3

3 × 26 = 3 × ( =(

60

+ ×

18

) )+(

×

)

= 60 + 18 =

48

PROBLEM SET

EM2_0402SE_B_L07_problem_set.indd 48

© Great Minds PBC •

29-Nov-21 12:10:51 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 7

6. 4 × 17

4 × 17 =

Use the distributive property to multiply. You may draw an area model to help you. 7. 3 × 23 = 3 × (20 + 3)

= (3 ×

) + (3 ×

)

= (30 ×

= 60 +

=

=

=

© Great Minds PBC •

EM2_0402SE_B_L07_problem_set.indd 49

8. 32 × 3 = (30 + 2) × 3

) + (2 ×

)

+6

PROBLEM SET

49

29-Nov-21 12:10:51 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 7

9. 4 × 24

10. 18 × 5

11. Robin paints a mural orange and blue. Write an expression and find the total area of the mural. Show your work by using the distributive property.

4m

20 m

7m

Use the Read–Draw–Write process to solve the problem. 12. Mr. Endo buys 3 boxes of pears. Each box has 28 pears. How many pears does he buy?

50

PROBLEM SET

EM2_0402SE_B_L07_problem_set.indd 50

© Great Minds PBC •

29-Nov-21 12:10:51 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 7

Name

7

Date

Think about 4 × 24. a. Fill in the area model.

b. Complete the equations.

4 × 24 = 4 × ( =( =

+ ×

) )+(

×

)

+

=

© Great Minds PBC •

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51

29-Nov-21 12:07:22 PM

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29-Nov-21 12:07:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 8

Name

8

Date

Use the distributive property to multiply. You may draw an area model to help you. 1. 5 × 17 = 5 × (10 +

= (5 ×

) ) + (5 ×

)

= 50 + = 10

7

5

2. 31 × 5 = (30 +

=(

)×5 × 5) + (

× 5)

= 150 + =

© Great Minds PBC •

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53

29-Nov-21 12:20:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 8

3. 6 × 41

5. 3 times as much as 29 is

7. 7 times as much as 63 mL is

54

PROBLEM SET

EM2_0402SE_B_L08_problem_set.indd 54

4. 42 × 7

6. 52 times as much as 4 is

.

.

8. 48 times as long as 8 km is

© Great Minds PBC •

.

.

29-Nov-21 12:20:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 8

Use the Read–Draw–Write process to solve each problem. 9. Mr. Lopez’s rectangular garden is 28 meters long and 9 meters wide. What is the area of the garden?

10. Mr. Davis works 8 hours a day. How many hours does he work in 45 days?

© Great Minds PBC •

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PROBLEM SET

55

29-Nov-21 12:20:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 8

11. A lizard weighs 86 grams. A snake weighs 7 times as much as the lizard. What is the weight of the snake?

56

PROBLEM SET

EM2_0402SE_B_L08_problem_set.indd 56

© Great Minds PBC •

29-Nov-21 12:20:04 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 8

Date

8

Use the distributive property to find 3 × 46.

© Great Minds PBC •

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57

29-Nov-21 12:19:54 PM

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29-Nov-21 12:19:54 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 9

Date

9

Use the Read–Draw–Write process to solve each problem. 1. A rectangle is 3 times as long as it is wide. The width of the rectangle is 35 centimeters. What is the length of the rectangle?

2. A worm is 21 centimeters long. A snake is 6 times as long as the worm. How long is the snake?

© Great Minds PBC •

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59

29-Nov-21 12:19:44 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 9

3. Liz does 25 push-ups each day. How many push-ups does Liz do in 7 days?

4. Luke’s dog weighs 24 kilograms. His pony weighs 9 times as much as his dog. How much does Luke’s pony weigh?

60

PROBLEM SET

EM2_0402SE_B_L09_problem_set.indd 60

© Great Minds PBC •

29-Nov-21 12:19:44 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 9

5. A cafeteria serves 94 liters of milk each day. How many liters of milk does the cafeteria serve in 5 days?

6. Mia buys grapes and apples. The apples weigh 8 times as much as the grapes. The grapes weigh 98 grams. How much do the apples weigh?

© Great Minds PBC •

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PROBLEM SET

61

29-Nov-21 12:19:44 PM

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29-Nov-21 12:19:44 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 9

Date

9

Use the Read–Draw–Write process to solve the problem. A puppy weighs 18 pounds. Jayla says her dog weighs 4 times as much as the puppy. What is the weight of Jayla’s dog?

© Great Minds PBC •

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63

29-Nov-21 12:19:35 PM

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29-Nov-21 12:19:35 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 10

Date

10

Multiply. Show your strategy. 1. 4 × 76 =

2. 4 × 43 =

3. 6 × 82 =

4. 8 × 72 =

5. 3 × 60 =

6. 3 × 59 =

© Great Minds PBC •

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65

29-Nov-21 12:19:25 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 10

7. 6 × 78 =

8. 8 × 67 =

Use the Read–Draw–Write process to solve each problem. 9. Jayla has 4 times as many stickers as Ivan. Ivan has 63 stickers. How many stickers does Jayla have?

66

PROBLEM SET

EM2_0402SE_B_L10_problem_set.indd 66

© Great Minds PBC •

29-Nov-21 12:19:25 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TB ▸ Lesson 10

10. Mr. Endo buys 7 boxes of crayons. Each box has 48 crayons. How many crayons does he buy in all?

11. Oka and Ray use a compensation strategy to find 6 × 37. Oka’s Way

Ray’s Way

6 x 37 = (6 x 40 40)) - 6

6 x 37 = (6 x 40) - 18

= 240 - 6

= 240 - 18

= 234

= 222

Whose work is correct? How do you know?

© Great Minds PBC •

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PROBLEM SET

67

29-Nov-21 12:19:25 PM

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29-Nov-21 12:19:25 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TB ▸ Lesson 10

Date

10

Multiply. Show your strategy. a. 7 × 40 =

© Great Minds PBC •

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b. 7 × 39 =

69

29-Nov-21 12:19:16 PM

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29-Nov-21 12:19:16 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TC ▸ Lesson 11

Date

11

Find the unknown. Show or explain your strategy. 1. 6 people equally share 78 dollars. How much money does each person get?

2. 7 equal groups of how many is 161?

© Great Minds PBC •

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71

29-Nov-21 12:25:06 PM

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29-Nov-21 12:25:06 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TC ▸ Lesson 11

Date

11

Find the unknown. Show or explain your strategy. 1. 48 pears are shared equally by 3 people. How many pears does each person get?

2. 4 equal groups of how many is 68?

© Great Minds PBC •

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73

29-Nov-21 12:24:52 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 11

3. How many groups of 5 are in 135?

4. Think about 210 ÷ 6. a. Use two different strategies to find the quotient.

b. Put a star next to the more efficient strategy.

74

PROBLEM SET

EM2_0402SE_C_L11_problem_set.indd 74

© Great Minds PBC •

29-Nov-21 12:24:52 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TC ▸ Lesson 11

Date

11

Mrs. Smith buys 8 cans of paint for a total of $120. The cans of paint are all the same. How much does 1 can of paint cost? Show or explain your strategy.

© Great Minds PBC •

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75

29-Nov-21 12:22:52 PM

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29-Nov-21 12:22:52 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 12

Name

Date

12

Complete the area model to help you divide. Then write the quotient. 1. 64 ÷ 2 = tens

2

6 tens 60

ones

4 ones 4

2. 136 ÷ 4 = tens

4

© Great Minds PBC •

EM2_0402SE_C_L12_problem_set.indd 77

12 tens 120

ones

16 ones 16

77

29-Nov-21 12:22:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 12

Complete the area model to help you divide. Then complete the equations. 3. 96 ÷ 3

3

90

6

96 ÷ 3 = (9 tens + 6 ones) ÷ 3 = (9 tens ÷ 3) + (6 ones ÷ 3) =

+

=

4. 159 ÷ 3

3

3

150

159 ÷ 3 = (15 tens + = (15 tens ÷ 3) + ( =

)÷3 ÷ 3)

+3

=

78

PROBLEM SET

EM2_0402SE_C_L12_problem_set.indd 78

© Great Minds PBC •

29-Nov-21 12:22:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 12

5. 52 ÷ 4

4

40

12

52 ÷ 4 = (40 + 12) ÷ 4 =( =

÷ 4) + (

÷ 4)

+

=

6. 148 ÷ 4

4

120

148 ÷ 4 = (120 +

)÷4

= (120 ÷ 4) + ( =

÷ 4)

+

=

© Great Minds PBC •

EM2_0402SE_C_L12_problem_set.indd 79

PROBLEM SET

79

29-Nov-21 12:22:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 12

Break apart and distribute the total to divide. You may draw an area model to help you. 7. 86 ÷ 2 = (80 +

)÷2

= (80 ÷ 2 ) + ( =

8. 168 ÷ 4

÷ 2)

+

=

9. 78 ÷ 3 = (60 +

)÷3

= (60 ÷ 3) + ( =

10. 185 ÷ 5

÷ 3)

+

=

80

PROBLEM SET

EM2_0402SE_C_L12_problem_set.indd 80

© Great Minds PBC •

29-Nov-21 12:22:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 12

Name

12

Date

Complete the area model and the equations to find 72 ÷ 3.

3

12 72 ÷ 3 = ( =( =

+ ÷ 3) + (

)÷3 ÷ 3)

+

=

© Great Minds PBC •

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81

29-Nov-21 12:22:21 PM

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29-Nov-21 12:22:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

Name

Date

13

Complete the area model. Then complete the equations. 1. 85 ÷ 5 =

5

50

35

85 ÷ 5 = (50 + 35) ÷ 5 = (50 ÷ 5) + (35 ÷ 5) =

+

=

2. 138 ÷ 3 =

3

120

18

138 ÷ 3 = (120 + 18) ÷ 3 = (120 ÷ 3) + (18 ÷ 3) =

+

=

© Great Minds PBC •

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83

29-Nov-21 12:29:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

3. 172 ÷ 4 =

3

4

160

172 ÷ 4 = (160 +

)÷4

= (160 ÷ 4) + ( =

÷ 4)

+3

=

4. 106 ÷ 2 =

50

2

6

106 ÷ 2 = ( =(

+ 6) ÷ 2 ÷ 2) + (6 ÷ 2)

= 50 + =

84

PROBLEM SET

EM2_0402SE_C_L13_problem_set.indd 84

© Great Minds PBC •

29-Nov-21 12:29:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

5. 201 ÷ 3 =

3

180

6. 304 ÷ 4 =

© Great Minds PBC •

EM2_0402SE_C_L13_problem_set.indd 85

PROBLEM SET

85

29-Nov-21 12:29:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

Break apart and distribute the total to divide. You may draw an area model to help you. 7. 430 ÷ 5 = (400 +

)÷5

= (400 ÷ 5) + ( =

8. 504 ÷ 6 = (

÷

)

=(

+

=

=

9. 406 ÷ 7

86

PROBLEM SET

EM2_0402SE_C_L13_problem_set.indd 86

+ 24) ÷ 6 ÷

) + (24 ÷ 6)

+

=

10. 368 ÷ 8

© Great Minds PBC •

29-Nov-21 12:29:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

Use the Read–Draw–Write process to solve the problem. 11. Oka puts 474 books equally into 6 boxes. How many books are in each box?

© Great Minds PBC •

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PROBLEM SET

87

29-Nov-21 12:29:22 PM

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29-Nov-21 12:29:22 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 13

Name

13

Date

Complete the area model and the equations to find 308 ÷ 7.

7

280

308 ÷ 7 = ( =( =

+ ÷ 7) + (

)÷7 ÷ 7)

+

=

© Great Minds PBC •

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89

29-Nov-21 12:29:12 PM

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

Name

Date

14

Draw on the place value chart to multiply. Then complete the equation. Problem 1 has been started for you. 1. 46 ÷ 2 = tens

ones

tens ones

2. 72 ÷ 3 = tens

© Great Minds PBC •

EM2_0402SE_C_L14_problem_set.indd 91

ones

91

29-Nov-21 12:29:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

Draw on the place value chart to divide. Then complete the equations. 3. 69 ÷ 3 tens

ones

69 ÷ 3 = (6 tens + =( =

ones ) ÷ 3 ÷ 3) + (

÷ 3)

+

=

92

PROBLEM SET

EM2_0402SE_C_L14_problem_set.indd 92

© Great Minds PBC •

29-Nov-21 12:29:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

4. 56 ÷ 2 tens

ones

56 ÷ 2 = (4 tens + =( =

)÷2 ÷ 2) + (

÷ 2)

+

=

© Great Minds PBC •

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PROBLEM SET

93

29-Nov-21 12:29:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

5. 48 ÷ 3 = tens

ones

48 ÷ 3 = (

+

=(

÷

=

)÷ )+(

÷

)

+

=

94

PROBLEM SET

EM2_0402SE_C_L14_problem_set.indd 94

© Great Minds PBC •

29-Nov-21 12:29:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

6. 96 ÷ 4 = tens

ones

96 ÷ 4 = (

+

=(

÷

=

)÷ )+(

÷

)

+

=

© Great Minds PBC •

EM2_0402SE_C_L14_problem_set.indd 95

PROBLEM SET

95

29-Nov-21 12:29:04 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

7. Mrs. Smith writes three division equations. She asks her class which equation they would represent on a place value chart.

35 ÷ 5 =

78 ÷ 3 =

a. Ivan chooses 78 ÷ 3 =

80 ÷ 8 =

. Explain why you think he chose that equation.

b. Draw on the place value chart to represent 78 ÷ 3. Then fill in the blanks. tens

÷

ones

=(

+

=(

÷

=

)÷ )+(

÷

)

+

= 96

PROBLEM SET

EM2_0402SE_C_L14_problem_set.indd 96

© Great Minds PBC •

29-Nov-21 12:29:05 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 14

Name

14

Date

Draw on the place value chart and complete the equations to find 84 ÷ 4. tens

84 ÷ 4 = ( =( =

ones

tens + tens ÷ 4) + (

ones) ÷ 4 ones ÷ 4)

+

=

© Great Minds PBC •

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97

29-Nov-21 12:28:53 PM

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29-Nov-21 12:28:53 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ 10 Times as Much

Sprint Write the product. 1.

10 × 4

2.

10 × 60

3.

10 × 200

© Great Minds PBC •

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99

30-Nov-21 12:30:56 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ 10 Times as Much

A

Number Correct:

Write the product. 1.

10 × 1

23.

10 × 30

2.

10 × 3

24.

10 × 500

3.

10 × 5

25.

10 × 7,000

4.

10 × 10

26.

10 × 40,000

5.

10 × 50

27.

60 × 10

6.

10 × 70

28.

300 × 10

7.

10 × 100

29.

5,000 × 10

8.

10 × 700

30.

70,000 × 10

9.

10 × 900

31.

10 × 80

10.

10 × 1,000

32.

900 × 10

11.

10 × 8,000

33.

10 × 4,000

12.

10 × 4,000

34.

60,000 × 10

13.

10 × 4

35.

10 × 7

14.

10 × 8

36.

10 × 8

15.

10 × 40

37.

10 × 200

16.

10 × 90

38.

30,000 × 10

17.

10 × 400

39.

10 × 9,000

18.

10 × 600

40.

50,000 × 10

19.

10 × 800

41.

10 × 90,000

20.

10 × 3,000

42.

800,000 × 10

21.

10 × 6,000

43.

10 × 500,000

22.

10 × 9,000

44.

900,000 × 10

100

EM2_0402SE_C_L15_removable_fluency_sprint_10_times_as_much.indd 100

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29-Nov-21 12:37:16 PM

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29-Nov-21 12:37:16 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ 10 Times as Much

B

Number Correct: Improvement:

Write the product. 1.

10 × 1

23.

10 × 20

2.

10 × 2

24.

10 × 400

3.

10 × 4

25.

10 × 6,000

4.

10 × 10

26.

10 × 30,000

5.

10 × 40

27.

50 × 10

6.

10 × 60

28.

200 × 10

7.

10 × 100

29.

4,000 × 10

8.

10 × 600

30.

60,000 × 10

9.

10 × 800

31.

10 × 70

10.

10 × 1,000

32.

800 × 10

11.

10 × 7,000

33.

10 × 3,000

12.

10 × 3,000

34.

50,000 × 10

13.

10 × 3

35.

10 × 6

14.

10 × 7

36.

10 × 7

15.

10 × 30

37.

10 × 200

16.

10 × 80

38.

20,000 × 10

17.

10 × 300

39.

10 × 8,000

18.

10 × 500

40.

40,000 × 10

19.

10 × 700

41.

10 × 80,000

20.

10 × 2,000

42.

700,000 × 10

21.

10 × 5,000

43.

10 × 400,000

22.

10 × 8,000

44.

800,000 × 10

102

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© Great Minds PBC •

29-Nov-21 12:37:16 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 15

Name

15

Date

Draw on the place value chart to divide. Then complete the equations. 1. 148 ÷ 2

2. 129 ÷ 3

tens

ones

tens

148 ÷ 2 = (14 tens + 8 ones) ÷ 2 =( =

÷ 2) + (

129 ÷ 3 = ( ÷ 2)

+

=

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ones

tens +

=( =

÷ 3) + (

ones) ÷ 3 ÷ 3)

+

=

103

29-Nov-21 12:36:46 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 15

3. 108 ÷ 2

4. 165 ÷ 3

tens

ones

108 ÷ 2 = ( =( =

+ ÷ 2) + ( +

=

104

PROBLEM SET

EM2_0402SE_C_L15_problem_set.indd 104

tens

)÷2 ÷ 2)

ones

165 ÷ 3 = (150 + =( =

)÷ ÷

)+(

÷

)

+

=

© Great Minds PBC •

29-Nov-21 12:36:46 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 15

5. 132 ÷ 4

6. 102 ÷ 3

tens

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ones

tens

ones

PROBLEM SET

105

29-Nov-21 12:36:47 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 15

7. Ray draws on a place value chart to find 108 ÷ 3. Liz uses a number bond to break apart the total to help her find 108 ÷ 3. Liz’s Way

Ray’s Way

tens

ones

108 ÷ 3 = 36 90

18

= (90 ÷ 3) + (18 ÷ 3) = 30 + 6 = 36

3 tens 6 ones

108 10 8 ÷ 3 = 36 How do both strategies show that 108 ÷ 3 can be found by breaking apart 108 into 90 and 18?

106

PROBLEM SET

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© Great Minds PBC •

29-Nov-21 12:36:47 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 15

Name

15

Date

Draw on the place value chart to find 135 ÷ 3. Then complete the equations. tens

ones

135 ÷ 3 = (

+

)÷

=(

÷

)+(

=

÷

)

+

=

© Great Minds PBC •

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107

29-Nov-21 12:36:33 PM

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29-Nov-21 12:36:33 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TC ▸ Lesson 16

Date

16

Divide. Show or explain your strategy. 1. 86 ÷ 2

2. 216 ÷ 4

3. 108 ÷ 3

4. 324 ÷ 6

© Great Minds PBC •

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109

29-Nov-21 12:36:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 16

5. Think about 308 ÷ 4. a. Use two different strategies to find the quotient.

b. Draw a star next to the strategy that is more efficient.

c. Explain why the strategy you chose is more efficient.

110

PROBLEM SET

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© Great Minds PBC •

29-Nov-21 12:36:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TC ▸ Lesson 16

Use the Read–Draw–Write process to solve each problem. 6. Amy pours a total of 460 milliliters of water equally into 5 containers. How many milliliters of water are in each container?

7. A baker sells 132 muffins. There are 6 muffins in each box. How many boxes of muffins does the baker sell?

© Great Minds PBC •

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PROBLEM SET

111

29-Nov-21 12:36:21 PM

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29-Nov-21 12:36:21 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TC ▸ Lesson 16

Date

16

Find 172 ÷ 4. Show or explain your strategy.

© Great Minds PBC •

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113

29-Nov-21 12:36:01 PM

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29-Nov-21 12:36:01 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 17

Name

17

Date

Circle the most reasonable measurement for each item. 1. The length of a crayon

7 inches

12 inches

2. The length from Mrs. Smith’s wrist to her elbow

3 inches

3. The height of a bookshelf

1 yard

© Great Minds PBC •

EM2_0402SE_D_L17_problem_set.indd 115

12 feet

20 inches

5 inches

1 foot

24 inches

4. The height of a tree

85 inches

85 yards

85 feet

115

10-Dec-21 1:52:56 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 17

5. Find three classroom items to measure in inches. Then complete the table.

Item

Estimate

Measurement

Complete the statement and equations.

1 foot is

6. 1 in

1 ft =

times as long as 1 inch.

× 1 in

1 foot =

inches

1 yard is

times as long as 1 foot.

1 ft 7.

1 ft

1 yd = 1 yard =

× 1 ft feet

1 yd

116

PROBLEM SET

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© Great Minds PBC •

12/20/2021 12:17:26 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 17

8. An ant is 1 inch long. A snake is 1 foot long. How many times longer is the snake than the ant? Use numbers or words to explain your thinking.

9. Oka and Shen measure the length of a ribbon. Oka says the ribbon is 3 feet long. Shen says the ribbon is 1 yard long. Mr. Davis says they are both correct. Use numbers or words to explain how Oka and Shen are both correct.

© Great Minds PBC •

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PROBLEM SET

117

10-Dec-21 1:52:57 PM

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10-Dec-21 1:52:57 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TD ▸ Lesson 17

Date

17

Estimate the length of each object in inches by using benchmark items. Then measure the length of each object in inches by using a ruler. 1.

Estimate:

inches

Measurement:

inches

2.

Estimate:

inches

Measurement:

inches

3. Draw and label a tape diagram to show the relationship between feet and yards. Use the tape diagram to complete the statement and equations.

1 yard is 1 yd = 1 yard = © Great Minds PBC •

EM2_0402SE_D_L17_exit_ticket.indd 119

times as long as 1 foot.

× 1 ft feet 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.

119

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29-Nov-21 12:41:28 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 18

Name

18

Date

Write an equation to find the perimeter of the rectangle. Complete the statement. 1.

2.

9 in 6 ft 2 ft

7 in

P = 2 × (l + w)

P = 2 × (l + w)

P=

P=

The perimeter is

feet.

3.

The perimeter is

inches.

4.

20 in

15 yd 8 yd

17 in

P=

P=

The perimeter is

© Great Minds PBC •

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yards.

The perimeter is

inches.

121

29-Nov-21 12:40:36 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 18

Find the unknown side length. Show your strategy and complete the statement. 5. The perimeter is 40 feet.

6. The perimeter is 72 inches.

c ft 27 in 8 ft

r in

c= The unknown side length is

r= feet.

The unknown side length is

inches.

Use the Read–Draw–Write process to solve each problem. 7. The width of a square poster is 36 inches. What is the perimeter of the poster?

122

PROBLEM SET

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© Great Minds PBC •

29-Nov-21 12:40:37 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 18

8. A rectangular basketball court is 50 feet wide. The perimeter of the court is 288 feet. What is the length of the basketball court?

9. A school wants to put a fence around a rectangular playground. The playground is 12 yards wide. The playground is 3 times as long as it is wide. a. What is the length of the playground?

b. To put a fence around the playground, how many yards of fencing does the school need?

© Great Minds PBC •

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PROBLEM SET

123

29-Nov-21 12:40:37 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 18

10. Mia and Gabe find the perimeter of the same rectangle. Who made a mistake? How do you know?

24 ft 8 ft

Mia’s Way

Gabe’s Way

P = 2 × ( 24 + 8) = 2 × 32 = 64

P = 24 × 8

feet.. The perime perimete terr is 64 feet

124

PROBLEM SET

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© Great Minds PBC •

= (20 × 8) + (4 × 8) = 160 + 32 = 192 The perimeter is 192 feet.

29-Nov-21 12:40:37 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 18

Name

Date

18

Write an equation to find the perimeter of the rectangle.

8 ft

6 ft

P= The perimeter is

© Great Minds PBC •

EM2_0402SE_D_L18_exit_ticket.indd 125

feet.

125

29-Nov-21 12:40:26 PM

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29-Nov-21 12:40:26 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Unknown Factor

Sprint Write the unknown factor. 1.

10 ×

= 40

2.

10 ×

= 700

3.

10 ×

© Great Minds PBC •

= 3,000

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127

30-Nov-21 12:48:35 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Unknown Factor

A

Number Correct:

Write the unknown factor. 1.

10 ×

= 10

23.

10 ×

2.

10 ×

= 30

24.

10 ×

= 1,000

3.

10 ×

= 50

25.

10 ×

= 10,000

4.

10 ×

= 70

26.

× 10 = 300

5.

10 ×

= 100

27.

× 10 = 4,000

6.

10 ×

= 400

28.

× 10 = 50,000

7.

10 ×

= 600

29.

8.

10 ×

= 800

30.

10 ×

= 7,000

10 ×

= 80,000

10 ×

= 100

= 600

9.

10 ×

= 1,000

31.

10.

10 ×

= 5,000

32.

× 10 = 900

11.

10 ×

= 7,000

33.

× 10 = 8,000

12.

10 ×

= 9,000

34.

× 10 = 90,000

13.

10 ×

= 20

35.

10 ×

= 40

14.

10 ×

= 40

36.

10 ×

= 30

15.

10 ×

= 60

37.

16.

10 ×

= 300

38.

17.

10 ×

= 500

39.

18.

10 ×

= 700

40.

19.

10 ×

= 2,000

41.

20.

10 ×

= 4,000

42.

21.

10 ×

= 6,000

43.

22.

10 ×

= 9,000

44.

128

EM2_0402SE_D_L19_removable_fluency_sprint_unknown_factor.indd 128

× 10 = 800 10 ×

= 6,000 × 10 = 40,000

10 ×

= 200,000 × 10 = 30,000

10 ×

= 500,000 × 10 = 70,000

10 ×

© Great Minds PBC •

= 900,000

29-Nov-21 12:45:10 PM

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29-Nov-21 12:45:10 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Unknown Factor

B

Number Correct: Improvement:

Write the unknown factor. 1.

10 ×

= 10

23.

10 ×

2.

10 ×

= 20

24.

10 ×

= 1,000

3.

10 ×

= 40

25.

10 ×

= 10,000

4.

10 ×

= 60

26.

× 10 = 200

5.

10 ×

= 100

27.

× 10 = 3,000

6.

10 ×

= 300

28.

× 10 = 40,000

7.

10 ×

= 500

29.

8.

10 ×

= 700

30.

10 ×

= 6,000

10 ×

= 70,000

10 ×

= 100

= 500

9.

10 ×

= 1,000

31.

10.

10 ×

= 4,000

32.

× 10 = 800

11.

10 ×

= 6,000

33.

× 10 = 7,000

12.

10 ×

= 8,000

34.

× 10 = 80,000

13.

10 ×

= 20

35.

10 ×

= 30

14.

10 ×

= 30

36.

10 ×

= 20

15.

10 ×

= 50

37.

16.

10 ×

= 200

38.

17.

10 ×

= 400

39.

18.

10 ×

= 600

40.

19.

10 ×

= 2,000

41.

20.

10 ×

= 3,000

42.

21.

10 ×

= 5,000

43.

22.

10 ×

= 8,000

44.

130

EM2_0402SE_D_L19_removable_fluency_sprint_unknown_factor.indd 130

× 10 = 700 10 ×

= 5,000 × 10 = 30,000

10 ×

= 100,000 × 10 = 20,000

10 ×

= 400,000 × 10 = 60,000

10 ×

© Great Minds PBC •

= 800,000

29-Nov-21 12:45:10 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TD ▸ Lesson 19

Date

19

1. A rectangular garden bed is 4 feet wide. It is 3 times as long as it is wide. a. Draw a rectangle to represent the garden bed. Label the side lengths.

b. Is 40 feet of wood enough to build a frame for the garden bed? How do you know?

c. What is the area of the garden bed?

2. The rectangular bed of a dump trailer has an area of 84 square feet. The width of the trailer is 2 yards. What is the length of the trailer in feet?

© Great Minds PBC •

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131

29-Nov-21 12:50:14 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 19

3. The area of the rectangle is 44 square feet. The perimeter is 30 feet. What are the length and width of the rectangle?

132

LESSON

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© Great Minds PBC •

29-Nov-21 12:50:15 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 19

Name

Date

19

Use the Read–Draw–Write process to solve each problem. 1. A rectangular carpet has a width of 8 feet and a length of 14 feet.

14 ft 8 ft

a. What is the area of the carpet?

b. What is the perimeter of the carpet?

2. Luke makes a rectangular blanket that is 2 times as long as it is wide. The blanket is 4 feet wide. a. What is the length of the blanket?

b. What is the area of the blanket?

c. What is the perimeter of the blanket?

© Great Minds PBC •

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133

29-Nov-21 12:50:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 19

3. Pablo draws a picture that has an area of 108 square inches. The picture is 9 inches wide. a. What is the length of the picture?

b. What is the perimeter of the picture?

4. A rectangular porch is 2 yards 1 foot wide and 3 yards long. a. What is the area, in square feet, of the porch?

b. What is the perimeter, in feet, of the porch?

134

PROBLEM SET

EM2_0402SE_D_L19_problem_set.indd 134

© Great Minds PBC •

29-Nov-21 12:50:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 19

5. Amy uses 38 yards of string to mark the outside edges of her rectangular garden. The garden is 6 yards wide. a. What is the length of the garden?

b. What is the area of the garden?

6. A rectangle has an area of 168 square inches. The perimeter of the rectangle is 62 inches. Can the rectangle have a length of 21 inches and a width of 8 inches? How do you know?

© Great Minds PBC •

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PROBLEM SET

135

29-Nov-21 12:50:03 PM

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29-Nov-21 12:50:03 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TD ▸ Lesson 19

Date

19

A rectangular piece of paper has an area of 88 square inches. The paper is 8 inches wide. a. What is the length of the paper?

b. What is the perimeter of the paper?

© Great Minds PBC •

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137

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29-Nov-21 12:49:53 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 20

Name

20

Date

Write an equation to represent the value of the unknown. Then find the value of the unknown. 1.

2.

18

18

3 d c

3.

Equation:

Equation:

c=

d=

4.

w

30

30

k

Equation:

Equation:

w=

k=

© Great Minds PBC •

EM2_0402SE_D_L20_problem_set.indd 139

5

139

29-Nov-21 12:49:37 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 20

5. Use problems 1–4 to answer parts (a) and (b). a. Which problem represents 3 times as many as 18?

b. Which problem represents 30 is 5 more than a number?

Use the Read–Draw–Write process to solve each problem. 6. A mouse weighs 34 grams. a. A kitten weighs 8 times as much as the mouse. How much does the kitten weigh?

b. A hamster weighs 8 more grams than the mouse. How much does the hamster weigh?

140

PROBLEM SET

EM2_0402SE_D_L20_problem_set.indd 140

© Great Minds PBC •

29-Nov-21 12:49:38 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TD ▸ Lesson 20

7. Container A has 84 milliliters of water. a. Container B has 27 more milliliters of water than container A. How many milliliters of water are in container B?

b. Container A has 6 times as much water as container C. How many milliliters of water are in container C?

8. A desk is 2 feet 3 inches long. a. The width of the desk is 9 inches less than the length of the desk. What is the width, in inches, of the desk?

b. A table is 3 times as long as the desk. What is the length, in inches, of the table?

© Great Minds PBC •

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PROBLEM SET

141

29-Nov-21 12:49:38 PM

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29-Nov-21 12:49:38 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TD ▸ Lesson 20

Date

20

Use the Read–Draw–Write process to solve each problem. 1. A hat costs $16. A sweatshirt costs 3 times as much as the hat. How much does the sweatshirt cost?

2. A hat costs $16. A T-shirt costs $3 more than the hat. How much does the T-shirt cost?

© Great Minds PBC •

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143

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29-Nov-21 12:49:24 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

Name

Number

1.

23

2.

35

3.

48

4.

2

© Great Minds PBC •

EM2_0402SE_E_L21_classwork.indd 145

21

Date

Multiplication Expressions

Odd or Even

Prime or Composite

Odd

Prime

Even

Composite

1×

Odd

Prime

5×

Even

Composite

Odd

Prime

Even

Composite

Odd

Prime

Even

Composite

List of Factors

1×

1,

145

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29-Nov-21 12:56:49 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

Name

21

Date

Complete each equation. Use the pictures to help you. Then answer each question. 1.

2.

1×

=5

1×

=6

2×

=6

What are the factors of 6?

What are the factors of 5?

,

,

,

,

Is 6 a prime or composite number?

Is 5 a prime or composite number?

Complete each equation. Then answer each question. 3. 8 = 1 ×

4. 11 = 1 ×

8=2× What are the factors of 8? ,

,

,

Is 8 a prime or composite number?

© Great Minds PBC •

EM2_0402SE_E_L21_problem_set.indd 147

What are the factors of 11? , Is 11 a prime or composite number?

147

29-Nov-21 12:57:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

Record the factor pairs for the given numbers as multiplication expressions. List the factors in order from least to greatest. Then circle prime or composite for each number. The first problem is done for you. Number

Multiplication Expressions

Factors

5.

3

1×3

1, 3

6.

4

7.

10

8.

18

9.

19

148

PROBLEM SET

EM2_0402SE_E_L21_problem_set.indd 148

Prime or Composite

Prime Composite

1×

Prime

2×

Composite

Prime Composite

Prime Composite

Prime Composite

© Great Minds PBC •

29-Nov-21 12:57:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

Find all the factor pairs for each number by writing multiplication expressions. Then circle prime or composite for each number. 10. 40

11. 41

1 × 40

Prime or Composite

Prime or Composite

12. Zara says the factors of 20 are 1, 2, 4, 5, and 10. a. Is Zara correct? Explain.

b. Zara says 20 is a prime number. Is she correct? Explain.

© Great Minds PBC •

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PROBLEM SET

149

29-Nov-21 12:57:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

13. David uses 24 cards to play a game. He lays the cards in equal rows. Color the boxes to show two ways that he can lay the cards in equal rows.

150

PROBLEM SET

EM2_0402SE_E_L21_problem_set.indd 150

© Great Minds PBC •

29-Nov-21 12:57:41 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 21

Name

21

Date

List the factors for each number. Then select whether the number is prime or composite. Number

Factors

7

12

25

© Great Minds PBC •

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Prime or Composite Prime Composite Prime Composite Prime Composite

151

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29-Nov-21 12:58:14 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

Name

Date

22

1. Luke counts a total of 75 soup cans.

30 of the cans are tomato soup. They are arranged together in equal rows to form an array. Draw a box around the cans to show one way the tomato soup cans could be arranged.

×

=

2. Complete the equation.

42 ÷ 3 =

© Great Minds PBC •

EM2_0402SE_E_L22_classwork.indd 153

153

29-Nov-21 12:58:28 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

Answer each question. Show or explain your thinking. 3. Is 3 a factor of 47?

4. Is 5 a factor of 85?

5. Is 7 a factor of 84?

154

LESSON

EM2_0402SE_E_L22_classwork.indd 154

© Great Minds PBC •

30-Nov-21 12:49:53 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

6. Is 4 a factor of 55?

7. Is 6 a factor of 73?

8. Use the associative property of multiplication to find factors of 72.

72 = 6 × 12

Some factors of 72 are

© Great Minds PBC •

EM2_0402SE_E_L22_classwork.indd 155

.

LESSON

155

29-Nov-21 12:58:28 PM

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29-Nov-21 12:58:28 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

Name

22

Date

Complete each equation. Use the picture to help you. Then answer each question. 1.

2.

10 = 1 ×

7=1×

10 = 2 × Is 1 a factor of 7?

Is 3 a factor of 10?

Is 2 a factor of 7?

Is 10 a factor of 10?

Complete each equation. Then answer each question. 3. 18 = 1 ×

4. 24 = 1 ×

18 = 2 ×

24 = 2 ×

18 = 3 ×

24 = 3 × 24 = 4 ×

Is 6 a factor of 18?

Is 10 a factor of 24?

Is 8 a factor of 18?

Is 12 a factor of 24?

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

Answer each question. Show or explain your thinking. 5. Is 2 a factor of 25?

6. Is 3 a factor of 54?

7. Is 4 a factor of 65?

8. Is 6 a factor of 78?

Use the associative property to find factors. Then answer the question. 9. 36 = 4 × 9

10. 48 = 6 ×

= 4 × (3 × =( =

) × 3) × 3

×3

= What are some factors of 36?

158

PROBLEM SET

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= (2 ×

) × (2 ×

= (2 × 2) × (3 ×

) )

=4× = What are some factors of 48?

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29-Nov-21 12:58:40 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 22

11. Miss Diaz needs 54 juice boxes. Juice boxes are sold in packs of 8. Can she buy exactly 54 juice boxes in packs of 8? Why?

12. Gabe and Deepa have 64 stamps to put into equal groups without having any left over. a. Gabe says, “We can make groups of 3.” Deepa says, “We can make groups of 4.” Who is correct? Explain.

b. Use words or numbers to show another way to put the 64 stamps into equal groups.

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PROBLEM SET

159

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TE ▸ Lesson 22

Date

22

Answer each question. Show or explain your thinking. a. Is 6 a factor of 84?

b. Is 4 a factor of 46?

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161

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29-Nov-21 2:00:25 PM

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Output

4 ▸ M2 ▸ TE ▸ Lesson 23 ▸ Horizontal Input–Output Table

Input

Pattern:

EUREKA MATH2 Tennessee Edition

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

Name

Date

23

1. Work with a partner to complete parts (a) and (b). a. List the multiples of 3.

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b. Write multiplication equations to represent the multiples of 3.

165

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

2. Follow the directions in parts (a)–(c) to complete the chart.

1

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 a. Circle the multiples of 2 in red. b. Shade the multiples of 3 in green. c. Put a blue square around the multiples of 6.

166

LESSON

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29-Nov-21 1:59:57 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

3. Complete the table in part (a). Then complete parts (b) and (c). a. Rule: Multiply the input by 8 Input

Output

1

8 16

5 6 80 b. How does the completed table show that 96 is a multiple of 8?

c. Is 92 a multiple of 8? How do you know?

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LESSON

167

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

Name

23

Date

Fill in the blanks. Use the pictures to help you. 1.

a. The first multiple of 3 is

.

b. The second multiple of 3 is

.

c. The fourth multiple of 3 is

.

2.

The first five multiples of 5 are

,

,

,

, and

.

3. Skip-count to complete the multiples of 6 pattern.

6, 12,

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,

,

, 36,

,

,

,

169

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

4. Think about the multiples of 7. a. Write the first 10 multiples of 7. Start with 7. ,

,

,

,

,

,

,

,

,

b. What is the third multiple of 7? c. What is the tenth multiple of 7? d. Is 40 a multiple of 7?

5. Complete the table in part (a) by using the rule. Then complete part (b). a. Rule: Multiply the input by 6 Input

Output

1

6 12

5 6 60 b. Deepa says she can use the completed table to tell that 96 is a multiple of 6. Explain her thinking.

170

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

Use mental math, division, or the associative property to complete problems 6–9. 6. Is 15 a multiple of 4?

7. Is 70 a multiple of 10?

8. Is 56 a multiple of 9?

9. Is 81 a multiple of 3?

10. Mr. Lopez asks his students how many numbers have 28 as a multiple. Casey and Eva write their answers. Casey

6, because 28 has three factor pairs

Eva

4 numbers

a. Write all the numbers that have 28 as a multiple.

b. Explain which student has the correct answer.

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PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 23

Name

23

Date

Think about the multiples of 4. a. Write the first 10 multiples of 4. Start with 4. ,

,

,

,

,

,

,

,

,

b. What is the fifth multiple of 4?

c. Is 14 a multiple of 4?

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173

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 24

Name

Date

24

1. Use the picture to complete parts (a)–(h).

a. List the factors of 8.

e. List the first five multiples of 4.

b. Is 4 a factor of 8?

f.

c. Is 5 a factor of 8?

g. Is 5 a multiple of 4?

d. Is 8 a factor of 8?

h. Is 8 a multiple of 4?

Is 4 a multiple of 4?

2. Complete the table in part (a) by using the rule. Then complete part (b). a. Rule: Multiply the input by 7

Input

Output

1

7

b. Decide whether 7 is a factor of 91. Explain your thinking.

3 35 10

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 24

3. Think about the number 16. a. What numbers have 16 as a multiple? b. What are the factors of 16? c. Are your answers from parts (a) and (b) the same? Explain.

4. Explain why the following statement is true. Any number that has 8 as a factor also has 4 as a factor.

5. Explain why the following statement is false. If a number has 3 as a factor, then it has 6 as a factor.

176

PROBLEM SET

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© Great Minds PBC •

30-Nov-21 12:53:53 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 24

6. Shen says, “3 is a factor of 129, so 9 must also be a factor of 129.” Use the associative property of multiplication or an input–output table to decide whether Shen is correct.

7. Use the associative property of multiplication to show that the given number is a factor of 90. a. 6

90 = 3 × 30

b. 10

90 = 2 × 45

c. 15

90 = 5 × 18

8. List all the factors of 90. Use your answers from problems 7(a)–(c) to help you.

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PROBLEM SET

177

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 24

Write true or false for each statement. 9. 90 is a factor of 90.

10. 90 is a multiple of 90.

11. 45 is a multiple of 90.

12. 45 is a factor of 90.

13. 90 is a factor of 18.

14. 90 is a multiple of 18.

178

PROBLEM SET

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30-Nov-21 12:53:53 PM

EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TE ▸ Lesson 24

Date

24

Decide whether each statement is true or false. Explain your thinking. a. Any number that has 8 as a factor also has 2 as a factor.

b. If a number has 5 as a factor, then it also has 10 as a factor.

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179

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Compare Numbers

Sprint Write >, =, or < to compare the two numbers. 1.

2,375

1,735

2.

45,162

45,189

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181

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Compare Numbers

A

Number Correct:

Write >, =, or < to compare the two numbers. 1.

100

1,000

23.

7,058

6,085

2.

1,000

199

24.

68,093

67,309

3.

2,573

1,573

25.

642,150

642,150

4.

1,365

1,365

26.

7,104

7,240

5.

2,936

2,836

27.

79,460

79,506

6.

2,521

2,612

28.

710,912

710,821

7.

2,494

2,494

29.

8,130

8,130

8.

2,258

2,184

30.

84,036

84,029

9.

3,887

3,891

31.

830,462

830,526

10.

3,653

3,647

32.

9,205

9,206

11.

3,432

3,428

33.

95,202

95,203

12.

3,281

3,279

34.

960,637

960,638

13.

4,000

40,000

35.

3,000

2,000

14.

40,000

4,999

36.

4,000

5,000

15.

51,593

41,593

37.

1,300

1,000 + 300

16.

47,628

47,628

38.

2,000 + 70

2,700

17.

58,531

59,135

39.

30,050

30,000 + 5

18.

57,742

57,742

40.

40,000 + 600

40,600

19.

56,319

56,291

41.

51,000

50,000 + 1,000

20.

55,682

55,728

42.

60 + 60,000

60,600

21.

54,957

54,968

43.

70,700

7,000 + 70,000

22.

53,528

53,519

44.

900 + 900,000

909,000

182

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29-Nov-21 2:06:21 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ Sprint ▸ Compare Numbers

B

Number Correct: Improvement:

Write >, =, or < to compare the two numbers. 1.

1,000

100

23.

6,085

7,058

2.

199

1,000

24.

67,309

68,093

3.

1,573

2,573

25.

642,150

642,150

4.

1,365

1,365

26.

7,240

7,104

5.

2,863

2,936

27.

79,506

79,460

6.

2,612

2,521

28.

710,821

710,912

7.

2,494

2,494

29.

8,130

8,130

8.

2,184

2,258

30.

84,029

84,036

9.

3,891

3,887

31.

830,526

830,462

10.

3,647

3,653

32.

9,206

9,205

11.

3,428

3,432

33.

95,203

95,202

12.

3,279

3,281

34.

960,638

960,637

13.

40,000

4,000

35.

2,000

1,000

14.

4,999

40,000

36.

3,000

4,000

15.

41,593

51,593

37.

1,000 + 300

1,300

16.

47,628

47,628

38.

2,700

2,000 + 70

17.

59,135

58,531

39.

30,000 + 5

30,050

18.

57,742

57,742

40.

40,600

40,000 + 600

19.

56,291

56,319

41.

50,000 + 1,000

51,000

20.

55,728

55,682

42.

60,600

60 + 60,000

21.

54,968

54,957

43.

7,000 + 70,000

70,700

22.

53,519

53,528

44.

909,000

900 + 900,000

184

EM2_0402SE_E_L25_removable_fluency_sprint_compare_numbers.indd 184

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30-Nov-21 12:57:11 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 25

Name

25

Date

1

2

3

4

5

6

7

8

9

10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TE ▸ Lesson 25

Date

25

1. Name a composite number. Explain how you know that it is composite.

2. Name a prime number. Explain how you know that it is prime.

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26 ▸ Vertical Input–Output Table

Pattern:

Input

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Output

189

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EUREKA MATH2 Tennessee Edition

Name

4 ▸ M2 ▸ TE ▸ Lesson 26

26

Date

1. Miss Wong’s class stands in line and works together to skip-count by fives. The first student says 5, and the next student in line says the next number in the skip-count. The student who says 100 sits down. Deepa is 18th in line. Will she sit down? How do you know? 5

Deepa

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

2. The rule for the shape pattern is add 3 circles.

Figure 1

Figure 2

Figure 3

a. Complete the table. Figure

Number of Circles

Figure 1

3

Figure 2 Figure 3 Figure 4 Figure 5

b. How many circles will be in figure 9?

192

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

3. The four terms keep repeating to make a pattern.

Stand

Beg

Sit

Lay

a. What will the dog be doing in the 5th term in the pattern?

b. What will the dog be doing in the 99th term? How do you know?

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LESSON

193

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

4. Mia makes a number pattern by using the rule: Add 9.

9, 18, 27, 36, 45 a. What is the 13th term in the pattern?

b. Are any numbers in the pattern prime? How do you know?

c. Write a statement to describe something else you notice about the numbers in the pattern. Show how you know your statement is true.

194

LESSON

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

Name

26

Date

1. The rule for the shape pattern is add 7 triangles.

Figure 1

Figure 2

Figure 3

a. Complete the table. Figure

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Number of Triangles

b. How many triangles would be in figure 7? c. In which figure is the number of triangles a prime number?

d. Is the number of triangles in figure 9 divisible by 3? How do you know?

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

2. Look at the shape pattern shown.

a. If the pattern continues, what is the next shape in the pattern?

b. Which shape will be the 49th term?

3. Draw a shape pattern that follows the rule. Rule: Go back and forth between a polygon with 3 sides and a polygon with 5 sides.

196

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

4. If the pattern of up, left, right, down continues, in which direction will the thumb point in the 101st term?

Up

Left

Right

Down

5. Adam creates a number pattern by using the rule: Add 10.

10, 20, 30, 40, 50 If the pattern continues, what will the 20th number be?

6. Write a number pattern with only odd numbers that follows the rule: Add 6. ,

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,

,

,

PROBLEM SET

197

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

7. Complete the number pattern in part (a) by using the rule. Then complete part (b). a. Rule: Subtract 9

90,

,

,

,

b. What do you notice about the numbers in the pattern?

8. Use the rule to continue the number pattern. Then circle True or False for each statement. Rule: Multiply by 2

1, 2,

198

,

,

,

,

The first number in the pattern is the only odd number.

True

False

The 8th number in the pattern will be the product of 8 × 2.

True

False

There are no multiples of 4 in the pattern.

True

False

PROBLEM SET

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

9. Carla scored 20 points in a game at level 1. Then her score doubled at each new level. a. Complete the table. Game Level

1

Number of Points

20

2

3

4

5

b. If the pattern continues, how many points will Carla score at level 7? c. What patterns do you notice for the number of points?

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PROBLEM SET

199

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EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

10. On Monday, Liz does 13 jumping jacks. Each day, she does 5 more jumping jacks than the day before. a. Complete the table to show the number of Liz’s jumping jacks. Day

Monday

Number of Jumping Jacks

13

Tuesday

Wednesday

Thursday

Friday

b. What patterns do you notice for the number of jumping jacks?

200

PROBLEM SET

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© Great Minds PBC •

29-Nov-21 2:12:03 PM

EUREKA MATH2 Tennessee Edition

4 ▸ M2 ▸ TE ▸ Lesson 26

Name

Date

26

Complete the number pattern in part (a) by using the rule. Then complete part (b). a. Rule: Add 7

5,

,

,

,

,

b. What do you notice about the numbers in the pattern?

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201

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EUREKA MATH2 Tennessee Edition

4 ▸ M2

Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. Cover, Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Arts, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York; page 193, Tartila/Shutterstock.com; All other images are the property of Great Minds. For a complete list of credits, visit http://eurmath.link/media-credits.

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EUREKA MATH2 Tennessee Edition

4 ▸ M2

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

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

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

ISBN 978-1-63898-509-9

9

781638 985099