4
A Story of Units®
Fractional Units LEARN ▸ Module 2 ▸ Place Value Concepts for Multiplication and Division
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because . . . .
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Ask for Reasoning
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related to
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Content Terms
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? Why?
What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York
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Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2022 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-509-9
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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.
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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.
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3
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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
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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
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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
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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 ×
=
× ×
=
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b. 6 × 50 = 6 ×
=
× ×
=
9
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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
=
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EM2_0402SE_A_L02_problem_set.indd 11
120 ÷ 3 = =
tens ÷ tens
=
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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
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5×
11. 270 ÷ 3 =
× 10 = 350
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3×
× 10 = 270
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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?
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PROBLEM SET
13
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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
=
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b. 60 ÷ 3 = 6 tens ÷
=
tens
=
15
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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 =
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EM2_0402SE_A_L03_removable_fluency_sprint_multiply_divide_within_100.indd 17
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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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
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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
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sq cm.
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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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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?
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PROBLEM SET
23
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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
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cm.
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25
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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
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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
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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
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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
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31
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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
+
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=
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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
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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?
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PROBLEM SET
35
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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)
+
=
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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)
+
=
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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
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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
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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)
+
=
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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
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EM2_0402SE_B_L07_removable_centimeter_grid.indd 45
4 ▸ M2 ▸ TB ▸ Lesson 7 ▸ Centimeter Grid
45
30-Nov-21 12:29:26 PM
EM2_0402SE_B_L07_removable_centimeter_grid.indd 46
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)
+
=
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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
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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 +
=
=
=
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8. 32 × 3 = (30 + 2) × 3
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) + (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
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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 × ( =( =
+ ×
) )+(
×
)
+
=
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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 + =
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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
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.
.
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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?
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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
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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.
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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?
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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
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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?
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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?
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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 =
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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
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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?
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PROBLEM SET
67
29-Nov-21 12:19:25 PM
EM2_0402SE_B_L10_problem_set.indd 68
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 =
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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?
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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?
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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
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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.
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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
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EM2_0402SE_C_L12_problem_set.indd 77
12 tens 120
ones
16 ones 16
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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
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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)
+
=
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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
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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)
+
=
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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) =
+
=
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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
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29-Nov-21 12:29:22 PM
EUREKA MATH2 Tennessee Edition
4 ▸ M2 ▸ TC ▸ Lesson 13
5. 201 ÷ 3 =
3
180
6. 304 ÷ 4 =
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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
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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?
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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)
+
=
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89
29-Nov-21 12:29:12 PM
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29-Nov-21 12:29:12 PM
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
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ones
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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
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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)
+
=
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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
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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
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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
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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
EM2_0402SE_C_L14_exit_ticket.indd 98
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
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EM2_0402SE_C_L15_removable_fluency_sprint_10_times_as_much.indd 99
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
EM2_0402SE_C_L15_removable_fluency_sprint_10_times_as_much.indd 101
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
EM2_0402SE_C_L15_removable_fluency_sprint_10_times_as_much.indd 102
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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)
+
=
© Great Minds PBC •
EM2_0402SE_C_L15_problem_set.indd 103
ones
tens +
=( =
÷ 3) + (
ones) ÷ 3 ÷ 3)
+
=
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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 + =( =
)÷ ÷
)+(
÷
)
+
=
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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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EM2_0402SE_C_L15_problem_set.indd 105
ones
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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
EM2_0402SE_C_L15_problem_set.indd 106
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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 •
EM2_0402SE_C_L15_exit_ticket.indd 107
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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
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EM2_0402SE_C_L16_problem_set.indd 109
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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
EM2_0402SE_C_L16_problem_set.indd 110
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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?
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EM2_0402SE_C_L16_problem_set.indd 111
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PROBLEM SET
111
29-Nov-21 12:36:21 PM
EM2_0402SE_C_L16_problem_set.indd 112
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.
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EM2_0402SE_C_L16_exit_ticket.indd 113
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113
29-Nov-21 12:36:01 PM
EM2_0402SE_C_L16_exit_ticket.indd 114
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
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EM2_0402SE_D_L17_problem_set.indd 115
12 feet
20 inches
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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
EM2_0402SE_D_L17_problem_set.indd 116
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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 •
EM2_0402SE_D_L17_problem_set.indd 117
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PROBLEM SET
117
10-Dec-21 1:52:57 PM
EM2_0402SE_D_L17_problem_set.indd 118
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
12/20/2021 12:20:19 PM
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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 •
EM2_0402SE_D_L18_problem_set.indd 121
yards.
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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
EM2_0402SE_D_L18_problem_set.indd 122
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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?
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EM2_0402SE_D_L18_problem_set.indd 123
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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
EM2_0402SE_D_L18_problem_set.indd 124
© Great Minds PBC •
= (20 × 8) + (4 × 8) = 160 + 32 = 192 The perimeter is 192 feet.
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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.
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125
29-Nov-21 12:40:26 PM
EM2_0402SE_D_L18_exit_ticket.indd 126
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 ×
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= 3,000
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EM2_0402SE_D_L19_removable_fluency_sprint_unknown_factor.indd 127
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 ×
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= 900,000
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29-Nov-21 12:45:10 PM
EM2_0402SE_D_L19_removable_fluency_sprint_unknown_factor.indd 129
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
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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?
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EM2_0402SE_D_L19_classwork.indd 131
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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
EM2_0402SE_D_L19_classwork.indd 132
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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?
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EM2_0402SE_D_L19_problem_set.indd 133
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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
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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?
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PROBLEM SET
135
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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?
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137
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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=
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5
139
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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
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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?
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PROBLEM SET
141
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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?
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143
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EUREKA MATH2 Tennessee Edition
4 ▸ M2 ▸ TE ▸ Lesson 21
Name
Number
1.
23
2.
35
3.
48
4.
2
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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×
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1,
145
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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?
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What are the factors of 11? , Is 11 a prime or composite number?
147
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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
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PROBLEM SET
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Prime or Composite
Prime Composite
1×
Prime
2×
Composite
Prime Composite
Prime Composite
Prime Composite
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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.
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PROBLEM SET
149
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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
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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
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Prime or Composite Prime Composite Prime Composite Prime Composite
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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 =
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153
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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
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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
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.
LESSON
155
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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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157
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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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Output
4 ▸ M2 ▸ TE ▸ Lesson 23 ▸ Horizontal Input–Output Table
Input
Pattern:
EUREKA MATH2 Tennessee Edition
163
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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.
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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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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,
,
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,
,
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
EM2_0402SE_E_L23_problem_set.indd 170
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29-Nov-21 1:59:15 PM
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
171
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29-Nov-21 1:59:15 PM
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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175
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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
EM2_0402SE_E_L24_problem_set.indd 176
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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
30-Nov-21 12:53:53 PM
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
EM2_0402SE_E_L24_problem_set.indd 178
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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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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
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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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185
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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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187
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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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191
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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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,
,
,
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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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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
204
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10-Dec-21 12:51:37 PM
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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10-Dec-21 12:51:38 PM
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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10-Dec-21 12:51:38 PM
MATH IS EVERYWHERE Do you want to compare how fast you and your friends can run? Or estimate how many bees are in a hive? Or calculate your batting average? Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars. Fueled by your curiosity to understand the world, math will propel you down any path you choose. Ready to get started?
Module 1 Place Value Concepts for Addition and Subtraction Module 2 Place Value Concepts for Multiplication and Division Module 3 Multiplication and Division of Multi-Digit Numbers Module 4 Foundations for Fraction Operations Module 5 Place Value Concepts for Decimal Fractions Module 6 Angle Measurements and Plane Figures
What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York
ISBN 978-1-63898-509-9
9
781638 985099