4
A Story of Units®
Fractional Units LEARN ▸ Module 5 ▸ Place Value Concepts for Decimal Fractions
Student
Talking Tool Share Your Thinking
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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
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related to
?
I heard you say . . . . said . . . . Another way to say that is . . . . What does that mean?
Content Terms
Place a sticky note here and add content terms.
? Why?
What does this painting have to do with math? American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square? On the cover Tahkt-I-Sulayman Variation II, 1969 Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York
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Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2022 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-512-9
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A Story of Units®
Fractional Units ▸ 4 LEARN
Module
EM2_0405SE_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
11/18/2021 4:35:22 PM
EUREKA MATH2 Tennessee Edition
4 ▸ M5
Contents Place Value Concepts for Decimal Fractions Topic A
Topic C
Exploration of Tenths
Comparison of Decimal Numbers
Lesson 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Compare measurements expressed as decimal numbers.
Organize, count, and represent a collection of money.
Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Decompose 1 one and express tenths in fraction form and decimal form.
Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Represent tenths as a place value unit.
Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Use pictorial representations to compare decimal numbers.
Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Compare and order decimal numbers.
Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Write mixed numbers in decimal form with tenths.
Topic D
Topic B
Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Apply fraction equivalence to add tenths and hundredths.
Tenths and Hundredths Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Decompose 1 one and express hundredths in
Addition of Tenths and Hundredths
Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
fraction form and decimal form.
Apply fraction equivalence to add mixed numbers with tenths and hundredths.
Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Represent hundredths as a place value unit.
Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Solve word problems with tenths and hundredths.
Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Write mixed numbers in decimal form with hundredths.
Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 114
Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Represent decimal numbers in expanded form.
2
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11/18/2021 11:05:50 AM
EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TA ▸ Lesson 1
1
Date
For this counting collection, I am partners with We are counting
. .
We think the total amount of the collection is
.
This is how we organized and counted the collection:
The total amount of the collection is An equation that describes how we found the total amount is
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. .
3
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 1
Self-Reflection Write one thing that worked well for you and your partner. Explain why it worked well.
Write one challenge you had. How did you work through the challenge?
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LESSON
5
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TA ▸ Lesson 1
Date
1
1. Explain how you counted your collection.
2. If you counted your collection again, would you choose the same strategy? Explain.
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 2 ▸ Tenths in Decimal Form and Fraction Form
0.2 kg
__ 3 liters
0.6 kg
__ 2 liters
10
10
0.4 kg 8 __ liters 10
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TA ▸ Lesson 2
2
Date
1.
2. Label the number line.
0
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1
11
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0.1 1 tenth
0
0 tenths tenths
tenths
tenths
tenths
tenths
tenths
tenths
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tenths
10 tenths
1
10 10
Name
c. Circle the number written in decimal form that represents the shaded part.
b. Shade the first 8 units of the tape diagram.
a. Label the number line by using fraction form, decimal form, and unit form.
1 10
0 10
1. Use the tape diagram and number line to complete parts (a)–(c).
EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TA ▸ Lesson 2
Date
2
13
11/18/2021 10:02:24 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 2
2. Write the length of the bee in centimeters. The drawing is not to scale.
8
9
10
8
7
11
12
13
14
15
7
1
16
17
6
9
6
18
5
5
19
20 21
4
10
4
22
23
3
3
24
25
26
2
2
27
28
1
11
0 CM 1
29
30
Inch
0 CM 12
a. Fraction form: _____ cm
cm
b. Decimal form:
Write the amount of water in fraction form and decimal form. 4.
3.
1L
1L
_____ L =
14
PROBLEM SET
EM2_0405SE_A_L02_problem_set.indd 14
_____ L =
L
© Great Minds PBC •
L
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11/18/2021 10:02:25 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 2
Write each fraction in decimal form. Shade the bottle to show the correct amount of water. 6.
5.
1L
1L 5 __ L = 10
9 __ L =
L
10
L
Write the total weight of the food in fraction form or decimal form. 8.
7.
kg
0.7 kg
_____ kg
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4 __ kg 10
PROBLEM SET
15
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 2
9.
10.
Flour
0 kg
0 kg
0.5
0.5
kg
kg
Match the equivalent numbers. 11.
2 tenths
0.7
2 10
12.
7 tenths
0.9
5 10
13.
5 tenths
0.2
9 10
14.
9 tenths
0.5
7 10
16
PROBLEM SET
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11/18/2021 10:02:26 AM
EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TA ▸ Lesson 2
2
Date
Write the amount of water in liters.
1L
a. Fraction form:
b. Decimal form:
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L
17
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 3 ▸ Area Models for Tenths
Each area model represents 1. A
B
C
D
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19
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 3
Name
3
Date
Write the decimal fraction as a decimal number. 2. 5 tenths
1. 2 tenths
2 = __ 10
3. 8 tenths
5 = __ 10
8 = __ 10
Write the decimal number as a decimal fraction. 4. 3 tenths 0.1
5. 7 tenths
0.1
0.1
0.3 = _____
© Great Minds PBC •
EM2_0405SE_A_L03_problem_set.indd 21
0.1
0.1
0.1
0.1
6. 9 tenths 0.1
0.7 = _____
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0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.9 = _____
21
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 3
Complete the table. Unit Form 7.
Fraction Form
Decimal Form
1 tenth
How Much to Get to 1?
0.9 4 __
8.
10
9.
6 tenths
10.
0.7
Complete the statements. Write each answer in decimal form. 11. 1 tenth more than 0.2 is 12. 1 tenth less than 0.5 is 13.
is 0.1 more than 0.6.
14.
is 0.1 less than 0.4.
15. 0.6 is
more than 0.5.
16. 0.9 is
less than 1.
22
PROBLEM SET
EM2_0405SE_A_L03_problem_set.indd 22
. .
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11/18/2021 10:03:29 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 3
Name
Date
3
1. Write the decimal fraction as a decimal number.
6 tenths
6 __ = 10
2. Write the decimal number as a decimal fraction.
4 tenths 0.1
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0.1
0.1
0.1
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0.4 = _____
23
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ Sprint ▸ Make 1
Sprint Write the unknown part as a fraction. 1.
_2 + 6
2.
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=1 + _ = 1 0 6
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25
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ Sprint ▸ Make 1
A
Number Correct:
Write the unknown part as a fraction. 1.
1 + 3
_
=1
2.
_
23.
2 + 3
=1
24.
3. 4.
_1 +
6.
2 + 4
10.
3 + 5
27.
=1
28.
3 4
29.
4
30.
_
=1
31.
=1
32.
+ _2 = 1 5
33.
0 5
34.
+ _ = 1
13.
_1 +
14.
6
6
_3 +
15.
=1
35.
=1
36.
+ _4 = 1
_1 +
18.
8
10 __ + 10
10
12
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=1 + _1 = 1 3
_
1 + 2
8
26
=1
__
12 + 12
40.
44.
6 12
5 12
=1
=1
=1
+ __ = 1
8
43.
6 10
__ 2 +
_1 + _1 +
=1
=1
+ __ = 1
39.
42.
5 10
0 __ +
=1
0 8
+ __ = 1
+ __ = 1
6
+ _ = 1 10
10
_1 +
41.
=1
__ 2 +
38.
6 8
+ _ = 1
_
8 + 8
6 6
+ _ = 1
=1 5 8
_1 + _1 +
_4 +
__ 1 +
_
2 + 8
37.
8
19.
8
6
+ _ = 1
17.
22.
=1
+ _ = 1
5
11.
21.
26.
+ 4_ = 1
_1 +
20.
0 3
_
9.
16.
25.
4
7.
12.
3
+ _ = 1
5.
8.
+ _2 = 1
+ 4_ = 1
6
_2 +
10
+ 2_ = 1 6
=1
8
+ _ = 1 3 8
10
10
+ __ = 1 3 10
+ __ 1 + __ 2 = 1
__ 2 +
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=1
6
+ __ 1 + __ 2 = 1
3 __ +
12
=1
12
12
+ __ = 1 5 12
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11/18/2021 4:41:47 PM
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ Sprint ▸ Make 1
B
Number Correct: Improvement:
Write the unknown part as a fraction.
_
=1
_1 +
23.
=1
24.
1.
2 + 3
2.
3
3. 4.
+ _1 = 1 3
25.
3 3
26.
+ _ = 1
5.
_3 +
6.
2 + 4
4
_
=1
27.
=1
28.
7.
+ _1 = 1
8.
0 + = 1 4
30.
=1
31.
=1
32.
4
_
9.
_4 +
10.
2 + 5
5
_
11. 12.
_5 +
14.
3 + 6
=1
35.
=1
36.
+ _2 = 1
18.
8
10
0 __ + 10
10
10
__
10 + 10
12
EM2_0405SE_A_L04_removable_fluency_sprint_make_1_whole.indd 28
3
=1
_ _
8
28
=1
2
40.
44.
7 12
_1 +
=1
=1
+ __ = 1
+ _2 = 1
8
43.
=1
0 __ +
_1 + _1 +
=1
+ __ = 1
__
10 + 12
39.
42.
=1 6 12
=1
8 8
=1 + __ 4 = 1
6
41.
5 10
8 __ +
_2 +
_
=1 + __ = 1
38.
+ _ = 1
9 __ +
8
0 6
+ 2 = 1 8
3 8
_0 +
1 1 + + 6 6
_4 +
=1 + _ = 1
37.
8
19.
8
6
+ _ = 1
_7 +
22.
34.
_
17.
21.
5 5
6
15.
20.
33.
8
_6 +
29.
3 5
+ _ = 1
13.
16.
+ _ = 1
+ 4_ = 1
_3 +
10
6
=1
8
+ _2 = 1 8
+ 2 + 1 = 1 10 10 + __ = 1 3 10
+ __ 2 + __ 1 = 1
5 __ +
© Great Minds PBC •
+ 1_ = 1
__ __
3 __ +
12
=1
12
12
+ __ 2 = 1 12
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11/18/2021 4:41:47 PM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 4
Name
4
Date
Write the number as a mixed number. 1. 1 one 2 tenths 0. 1
1
0. 1
2. 1 one 4 tenths 1
0. 1
3. 2 ones 7 tenths
0.1
0.1
1.4 =
1.2 =
0. 1
1
1
0. 1
0. 1
0. 1
0. 1
0. 1
0. 1
0.1
2.7 =
For problems 4–6, represent the number on the number line by completing the following steps: •
Partition and label the number line.
•
Plot and label the point.
•
Write the number in decimal form.
4. 1 one 3 tenths
3 1 __ = 10
5. 1 one 5 tenths
5 1 __ = 10
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29
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 4
6. 2 ones 9 tenths
9 2 __ = 10
Write the number in expanded form by using decimal form. 7. 1.8 =
+
8. 2.2 =
+
Complete the table.
9.
Unit Form
Fraction Form
1 one 1 tenth
1__ 1 1.6
0.4
9 1 __
11.
10
2 ones 1 tenth
0.9 2.3
13. 8 2 __
14.
30
How Much to Get to the Next One?
10
10.
12.
Decimal Form
10
PROBLEM SET
EM2_0405SE_A_L04_problem_set.indd 30
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11/18/2021 10:05:37 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TA ▸ Lesson 4
Name
4
Date
1. Write the number as a mixed number.
2 ones 6 tenths 1
1
0.1
0.1
0.1
0. 1
0.1
2.6 =
0.1
2. Partition the number line to plot and label the number. Then write the number in decimal form.
1 one 8 tenths
8 1 __ = 10
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5 ▸ Hundredths in Fraction Form and Decimal Form
1 liter
0.07 kg
___ 34 liters 100 1 liter
0.85 kg
___ 7 liters 100 1 liter
0.70 kg
___ 50 liters 100 © Great Minds PBC •
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5
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EM2_0405SE_B_L05_classwork.indd 35
5
1
Date
2.
1.
1
Name
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35
11/18/2021 10:07:05 AM
EUREKA MATH2 Tennessee Edition
36
LESSON
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0
0
1
1
4 ▸ M5 ▸ TB ▸ Lesson 5
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11/18/2021 10:07:05 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5
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EM2_0405SE_B_L05_problem_set.indd 37
1 0
10
0.01 0.00
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5
hundredths hundredth hundredths hundredths hundredths hundredths hundredths hundredths hundredths hundredths hundredths
1 100 0 100
1
1. Label the number line by using fraction form, decimal form, and unit form.
0.10
Date
10 100
Name
37
11/18/2021 10:18:47 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5
Complete the number bond. Write each part as a decimal fraction. 2.
1
0.13
10 100
3.
1
4.
1
38
PROBLEM SET
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100
0.24
0.46
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11/18/2021 10:18:48 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5
Write the weight of the animal in fraction form or decimal form. 6.
5.
7.
kg
0.24 kg
____ kg
___ 68 kg 100
____ kg
Match the equivalent numbers. 8.
4 hundredths
0.14
9.
40 hundredths
0.40
10.
14 hundredths
0.41
11.
41 hundredths
0.04
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0.97 kg
41 ___ 100
14 ___ 100
4 ___ 100 40 ___ 100
PROBLEM SET
39
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 5
Name
Date
5
Write the shaded amount in unit form, fraction form, and decimal form.
1
a. Unit form: b. Fraction form: ____ c. Decimal form:
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11/18/2021 10:16:17 AM
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11/18/2021 10:16:17 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6 ▸ Area Models for Hundredths
Each area model represents 1.
A
B
C
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43
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11/18/2021 10:35:24 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6
Name
6
Date
Write the decimal fraction in decimal form. 1. 8 hundredths
2. 48 hundredths
8 ___ 100 =
___ 48 = 100
4. 70 hundredths
3. 50 hundredths
___ 50 =
70 ___ = 100
100
5. Use division to show ___ = __ . 50 100
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5 10
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6. Use multiplication to show __ = ___ . 7 10
70 100
45
11/18/2021 10:35:15 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6
Write the decimal number in fraction form. 7. 2 hundredths
8. 12 hundredths
0.02 = ____
0.12 = _____
Use the place value disks, unit form, and number bond to answer problems 9 and 10. •
Circle hundredths to compose as many tenths as you can.
•
Complete the unit form.
•
Use the number bond to break apart the tenths from the hundredths.
9.
14 hundredths =
tenth
hundredths
0.14
0.1
46
PROBLEM SET
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11/18/2021 10:35:16 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6
10.
26 hundredths =
tenths
hundredths
0.26
Complete the table. Unit Form 11.
Fraction Form
5 hundredths
12.
tenths
hundredths
13.
tenths
hundredths
14.
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Decimal Form
50 ___ 100
0.25
5 tenths 2 hundredths
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PROBLEM SET
47
11/18/2021 10:35:16 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6
Complete the statements. Write the answer in decimal form. 15. 1 hundredth more than 0.04 is 16. 1 hundredth less than 0.14 is 17.
is 0.01 more than 0.27.
18.
is 0.01 less than 0.07.
19. 0.09 is 20. 0.9 is
48
.
more than 0.08. less than 0.91.
PROBLEM SET
EM2_0405SE_B_L06_problem_set.indd 48
.
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11/18/2021 10:35:16 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 6
Name
6
Date
1. Write the decimal fraction in decimal form.
39 hundredths
39 ___ 100 =
2. Write the decimal number in fraction form.
17 hundredths 0.17 = ____
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EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TB ▸ Lesson 7 ▸ Open Number Line
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 7
Name
Date
7
Write the number in unit form and decimal form. 1.
one
tenths
hundredths =
2.
ones
tenths
ones
hundredths =
hundredths =
3.
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53
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 7
Write the number in unit form and fraction form. 4.
one
tenths
hundredths =
5.
ones
tenths
ones
hundredths =
hundredth =
6.
54
PROBLEM SET
EM2_0405SE_B_L07_problem_set.indd 54
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11/18/2021 10:35:44 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 7
Represent the number on the number line. •
Partition and label the number line.
•
Plot and label the point.
7. 2 ones 3 tenths 7 hundredths
8. 1 one 8 hundredths
Complete the table.
9.
10.
11.
12.
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EM2_0405SE_B_L07_problem_set.indd 55
Unit Form
Fraction Form
1 one 6 tenths 4 hundredths
64 1 ___
ones
tenth
Decimal Form
100
3.17
hundredths
2 ones 9 hundredths
ones
hundredths
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5 5 ___ 100
PROBLEM SET
55
11/18/2021 10:35:44 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 7
Match the equivalent numbers. 13.
6 ones 8 hundredths
6.13
80 6 ___
14.
6 ones 8 tenths
6.03
8 6 ___
15.
6 ones 3 hundredths
6.08
13 6 ___
16.
6 ones 1 tenth 3 hundredths
6.80
3 6 ___
56
PROBLEM SET
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100
100
100
100
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11/18/2021 10:35:44 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 7
Name
Date
7
Write the number in unit form, decimal form, and fraction form. a.
Unit form:
one
tenths
hundredths
Decimal form: Fraction form:
b.
Unit form:
ones
tenths
hundredths
Decimal form: Fraction form:
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57
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11/18/2021 10:35:33 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 8
Name
8
Date
Write an expression to show the total value of the place value disks. Use unit form. 1.
2.
Write an expression to show the total value of the place value disks. Use decimal form. 3.
3 ones
6 tenths +
4 hundredths +
4.
2 tens
8 hundredths +
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59
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 8
Write each number in expanded form. Use decimal form or fraction form. 5. 3 ones 2 tenths
6. 5 ones 4 tenths 9 hundredths
7. 1 ten 3 tenths 3 hundredths
8. 3 tens 1 one 8 hundredths
Write the value of each digit. Use decimal form. 9.
60
10.
PROBLEM SET
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11/18/2021 10:58:19 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 8
Use the place value chart to complete each statement. Express the value of each digit in decimal form. 11.
tens
ones
tenths
hundredths
9
2
5
a. The digit
is in the ones place. It has a value of
b. The digit
is in the tenths place. It has a value of
c. The digit
is in the hundredths place. It has a value of
12.
tens
ones
tenths
hundredths
4
0
7
6
. .
a. The digit 4 is in the
place. It has a value of
.
b. The digit 0 is in the
place. It has a value of
.
c. The digit 7 is in the
place. It has a value of
.
d. The digit 6 is in the
place. It has a value of
.
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PROBLEM SET
61
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11/18/2021 10:58:20 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TB ▸ Lesson 8
Name
8
Date
1. Use the place value chart to complete each statement. tens
ones
tenths
hundredths
7
4
9
a. The digit
is in the ones place. It has a value of
b. The digit
is in the tenths place. It has a value of
c. The digit
is in the hundredths place. It has a value of
. . .
2. Write 7.49 in expanded form. Use unit form, decimal form, or fraction form.
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63
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11/18/2021 10:58:08 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9 ▸ Blank Tape Diagrams, Area Models, and Number Line
1
1
1
Each area model represents 1.
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9
Name
9
Date
Write the lengths of the shaded parts in decimal form. Then complete the statement.
1 meter
1.
meters
1 meter meters meters is longer than
meters.
1 meter
2.
meters
1 meter meters meters is shorter than
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meters.
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67
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9
3. Use the scales to complete parts (a)–(c). Grapes
Lettuce
Carrots
Bananas
0 kg
0 kg
0 kg
0 kg
0.5
0.5
0.5
0.5
0.17 kg
0.41 kg
0.4 kg
0.71 kg
a. Write an X over the items that are lighter than the lettuce. b. Write the mass of each item in the table. Mass of Food (kilograms)
Food Grapes Lettuce Carrots Bananas
c. Complete the statements by using the words heavier than or lighter than. The grapes are The lettuce is
68
PROBLEM SET
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the bananas. the carrots.
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11/18/2021 10:58:38 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9
4. Use the graduated cylinders to complete parts (a) and (b).
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EM2_0405SE_C_L09_problem_set.indd 69
A
B
C
1L
1L
1L
0.86 L
0.2 L
0.8 L
D
E
F
1L
1L
1L
0.35 L
0.18 L
0.5 L
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PROBLEM SET
69
11/18/2021 10:58:38 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9
a. Complete the table by writing the liquid volume of the water in each graduated cylinder. Cylinder
Liquid Volume of Water (liters)
A B C D E F
b. Circle the larger amount of water.
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0.2 L
0.18 L
0.35 L
0.5 L
0.8 L
0.86 L
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11/18/2021 10:58:38 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 9
Name
9
Date
Use the scales to complete parts (a) and (b).
A
B
C
0 kg
0 kg
0 kg
0.5
0.5
0.5
0.15 kg
0.48 kg
0.32 kg
a. Write the mass of each package in the table. Package
Mass of Package (kilograms)
A B C b. Complete the statements by using the words heavier than or lighter than. Package A is
package B.
Package B is
package C.
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71
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EUREKA MATH2 Tennessee Edition
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4 ▸ M5 ▸ TC ▸ Lesson 10 ▸ Area Models and Number Line
73
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11/18/2021 11:03:08 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 10
Name
10
Date
Use >, =, or < to compare the numbers. Shade the area models to help you. Each square represents 1. 1. 0.26
0.2
2. 0.80
0.8
Use >, =, or < to compare the numbers. 3.
0.1
0.1
0.1
0.1
0.1
0.01
0.5
4.
1
0.1
0.1
0.1
0.01
0.01
EM2_0405SE_C_L10_problem_set.indd 75
0.01
0.05
0.01
0.01
0.01
0.01
0.01
0.01
0.01
1.37
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0.01
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1
0.1
0.1
0.1
0.1
0. 1
0. 1
0.1
0.01
0.01
0.01
1.73
75
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 10
Use >, =, or < to compare the numbers. Locate the numbers on the number line to help you. 5. 6.03
6.3
6.0
6. 15.68
6.1
6.2
6.3
15.7
15.8
15.9
15.8
15.6
Use >, =, or < to compare the numbers. 7. 0.79
0.9
8. 0.41
0.38
9. 1.85
1.92
10. 1.06
1.6
11. 7.23
7.32
12. 3.5
3.50
13. 34.9
34.19
14. 25.28
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PROBLEM SET
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25.2
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11/18/2021 11:03:00 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 10
Name
10
Date
1. Use >, =, or < to compare the numbers. 0.1
0.1
0.1
0.01
0.01
0.32
0.1
0.1
0.01
0.01
0.01
0.23
2. Use >, =, or < to compare the numbers. Locate the numbers on the number line to help you.
4.2
4.0
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4.02
4.1
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4.2
4.3
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EUREKA MATH2 Tennessee Edition
8.2
A
0.49
A
7.2
A
8.04
A
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31 ___ 2
4 ▸ M5 ▸ TC ▸ Lesson 11 ▸ Comparison Cards
B
2.1
B
1.09
B
2 __ 1 10
B
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 11
Name
11
Date
1. Use the scales to complete parts (a)–(c).
Rice
Rice
Rice
Rice
0 kg
0 kg
0 kg
0 kg
0.5
0.5
0.5
0.5
0.13 kg
0.3 kg
0.25 kg
0.1 kg
a. Plot numbers to represent the weight of each bag of rice. Label each point.
0
0.1
0.2
0.3
b. Use >, =, or < to compare the numbers.
0.3
0.1
0.13
0.25
0.25
0.3
c. List the numbers from least to greatest.
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81
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 11
2. Use the numbers to complete parts (a)–(c).
1.2, 1.18, 1.02, 1.28 a. Plot and label the numbers.
1.0
1.1
1.2
1.3
b. Use >, =, or < to compare the numbers.
1.18
1.28
1.02
1.18
1.2
1.02
c. List the numbers from greatest to least.
Arrange the numbers from least to greatest. 3. 2.5, 0.85, 2.8, 2.05
4. 1.31, 13.01, 1.3, 13.1
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PROBLEM SET
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11/18/2021 11:03:25 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 11
List the numbers from greatest to least. 49 __6 ___ 5. 6.08, 5 , 4.95, 6.2, 5 10 100
37 7 ___ __1 ___ 6. 43 , 71.04, 70 , 7 , 47.3 100 10 100
7. Four students record the weights of their rocks, as shown in the table. Jayla
__
13 kg 10
Tom
Amy
Shen
1.38 kg
1 and 4 tenths kg
104 kg 100
___
a. Whose rock is the lightest?
b. Jayla says her rock weighs more than Amy’s because 13 tenths is greater than 4 tenths. Do you agree? Explain.
c. List the weights of the rocks from the lightest to the heaviest.
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PROBLEM SET
83
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 11
8. Eva records her 100-meter dash times for the week. On Monday, she runs the dash in 16.01 seconds. On Tuesday, she runs it in 15.58 seconds. On Wednesday, she runs it in 15.56 seconds. On Thursday, she runs it in 16.1 seconds. a. On which day does Eva run the fastest?
b. Arrange Eva’s times from the slowest to the fastest.
84
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11/18/2021 11:03:26 AM
EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TC ▸ Lesson 11
Name
Date
11
Use the numbers to complete parts (a) and (b).
2.36, 2.5, 2.05, 2.46 a. List the numbers from least to greatest.
b. Use >, =, or < to compare the numbers.
2.36 2.5
2.05
2.46
2.5
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2.46
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85
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TD ▸ Lesson 12
Date
12
Add.
2 ___ 10 + 100 4 1. __
2. ___ 48 + __ 3 100 10
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87
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TD ▸ Lesson 12
Name
12
Date
Add. 1. 1 hundredth + 7 hundredths =
2. 6 hundredths + 3 hundredths =
hundredths
hundredths
3. 14 hundredths + 72 hundredths =
hundredths
4. 61 hundredths + 35 hundredths =
hundredths
Add. Shade the area model to help you. 5. __ 1 + ___ 4 = _____ + _____ 10 100 100 100
6. ___ 27 + __ 3 100 10
= _____ 100
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4 ▸ M5 ▸ TD ▸ Lesson 12
Add. Use the number line to help you.
4 + ___ 7 7. __ 10 100
8. __ 4 + ___ 17 10 100
90
PROBLEM SET
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EUREKA MATH2 Tennessee Edition
Add.
4 ▸ M5 ▸ TD ▸ Lesson 12
9 + ___ 2 9. __ 10 100
10. ___ 7 + __ 4 100 10
11. __ 2 + ___ 9 10 100
12. ___ 37 + __ 4 100 10
13. __ 3 + ___ 40 10 100
14. ___ 60 + __ 4 100 10
3 67 15. Miss Diaz walks ___ kilometers to the library. Then she walks __ kilometers to the gym. 100
How many kilometers does Miss Diaz walk altogether?
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10
PROBLEM SET
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TD ▸ Lesson 12
Date
12
Add.
5 + ___ 7 1. __ 10 100
2. ___ 25 + __ 6 100 10
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EUREKA MATH2 Tennessee Edition 4 ▸ M5 ▸ TD ▸ Lesson 13 ▸ Methods Recording Page
=
=
Method 1
Method 2
Method 3
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Name
4 ▸ M5 ▸ TD ▸ Lesson 13
Date
Add.
6 2 + 3 __ 1. 1 __ 10 10
25 64 2. 1 ___ + 3 ___ 100 100
3. __ 7 + ___ 21 10 100
83 4. ___ + __ 7 100 10
7 5. 1 __ + ___ 51 10 100
83 6. __ 6 + 1 ___ 10 100
46 4 7. 1 __ + 3 ___ 10 100
96 4 8. 1 __ + 3 ___ 10 100
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13
97
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4 ▸ M5 ▸ TD ▸ Lesson 13
6 64 9. 3 __ + 3 ___ 10 100
85 2 10. 3 ___ + 4 __ 100 10
98 8 11. Zara and David find the sum of 4 ___ and 5 __ . Who made a mistake? Explain. 100
10
Zara’s Work 98
8
78
9 100 + 10 = 10 100 2 100
98
PROBLEM SET
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78 100
David’s Work 98
8
6
9 100 + 10 = 10 10 2 10
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6 10
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EUREKA MATH2 Tennessee Edition
Name
Add. 1.
4 ▸ M5 ▸ TD ▸ Lesson 13
Date
13
__3 + ___ 98 10
100
57 7 2. 4 ___ + 1 __ 100 10
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4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions
Sprint Write the unknown numerator or denominator. 1. 2. 3. 4.
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1_ = ___ 6
3 9 3_ = ___ 4
_3 = ___ 2 6 3 6 __ = ___ 10
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions
A
Number Correct:
Write the unknown numerator or denominator. 2_3 = ___ 9
1.
1_2 = ___ 4
21.
2.
1_3 = ___ 9
22.
_4 = ___
4_5 = ___ 10
3
6
3.
3 _1 = ___ 4
23.
4.
2 1_5 = ___
24.
4_6 = ___
5.
_1 = ___ 6 12
25.
2 __ = ___ 10 100
6.
2_3 = ___ 6
26.
3_ ___ 6 = 2
7.
2_4 = ___ 8
27.
2 _4 = ___ 6
__ = ___ 12 3
8
8.
9 _3 = ___ 4
28.
9.
_5 = ___
29.
__ = ___ 12
10.
_6 = ___ 12
30.
___ = ___ 100 10
11.
2_4 = ___ 2
31.
1_2 = ___
12.
2_6 = ___ 3
32.
1_3 = ___
3
6
3
8
10
5
30
3 3
13.
__ = ___ 1 12
33.
14.
__ 2 = ___ 1
1_2 = ___ 8
10
34.
__ = ___ 12 4
15.
2 __ = ___ 12 6
35.
2_4 = ___
16.
4_6 = ___ 3
36.
__ = ___ 1 10
37.
__ = ___ 10 100
3
9
6
5
18.
_6 = ___ 3 9 9 3 __ 12 = ___
19.
4 2 __ = ___ 10
39.
__ = ___ 10
20.
8 __ = ___
40.
___ = ___ 100
17.
12
6
102
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38.
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6
___ = ___ 100 10 40 7
90
70 9
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ Sprint ▸ Equivalent Fractions
B
Number Correct: Improvement:
Write the unknown numerator or denominator. 1.
1_2 = ___ 2
21.
2.
1_3 = ___
22.
3.
_1 = ___ 4 12
23.
3_ ___ 4 = 8 8 _4 = ___ 5
24.
4_6 = __ 12
3
5.
_1 = ___ 5 10 1_6 = ___ 2
6.
4.
2_3 = ___ 6
25.
2 __ = ___ 10
4 2_3 = ___
26.
_6 = ___ 1
7.
4 2_4 = ___
27.
8.
3_ ___ 4 = 12
28.
_4 = __ 3 6 8 2 __ = ___ 12
29.
__ = ___ 12 6
10.
_3 = ___ 5 10 3_ ___ 6 6 =
11.
9.
20
3
10
30.
30 3 ___ = ___
1 _2 = ___ 4
31.
2 1_2 = ___
12.
1 2_6 = ___
32.
2 _1 = ___ 3
13.
__ = ___ 12 4
33.
4 _1 = ___
14.
__ 2 = ___
34.
9 3 __ = ___
15.
2 __ = ___ 1 12
35.
16.
2 _4 = ___ 6
_2 = __ 4 12
36.
17.
_9 = ___ 2
__ = __ 10 2
37.
__ = ___ 10
18.
__ = ___ 12 4
38.
4 ___ = ___ 100
19.
__ 4 = ___
39.
20.
3
10
5
6
9
5 10 8 __ = ___ 4 12
104
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40. © Great Minds PBC •
100
2
12
5 6
60
40
__ = ___ 10 100 7
___ = ___ 100 10 90
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TD ▸ Lesson 14
Date
14
Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number. A wall in Mrs. Smith’s living room is 0.78 meters longer than a wall in her bedroom. The wall in Mrs. Smith’s bedroom is 4.32 meters long. How long is the wall in her living room?
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TD ▸ Lesson 14
Date
14
Use the Read–Draw–Write process to solve each problem. Write the solution statement by using a decimal number. 1. Mr. Endo’s chicken drink 5.6 liters of water on Monday. They drink 6.17 liters on Tuesday. In total, how many liters of water do the chickens drink on both days?
2. A watermelon weighs 4.79 kilograms. A pineapple weighs 1.4 kilograms. What is the combined weight of the watermelon and pineapple?
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TD ▸ Lesson 14
3. A sheep is 1.17 meters long. A pig is 0.47 meters longer than the sheep. What is the length of the pig?
4. Gabe solves a magic cube puzzle in 7.64 seconds. That is 4.93 seconds faster than the time it takes his brother to solve the puzzle. How long does it take Gabe’s brother to solve the puzzle?
108
PROBLEM SET
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EUREKA MATH2 Tennessee Edition
4 ▸ M5 ▸ TD ▸ Lesson 14
5. Robin jogs 5.3 kilometers on Saturday. She jogs 1.85 kilometers more on Sunday than she jogs on Saturday. How many kilometers does Robin jog on Sunday?
6. Pablo has 4 one-dollar bills, 3 dimes, and 9 pennies. Mia has 4 one-dollar bills and 4 pennies. How much money do they have altogether?
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PROBLEM SET
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EUREKA MATH2 Tennessee Edition
Name
4 ▸ M5 ▸ TD ▸ Lesson 14
Date
14
Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number. Miss Diaz’s class drinks 2.9 liters of juice. Mrs. Smith’s class drinks 3.15 liters of juice. How many liters of juice do both classes drink altogether?
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4 ▸ M5
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; 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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4 ▸ M5
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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12/2/2021 9:56:44 AM
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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11/20/2021 12:41:06 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 978-1-63898-512-9
9
781638 985129