Eureka Math2 Tennessee | Apply Grade 5 Module 4

5

A Story of Units®

Fractions Are Numbers APPLY ▸ Module 4 ▸ Place Value Concepts for Decimal Operations

Student

A Story of Units®

Fractions Are Numbers ▸ 5 APPLY

Module

1 2 3 4 5 6

Place Value Concepts for Multiplication and Division with Whole Numbers

Addition and Subtraction with Fractions

Multiplication and Division with Fractions

Place Value Concepts for Decimal Operations

Addition and Multiplication with Area and Volume

Foundations to Geometry in the Coordinate Plane

Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4

Contents Place Value Concepts for Decimal Operations Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Understanding Decimal Numbers with Place Value and Fraction Thinking

Subtract decimal numbers by using different methods.

Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Model and relate decimal place value units to thousandths.

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Subtract decimal numbers by using place value understanding.

Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Represent thousandths as a place value unit.

Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Represent decimal numbers to the thousandths place in different forms.

Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Relate the values of digits in a decimal number by using place value understanding.

Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Multiply and divide decimal numbers by powers of 10.

Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Compare decimal numbers to the thousandths place.

Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Round decimal numbers to the nearest one, tenth, or hundredth.

Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Round decimal numbers to any place value unit.

Topic B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Addition and Subtraction of Decimal Numbers Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Add decimal numbers by using different methods.

Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Solve word problems involving addition and subtraction of decimal numbers and fractions.

Topic C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Multiplication of Decimal Numbers Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Multiply decimal numbers to hundredths by one-digit whole numbers by using different models.

Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Multiply decimal numbers to hundredths by one-digit whole numbers and multiples of 10, 100, or 1,000 by using different written methods.

Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Multiply decimal numbers to hundredths by two-digit whole numbers by using area models and vertical form.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Multiply decimal numbers to hundredths by two-digit whole numbers by using different methods.

Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Relate decimal-number multiplication to fraction multiplication.

Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Multiply a decimal number by a decimal number.

Add decimal numbers by using place value understanding. © Great Minds PBC •

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EUREKA MATH2 Tennessee Edition

5 ▸ M4

Topic D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Division of Decimal Numbers Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Divide decimal numbers to hundredths by one-digit whole numbers and multiples of 10, 100, or 1,000 by using unit form and place value understanding.

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Divide decimal numbers to hundredths by one-digit whole numbers and multiples of 10, 100, or 1,000 by using place value understanding and vertical form.

Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Divide decimal numbers to hundredths by two-digit whole numbers.

Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Relate division by 0.1 and 0.01 to division by a unit fraction.

Lesson 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Divide decimal numbers by decimal numbers, resulting in whole-number quotients. (Optional)

Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Divide decimal numbers by decimal numbers, resulting in decimal-number quotients. (Optional)

Topic E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Applications of Decimal Numbers Lesson 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Solve a real-world problem involving metric measurements.

Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Convert metric measurements involving decimals.

Lesson 28. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Convert customary measurements involving decimals.

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 171

2

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Module 4 Topic A

FAMILY MATH Understanding Decimal Numbers with Place Value and Fraction Thinking Dear Family,

Your student is learning that the place value unit thousandths Key Term is made by decomposing 1​ ​​ ​hundredth into ​​10​​equal parts. thousandths Students represent decimal numbers to thousandths by using models. They also name decimal numbers to thousandths in unit form, fraction form, decimal form, standard form, and expanded form, as well as expanded notation. Your student describes the relationships between place value units as ​​ 1 10​​ times as much as the next smaller unit and __ ​​ ​​ as much as the next larger unit. This helps 10 students multiply and divide decimal numbers by powers of 10​ ​​ ​. Students also use place value to compare the value of digits in decimal numbers and to round to any place value. Students recognize that the thinking and reasoning used to multiply, divide, compare, and round whole numbers are the thinking and reasoning used to multiply, divide, compare, and round decimal numbers.

ones

tenths

hundredths thousandths

× 10

16 thousandths

16 0.016 1,000 sixteen thousandths

1 hundredth 6 thousandths 16 0.016 1,000 sixteen thousandths

Composing 10 thousandths makes 1 hundredth, and decomposing 1 hundredth makes 10 thousandths.

Decimal numbers can be written in the same forms as other numbers. ones

tenths

​​3​hundredths is 10​ ​​ ​times as much as ​​ 3​​ thousandths.

0​ .​0​ 3​​ = 1​ 0​ × 0​​ .​0​ 03​

hundredths thousandths

×1

10

__

1 ​​3​​thousandths is ​​ ​​ as much as 3 hundredths.

10 1 0​ .​0​ 03​ = 10 ​​ ​​ × 0 ​ .​0 ​ 3​ © Great Minds PBC •

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__

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA

At-Home Activities Calculator Patterns Using a calculator, help your student explore how multiplying and dividing by powers of 10​ ​​ ​ changes the value of a digit. First, have your student enter a one-digit number, such as 3​ ​​ ​, ​​ ​. Then, have them divide by 10​ ​​ ​ on the calculator. Next, have them multiply by 10​ ​​ ​to get 30​ ​​ ​again to get 0​ ​​ .3 ​ ​. Discuss how the value of once to get back to ​​3​​. Finally, have them divide by 10​ 1 ​​ ​​ the digit changes each time. Help your student use the language 10​ ​​ ​ times as much as and __ 10 as much as to describe the changes. Encourage your student to continue experimenting with multiplying or dividing by ​​10​​and describing the changes in the value of digits.

Shop-A-Round Find prices of various items at the store or in an advertisement. Begin by asking your student to round the prices to the nearest whole dollar, and then to the nearest tenth of a dollar, or ​​10​​ cents.

•

​ 9​​rounded to the nearest dollar?” (​$​4​.0 ​ 0​​) “What is ​$​3​.7

•

​ 9​​rounded to the nearest tenth of a dollar, or 10​ ​​ ​cents?” (​$​3​.​80​​) “What is ​$​3​.7

To offer more practice, complete this activity again with different prices.

4

FA M I LY M AT H ▸ Module 4 ▸ Topic A

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 1

Name

1

Date

1. Use the area model to complete parts (a) and (b). The area model represents 1.

The area model represents ​1​ whole and each shaded area represents part of the whole.

I see the model is divided into 100 equal parts. Each part represents 1 hundredth, written as ____ ​​ 1 ​​ or 0.01.

100

a. The shaded area represents ​5​ thousandths . b. Express the shaded area in fraction form and decimal form.

5 ____ ​​ ​​ = 1,000

Each hundredth is divided into 10 equal parts. Each of these smaller parts represents 1 thousandth, written as _____ ​​ 1 ​​ or 0.001.

1,000

I see 5 thousandths shaded.

5 This is written as ​​ _____ ​​ or 0.005.

1,000

0.005

2. Use the place value disks shown to complete the statements and equations.

1 tenth is

10

times as much as ​1

1 tenth =

10

× 1 hundredth .

hundredth ​ .

1 hundredth is ___ ​​ ​​ as much as 1 tenth .

1

10

1 hundredth =

1 __ ​​ ​​ 10

× 1 tenth .

The place value disks show that 1 tenth = 10 hundredths.

That means that 1 tenth is 10 times as much as 1 hundredth.

I can also describe this 1 relationship by using ​​ __ ​​ .

10

1 1 hundredth is ​​ __ ​​ as much as 10 1 tenth.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 1

3. Express the amount of water in the container in fraction form and decimal form.

0.01

The container is labeled 0.01 at the top. This means that it holds 0.01 of a unit.

4

_____ ​​ ​​ =

0.004

1,000

I see 10 equal parts. Each part represents 0.001 because 1 0.001 = ​​ __ ​​ × 0.01. This can also be 10 1 written as 1 thousandth or ​​ _____ ​​ .

1,000

The container is filled to the fourth mark. This represents 4 thousandths.

REMEMBER 4. Add. Show your thinking.

1 ​​ __ ​​ + 2 ​​ __ ​​ 12 12 11

6

1 11 + 12 1 12

4 ​​ __ ​​ 12 5

2

5 + 2 12

4

5 12

I use the arrow way to show how to add.

11 __ 1 ​​ is ​​ 1 ​​ away from 2. I add ​​ __ ​​ from I know that 1 ​​ __ 12 12 12 the other addend to get 2.

I add what is left over from the other addend: __5 ​​ = 4 ​​ __5 ​​ .

2 + 2 ​​ 12 12

6

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 1

5. Subtract. Show your thinking.

8 ​​ __ ​​ − 2 ​​ __ ​​ 12 12 5

9 212

I write a related addition problem with an unknown part.

9

3 + 12

3

+5

8

5 + 12

5 ​​ __ ​​ 12

9 5 ​2 ​ __ ​​ + = ​8 ​ __ ​​ 12 — 12

5 812

9 5 I count on from ​2 ​ __ ​​ to 8 ​ ​ __ ​​ to find the 12 12 difference.

8

9 3 •I add ​​ __ ​​ to ​2 ​ __ ​​ to get to the benchmark 12 12

number 3.

•I add 5 to get to 8.

5 5 •Then, I add ​​ __ ​​ to get to 8 ​ ​ __ ​​ .

12 12

To find the difference, I add the parts I counted on.

8 5 __ ​​ = 5 ​ ​ __ ​​ ​​ 3 ​​ + 5 + ​​ __ 12

12

12

6. Complete the equation and statement. Then represent the equation with a number line.

_​​ 3​​ = _​​ 1​​ + _​​ 1​​ + _​​ 1 ​​ 6 6 6 6 1 3 ​​ _​​ = 3 × __ ​ ​ 6

6

6

third

_​​ 3​​ is the 0

multiple of

__​​ 1 ​​ 6

.

3 6

I write the addition equation as ­multiplication. The addition ­equation shows ​​ __61 ​​ added 3 times. ​​ __63 ​​ = 3 × ​​ __61 ​​

My multiplication equation shows that ​​ __63 ​​ is the third multiple of ​​ __61 ​​ .

I draw a tick mark on the n ­ umber line and label it 0. I represent __ ​​ 63 ​​ on the number line by drawing 3 e ­ qually spaced tick marks. The length ­between tick marks is __6​​ 1 ​​ . I shade the number line from 0 to __ ​​ 63 ​​ to ­represent the equation ​​ __63 ​​ = 3 × __6​​ 1 ​​ .

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P R ACT I C E PA R T N E R

7

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 1

Name

1

Date

1. Use the area model to complete parts (a) and (b). The area model represents 1. a. The shaded area represents 1

.

b. Express the shaded area in fraction form and decimal form.

____ =

2. Use the place value disks shown to complete the statements and equations.

1 hundredth is ​

times as much as 1

1 hundredth =

×1

. 1 thousandth is ___ ​​ ​as much as 1

1 thousandth =

.

×1

3. Express the amount of water in the container in fraction form and decimal form.

0.01

_____ ​​ ​​ = ​

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 1

REMEMBER 4. Add. Show your thinking.

1 ​ _8 ​+ 1 ​ _8 ​ 7

6

​ 5. Subtract. Show your thinking.

4 ​ __ ​ − 1 ​ __ ​ 10 10 4

8

6. Complete the equation and statement. Then represent the equation with a number line.

_​ 8​ = _​ 1​ + ​ _1​ + ​ _1​ + ​ _1​ + ​ _1​ + ​ _1​ + ​ _1​ + ​ _1​ 6 6 6 6 6 6 6 6 6 _​ 8​= __ × ​ 6 ​ 6 8 ​​ _​​ is the multiple of 6

10

P R ACT I C E

.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 2

Name

Date

2

1. Write the number in decimal form.

384 thousandths

I see ​3​columns completely shaded.

That represents 3 ​ 00​ thousandths.

I also see 8 ​ 0​ more thousandths ­shaded in the next column.

I see ​4​thousandths shaded in the zoomed-in square.

384 ____ ​​ ​​ = 1,000

There are ​384​thousandths shaded ­because ​300 thousandths + 80 thousandths + ​​4 thousandths​ ​=​ ​ 384 thousandths​.

0.384

I write ​384​thousandths in decimal form as ​0.384​.

I see ​1​place value disk for ones, or ​1​one (​1 ​).

I see ​7​place value disks for​​tenths, or ​7​ tenths (​0.7​).

I see ​2​place value disks for hundredths, or ​2​hundredths (​0.02​).

I see ​4​place value disks for thousandths, or ​4​thousandths (​0.004​).

I represent this number in decimal form as ​1 .724​.

2. Write the unit form and decimal form of the number the place value disks show.

1 one 7 tenths 2 hundredths 4 thousandths = 1.724 © Great Minds PBC •

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11

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 2

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

__5

__7

3. Toby has a container with 4 ​​ 12 ​​ cups of rice. He uses 1 ​​ 12 ​​ cups of rice when he cooks dinner.

How many cups of rice are left in the container?

4 ​​ __ ​​ − 1 ​​ __ ​​ = 2 ​​ __ ​​ 12 12 12 5

10

7

10 __

There are 2 ​​ 12 ​​ cups of rice left in the container.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the total, 4 __ ​5 ​cups of rice.

12 I draw one part in the tape diagram to represent the 1 __ ​7 ​cups 12 of rice Toby uses for dinner. The other part, which represents the amount of rice left in the container, is unknown.

4 1

5 12

7 12

?

I subtract to find how much rice is left in the container.

5 4 ​__ ​− 1 __ ​7 ​ 12 12

7 I subtract the whole numbers. Then, I subtract ​__ ​. I use a number 12 5 __ bond to decompose 3 12 ​ ​so I can subtract from 1.

4

5 7 5 7 10 - 1 =3 - =2 12 12 12 12 12

2

5 12

1

10 There are 2 ​__ ​cups of rice left in the container.

12

12

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 2

4. Blake measures the weights of ​10​ eggs and lists the data in a table. a. Use the data in the table to create a line plot.

Egg

Weight (ounces)

A

2 ​​ _8 ​​ 4

B

C

D

2 ​​ _82 ​​

2 ​​ _8 ​​ 6

E

F

2 ​​ _8 ​​

2 ​​ _82 ​​

G

2 ​​ _8 ​​

7

6

5

I

2 ​​ _8 ​​

2 ​ _8 ​

2 ​​ _8 ​​

7

H

6

J

2 ​​ _84 ​​

Weights of Eggs

× × 0

2

1

2

3

× × 4

×

× × ×

× ×

5

6

7

28 28 28 28 28 28 28

3

Weight (ounces)

b. What is the combined weight of the two lightest eggs?

​4 ​ _8 ​​ounces 4

First, I create a scale for the line plot. The lightest egg 2 7 is 2 ​​ __ ​​ ounces. The heaviest egg is 2 ​​ __ ​​ ounces. So, I know 8 8 that all the data values on the line plot are between 2 and 3.

0

2

3

The data in the table are mixed numbers with eighths as the fractional unit. I partition the interval into eighths.

0

2

1

2

3

4

5

6

7

28 28 28 28 28 28 28

3

I look at each data point, one at a time, and mark an X for each measurement on the line plot. I write a title and a label for the line plot.

I look on the line plot for the weights of the two lightest eggs.

2 I see two marks at 2 ​​ __ ​​. I add to find the combined weight.

8 2 2 2 ​​ __ ​​ + 2 ​​ __ ​​ = 4 ​​ __ ​​ 8 8 8 4

The combined weight of the two lightest eggs is 4 ​​ __ ​​ ounces.

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P R ACT I C E PA R T N E R

13

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 2

Name

Date

2

Write the number in decimal form.

1. 7 ​ ​ thousandths

2. ​45​ thousandths

7 ____ ​​ ​= ​

45 ____ ​​ ​​ =

1,000

1,000

3. ​236​ thousandths

4. ​452​ thousandths

236 ____ ​​ ​​ =

452 ____ ​​ ​​ =

1,000

1,000

5. Write the unit form and decimal form of the number the place value disks show.

one © Great Minds PBC •

tenths

hundredths

thousandths =

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 2

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

__9

__7

6. Yuna wants to dive to a depth of 16 ​​ 12 ​​ feet. She dives to a depth of 14 ​​ 12 ​​ feet. How many more feet does Yuna need to dive to reach her goal?

7. Leo measures the amount of milk produced by 10 cows and lists the data in a table. a. Use the data in the table to create a line plot.

Cow

A

B

C

D

E

F

G

H

I

J

Milk (liters)

3 ​​ _2 ​​

​3​

4 ​​ _2 ​​

​5​

4 ​​ _2 ​​

​4​

3 ​​ _2 ​​

​4​

4​ ​

3 ​​ _2 ​​

1

1

1

1

1

_1

b. How much milk is produced altogether by the cows that produce 4 ​​ 2 ​​ liters of milk?

16

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 3

Name

3

Date

1. Use the place value disks shown to complete parts (a)–(f).

a. The place value disks represent the number b. The digit

3

32.154 .

c. The digit 2 is in the ones place. It has a value of d. The digit

1

30 .

is in the tens place. It has a value of

2

.

is in the tenths place. It has a value of 0.1 .

e. The digit 5 is in the hundredths place. It has a value of 0.05 . f.

The digit

4

is in the thousandths place. It has a value of 0.004 .

I see ​3​ tens ​2​ ones ​1​ tenth ​5​ hundredths ​4​ thousandths.

I use the place value disks to help me find the value of each digit in the number ​32.154​.

For example, the digit ​3​ is in the tens place. I look at the tens place value disks.

The value of ​3​ tens is ​30​.

2. Use the place value chart shown to complete parts (a)–(e). Express the value of each digit in decimal form. tens

ones

tenths

5

8

2

a. The digit

2

hundredths thousandths

9

3

is in the tenths place. It has a value of

b. The digit 8 is in the ones place. It has a value of

0.2

8

.

50

I use the place value chart to help me find the value of each digit in the number 58.293.

For example, the digit 9 is in the hundredths place in the number and on the . place value chart. The value of 9 hundredths 9 ​​ or 0.09. is ​​ ____ 100

c. The digit

5

is in the tens place. It has a value of

d. The digit

3

is in the thousandths place. It has a value of 0.003 .

.

e. The digit 9 is in the hundredths place. It has a value of 0.09 . © Great Minds PBC •

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17

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 3

3. Represent 73.052 in two different ways by using expanded form or expanded notation.

Sample:

70 + 3 + 0.05 + 0.002

____​​ 7 × 10 + 3 × 1 + 5 × ​​ ___ ​​ + 2 × ​​ 1,000 100 1

1

I write the number in expanded form by using addition, where each addend represents the value of one digit.

For example, to represent 73.052, I write 70 + 3 + 0.05 + 0.002.

I write the number in expanded notation by representing the value of each digit by using multiplication.

For example, to represent the value of the digit 5 in 73.052, I write 5 × 0.01.

REMEMBER

Acute angles are less than 9 ​ 0°​.

4. Use the trapezoid to complete parts (a) and (b).

W

X

Y

Each of the measures of ∠ ​ W​and ​∠Z​ is less than ​9 0°​.

Obtuse angles are greater than ​9 0°​.

Each of the measures of ​∠X​ and ​∠Y​ is greater than ​9 0°​.

a. Name the acute angles shown in the trapezoid. ​∠W​and ​∠Z​ b. Name the obtuse angles shown in the trapezoid. ​∠X​and ​∠Y​

Z 18

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EUREKA MATH2 Tennessee Edition

5. Multiply.

3 × 2 __ 6 2 3 × ​​ __​​ = ____ ​​ ​​ = ​​ ​​ 10

10

10

5 ▸ M4 ▸ TA ▸ Lesson 3

I use unit form and the associative property to ­multiply a whole number by a fraction.

I write __ ​​ 2 ​​ in unit form as 2 tenths.

10

3 × 2 tenths

I use the associative property to group 3 × 2.

(3 × 2) tenths I find 3 × 2 and the units stay the same, tenths.

(3 × 2) tenths = 6 tenths I write the equation in fraction form.

2 3 × 2 __ 6 3 × ​​ __ ​​ = ​​ _____ ​​ = ​​ 10 ​​ 10 10

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

__3

​​ ​​ pints of juice. How many pints of juice does 6. Adesh pours 6 glasses of juice. Each glass holds 12 Adesh pour in all?

__ 6 × ​__ ​ 12 ​​ = ​​ 12 ​​ 3

18

_1

Adesh pours 1​​ 2 ​​ pints of juice in all.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with 6 parts to represent the 6 glasses 3 ​​ because Adesh pours __ ​​ 3 ​​ pints of of juice. I label each part as ​​ __ 12 12 juice into each glass. The unknown is the total pints of juice. ?

3 12

3 12

3 12

3 12

3 12

3 12

I multiply to find the unknown.

__ ​ 1 ​​​​)​ ​6 × __ ​​ 3 ​​ = 6 × (​ ​​3 ​ × 12 12 1 = (6 × 3)​​ × ​​ __ ​​ 12

= 18 × __ ​​ 1 ​​ 12 18 = ​​ ___ ​​ 12

18 18 Adesh pours ​​ ___ ​​ pints of juice in all. I rename ​​ ___ ​​ as a 12 12 1 __ mixed ­number because 1 ​​ 2 ​​ pints of juice makes more sense 18 than ​​ ___ ​​ pints of juice.

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19

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 3

Name

3

Date

1. Use the place value disks shown to complete parts (a)–(f).

a. The place value disks represent the number is in the tens place. It has a value of

b. The digit

c. The digit ​3​is in the

.

place. It has a value of

.

is in the tenths place. It has a value of

d. The digit

e. The digit ​4​is in the f.

.

.

place. It has a value of

.

is in the thousandths place. It has a value of

The digit

.

2. Use the place value chart to complete parts (a)–(e). Express the value of each digit in decimal form.

a. The digit

tens

ones

tenths

2

4

6

hundredths thousandths

1

7

is in the tenths place. It has a value of

b. The digit ​4​is in the

place. It has a value of

. .

c. The digit

is in the tens place. It has a value of

d. The digit

is in the thousandths place. It has a value of

e. The digit ​1​is in the

place. It has a value of

3. Represent 2.963 in two different ways by using expanded form or expanded notation.

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. . .

4. Represent 48.036 in two different ways by using expanded form or expanded notation.

21

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 3

REMEMBER 5. Use the parallelogram to complete parts (a) and (b).

E

H

F

a. Name the acute angles shown in the parallelogram. b. Name the obtuse angles shown in the parallelogram.

G

6. Multiply. You may draw a model to help you.

8 × ​​ _6 ​​ 5

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

__9

7. Jada puts 8 ice cubes in her water bottle. Each ice cube weighs 10 ​​ ​​ grams. How many grams of ice does Jada put in her water bottle?

22

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 4

Name

4

Date

Use the place value chart to complete the statement and equation.

1.

tens

ones

tenths

hundredths thousandths

When I multiply a number by ​1​0​​, the digits shift one place to the left.

× 10

I multiply 0 ​ .003​by ​1 0​. The digit ​3​moves one place to the left.

3 hundredths is 10 times as much as 3 thousandths .

0.03 = 10 × 0.003 2.

tens

ones

tenths

hundredths thousandths

× 1

10

8 hundredths is __ ​​ ​​ as much as 8 tenths .

10 1

0.08 = __ ​​ ​​ × 10 1

0.8

3. Consider the number shown.

23.6 4 4 a. What is the value of the boxed digit?

0.04 b. What is the value of the underlined digit?

0.004 c. Complete the equations to show the relationship between the boxed digit and the underlined digit.

0.04 = 10 × 0.004

0.004 = __ ​​ 10 ​​ × 0.04 1

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When I multiply a number 1 by ​​ __ ​​, the digits shift one 10 place to the right.

I multiply 0.8 by __ ​​ 1 ​​. The 10 digit 8 moves one place to the right.

The boxed digit is in the hundredths place. 4 hundredths has a value of 0.04.

The underlined digit is in the ­thousandths place. 4 thousandths has a value of 0.004.

4 hundredths is 10 times as much as 4 thousandths.

1 4 thousandths is ​​ __ ​​ as much as 10 4 hundredths.

23

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 4

REMEMBER 4. Use polygons A–G to complete parts (a) and (b).

Polygon A

Polygon B

Polygon E

Polygon C

Polygon F

Polygon D

Polygon G

a. Use a right-angle tool to find right angles in the polygons. Mark each right angle with a small square. b. Write the name of each polygon in the category that best describes it.

2​ ​or more pairs of perpendicular sides Polygon ​E​ Polygon G ​ ​

1 pair of perpendicular sides Polygon B ​​ Polygon F ​​

No pairs of perpendicular sides Polygon A ​ ​ Polygon C ​ ​ Polygon ​D​

Perpendicular sides form a right angle.

Polygon E

Polygon G

The polygons must have at least 2 pairs of perpendicular sides to belong in the first category.

24

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 4

5. How many zeros are in the product of the expression shown? Explain how you know.

26 × ​104​​ ​ ​ 04​​ ​ represents 4 factors of 10. Each factor of 10 shifts the digits one The product has 4 zeros. 1 4 place to the left. So ​10​​ ​shifts the digits 2 and 6 to the left 4 places. There are no zeros in 26, so the number of zeros in the product of the expression 26 × ​104​​ ​matches the exponent.

The exponent represents the number of times 1​ 0​is a factor. ​​1 0​​4​​is equal to 1​ 0 × 10 × 10 × 10​. ​26 × ​1 0​​4​​ represents ​26 × 10 × 10 × 10 × 10​.

There are no zeros in 2​ 6​, so the number of zeros in the product matches the exponent. The exponent is ​4​.

The product of the expression 2​ 6 × ​1 0​​4​​ has ​4​ zeros.

6. Write the number in standard form. ​105​​ ​ = 100,000

​​ 10​​5​​is a number represented in exponential form. To write this number in standard form, I look at the exponent.

The exponent is 5 ​ ​. ​​1 0​​5​​ represents ​1 0 × 10 × 10 × 10 × 10​.

In standard form, the number is ​1 00,000​.

There are ​5​zeros in the number, and the exponent is also the number 5 ​ ​.

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25

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 4

Name

4

Date

Use the place value chart to complete the statement and equation.

1.

tens

ones

tenths

hundredths thousandths

× 10

is ​10​times as much as

.

​= ​ ​10 ​×​ ​ 2.

tens

ones

tenths

hundredths thousandths

× 10

is 1 ​ 0​times as much as

.

​= ​ ​10 ​×​ ​ 3.

tens

ones

tenths

×

hundredths thousandths

1 10

5​ hundredths is ​​ __ ​​ as much as 10 1

0.05 = __ ​​ 10 ​​ × 1

.

4. Consider the number shown.

52.422 a. What is the value of the boxed digit?

b. What is the value of the underlined digit?

c. Complete the equations to show the relationships between the boxed digit and the underlined digit. ​= ​ ​10 ​×

__ =​10 ​ ​ ​× 1

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27

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 4

REMEMBER 5. Use polygons ​A​–G ​ ​to complete parts (a) and (b).

Polygon A

Polygon B

Polygon E

Polygon C

Polygon F

Polygon D

Polygon G

a. Use a right-angle tool to find right angles in the polygons. Mark each right angle with a small square. b. Write the name of each polygon in the category that best describes it.

​2​or more pairs of perpendicular sides

1 pair of perpendicular sides

No pairs of perpendicular sides

6. How many zeros are in the product of the expression shown? Explain how you know. ​61 ​×​ ​107​​ ​​

7. Write the number in standard form. ​​10​​6​ = ​ ​​ 28

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 5

Name

5

Date

Use the place value chart to complete the equations.

1.

tens

ones

tenths

hundredths thousandths

​0.9 × 10 × 10 = × 10

90

​

​0.9 × 100 = ​ 90 2

​0.9 × ​10​​ ​ = ​ 90

× 10

​​

There are ​9​ tenths. In standard form, this is ​0.9​​.

For every 10​ ​​ that I multiply by, the digits shift one place to the left. ​​0.9 × 10​​moves the digit ​9​ to the left one place, from ​​0.9​to ​9​. ​9 × 10​​moves the digit ​9​ to the left one place, from ​​9​to ​9 0​.

Multiplying by ​1 0​ twice is the same as multiplying by 100​ ​​ ​ or ​​1 0​​2​​​. ​1 0 × 10 = 100 = ​10​​2​ 2.

tens

ones

tenths

hundredths thousandths

​20 ÷ 1,000 = ​ 0.02 ÷ 1000

3

​20 ÷ ​10​​​ ​​= ​ 0.02

There are ​​2​tens. In standard form, this is ​20​.

I know that each digit shifts three places to the right when I divide by ​​1 ,000​​. ​20 ÷ 1,000 = 0.02​ I represent dividing by ​1 ,000​as dividing by a power of 10 with an exponent of 3. © Great Minds PBC •

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29

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 5

Find the product or quotient and write it in standard form.

For every 10​ ​​ ​that I divide by, the digits shift one place to the right.

2

3. ​0.3 ÷ ​10​​ ​= ​ 0.003

​​1 0​​2​​​ means dividing by ​​1 0​​two times or dividing by ​​100​ .

3

4. ​5.107 × ​10​​ ​= ​ 5,107

Dividing ​0.3​ by ​​1 0​​2​​shifts the digit ​3​ two places to the right.

For every ​1 0​ that I multiply by, the digits shift one place to the left. ​​1 0​​3​​​ = ​1 0 × 10 × 10​ Multiplying ​5.107​ by ​​1 0​​3​​shifts the digits to the left three places.

REMEMBER 5. Make like units. Then add. Show your work.

25 7 11 __ ​​ ​​ + ​​ __​​ = __ ​​ ​​

12 24 24 7×2 7 11 11 ​​ + ​​ ​​ ​​ ​​ + ​​ ​​ = ​​ 12 24 12 × 2 24 14 11 = ​​ 24 ​​ + ​​ 24 ​​ 25 = ​​ 24 ​​

__ __ _____ __ __ __ __

I notice that the units are related. I know that ​1 2​ is a factor of 24​ . So ​24​ is a common denominator for the two fractions.

I rename __ ​​ 7 ​​ as an equivalent fraction. I know that 12 × 2 = 24​ .

12 I rename twelfths as twenty-fourths.

I add like units.

7×2 ​​ _____ ​​ = ​​ ___​​ 12 × 2 14 24

25 11 ​​ ___​​ + ​​ ___ ​​ = ​​ ___ ​​ 14 24

30

P R ACT I C E PA R T N E R

24

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 5

Use the Read–Draw–Write process to solve the problem. ​​ ​grams. His 6. Eddie can pack ​11 ​kilograms​​ 793 ​grams into his suitcase. His clothes weigh 8,652​ ​grams. How many more grams can Eddie pack into his suitcase? shoes weigh 1,134​ ​​

​11 ​kg​ = 11,000 g​ ​ ​11 ​kg​ 793 g​ ​ = 11,793 g​ ​ ​8,652 ​g​ + 1,134 g​ ​ = 9,786 g​ ​ 1​​ 1,793 − 9,786 = 2,007​ Eddie can pack 2,007​ ​​ ​grams more into his suitcase.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent that Eddie can pack ​​1 1​​ kilograms ​​7 93​grams in his suitcase. I draw and label one part to represent the weight of his clothes. I draw and label another part to represent the weight of his shoes. The unknown is how many more grams Eddie can pack.

11 kg 793 g 8,652 g

1,134 g

?

I convert ​1 1 kilograms 793 grams to grams. ​1 ​kg​ = 1,000 ​g​ ​1 1 ​kg ​×​ ​1 ,000 ​​=​​ ​​1 1,000​g​ ​1 1,000​ g ​+​ ​7 93​g​ =​​ 11,793​g​ The total weight Eddie can pack is ​​11,793​g​.

I find the combined weight of Eddie’s clothes and shoes. ​8,652​ ​+​ ​1 ,134 ​​= 9,786​ I subtract to find the difference between the total weight and the weight of the clothes and shoes. ​1 1,793​ ​−​ ​9,786 ​​= ​​2,007​​

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31

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 5

Name

5

Date

Use the place value chart to complete the equations.

1. ​​ tens ones tenths hundredths thousandths 0.8 × 10 × 10 =

​0.8 × 100 = × 10 ​​ 0.8 × ​10​​​ ​ ​ = × 10

2. ​​ tens ones tenths hundredths thousandths 0.6 ÷ 100 = ​​0.6 ÷ ​10​​​ ​ ​ =

÷ 100

3. ​​ tens ones tenths hundredths thousandths 30 ÷ 1,000 =

​​30 ÷ ​10​​​ ​ ​ =

÷ 1000

Find the product or quotient and write it in standard form.

4. 3 ​​ .04 ÷ 10 = 6. ​3.205 × ​10​​3​ =

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5. ​0.205 × 10 =

​ ​​​

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7. ​0.9 ÷ ​10​​2​ =

​​ ​

33

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 5

REMEMBER 8. Make like units. Then add. Show your work.

13 _​​ 5​​ + ​​ __ ​​ = 6

18

Use the Read–Draw–Write process to solve the problem. ​ 00​grams​. All of the potatoes need 9. A restaurant has a bag of potatoes that weighs 4​ ​​ kilograms 5 ​grams of potatoes. Lacy peels 2,358​ ​​ ​grams of potatoes. How to be peeled. Kayla peels 1,841​ ​​ many grams of potatoes still need to be peeled?

34

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 6

Name

6

Date

Use ​​>​,​ ​=​, or ​<​​to compare the numbers.

1. ​2 hundredths ​ 2. ​73 hundredths ​

< >

The digits are the same, but the units are different. I can use the units to help me compare.

2 tenths​

I know hundredths are less than tenths.

73 thousandths ​

​2 hundredths < 2 tenths​ I know hundredths are greater than thousandths. ​73 hundredths > 73 thousandths​

3. Plot and label each number on the number line. Then use >​ ​​ ​, ​=​, or ​<​​to compare the numbers.

​0.436 ​

<

0.438​

0.43

0.436

0.438

0.44

The interval between ​​0.43​and ​0.44​ is partitioned into ​​1 0​parts, which represent thousandths. I count by ​1​​ ­thousandths to plot and label each number.​ ​0.438​ is to the right of 0.436​ ​​ on the number line.

So 0.436 is less than 0.438.

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35

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 6

4. Write each number on the place value chart. Then use >​ ​​ , ​=​, or ​<​​to compare the numbers.

​3.065

< tens

​ 3.65​ ones

tenths

hundredths thousandths

3

0

6

3

6

5

5

I compare the numbers in the ones place. Both numbers have 3​ ​​ ​in the ones place.

I compare the numbers in the tenths place. ​​ 3.065​​ has a ​0​​in the tenths place. ​3.65​ has a ​6​ in the tenths place. ​​0​is less than ​6​, so ​3.065​ is less than 3.65​ ​​ ​.

5. Order the numbers from least to greatest. ​​ , 5.174​ ​​ ​​5.17​, ​51.74​, 0.174​

0.174​, ​5.17​, ​5.174​, ​51.74​

I see which number has the largest place value unit. ​​51.74​ ​ has a digit in the tens place. No other numbers have a digit in the tens place, so ​51.74​ is the greatest number in the list. ​ .174​ is the smallest number because it is the only number 0 without any ones or tens.

I compare the remaining numbers, ​5.17​ and ​5.174​ . ​5.17​ is less than ​5.174​because there are ​4​ more thousandths in ​5.174​.

36

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 6

REMEMBER 6. For each figure, draw all lines of symmetry. Circle any figure that does not have a line of symmetry.

I imagine folding each figure in half.

I want two sides to match exactly on either side of the fold. I can imagine folding horizontally, vertically, and diagonally.

Each fold where the two sides are ­exactly the same is a line of symmetry.

A figure can have no lines of symmetry, one line of symmetry, or multiple lines of symmetry.

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37

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 6

Name

6

Date

Use ​​>​,​ ​​=​,​ or ​​<​​to compare the numbers.

1. ​​6​tenths

6​ ​hundredths​

2. ​​19​thousandths ​

19​hundredths ​

3. Plot and label each number on the number line. Then use >​ ​​ ​, ​​=​,​ or ​​<​to compare the numbers. ​​0.576

0​ .574​

0.57

0.58

4. Write each number on the place value chart. Then use >​ ​​ ​, ​​=​,​ or ​​<​to compare the numbers.

5​​ .41

5.041​ tens

ones

tenths

hundredths thousandths

Order the numbers from least to greatest.

5. 3 ​​ .742​​, ​​37.42​​, ​​3.74​​, ​​0.742​

<

<

<

6. 2.423​​, ​​24.23​​, ​​2.42​​, ​​0.423​

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39

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 6

REMEMBER 7. For each figure, draw all lines of symmetry. Circle any figure that does not have a line of symmetry.

40

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 7

Name

Date

7

1. Round the number to the given place. Show your thinking on the number line.

Nearest tenth

7.8 = 78 tenths

7.76 7.75 = 77 tenths 5 hundredths

7.7 = 77 tenths 7.76 ≈

7.8

There are ​7 7​tenths in 7​ .76​. I label the bottom tick mark on the number line ​7 7​tenths or ​7.7​.

1​ ​more tenth than ​7 7​tenths is 7​ 8​tenths. I label the top tick mark on the number line ​78​tenths or ​7.8​.

Halfway between 7​ 7​tenths and ​78​tenths is ​7 7​tenths 5 ​ ​hundredths. I label the halfway mark ​7 7​tenths 5 ​ ​hundredths or ​7.75​.

I plot and label ​7.76​.

The number line helps me see that ​7.76​is more than halfway between 7​ .7​and ​7.8​. ​7.76​rounded to the nearest tenth is ​7.8​.

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41

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 7

REMEMBER

_7

2. The maximum weight a box can hold is 18 pounds. Lisa has a doll that weighs 8 ​​ 8 ​​ pounds 15 __

and a train that weighs 9 ​​ 16 ​​ pounds. Is the combined weight of the doll and train less than the

maximum weight the box can hold? Without evaluating, explain whether the combined weight of the doll and train is greater than or less than the maximum weight the box can hold.

_7

_1

15 __

_1

I know that 8 + 9 = 17. I know that ​​ 8 ​​ is greater than ​​ 2 ​​ . I know that ​​ 16 ​​ is greater than ​​ 2 ​​ .

So I know that the sum of the fractions is greater than 1. The sum of the whole numbers and the fractional parts is greater than 18. The combined weight of the doll and train is greater than the maximum weight the box can hold.

I add the whole numbers. ​8 + 9​ ​=​ ​17​ I know that the difference between the whole numbers and the maximum weight the box can hold is ​1​ pound.

If the sum of the fractional parts is less than ​1​, then the combined weight of the doll and train is less than the weight the box can hold.

If the sum of the fractional parts is greater than ​1​, then the combined weight of the doll and train is greater than the weight the box can hold.

Both fractional parts are greater than __2​​ 1 ​​ , so the sum of the fractional parts is greater than ​1​.

The combined weight of the doll and train is greater than the maximum weight the box can hold.

42

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 7

3. Use the number shown to complete parts (a) and (b).

85 9 ,924 a. Write a number in each blank to correctly complete each statement.

The value of the underlined 9 is

900 .

The value of the boxed 9 is 9,000 . b. Circle one answer in each box to make the statement true. boxed The

underlined

boxed

9 represents 10 times as much as the

9. underlined

The underlined 9 in 859,924 is in the hundreds place. It represents 900.

9 × 100 = 900 The boxed 9 in 859,924 is in the thousands place. It represents 9,000.

9 × 1,000 = 9,000 Both digits are 9 and they are next to each other in the number. The value of the digit to the left is 10 times as much as the value of the digit to the right.

9,000 is 10 times as much as 900.

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43

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 7

Name

7

Date

Round the number to the given place. Show your thinking on the number line.

1. Nearest one

4 = 4 ones

2. Nearest one

12 = 12 ones

0.9 = 9 tenths

0.85 = 8 tenths 5 hundredths

3.5 = 3 ones 5 tenths

3 = 3 ones

3. Nearest tenth

11 = 11 ones

0.8 = 8 tenths

​3.6 ≈

​11.6 ≈ ​ ​​

​0.84 ≈ ​ ​​

4. Nearest tenth

5. Nearest hundredth

6. Nearest hundredth

15.​09 ≈ ​ ​​

​3.694 ≈ ​ ​​

​3.278 ≈ ​ ​​

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45

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 7

REMEMBER

_2

7. A fish tank holds 10 gallons of water. Tyler pours 5 ​​ 8 ​​ gallons of water into the tank. Can Tyler _3 pour another 4 ​​ 16 ​​ gallons of water into the tank without overfilling the fish tank? Without evaluating, explain whether the combined amount of water is greater or less than 10 gallons.

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

90​4​, ​_​ 4 12 a. Write a number in each blank to correctly complete each statement.

The value of the underlined 4 is The value of the boxed 4 is

. .

b. Circle one answer in each box to make the statement true. boxed

boxed

4 represents 10 times as much as the

The underlined

46

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4. underlined

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 8

Name

8

Date

1. Round the number to the given place. Show your thinking on the number line.

3.783 a. Nearest one

b. Nearest tenth

c. Nearest hundredth

3.8 = 38 tenths 3.783

3.79 = 379 hundredths

3.5 = 3 ones 5 tenths

3.75 = 37 tenths 5 hundredths

3.785 = 378 hundredths 5 thousandths 3.783

3 = 3 ones

3.7 = 37 tenths

3.78 = 378 hundredths

4 = 4 ones 3.783

3.783​ ≈​

4

To round to the nearest one, I look at the tenths place. ​ .783​has the digit ​7​ 3 in the tenths place.

I plot ​3.783​ above ​ 3.5​on the number line. Because 3 ​ .783​ is more than halfway between 3 ​ ​and ​4​, I round ​3.783​to 4 ​ ​.

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3.783​ ≈​ 3.8 To round to the nearest tenth, I look at the hundredths place. ​ .783​has the digit ​8​in the 3 ­hundredths place. I plot ​3.783​ above 3 ​ .75​on the number line.

Because ​3.783​is more than ­halfway between 3 ​ .7​and ​3.8​, I round ​3.783​to ​3.8​.

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3.783​ ≈​ 3.78 To round to the nearest hundredth, I look at the thousandths place. ​ .783​has the digit ​ 3 3​in the thousandths place. I plot ​3.783​ below 3 ​ .785​on the number line. Because ​ 3.783​is less than halfway between ​ 3.78​and ​3.79​, I round ​ 3.783​to ​3.78​.

47

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 8

REMEMBER

__3

_4

2. Leo correctly added 14 ​​ ​​ and ​​ 6 ​​ . Explain how Leo chose the units he used. Explain why Leo could have used other units.

4 × 14 18 3×6 56 74 + + = = 14 × 6 6 × 14 84 84 84

Leo multiplied the denominators to find like units. He could have found a common multiple for 14 and 6, such as 42.

I see that Leo multiplied the denominators to find like units.

4 × 14 ______ ​​ 3 × 6 ​​ +​ ​​______​​ 14 × 6 6 × 14

I know Leo could have used other units.

He could have used a common multiple to find like units.

To find like units, I skip-count by fourteens.

14, 28, 42​, . . .

Then, I skip-count by sixes.

6, 12, 18, 24, 30, 36, 42, . . .

42 is a multiple of 14 and 6. Leo could rename each fraction by using 42 as the like unit.

4 × 7 ___ ______ ​​ 3 × 3 ​​ +​ _____ ​​ ​​ = ​​ 9 ​​ + ___ ​​ 28​​ = ___ ​​ 37​​ ​ 14 × 3

48

P R ACT I C E PA R T N E R

6×7

42

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42

42

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 8

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

_3

_5

3. Jada makes trail mix with nuts. She uses 2 ​​ 4 ​​ cups of almonds and 1 ​​ 6 ​​ cups of pecans. How many cups of nuts are in the trail mix in all?

2 ​​ _4 ​​ + 1 ​_​ 6 ​​ = 4 ​__ ​ 12 ​​ 3

5

7

__7

There are 4 ​​ 12 ​​ cups of nuts in all.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with two parts. One part represents 5 ​​ cups of 2​​ __3 ​​ cups of almonds and the other part represents 1 ​​ __ 6 4 pecans. The total number of cups of nuts in the trail mix is unknown. ?

2

3 4

1

5 6

I add the amounts to find the total number of cups of nuts in the trail mix.

5 2 ​​ __3 ​​ + 1 ​​ __ ​​ 6 4

First, I make equivalent fractions with like units. I know that 12 is a common multiple of the denominators 4 and 6.

3 × 3 __ __​​ 3 ​​ = ​​ _____ ​​ = ​​ 9 ​​ 4 4 × 3 12 10 5 _____ ​​ __ ​​ = ​​ 5 × 2 ​​ = ​​ ___ ​​ 6

6×2

12

I add the whole numbers and fractions.

9 19 10 2 ​​ __ ​​+ 1 ​​ ___ ​​ = 3 + ​​ ___ ​​ 12 12 12

19 7 7 I rename ​​ ___ ​​ as 1 + ​​ __ ​​ , and add it to 3 to find the sum, 4 ​​ __ ​​ .

12 12 12

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P R ACT I C E PA R T N E R

49

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 8

Name

8

Date

Round the number to the given place. Show your thinking on the number line.

1. 5.416 a. Nearest one

b. Nearest tenth

c. Nearest hundredth

​5.416​ ≈

​5.416​ ≈

​5.416​ ≈

a. Nearest one

b. Nearest tenth

c. Nearest hundredth

​12.603​ ≈

​12.603​ ≈

​12.603​ ≈

2. 12.603

3. Round the number to the nearest tenth. ​2.385​ ≈

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4. Round the number to the nearest hundredth. ​4.237​ ≈

51

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TA ▸ Lesson 8

REMEMBER

__9

_5

5. Jada correctly added ​​ 12 ​​ and ​​ 9 ​​ . Explain how Jada chose the units she used. Explain why Jada could have used other units.

5 × 12 141 60 81 9×9 + = + = 12 × 9 9 × 12 108 108 108

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

_2

_3

6. Adesh has 4 ​​ 3 ​​ cups of water in his water bottle. He pours another 3 ​​ 4 ​​ cups of water into the bottle. How many cups of water are now in the bottle?

52

P R ACT I C E

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Module 4 Topic B

FAMILY MATH Addition and Subtraction of Decimal Numbers Dear Family,

Your student is adding and subtracting decimal numbers by using familiar methods. They notice the strategies they used to add and subtract whole numbers and fractions can also be used to add and subtract decimal numbers. Your student estimates to check that their answer is reasonable. They also rename a fraction as a decimal number to solve addition and subtraction word problems.

​2.9 + 6.6 = 9.5​

​6.27 − 4.68 = 1.59​

2.9 + 6.6 = 3 + 6.5 = 9.5 0.1

ones

tenths

hundredths

11 5 1 17

6.2 7 – 4.6 8 1.5 9

6.5

To add and subtract decimal numbers, students can use methods and tools such as making the next unit, vertical form, and place value charts.

2 5

5.83 – 3 = 5.83 – 3.4 = 2.43

3

2 5

2 2×2 = = 4 5 5 × 2 10

5.83 – 3.4 2.43

4 = 0.4 10 When an addition or subtraction problem gives one number as a fraction and the other as a decimal number, students can rename one of the numbers so that both numbers are in the same form.

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53

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB

At-Home Activities Shopping Receipts Use shopping receipts to help your student practice adding and subtracting decimal numbers.

Save a receipt from a shopping trip or look at prices online and ask your student to find sums and differences. For example, invite your student to •

add to find the total cost of two items, such as the total cost of two cans of soup or the total cost of a ball and a stuffed animal.

•

subtract to find the difference in cost between two items or two different brands of the same type of item.

Fractions to Decimal Numbers Invite your student to practice renaming fractions as decimal numbers to make adding and subtracting simpler. Discuss situations where one number is a fraction and the other is a decimal number.

•

​ .25​feet tall. How many feet taller is Sasha than Leo? Leo is ​4 ​ _​ ​feet tall. Sasha is 5 1 2

(​5.25 − 4.5​) •

Lacy is buying wood to build a rectangular fence for her garden. She needs a total of

​6.75​yards for the length and a total of 3 ​ ​ _ ​​ yards for the width. How many yards of wood 5 2

does Lacy need to buy altogether? (6.75 + 3.4)

•

Adesh is making pizza dough for a family dinner. He needs 1​​ _​​ cups of flour for a 1 4

medium pizza and 0.75 cups of flour for a small pizza. How many cups of flour does

Adesh need to make both pizzas? (1.25 + 0.75)

54

FA M I LY M AT H ▸ Module 4 ▸ Topic B

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 9

Name

9

Date

Add. Show your work.

1. 2.3 + 1.9 = + 0.1

1.9

4.2 + 2.2

2

I use the arrow way to show how to add ​2 .3​ and ​1 .9​.

4.2

I start with ​1 .9​because it is close to the next one, 2​ ​. I add 0 ​ .1​from the other addend, ​2 .3​.

I add what is left over from the other addend,​ 2 + 2.2​​=​ ​4.2​.

2. 1.74 + 4.87 = 6.61

1.61

0.13

​ .87​is close to the next one, 5. I use a 4 number bond to decompose 1​ .74​ into ​ 0.13​and ​1 .61​. ​0.13 + 4.87​​=​ ​5​ I make a new addition problem with 5 ​​ and the other part that is left over from the first addend, ​1 .61​. ​1 .61 + 5​​=​ ​6.61​

3. 2.7 + 1.4 =

I draw a number line to show how to add ​2 .7​and ​1 .4​.

4.1 + 0.3

2

2.7

3

+ 1.1

4 4.1

5

I start at ​2 .7​because it is close to the next one, 3 ​ ​. I add 0 ​ .3​ from the other addend to get to ​3​.

Then I add 1​ .1​, which is what is left over from the other addend. ​2 .7 + 0.3​​=​ ​3​ ​3 + 1.1​​=​ ​4.1​

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55

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 9

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

_1

4. Tyler has 7 ​ ​ 4 ​pounds of ham.

_7 He uses 3 ​ ​ ​pounds of ham 9

to make sandwiches.

How many pounds of ham are left over?

9 28 1 7 7 4 − 3 9 = 7 36 − 3 36

3 9

9 − 28 4 36 36 9

3 36

As I reread, I think about what I can draw.

I draw a tape diagram to represent the ​7​ __1 ​​ pounds 4 of ham Tyler has and the ​3​ __97​​ pounds of ham he uses to make sandwiches. The unknown is how many pounds of ham are left over.

1

74

28 36

7 ​​ __ ​​ − 3 = 4 ​​ __ ​​ 36 36 9

I read the problem. I read it again.

7

?

39

I subtract 3 ​ ​ __97 ​​from ​7​ __1 ​​to find the unknown part. First, 4 I make equivalent fractions with like units. I know that ​ 36​is a common multiple of the ­denominators ​4​and ​9​.

28 1×9 9 ​​ - 3 ​​ _____​​ = 7 ​​ ___ ​​ − 3 ​​___ ​​ 7 ​​ _____

1

7×4 9×4

4×9

28 __ 8 1 − ​​__ ​​ = ​​ ​​ 36 36 9 8 17 3 ​​ __ ​​ + ​​ __​​ = 3 ​​__ ​​ 36 36 36 17 There are 3 ​ ​ 36 ​​pounds of ham left over.

__

36

36

Now, I subtract the ones: ​7 − 3​​=​ ​4​.

28 28 9 9 7 ​​ ___ ​​ − 3 ​​___ ​​ = 4 ​​ ___ ​​ − ___ ​​ ​​ 36

36

36

36

I look at the numerators. I notice that ​9​is less than 2​ 8​.

9 28 ___9 ​​ and 1, so I can subtract ___ ​​ into 3​​ 36 ​​ ​​ I decompose 4​​ ___ 36 36 from 1.

9 28 4 36 – 36

9

I subtract ___ ​​ 28 ​​ from 1.

36

1

3 36

28 36 28 1 − ​​___ ​​ = ​​___​​ − ​​___ ​​ = ___ ​​ 8 ​​ 36

36 36 36 9 I add the difference to 3 ​​ 36 ​.​ 9 17 8 3 ​​ ___ ​​ + ​​ ___ ​​ = 3 ​​ ___ ​​ 36 36 36

56

P R ACT I C E PA R T N E R

___

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TB ▸ Lesson 9

9

Date

Add. Show your work.

1. ​4.8 + 0.3 =​

2. ​2.4 + 5.7 =​

3. ​0.08 + 0.04 =

​

5. ​3.26 + 6.95 =

7. 4 ​ .07 + 1.34 =

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​

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4. ​0.98 + 1.03 =​

6. ​4.97 + 1.06 =​ ​

​

8. ​6.13 + 2.98 =​ ​

​

57

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 9

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

_2

_2

​ ​ 3 ​quarts of paint on a banner. How many quarts of paint 9. Julie has 1 ​ 7 ​ 5 ​quarts of paint. She uses 9 does she have left over?

58

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 10

Name

Date

10

1. Add. Circle to show when you can compose a unit. Then record in vertical form.

​0.16 + 0.28​ 0.1

0.01

0.01

0.01

0.01

0.16 + 0.28 1 0.44

0.01

0.01

0.1

0.1

0.01

0.01

0.01

0.01

0.01

0.01

0.01

I start with the smallest unit, ­hundredths.

I add the hundredths: ​6​ hundredths ​​+ 8​hundredths ​​= 14​hundredths.

I circle ​1 0​ hundredths to make a unit of 1​ ​​ tenth.

0.01

Then, I add the tenths: ​1​ tenth ​+ 2​​ tenths ​+ 1​​ tenth ​= 4​​ tenths.

2. Add. Show your work on the place value chart. Then record in vertical form.

​2.75 + 2.83​ ones

tenths

hundredths

2.75 + 2.83 1 5.58 I represent each number in the place value chart.

I add the hundredths: ​​5​hundredths ​​+ 3​hundredths = ​ 8​hundredths.

I add the tenths:​​ 7​​ tenths ​+ 8​​ tenths ​= 15​tenths.

I can regroup 10​ ​​ ​ tenths as ​1​ one.

Then, I add the ones: ​2​ ones ​+ 2​​ ones ​+ 1​​ one ​= 5​​ ones.

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59

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 10

3. Add by using the standard algorithm.

​4.35 + 9.78 = ​ 14.13 4.35 + 9.78 1 1 14.13 REMEMBER Use the Read–Draw–Write process to solve the problem.

_2

4. There are ​​ 6 ​as many art students as music students. There are ​30​ music students. How many music students and art students are there altogether?

2 3​ 0 + ​(_​6​× 30)​= 40​ There are ​​40​music students and art students altogether.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram that represents the ​30​ music students. I draw another tape diagram that represents there are __​​ 62 ​​as many art students as music students. The unknown is the total number of art students and music students.

30 music ?

art To find the number of art students, I multiply to find ​​ __62 ​​ of ​​30​ .

__​​ 2 ​× 30 = 10​ 6

I add the ​30​ music students to the ​1 0​ art students. ​30 + 10 = 40​​ 60

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 10

Name

10

Date

1. Add. Circle to show when you can compose a unit. Then record in vertical form. ​​0.27 + 0.15​

0.1

0.1

0.1

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.27 + 0.15

Add. Show your work on the place value chart. Then record in vertical form.

2. ​1.35 + 2.82​

ones

tenths

hundredths

1.35 + 2.82

Add by using the standard algorithm.

3. ​0.79 + 0.4 =

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0.79 + 0.4

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4. ​6.48 + 5.93 = ​

+

61

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 10

REMEMBER 2 5. There are _ ​​ ​​as many students who wrestle as students who play basketball. There are ​ 5 20​students who play basketball. How many wrestlers and basketball players are there altogether?

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

​

62

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 11

Name

11

Date

1. Use a related addition equation to subtract. Let the letter represent the unknown part. Fill in the blanks and use the arrow way to record your thinking.

​5.34 − 2.89​ Related addition equation with unknown part ​​c​​:

2.89 + c = 5.34 ​ Arrow way:

+ 0.11

2.89

3

+ 2.34

5.34

​5.34 − 2.89 = ​ 2.45 ​

I use the letter c ​for the unknown addend. ​2 .89 + c = 5.34​ I use the arrow way to show how to count on from ​​2.89​​ to ​​5.34​.

2. Subtract. Show your work.

I add ​0.11​​ to ​2 .89​ to get to ​​3​ .

Next, I add ​​2.34​to ​3​​to get to 5.34​ ​​ .

​4.3 − 0.9 = ​ 3.4 ​ 4.3 − 0.9 = 3.3 + 0.1 = 3.4 3.3

First, I write the related addition equation.

I add the amounts I counted on. ​0.11 + 2.34 = 2.45​

1 I decompose ​4.3​ into ​3.3​ and ​1​.

Now, I subtract 0.9​ ​​ ​from ​1​​ to get ​​0.1​. ​​1 − 0.9 = 0.1​ I add ​3.3​ and ​​0.1​. ​3.3 + 0.1 = 3.4​

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63

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 11

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

_2

3. Jada has ​25​ tulip bulbs. She plants ​​ 5 ​of the tulip bulbs.

How many tulip bulbs does Jada plant?

2 ​× 25 = 10​ ​ ​_ 5 Jada plants 10​ ​​ tulip bulbs.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram that represents that Jada has ​ 25​tulip bulbs and she plants __ ​​ 2 ​​ 5 of the tulip bulbs. The unknown is the number of tulip bulbs Jada plants.

25

?

I multiply to find __ ​​ 2 ​​ of ​25​.

5

__​​ 2 ​× 25 = ​50 ___​= 10​ 5

64

P R ACT I C E PA R T N E R

5

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TB ▸ Lesson 11

11

Date

Use a related addition equation to subtract. Let the letter represent the unknown part. Fill in the blanks and use the arrow way to record your thinking.

1. ​7.5 − 4.8​

2. ​7.23 − 2.84​

Related addition equation with unknown part ​​b​​:

​ + b = ​

​ ​​ + h = ​

Arrow way:

​7.5 − 4.8 =

Related addition equation with unknown part ​​h​​:

Arrow way:

​7.23 − 2.84 =

​

​

Subtract. Show your work.

3. ​7.2 − 0.5 = ​

5. ​​6.35 − 1.96 = ​

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​

4. ​9.5 − 3.7 = ​

​

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6. ​5.3 − 2.75 = ​

​

​

65

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 11

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

_5

7. Riley serves 60​ ​​ ​chicken wings to his friends. Riley and his friends eat ​​ 6 ​of the wings. How many wings do Riley and his friends eat?

66

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 12

Name

Date

12

1. Subtract. Show your work on the place value chart. Then record in vertical form. ​2.14 − 1.42​

ones

tenths

hundredths

1 11

2.14 – 1.42 0.72

I draw to represent 2​ .14​in the place value chart.

I need to subtract ​1 .42​.

I start with the hundredths. ​4​ hundredths ​− 2​ hundredths ​= 2​ hundredths Next, I subtract the tenths. I do not have enough tenths to subtract. So, I regroup 1​ ​one into 1​ 0​ tenths.

Now, I see ​1​one 1​ 1​ tenths.

I subtract the tenths. ​1 1​ tenths ​− 4​ tenths ​= 7​ tenths Then, I subtract the ones. ​1 one − 1 one = 0 ones​

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67

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 12

2. Subtract by using the standard algorithm.

​8.02 − 2.71 = 7 10

8.02 – 2.71 5.31

5.31

​

I subtract the digits in each place value, starting with the smallest unit. ​2​ hundredths ​− 1​ hundredth ​= 1​ hundredth Next, I subtract the tenths. There is a 0 in the tenths place in 8.02, but I need to subtract 7 tenths.

I rename 1​ ​one as 1​ 0​tenths. I now have ​ 7​ ones ​1 0​ tenths.

I subtract the tenths. ​1 0​ tenths ​− 7​ tenths ​= 3​ tenths Then, I subtract the ones. ​7​ ones ​− 2​ ones ​= 5​ ones

68

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 12

REMEMBER 3. Draw a model to divide.

1 _​ 1​÷ 4 = _ ​​ ​​ 20

5

0

1 5

1

1 I think about __ ​​ 1 ​÷ 4​by asking myself, ​​ __ ​​is ​4​groups of 5 5 what?

I draw a number line partitioned into fifths. I draw a tape diagram above the number line. I partition each ​1​fifth of the tape diagram into 4 ​ ​equal parts. I find the value of ​1​part of the tape diagram to find __ ​​ 1 ​÷ 4​.

5

0

1 5

1

I see that the tape diagram has 2​ 0​total parts. The 1 value of ​1​ part is ​​ ___ ​ ​.

20

1 So, ​​ __ ​÷ 4 = ___ ​ 1 ​ ​.

5 20

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P R ACT I C E PA R T N E R

69

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 12

Name

12

Date

1. Subtract. Show your work on the place value chart. Then record in vertical form. ​3.45 − 1.63​ ones

tenths

hundredths

3.45 – 1.63

Subtract by using the standard algorithm.

2. 8.1 ​−​3.5 =

3. 4.1 ​−​1.4 =

8.1 – 3.5

4. 9.27 ​−​4.09 =

5. 7.08 ​−​4.12 =

6. 6.44 ​−​2.7 =

7. 5.5 ​−​3.13 =

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71

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 12

REMEMBER 8. Draw a model to divide.

_​​ 1​÷ 3 = 8

72

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 13

Name

13

Date

Use the Read–Draw–Write process to solve each problem. Write each answer as a decimal number.

_3

​ ​ 5 ​liters more water to the container.

1. Yuna has 2 ​ .2​liters of water in a container. She adds 1 a. Rename the number of liters of water Yuna adds to the container as a decimal number.

3 × 2 __ 3 ____ 6 ​= ​ ​ = ​ ​​ ​​_ 5 5 × 2 10

_3​​ ​= 0.6​ 5

3 ​1 ​_ ​= 1.6​ 5

b. How many liters of water are in the container after Yuna adds more water? ​2.2 + 1.6 = 3.8​ There are 3 ​ .8​liters of water in the container.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the amounts of water in the container, ​2 .2​liters and ​ 3 1 ​ __ ​​liters. The total is unknown.

5 ?

2.2 liters

1 3 liters 5

3 I add to find the total. I need to rename 1​ ​ __ ​​as a 5 decimal number to add.

__​​ 3 ​= _____ ​ 3 × 2 ​= __ ​ 6 ​​

5 5×2 I know ​​ 53 ​= 0.6​, so ​1 ​ 53 ​= 1.6​.

__

__

10

Now, I add the two decimal numbers. ​2 .2 + 1.6 = 3.8​

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73

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 13

_1

2. A piece of wood is 6 ​ ​ 2 ​feet long. Kelly cuts 1 ​ .45​feet off the piece of wood. How long is the piece of wood after Kelly cuts it?

6 ​ _2 ​= 6.5 1

6.5 − 1.45 = 5.05 The piece of wood is 5 ​ .05​feet long after Kelly cuts it.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the total length of the piece of wood, ​6 ​ 2__1 ​​ feet.

Then I draw and label one part to represent how much Kelly cuts off, 1​ .45​feet. The other part is unknown.

6 1 feet 2

1 .45 feet

?

I subtract to find the unknown part.

I rename 6 ​ ​ __21 ​​as a decimal number to subtract. ​​ __21 ​= 2_____ ​ 1 ×× 55 ​= __ ​ 5 ​​ 10

I know __2​​ 1 ​= 0.5​, so ​6 ​ __21 ​= 6.5​.

Now, I subtract the two decimal numbers. ​6.5 − 1.45 = 5.05​

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 13

REMEMBER 3. The line plot shows the amount of juice in 8 ​ ​pitchers. The amounts shown are in cups.

Amount of Juice in Pitchers

×

× 0

21

2

21

8

23

4

21

8

2

× ×

× ×

×

×

25

23

27

3

8

4

8

Amount of Juice (cups)

The juice is redistributed evenly among the 8 ​ ​pitchers. How many cups of juice are in each pitcher after redistribution?

3

5

28 2

5

28 3 8

2

3

28 5 8

2

3

24 5 8

2

7

24 6 8

2

28 6 8

2

7 8

​2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 = 17​ 3_ 5_ 5_ 6_ 6_ 7_ 32 ​​ ​+ ​ ​+ ​ ​+ ​ ​+ ​ ​+ ​ ​= __ ​ ​= 4​ 8 8 8 8 8 8 8 ​17 + 4 = 21​ 5 21 2​ 1 ÷ 8 = __ ​ ​= 2 ​_​ 8 8 5 _ There are ​2 ​ 8 ​cups of juice in each pitcher after redistribution.

Each X represents 1​ ​ pitcher.

I add the whole number amount in each pitcher. ​2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 = 17​ I add the fractional amount in each pitcher.

3 __ 6 __ 5 __ ​​ __ ​​ + ​​ 5 ​​ + ​​ __ ​​ + ​​ 6 ​​ + ​​ __ ​​ + ​​ 7 ​​ =​ 32 ​ __ ​​ = 4 8 8 8 8 8 8 8

Then I add the two sums: ​17 + 4 = 21​.

I divide ​2 1​cups by 8 ​ ​ pitchers.

5 ​2 1 ÷ 8 = 21 ​__ ​= 2 ​ __ ​​ 8 8

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75

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 13

Name

Date

13

Use the Read–Draw–Write process to solve each problem. Write each answer as a decimal number.

_3

​ ​ 4 ​feet to the length of the garden.

1. Adesh’s garden is 6 ​ .5​feet long. He adds another 2 a. Rename the number of feet Adesh adds to the length of the garden as a decimal number.

b. How many feet long is the garden after Adesh adds to it?

_1

2. A string is 2 ​ 0​inches long. Mr. Perez cuts 1 ​ 3 ​ 4 ​inches off the string. How long is the string now?

_2

3. Lacy rides her bike ​8 ​ 5 ​miles on Tuesday. She rides her bike 5 ​ .17​miles on Wednesday. How many more miles did Lacy ride her bike on Tuesday than on Wednesday?

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77

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TB ▸ Lesson 13

REMEMBER 4. The line plot shows the amount of maple tree sap in 8 ​ ​buckets. The amounts shown are in gallons.

Amount of Maple Tree Sap in Buckets

0

×

×

×

×

1

11

11

13

8

4

8

11 2

×

×

×

×

15

13

17

2

8

4

8

Amount of Maple Tree Sap (gallons)

The sap is redistributed evenly among the 8 ​ ​buckets. How many gallons of sap are in each bucket after redistribution?

78

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Module 4 Topic C

FAMILY MATH Multiplication of Decimal Numbers Dear Family,

Your student is learning to multiply decimal numbers by using methods that are familiar from whole-number multiplication. Students multiply a decimal number by a one-digit whole number; by a multiple of 10, 100, or 1,000; by a two-digit whole number; and by another decimal number.

To multiply, students use number lines, place value charts, area models, and vertical form. They relate decimal multiplication to fraction multiplication. Students use their experience multiplying whole numbers to select the most efficient strategy and determine the reasonableness of their answers, with a focus on the placement of the decimal point in the product.

6 tenths

7

42 tenths

10

60 tenths

2 hundredths

14 hundredths

20 hundredths

4.2 + 6 + 0.14 + 0.20 = 10.54 0.62 × 17 = 10.54

Area models can help students find all of the partial products.

4 10 7 10 4 7 4×7 10 × 10 = 10 × 10 28 = 100

When multiplying two decimal numbers, students can rename the numbers as fractions.

×

7 2 6 hundredths 1 5 tenths 1 3

3 630 + 7 260 1 0, 8 9 0 thousandths Vertical form is an efficient way to multiply two decimal numbers.

At-Home Activities Cost of Multiples Help your student practice multiplying decimal numbers by whole numbers. Ask your student to calculate the cost of buying multiples of an item.

•

If the cost of 1 box of crackers is $3.27, calculate the cost of 3 boxes of crackers.

(3 × 3.27)

•

If the cost of 1 pound of tomatoes is $1.68, calculate the cost of 4 pounds of tomatoes.

(4 × 1.68)

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79

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC

Multiply Decimal Numbers Help your student practice multiplying decimal numbers by decimal numbers. Cut a piece of paper into 9 strips, number the strips 1 to 9, and place the strips in a container. Have your student generate decimal numbers by picking a strip from the container, writing the number down, and putting the strip back. Then, repeat to create different decimal numbers. Focus on making decimal numbers that result in multiplying tenths by tenths and hundredths by tenths.

•

80

If your student picks the numbers 3, 1, and 6, they could use decimal points to make decimal numbers, and then multiply: 0.31 × 0.6, 3.1 × 0.6, or 0.3 × 1.6.

FA M I LY M AT H ▸ Module 4 ▸ Topic C

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 14

Name

14

Date

1. Multiply. Show your work by using a number line.

5 × 0.3 =

1.5 0.3

0.3

0.3

0

0.3

0.3

1

1.5

2

Each interval on the number line is ­partitioned into tenths.

Each tick mark represents 1 tenth.

I start at 0 and draw arrows to show 5 groups of 3 tenths. I plot and label a point to represent the product.

5 groups of 3 tenths is 15 tenths, or 1.5.

I use repeated addition to check my work.

0.3 + 0.3 + 0.3 + 0.3 + 0.3 = 1.5 2. Multiply. Show your work by using a place value chart. Then record your work in vertical form.

4 × 0.31 = 1.24 ones

0.

tenths

3

× 1

1.

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2

hundredths

I know 0.31 is 3 tenths 1 hundredth.

I draw 4 groups of 3 tenths 1 hundredth.

There are 12 tenths 4 hundredths.

I regroup 10 tenths as 1 one.

Now, the place value chart shows 1 one 2 tenths 4 hundredths.

1

I record my work in vertical form by multiplying one place v ­ alue at a time, starting with the ­hundredths.

4

4 × 1 hundredth = 4 hundredths

4

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4 × 3 tenths = 12 tenths I rename 12 tenths as 1 one 2 tenths. I multiply 4 and 0 ones, which is 0. Then, I add 1 one.

81

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 14

3. Multiply. Show your work by using the area model to find the partial products. Add the partial products to find the product.

3 × 1.35 1

3

3

+

0.9

3

one

3 ones

5

tenths

9 tenths

hundredths

15 hundredths

+ 0.15 = 4.05

3 × 1.35 = 4.05

I break apart 1 .35 into 1 one 3 tenths 5 hundredths to label the side lengths of the parts of the rectangle in the area model.

I multiply each side length by 3 to find the area of each part of the rectangle. The areas of the parts are the partial products.

3 × 1 one = 3 ones 3 × 3 tenths = 9 tenths 3 × 5 hundredths = 15 ­hundredths I add the partial products.

+

3.

0

0

0.

9

0

0.

1

5

4.

0

5

1

3 × 1 .35 = 4.05

82

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 14

REMEMBER 4. Write the decimal fraction in decimal form.

26 hundredths

26 ___ ​​ ​​ = 100

0.26

The area model shows 1 one decomposed into 100 hundredths.

26 ­hundredths are shaded.

I write 26 hundredths as a decimal number. I write 0 ones, a decimal point, and then 26.

26 26 hundredths = ​​ ____ ​​ = 0.26 100

Divide. Then check your work.

5. 90 ÷ 30

9 tens ÷ 3 tens = 3

3 3 0 9 0 − 9 0 0

I write 3 above the 0 ones in 90 in vertical form. I know that 3 represents 3 ones. The ones digit in the quotient goes above the ones digit in the total, or dividend.

3

Quotient: Remainder:

I think about unit form to help me divide.

I know that 3 groups of 30 is 90: 3 × 30 = 90.

0

I write 90 below 90 so I can subtract to see how much is left to divide. The difference is 0.

Check:

30 × 3 = 90 I check division with multiplication.

I multiply the quotient, 3, by the divisor, 30.

30 × 3 = 90 My answer matches the dividend. I know my work is correct.

3

3 0 9 0 − 9 0 0 I cannot make another group of 30. The quotient is 3. There is no remainder.

90 ÷ 30 = 3

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83

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 14

Name

14

Date

1. Multiply. Show your work by using a number line.

4 × 0.7 =

0

1

2

3

2. Multiply. Show your work by using a place value chart. Then record your work in vertical form.

3 × 0.15 = ones

tenths

hundredths

×

3. Multiply. Show your work by using the area model to find the partial products. Add the partial products to find the product.

6 × 2.18 ones

tenth

hundredths

6

+

+

=

6 × 2.18 =

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85

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 14

REMEMBER 4. Write the decimal fraction in decimal form.

88 hundredths

88 ___ ​​ ​​ = 100

Divide. Then check your work.

5. 60 ÷ 30

Quotient: Remainder: Check:

86

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 15

Name

15

Date

1. Find the product. Show your work.

2.47 × 30 = 74.1

I rewrite 30 as a product of two numbers.

2.47 × 30 = 2.47 × (10 × 3) = (2.47 × 10) × 3 = 24.7 × 3 = 74.1

I use the associative property of ­multiplication to regroup the factors.

×

2 4 7 tenths 3 1 2

7 4 1 tenths

2.47 × (10 × 3)

(2.47 × 10) × 3 When I multiply by 10, I shift the digits in 2.47 one place to the left.

2.47 × 10 = 24.7 I rewrite the expression so that the s­ econd ­factor is a one-digit number.

24.7 × 3 Now, I use vertical form and unit form to multiply.

The product of 3 and 247 tenths is 741 tenths, or 74.1.

REMEMBER 2. Plot and label each number on the number line. Then use >, =, or < to compare the numbers.

7.64 7.63

>

7.639 7.639

7.64

I see that the interval on the number line is 7.63 to 7.64. I know that when I decompose 1 hundredth into 10 equal parts, each part is 1 thousandth. So I know that the interval is partitioned into thousandths.

I plot 7.64 and 7.639 on the number line. 7.64 is to the right of 7.639 on the number line. This shows that 7.64 is greater than 7.639.

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87

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 15

3. Write the number shown in the area model in decimal form.

0.453 I see an area model decomposed into tenths, hundredths, and thousandths.

I know that each column represents 1 tenth. There are 4 tenths completely shaded.

I know that each tenth is decomposed into 10 hundredths.

I see 5 hundredths c ­ ompletely shaded.

I know that each hundredth is decomposed into 10 thousandths. The zoomed-in square helps me see the thousandths. I see 3 thousandths completely shaded.

Altogether, there are 4 tenths 5 ­hundredths 3 thousandths. I write the ­number in decimal form as 0.453.

88

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 15

4. Round 4.285 to each given place. a. Nearest one

4 b. Nearest tenth

4.3 c. Nearest hundredth

4.29

To round to the nearest one, I think about which two ones 4.285 is between. It is between 4 and 5.

I also think about the halfway point between 4 and 5, which is 4.5.

4.285 is closer to 4 because it is less than halfway ­between 4 and 5.

4.285 rounded to the nearest one is 4.

To round to the nearest tenth, I think about which two tenths 4.285 is between. It is between 42 tenths and 43 tenths, or 4.2 and 4.3.

I also think about the halfway point between 4.2 and 4.3, which is 4.25.

4.285 is closer to 4.3 because it is more than halfway between 4.2 and 4.3.

4.285 rounded to the nearest tenth is 4.3.

To round to the nearest hundredth, I think about which two ­hundredths 4.285 is between. It is between 428 hundredths and 429 hundredths, or 4.28 and 4.29.

I also think about the halfway point between 4.28 and 4.29, which is 4.285.

4.285 is exactly halfway between 4.28 and 4.29. So I round up to 4.29.

4.285 rounded to the nearest hundredth is 4.29.

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89

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TC ▸ Lesson 15

15

Date

Multiply. Show your work by using vertical form.

1. 4 × 2.9 =

2. 3 × 1.62 =

2

×

9

tenths

4

×

1

6

2

hundredths

3

Find the product. Show your work.

3. 0.32 × 4 =

4. 8 × 11.3 =

5. 6.13 × 20 =

6. 4.24 × 50 =

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91

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 15

REMEMBER 7. Write the number shown in the area model in decimal form.

8. Plot and label each number on the number line. Then use >, =, or < to compare the numbers.

8.52

8.522

8.52

8.53

9. Round 7.763 to each given place. a. Nearest one

b. Nearest tenth

c. Nearest hundredth

92

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 16

Name

16

Date

1. Use the area model to find the product.

32 × 0.59 = 5

18.88

tenths

9

hundredths

2

10 tenths

18 hundredths

30

150 tenths

270 hundredths

I break apart 0.59 into 5 tenths and 9 ­hundredths.

I multiply to find the area of each rectangle in the area model. The areas are the partial ­products.

2 × 5 tenths = 10 tenths 2 × 9 hundredths = 18 hundredths 30 × 5 tenths = 150 tenths

1 + 15 + 0.18 + 2.7 = 18 . 88

30 × 9 hundredths = 270 hundredths Now, I add the partial products.

1 + 15 + 0.18 + 2.7

2. Find the partial products. Then add to find the product.

26 × 7.4 =

7 × 2 2 4 2 8 + 1 4 0 1 1, 9 2

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192.4

4 tenths 6 4 0 0 0 4 tenths

I multiply in unit form and record the products in vertical form.

I rename 7.4 by using the smallest unit: tenths.

7.4 = 74 tenths Now, I multiply each unit and r­ ecord the partial products.

6 × 4 = 24 6 × 70 = 420 20 × 4 = 80 20 × 70 = 1,400 I add the partial products.

24 + 420 + 80 + 1,400 = 1,924 1,924 tenths is equal to 192.4.

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93

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 16

REMEMBER 3. Fill in the blank to make the equation true. ​60​ 6 __ ___ ​​ ​​ = ​​ ​​ 10

100

I multiply the numerator and denominator by 10 to rename tenths as hundredths.

6 10 × 6 60 ​​ __ ​​ = ​​ _______ ​​ = ​​ ____ ​​ 10 10 × 10 100

6 The equation shows how to decompose ​ __ ​ 10 into hundredths.

6 60 ​​ __ ​​ = ​​ ____ ​​ 10 100

Consider the expression shown.

2.574 × 104 4. How does the exponent help you think about shifting the digits in the first factor to find the product?

The exponent of 4 helps me know that I need to shift the digits 4 places. Because I am multiplying 2.574 by 10 four times, I need to shift the digits 4 places to the left.

The exponent in the power of 10 tells me how many times I multiply by 10. So the exponent of 4 tells me that I multiply 2.574 by 10 four times.

2.574 × 104 = 2.574 × 10 × 10 × 10 × 10 When I multiply by 104 , the digits shift to the left 4 places.

2.574 × 104 = 25,740

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 16

Name

16

Date

Use the area model to find the product.

1. 24 × 0.71 =

2. 2.6 × 34 = tenths

hundredth

ones

4

4

20

30

tenths

Find the partial products. Then add to find the product.

4. 54 × 3.12 =

3. 37 × 5.8 =

×

5 8 tenths 3 7

+

+

Multiply. Show your work.

5. 42 × 0.4 =

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×

3 1 2 hundredths 5 4

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6. 5.04 × 32 =

95

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 16

REMEMBER 7. Fill in the blank to make the equation true.

4 __ ​​ ​​ = ​​ ___​​ 10

100

Consider the expression shown.

3.285 × 107 8. How does the exponent help you think about shifting the digits in the first factor to find the product?

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EUREKA MATH2 Tennessee Edition 5 ▸ M4 ▸ TC ▸ Lesson 17

Name

17

Date

Multiply. Express the product in unit form and standard form.

1. 42 × 0.4

42

×

4

tenths = 168 tenths = 16.8

1

hundredth =

2. 42 × 0.01

42

×

42

hundredths = 0.42

I rename the second factor in each expression in unit form.

Then, I multiply.

42 × 4 tenths = 168 tenths = 16.8 42 × 1 hundredth = 42 hundredths = 0.42

3. Use your answers in problems 1 and 2 to help you find 42 × 0.41. Show your work.

42 × 0.41 = 42 × 0.4 + 42 × 0.01 = 16.8 + 0.42 = 17.22 I break apart 0.41 into 0.4 and 0.01.

Then, I multiply each part by 42.

42 × 0.41 = (42 × 0.4) + (42 × 0.01) From problem 1, I know the product of 42 and 0.4 is 16.8.

From problem 2, I know the product of 42 and 0.01 is 0.42.

I add the partial products to find the product.

16.8 + 0.42 = 17.22

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97

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 17

4. Consider the expression.

To estimate the product, I round 38 to 40 and I round 3.4 to 3.

I know 40 × 3 = 120.

I use compensation to find the product. 38 groups of 3.4 is equal to 40 groups of 3.4 minus 2 groups of 3.4.

38 × 3.4 = (40 × 3.4) − (2 × 3.4) = 136 − 6.8 = 129.2

38 × 3.4 a. Estimate the product. Show your work.

38 × 3.4 ≈

120

38 × 3.4 ≈ 40 × 3 40 × 3 = 120

b. Find the product. Show your work.

38 × 3.4 = 40 × 3.4 − 2 × 3.4 = 136 − 6.8 = 129.2

The estimated product and the ­actual product are close. So I know my answer is reasonable.

c. Is the answer you wrote in part (b) reasonable?

How do you know?

Yes. My answer is reasonable because 129.2 is close to my estimate of 120.

REMEMBER 5. Use the tape diagram to represent the problem.

Then divide.

7 ÷ ​​ _3​​ = 21 1

7

21 thirds

To think about 7 ÷ ​​ 3__1 ​​ , I ask ­myself, How many thirds are in 7?

The tape diagram represents a total of 7. I partition each part of the tape diagram into thirds. Now, there are 21 parts in the tape diagram. Each part ­represents ​​ __31 ​​. So there are 21 thirds in 7.

7 ÷ ​​ __1 ​​ = 21 3

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 17

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

_1

6. Mr. Perez uses ​​ 4 ​​ gallon of water to water 4 plants. He uses an equal amount of water for each plant. How many gallons of water does Mr. Perez use to water each plant?

1 _1​​ ​​ ÷ 4 = ​​ __ ​​ 4 16

__1

Mr. Perez uses 16 ​​ ​​ gallon of water to water each plant.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the ​​ __1 ​​ gallon of water 4 Mr. Perez uses. I partition the tape diagram into 4 equal parts because I know Mr. Perez uses the water equally ­between 4 plants. The unknown is how many gallons of water Mr. Perez uses for each plant.

1 4

?

I divide to find how many gallons of water Mr. Perez uses for each plant. ​​ __1 ​​ ÷ 4 = __ ​​ 1 ​​ 16 4

Mr. Perez uses __ ​​ 1 ​​ gallon of water for each plant.

16

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99

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 17

Name

Date

17

Multiply. Express the product in unit form and standard form.

1. 43 × 0.2

×

tenths =

tenths =

2. 43 × 0.03

×

hundredths =

hundredths =

3. Use your answers in problems 1 and 2 to help you find 43 × 0.23. Show your work.

4. Consider the expression.

27 × 4.2 a. Estimate the product. Show your work.

27 × 4.2 ≈

b. Find the product. Show your work.

c. Is the answer you wrote in part (b) reasonable? How do you know?

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101

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 17

REMEMBER 5. Use the tape diagram to represent the problem. Then divide.

6 ÷ ​​_4​​ = 1

6

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

_1

6. Lisa uses ​​ 2 ​​ gallon of yogurt to make 8 smoothies. She uses an equal amount of yogurt in each smoothie. How many gallons of yogurt are in each smoothie?

102

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 18

Name

18

Date

1. Complete the area model. Rename the numbers as fractions to multiply. Express the product in fraction form and standard form. The area model represents 1.

0.5 × 0.9 = 0.45 5

9

10

10

45

5×9 _____ ​​ ​​ × ​​_____​​ = ​​ ______​​ = _____ ​​ ​​ 10 × 10

100

5 10 9 10

The area model is partitioned into 10 tenths vertically. It is also partitioned into 10 tenths horizontally. It shows hundredths.

9 I rename 0.5 as __ ​​ 5 ​​ and 0.9 as ​​ __ ​​.

10 10

9 ​​ as __ ​​ 5 ​​ of __ ​​ 9 ​​ .

I think about __ ​​ 5 ​​ × ​​ __ 10 10 10 10

​​ 9 ​​ .

I use the area model to help me find __ ​​ 5 ​​ of __ 10 10

5 ​​ horizontally. I draw a box to show the I label __ ​​ 9 ​​ vertically and ​​ __ 10 10

​​ 9 ​​ . area that represents __ ​​ 5 ​​ of __ 10 10

9 ​​ 9 ​​ is ____ ​​ ​​ . So __ ​​ 5 ​​ × ​​ __ ​​ = ____ ​​ ​​ .

I use the area model to see that __ ​​ 5 ​​ of __ 10 10 100 10 10 100 45

Rename the decimal numbers as fractions to multiply.

Express the product in fraction form and standard form.

2. 3.2 × 0.4 = 1.28 32

4

10

10

32 I rename 3.2 as ___ ​​ 10 ​​ and 0.4 as __ ​​ ​​ .

10 4

I multiply the fractions.

32 × 4 ​​_____​​ × ​​_____​​ = ​​ ______​​ 10 × 10 128

= ​​_____​​ 100 © Great Minds PBC •

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32 × 4 = 128 10 × 10 = 100

128 So the product is ​​ ____ ​​.

100 128 I rename ​​ ____ ​​ as 1.28.

100

103

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 18

3. 3.2 × 0.04 = 0.128 32

4

10

100

32 I rename 3.2 as ___ ​​ 10 ​​ and 0.04 4 ____ as ​​ 100 ​​ .

32 × 4 _____ ​​ ​​ × ​​_____ ​​ = ​​ ______ ​​ 10 × 100

I multiply the fractions.

128

= ​​_____​​

32 × 4 = 128 10 × 100 = 1,000

1,000

128 So the product is ​​ _____ ​​ .

1,000

128 I rename ​​ _____ ​​ as 0.128.

1,000

REMEMBER Estimate the product. Then multiply.

4. 321 × 184 ≈

=

300

×

200

60,000

321 × 184 1284 1 25680 + 32100 1 1 5 9, 0 6 4

I estimate the product by rounding each factor to the nearest hundred.

I multiply by using vertical form.

I multiply 321 by 4 ones. The partial product is 1,284.

I multiply 321 by 8 tens. The partial product is 25,680.

I multiply 321 by 1 hundred. The partial product is 32,100.

I add the partial products.

1,284 + 25,680 + 32,100 = 59,064 321 × 184 = 59,064 My answer is reasonable because 59,064 is close to my ­estimate of 60,000.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 18

5. Use >, =, or < to compare the numbers. Plot the location of each number on the number line to justify your answer.

19.67 19.4

19.47 19.5

>

19.47 19.67 19.7

19.6

The interval between each number on the number line represents 1 tenth. Each tenth is partitioned into 10 equal parts, which represents hundredths.

I know that 19.67 has 6 tenths 7 hundredths. I start at 19.6 and count 7 hundredths. I plot and label the point 19.67.

I know that 19.47 has 4 tenths 7 hundredths. I start at 19.4 and count 7 hundredths. I plot and label the point 19.47.

I see that 19.67 is to the right of 19.47. I know 19.67 is greater than 19.47.

I write the symbol for greater than, >.

19.67 > 19.47

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105

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TC ▸ Lesson 18

18

Date

1. Complete the area model. Rename the numbers as fractions to multiply. Express the product in fraction form and standard form. The area model represents 1.

0.6 × 0.7 = × _____​​ × ​​_____​​ = ​​ ______ = ​​ _____​​ 10

10

×

Rename the decimal numbers as fractions to multiply. Express the product in fraction form and standard form.

2. 2.1 × 0.5 =

3. 2.1 × 0.05 =

× _____​​ × ​​_____​​ = ​​ ______ 10

10

×

× ___ ​​ × ​​_____​​ = ​​ _______ ×

= ​​ _____

= ​​ _____​​

Multiply. Show your work.

4. 0.3 × 0.8 =

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5. 0.06 × 0.7 =

107

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 18

REMEMBER Estimate the product. Then multiply.

6. 293 × 118 ≈

×

=

7. Use >, =, or < to compare the numbers. Plot the location of each number on the number line to justify your answer.

8.32

8

108

8.1

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8.07

8.2

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8.4

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 19

Name

19

Date

1. Multiply. Express the product in unit form and in standard form. Write an equation in fraction form to check the units in your product.

2.3 × 0.8 = 1.84 2

×

1

2

8

3

tenths

8

tenths

4

hundredths

184

23

8

10

10

_____​​ × ​​_____​​ = ​​_____​​ 100

I rename the numbers as tenths and multiply.

When I multiply tenths by tenths, the unit of the product is hundredths.

The product is 184 hundredths, or 1.84.

I use fraction form to check my answer.

2. Multiply. Show your work.

3.61 × 0.7 = 2.527 ×

3 6 1 hundredths 7 tenths

8 I rename 2.3 as ___ ​​ 23 ​​ and 0.8 as ​​ __ ​​ . I multiply the 10 10

two fractions and get ​​ ____ ​​ , which is 1.84.

100 184

4

2 , 5 2 7 thousandths

I rename 3.61 as 361 hundredths and 0.7 as 7 tenths.

When I multiply tenths by hundredths, the unit of the product is thousandths.

I think of the numbers as whole numbers when multiplying.

361 × 7 = 2,527 The product is 2,527 thousandths, or 2.527.

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109

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 19

REMEMBER Complete the tape diagram. Then complete the vertical form and check your work.

3. 210 ÷ 70 a.

b.

210 70

70

3 70

7

0

2

1

0

−

2

1

0 0

Check:

210 =

3

× 70

The tape diagram represents a total of 210. The ­divisor, 70, is the size of each group.

I use unit form to help me think about 210 ÷ 70.

21 tens ÷ 7 tens = 3 There are 3 groups of 70 in 210.

I partition the tape diagram to show 3 groups and label each group 70.

I record the division in vertical form.

I multiply to check my work.

The product matches the dividend, 210. My work is correct.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 19

4. Use the place value chart to complete the statement and equation. ones

tenths

hundredths thousandths ×

10

tens

5

hundredths

is 10 times as much as

5

thousandths

.

0.05 = 10 × 0.005

The place value chart shows that 5 hundredths is 10 times as much as 5 thousandths.

The digits shift one place to the left to move from thousandths to the next larger unit of hundredths.

I write a multiplication equation to represent this relationship.

0.05 = 10 × 0.005

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111

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TC ▸ Lesson 19

19

Date

Multiply. Express the product in unit form and in standard form. Write an equation in fraction form to check the units in your product.

1. 1.9 × 0.4 =

×

1

2. 2.7 × 0.03 =

9

tenths

4

tenths

_____​​ × ​​_____​​ = ​​_____​​ 10

10

×

2

7

tenths

3

hundredths

_____​​ × ​​_____​​ = ​​_____​​ 10

100

Multiply. Show your work.

3. 0.9 × 8.1 =

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4. 1.45 × 3.2 =

113

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TC ▸ Lesson 19

REMEMBER Complete the tape diagram. Then complete the vertical form and check your work.

5. 320 ÷ 80 a.

b.

320 80

8

0

3

2

0

Check:

320 = 80 × 6. Use the place value chart to complete the statement and equation. ones

tenths

hundredths thousandths ×

10

tens

is 10 times as much as

.

= 10 ×

114

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Module 4 Topic D

FAMILY MATH Division of Decimal Numbers Dear Family,

Your student is learning to divide decimal numbers by using methods that are familiar from whole-number division. Students divide decimal numbers by one-digit whole numbers; by multiples of 10, 100, or 1,000; and by two-digit whole numbers. By renaming decimal numbers as fractions, students connect division with decimal numbers to division with fractions. Your student sees division expressions as equal groups (e.g., 3 groups of 4 tenths make 12 tenths) and parts of a

whole (e.g., 5 tenths is ___ ​​ ​​ of 50). Students use their experience dividing whole numbers to select 1 100

the most efficient strategy and determine the reasonableness of their answers, with a focus on the placement of the decimal point in the quotient.

249.6 ÷ 52 = 2,496 tenths ÷ 52 = 48 tenths = 4.8 6.72 ÷ 32 =

3.6 ÷ 3 = 1.2 36 tenths ÷ 3 = 12 tenths

Unit thinking allows students to use whole-number division strategies to divide before renaming the quotient in decimal form.

32

0.21

2 tenths

1 hundredth

64 tenths

32 hundredths

Students draw an area model to divide decimal numbers by two-digit whole numbers.

8 40 52 2 4 9 6 –2080 416 –416 0

Students use unit form and long division to divide decimal numbers by two-digit whole numbers.

At-Home Activity Find the Cost Turn daily situations into questions to help your student practice dividing with decimal numbers.

•

“A box of crackers costs $3.75. What is the cost per serving if there are 10 servings in the box?” (3.75 ÷ 10)

•

“A gym membership costs $39.50 per month. What is the cost per day if there are 30 days in the month?” (39.50 ÷ 30) “What is the cost per visit if you visit the gym 15 times in the month?” (39.50 ÷ 15)

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115

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 20

Name

Date

20

1. Divide. Express the quotient in unit form and standard form.

42 hundredths ÷ 7 = 0.42

÷7=

6

hundredths

0.06

2. Draw on the place value chart to divide.

Then complete the equation.

7.59 ÷ 3 = ones

2.53 tenths

I use unit form and mental math to find the quotient.

42 ÷ 7 = 6, so 42 hundredths ÷ 7 = 6 hundredths.

I write the equation in standard form, 0.42 ÷ 7 = 0.06.

hundredths

2 ones 5 tenths 3 hundredths

I draw to represent 7 ones 5 tenths 9 hundredths, or 7.59, on the place value chart.

The divisor is 3. So I draw lines to represent 3 groups.

To divide, I distribute the units into the 3 groups, crossing them out as I go.

I start with the largest units: ones. After equally distributing the ones into 3 groups, there is 1 one remaining. I rename the remaining one as 10 tenths. Now, there are 15 tenths.

I distribute the tenths equally into 3 groups. There are no tenths remaining.

Next, I distribute the hundredths equally into 3 groups. There are no hundredths remaining.

Now, I see 2 ones 5 tenths 3 hundredths in each group, or 2.53.

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117

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 20

REMEMBER 3. Add.

8 11 __ ___ ​​ 10​​ + 100 ​​ ​​ 91 ​​ ___​​ 100

I need like units to add. I rename tenths as hundredths.

100 is 10 times as much as 10.

8 I multiply the numerator and the denominator of ​​ __ ​​ by 10 to 10 rename tenths as hundredths.

10× 8 80 __ ​​ 8 ​​ = ​​ ______ ​​ = ​​ ____ ​​

Now, I add like units.

4. Evaluate. a. 12 + (8 × 3) −1

35 b. (12 + 8) × (3 − 1)

40

10

10× 10

100

I read the first expression: 12 + (8 × 3) − 1.

I evaluate the expression in parentheses first.

I find 8 × 3, and then I add and subtract.

12 + (8 × 3) − 1 = 12 + 24 − 1 = 35 I read the second expression: (12 + 8) × (3 − 1).

I notice that the expressions in part (a) and part (b) use the same numbers and operations, but the parentheses group the numbers and operations differently.

I evaluate the expressions in parentheses first.

I find 12 + 8 and 3 − 1 before I multiply.

(12 + 8) × (3 − 1) = 20 × 2 = 40

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 20

Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number.

5. Kayla swims two legs of a race. She swims the first leg in 1.4 minutes. She swims the second leg in 1.68 minutes. How many minutes does Kayla swim altogether during the race?

1.4 + 1.68 = 3.08 Kayla swims for 3.08 minutes.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with two parts. I label each part to represent the number of minutes Kayla swims each leg of the race. The total number of minutes Kayla swims is unknown, so I label it m. m 1.4

1.68

I add to find the unknown number of minutes.

1.4 + 1.68 = m 1.40 + 1.68 1 3. 0 8

m = 3. 0 8

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119

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 20

Name

Date

20

Divide. Express the quotient in unit form and standard form.

1. 12 tenths ÷ 4 =

tenths

1.2 ÷ 4 = 2. 396 tenths ÷ 3 =

tenths

÷3= 3. 720 hundredths ÷ 9 =

hundredths

÷9= Draw on the place value chart to divide. Then complete the equations.

4. 6.15 ÷ 5 = ones

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hundredths

121

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 20

REMEMBER 5. Add.

3 57 __ ​ ​ + ​​ ___​​ 10

100

6. Evaluate. a. (40 − 30) ÷ (10 − 5)

b. 40 − (30 ÷ 10) − 5

Use the Read–Draw–Write process to solve the problem. Write the solution statement by using a decimal number.

7. Scott puts 3.76 grams of blueberries in his oatmeal. He feeds his bird 1.3 grams of blueberries.

How many grams of blueberries does Scott use altogether?

122

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 21

Name

21

Date

1. Draw on the place value chart to divide. Then record your work in vertical form.

4.5 ÷ 3 = ones

1.5 tenths

hundredths

3

– –

I draw to represent 4 ones 5 tenths, or 4.5, on the place value chart. The divisor is 3, so I draw lines to represent 3 groups.

To divide, I equally distribute the units into the 3 groups, crossing them out as I go.

I start with the largest unit: ones. After equally distributing the ones into 3 groups, there is 1 one remaining. I rename the remaining one as 10 tenths. Now, there are 15 tenths.

I distribute the tenths equally into 3 groups. There are no tenths remaining.

Now I see 1 one 5 tenths in each group, or 1.5.

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0.

5

1.

0

4.

5

3.

0

1.

5

1.

5 0

I show the work in vertical form.

When I equally distribute the ones on the place value chart, the partial quotient is 1 one or 1.0. I record 1.0 in vertical form.

I distributed a total of 3 ones.

I record that below 4.5 as 3.0.

Then, I subtract: 4.5 − 3.0 = 1.5.

There are 15 tenths left to divide.

When I equally distribute the tenths on the place value chart, the partial quotient is 5 tenths or 0.5. I record 0.5 in vertical form. I distributed a total of 15 tenths. I record that below 1.5 as 1.5. Then, I subtract: 1.5 − 1.5 = 0. There is nothing left to divide. I add the partial quotients.

1.0 + 0.5 = 1.5 123

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 21

2. Divide. Show your work.

56.8 ÷ 800 =

0.071

I write a related expression for 56.8 ÷ 800.

56.8 ÷ 800 = 56.8 ÷ 8 ÷ 100

56.8 ÷ 8 ÷ 100

= 7.1 ÷ 100

I use vertical form to show how to divide 56.8 by 8.

= 0.071​

The quotient is 7.1. Then, I divide 7.1 by 100.

To divide by 100, I shift the digits in 7.1 two places to the right.

8

– –

0.

1

7.

0

5

6.

8

5

6.

0

0.

8

0.

8 0

7.1 ÷ 100 = 0.071 REMEMBER 3. Write a statement and expression to represent the tape diagram. Then evaluate your expression.

8

13

8

13

8

13

Statement: 3 times as much as the sum of 8 and 13 Expression: 3 × (​ 8 + 13)​​​ Value of expression:

63

In the tape diagram, I see the sum of 8 and 13 three times. I write a statement by using times as much as.

3 times as much as the sum of 8 and 13 I write an expression to represent the statement. I use parentheses to group 8 + 13.

3 × (8 + 13) To find the value of the expression, I add 8 and 13. Then, I multiply the sum by 3.

3 × (8 + 13) = 3 × 21 = 63 The value of the expression is 63.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 21

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

4. On Monday, workers load 45 delivery vans with boxes. Workers load 310 boxes in each van.

On Tuesday, workers load 232 more boxes in vans than the number of boxes they loaded on Monday. How many total boxes do the workers load on Tuesday?

45 × 310 = 13,950 13,950 + 232 = 14,182 The workers load 14,182 boxes on Tuesday.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent the number of boxes on Monday. I draw to show 45 vans with 310 boxes in each van.

I draw another tape diagram to represent the number of boxes on Tuesday. I draw one part to represent the number of boxes on Monday and another part to represent 232. The unknown is the number of boxes the workers load on Tuesday.

Monday

310 boxes

...

45 vans Tuesday

232

? boxes on Tuesday I multiply to find the total number of boxes on Monday.

45 × 310 = 13,950 I add to find the total number of boxes on Tuesday.

13,950 + 232 = 14,182

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125

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 21

Name

Date

21

Draw on the place value chart to divide. Then record your work in vertical form.

1. 1.05 ÷ 3 =

ones

tenths

hundredths

2. Divide. Show your work.

7.14 ÷ 60 =

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127

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 21

REMEMBER 3. Write a statement and expression to represent the tape diagram. Then evaluate your expression.

Statement:

12

23

12

23

12

23

12

23

Expression: Value of expression:

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

4. Last year, Ryan practiced guitar for 25 minutes every school day. There are 190 school days in a year. This year, Ryan wants to practice for 375 more minutes than he did last year. For how many minutes does Ryan want to practice guitar this year?

128

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 22

Name

22

Date

1. Complete the area model and vertical form. Then complete the equation.

414.4 ÷ 56 =

7.4

56

7

392

4

tenths

224 tenths

I use the area model to find partial quotients.

The first partial quotient is ​7​. I write ​7.0​ in ­vertical form and subtract ​392​ from ​417.4​ to see how much is left to divide. The difference is ​2 2.4​.

I rename ​2 2.4​ as ​2 24​ tenths and write ​2 24​ tenths in the area model. I use a related multiplication fact to think about dividing ​2 24​ by ​5 6​. I know 56 × 4 = 224.

The units are tenths. So the unknown side length is ​ 4​ tenths.

5

6

– –

0.

4

7.

0

4

1

4.

4

3

9

2.

0

2

2.

4

2

2.

4 0

I continue this work in vertical form. I write ​0.4​ above ​7.0​. Then, I subtract ​2 2.4​ from ​2 2.4​. The difference is ​0​.

I add the partial quotients: 7 ones + 4 tenths = 7.4.

2. Divide. Show your work.

164.7 ÷ 27 =

6.1

164.7 ÷ 27 = 1,647 tenths ÷ 27

= 61 tenths

= 6.1

1 60 2 7 1, 6 4 7 –1 6 2 0 27 –27 0

I rename the dividend in unit form and use vertical form to divide the whole numbers.

The quotient is 61, and the units are tenths.

164.7 ÷ 27 = 6.1

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129

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 22

REMEMBER 3. Write an expression that represents the word problem. Draw a tape diagram if it helps you.

Blake uses lights to create 3 displays that are all the same. Each display has 10 blue lights and 12 white lights. How many total lights are in Blake’s displays?

10

12

10

12

10

12

3 × (10 + 12) I draw and label parts in a tape diagram to represent the 10 blue lights and 12 white lights. There are 3 displays, so I draw 3 groups of 10 and 12.

I use parentheses to show 1 group of 10 and 12.

(10 + 12) I use multiplication to show 3 groups of 10 and 12.

3 × (10 + 12)

4. Use >, =, or < to compare the expressions.

31 × (14 + 23)

<

(14 + 23) × 54

I see the (14 + 23) in both expressions.

I can compare the expressions without multiplying.

I compare the number of groups.

I know 31 times as much as the sum of 14 and 23 is less than 54 times as much as the sum of 14 and 23.

I use the less than symbol to compare the expressions.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 22

5. Draw a model to represent the word problem. Explain how your model represents the product.

_​​ 2​​ of the shoes in the store are sneakers. _​​ 1​​ of the sneakers are white. What fraction of the shoes 3

6

in the store are white sneakers?

1 3 2 6

_1 _2

The area model represents the product ​​ 3 ​​ × ​​ 6 ​​ because the area is partitioned into sixths, and

_1 _2

then each sixth is partitioned into 3 equal parts. ​​ 3 ​​ of ​​ 6 ​​ is outlined. The model shows a product

__2

of ​​ 18 ​​ because there are 2 shaded parts out of 18 total parts.

I know that ​​ __62 ​​ of the shoes are ­sneakers and that __3​​ 1 ​​ of

those s­ neakers are white. I need to find ​​ __31 ​​ of __​​ 62 ​​ .

I draw an area model and partition it into sixths. I label __​​ 62 ​​.

I partition each sixth into 3 equal parts so I can find __3​​ 1 ​​ of __​​ 62 ​​ .

I shade and label ​​ __31 ​​ of __​​ 62 ​​ .

1 3 2 6

2 The shaded area represents ​​ ___ ​​ ­because the new unit is 18 eighteenths and there are 2 units shaded.

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131

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 22

Name

22

Date

Complete the area model and vertical form. Then complete the equation.

1. 42.77 ÷ 13 =

13

3

39

tenths

26 tenths

hundredths hundredths

1

3.

0

0

3

4

2.

7

7

–

3

9.

0

0

3.

7

7

–

–

Divide. Show your work.

2. 26.98 ÷ 38 =

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3. 96.35 ÷ 41 =

133

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 22

REMEMBER 4. Write an expression that represents the word problem. Draw a tape diagram if it helps you.

There are 32 fifth grade students in art class. There are 22 fifth grade students in music class.

The entire fifth grade has 3 times the number of students in art and music classes.

How many students are in the entire fifth grade?

5. Use >, =, or < to compare the expressions.

23 × (12 + 17)

(12 + 17) × 34

6. Draw a model to represent the word problem. Explain how your model represents the product.

_​​ 2​​ of the produce in the farmer’s market is apples. _​​ 1 ​​ of the apples are Golden Delicious. What 5

7

fraction of the produce in the farmer’s market are Golden Delicious apples?

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 23

Name

23

Date

Write the divisor as a fraction. Complete the statements to help you divide. Then complete the equation.

1. 6.8 ÷ 0.1 = 6.8 ÷ ___ ​​ ​​ 1

10

__1 1 __ groups of 10 ​​ ​​ make 0.8. __1 groups of ​​ ​​ make 6.8.

60

groups of 10 ​​ ​​ make 6.

8 68

10

6.8 ÷ 0.1 =

I rename 0.1 as __ ​​ 1 ​​.

10

1 I know 10 groups of ​​ __ ​​ make 1. So 10 1 __ 60 groups of ​​ 10​​ make 6, and 8 groups of __ ​​ 1 ​​ make 0.8.

10

68

I add to find the quotient.

60 + 8 = 68

1

2. 14.1 ÷ 0.01 = 14.1 ÷ ____ ​​ ​​ 100

6.8 ÷ 0.1 = 68

___ 1,400 groups of 100 ​​ ​​ make 14.

1

1 ___ 1 ___ groups of ​​ ​​ make 14.1.

10

groups of ​​ 100 ​​ make 0.1.

1,410

100

14.1 ÷ 0.01 = 1,410

I rename 0.01 as ____ ​​ 1 ​​ .

100

I know 100 groups of ____ ​​ 1 ​​ make 1. So 14 hundred, or 100 1,400, groups of ____ ​​ 1 ​​ make 14. I also know that 100 1 10 groups of ​​ ____ ​​ make 0.1.

100 I add to find the quotient.

1,400 + 10 = 1,410 14.1 ÷ 0.01 = 1,410

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135

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 23

3. Rewrite the expression as a decimal number divided by a fraction. Then divide.

76.3 ÷ 0.01 = 7,630

___​​ = 7,630 76.3 ÷ ​​ 100 1

1 I rename 0.01 as ​​ ____ ​​. The expression becomes 76.3 ÷ ____ ​​ 1 ​​.

100 100

I know there are 7,600 groups of ____ ​​ 1 ​​ in 76.

100

I know there are 30 groups of ____ ​​ 1 ​​ in 0.3.

100 I add to find the quotient.

7,600 + 30 = 7,630

REMEMBER 4. Order the numbers from least to greatest.

5.362,

5.36,

15.362,

5.326 5.326

<

5.36

<

5.362

<

15.362

I notice that 15.362 is the only number with a digit in the tens place.

So I know that 15.362 is the greatest number. ?

<

?

<

?

<

15.362

I notice that the rest of the numbers all have 5 ones. I think about the n ­ umbers in unit form by using ones and thousandths. 5.362 is 5 ones 362 ­thousandths. 5.36 is 5 ones 360 thousandths. 5.326 is 5 ones 326 thousandths.

I know that 326 thousandths is less than 360 thousandths, and 360 ­thousandths is less than 362 thousandths.

5.326

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<

5.36

<

5.362

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<

15.362

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 23

5. Represent 5.426 in expanded notation by using fractions.

5 × 1 + 4 × __ ​​ ​​+ 2 × ​​ ___ ​​ + 6 × ​​ ____ ​​ 10 100 1,000 1

1

1

To write a number in expanded notation, I represent the number as the sum of the value of each digit. I represent the value of each digit by using multiplication.

There are 5 ones. I represent 5 ones as 5 × 1.

There are 4 tenths. I represent 4 tenths as 4 × __ ​​ 1 ​​.

10

1 ​​.

There are 2 hundredths. I represent 2 hundredths as 2 × ​​ ____ 100

There are 6 thousandths. I represent 6 thousandths as 6 × _____ ​​ 1 ​​.

1,000

I add the expressions to represent 5.426 in expanded notation.

5 × 1 + 4 × __ ​​ 1 ​​ + 2 × ____ ​​ 1 ​​ + 6 × _____ ​​ 1 ​​ 10 100 1,000

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137

EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TD ▸ Lesson 23

23

Date

Write the divisor as a fraction. Complete the statements to help you divide. Then complete the equation.

___​​

1. 5.3 ÷ 0.1 = 5.3 ÷ ​​

__1 1 __ groups of 10 ​​ ​​ make 0.3. __1 groups of ​​ ​​ make 5.3. groups of 10 ​​ ​​ make 5.

10

5.3 ÷ 0.1 =

___​​

2. 34.7 ÷ 0.1 = 34.7 ÷ ​​

__1 1 __ groups of 10 ​​ ​​ make 0.7. __1 groups of ​​ ​​ make 34.7.

groups of 10 ​​ ​​ make 34.

10

34.7 ÷ 0.1 =

3. 6.4 ÷ 0.01 = 6.4 ÷ ___ ​​ ​​

600 groups of ___ ​​ ​​ make 6.

100 1

1 ___ 1 ___ groups of ​​ ​​ make 6.4.

groups of 100 ​​ ​​ make 0.4.

100

6.4 ÷ 0.01 =

4. 11.6 ÷ 0.01 = 11.6 ÷ ___ ​​ ​​ 1 ___ 1 ___ groups of 100 ​​ ​​ make 0.6.

1 ___ groups of ​​ ​​ make 11.6.

groups of 100 ​​ ​​ make 11.

100

11.6 ÷ 0.01 =

Rewrite the expression as a decimal number divided by a fraction. Then divide.

5. 62.1 ÷ 0.1 =

6. 8.64 ÷ 0.01 =

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139

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 23

REMEMBER 7. Order the numbers from least to greatest.

21.58, 12.584, 21.584, 21.54 <

<

<

8. Represent 4.859 in expanded notation by using fractions.

140

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 24

Name

24

Date

1. Use unit form to divide.

36.8 ÷ 0.4 = 368

I rename 36.8 and 0.4 as tenths.

92

tenths ÷

4

tenths =

92

2. Complete the equation.

1.86 ÷ 0.03 =

=

186

=

62

0.01

÷3

÷3

I think of dividing by 0.03 as dividing by 0.01 and then dividing by 3.

To divide 1.86 by 0.01, I shift the digits two places to the left. I get 186.

3. Divide. Show your work.

25.13 ÷ 0.07 =

359

25.13 ÷ 0.07 = 2,513 hundredths ÷ 7 hundredths 9 50 300 7 2, 5 1 3 –2 10 0 413 –35 0 63 –6 3 0

I use mental math to find the quotient.

368 tenths ÷ 4 tenths = 92

62

1.86 ÷ 0.03 = 1.86 ÷

36.8 ÷ 0.4 = 368 tenths ÷ 4 tenths

Now, the expression is 186 ÷ 3. I use mental math to divide.

186 ÷ 3 = 62

I rename the dividend and the divisor as hundredths.

25.13 ÷ 0.07 = 2,513 hundredths ÷ 7 hundredths Now, I divide whole numbers: 2,513 ÷ 7. I use vertical form to show how to divide.

25.13 ÷ 0.07 = 359

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141

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 24

REMEMBER 4. Add. Show your work.

4.63 + 2.9 = 7.53 4.53 0.1

I look at both numbers. 2.9 is close to the next one: 3.

I decompose 4.63 into 0.1 and 4.53.

I add 0.1 to 2.9 to make the next one.

2.9 + 0.1 = 3 I add 4.53 to 3 to find the sum.

4.53 + 3 = 7.53 So 4.63 + 2.9 = 7.53.

142

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 24

5. Subtract. Show your work.

5.4 − 1.37 =

4.03

3 10

5 .4 0 – 1.3 7 4.0 3

I can write subtraction vertically. I line up the digits by place value. I notice that 5.4 does not have a digit in the hundredths place but 1.37 has a digit in the hundredths place. I write 0 in the hundredths place to record 5.4 as 5.40.

5.40 - 1.37 There are not enough hundredths to subtract 7 hundredths.

I rename 1 tenth in 5.4 as 10 hundredths. Now, 5.4 is renamed as 5 ones 3 tenths 10 hundredths.

3 10

5.40 - 1.37 I subtract like units.

5.4 − 1.37 = 4.03

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143

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 24

Name

Date

24

1. Use unit form to divide.

4.97 ÷ 0.07 =

hundredths ÷

hundredths

= 2. Complete the equation.

12.6 ÷ 0.3 = 12.6 ÷ =

÷3 ÷3

= 3. 3.06 ÷ 0.06 = 3.06 ÷

=

÷6 ÷6

= 4. Divide. Show your work.

49.2 ÷ 0.3 =

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145

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 24

REMEMBER 5. Add. Show your work.

4.7 + 3.58 =

6. Subtract. Show your work.

6.7 − 1.56 =

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 25

Name

25

Date

1. Complete the equation by using unit form and whole numbers. Write the quotient in standard form.

3.8 ÷ 0.8 =

38

tenths ÷

=

38

÷

=

4.75

8

tenths

8

4 8 38 –32 6 4 ​​ _8 ​​ = 4 ​​ _4 ​​ = 4.75 6

3

I rewrite 3.8 ÷ 0.8 in unit form.

The dividend and divisor have the same unit.

So I can use whole numbers when dividing: 38 ÷ 8.

38 ÷ 8 is 4 with 6 left over.

I write the quotient as a mixed number and then rename as a decimal number.

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147

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 25

2. Complete the equation. Write the quotient in standard form.

9.74 ÷ 0.04 = 9.74 ÷ 0.01 ÷ 4 =

974

=

243.5

÷

4

0. 5 3. 0 4 0. 0 2 0 0. 0 4 9 7 4. 0 – 8 0 0. 0 1 7 4. 0 – 1 6 0. 0 1 4. 0 – 1 2. 0 2. 0 – 2.0 0

I think of dividing by 0.04 as dividing by 0.01 and then dividing by 4. When I divide by 0.01, I shift the digits in 9.74 two places to the left.

9.74 ÷ 0.01 = 974 I use vertical form to show how to divide 974 by 4.

974 ÷ 4 = 243.5, so 9.74 ÷ 0.04 = 243.5.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 25

REMEMBER 3. Use >, =, or < to compare the expressions. Explain how you can compare the expressions without evaluating.

_​​ 5​​

>

8

​​ _5 ​​ × _​​ 8 ​​ 5

4

​​ _8 ​​ is in both expressions, but the second expression is finding a part, or _​​ 5 ​​ , of ​​ _8 ​​ . So the value _5 of the second expression is less than ​​ 8 ​​ . The value of the first expression is greater than the 5

4

5

value of the second expression.

I see that __ ​​ 5 ​​ is in both expressions.

8

__​​ 5​​ as __​​ ​​ of __​​ 5​​ . I know that __​​ ​​ of __​​ 5​​ is I can think about __ ​​ 5 ​​ × 8 5 5 8 8 4

4

4

__​​ 5​​ . less than __ ​​ 5 ​​ because it is a part of 8 8

I do not need to evaluate the expressions because I know that the value of the first expression is greater than the value of the second expression.

4. Explain why the number sentence is true.

_​​ 4​​ × 3 > 3 3

4 4 ​​ _​​ × 3 is greater than 3 because ​​ _​​ is greater than 1. When you 3

3

multiply 3 by any number greater than 1, the product is greater than 3.

__​​ 4​​ × 3 has the same value as 3 groups of __​​ 4​​ . The total 3 3 4 of 3 groups of __ ​​ ​​ is greater than 3.

3

0

1

2

3

4

Multiplying a whole number by any number greater than 1 results in a product that is greater than the whole-number factor.

So I know that multiplying 3 by __ ​​ 3 ​​, which is greater than 1, results in a product that is greater than 3.

4

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149

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 25

Name

25

Date

1. Complete the equation by using unit form and whole numbers. Write the quotient in standard form.

1.3 ÷ 0.2 = =

tenths ÷

tenths

÷

= 2. Divide. Use unit form to help you. Write the quotient in standard form.

5.2 ÷ 0.16 =

3. Complete the equation. Write the quotient in standard form.

8.91 ÷ 0.06 = 8.91 ÷ 0.01 ÷ 6 =

÷

=

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151

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TD ▸ Lesson 25

REMEMBER 4. Use >, =, or < to compare the expressions. Explain how you can compare the expressions without evaluating.

_​​ 5​​

​​ _3 ​​ × _​​ 6 ​​ 2

6

5

5. Explain why the number sentence is true.

_​​ 8​​× 6 > 6 7

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Module 4 Topic E

FAMILY MATH Applications of Decimals Dear Family,

Your student is applying their understanding of decimal numbers in different ways. They use multiplicative relationships to convert metric and customary measurements involving decimals from larger units to smaller units. Students also convert a metric measurement involving a decimal to a mixed-unit measurement. For example, 3.5 liters is converted to the mixed-unit measurement of 3 liters 500 milliliters. They apply their understanding of rounding decimals to estimate conversions with customary units. Students solve word problems involving converting decimal measurements.

6.25 m = 6m

6

m

25

cm

0.25 m

0.25 m = 0.25 × 1 m = 0.25 × 100 cm = 25 cm

When students convert a decimal measurement to a mixed-unit measurement, they break apart the decimal measurement into the whole number part and the decimal part. Then they convert the decimal part to smaller units.

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3​ .5 gal ​=​ 3.5 ​×​ 1 gal ​ =​ 3.5 ​×​ 4 qt ​ =​ 14 qt​

When students convert a measurement from a larger unit to a smaller unit, they multiply by a whole number.

153

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE

At-Home Activity Unit Conversion Help your student convert measurements, such as length, capacity, and weight.

•

•

“The bag of rice weighs ​0.125​kilograms. What is the weight of the rice in grams?

Milligrams?” (0.125 kg = 125 g = 125,000 mg) •

​​ ​​1 ​ ,000​ grams ​1​ kilogram =

•

​ ,000​ milligrams ​1​ gram = 1

“Riley runs the ​100​-meter dash. How far does Riley run in centimeters?”

(100 m = 10,000 cm) •

•

“How many quarts are in ​2​gallons of milk?” (2 gal = 8 qt) •

154

1​ ​ meter = ​​ ​​ 1 ​ 00​ centimeters ​​ ​4​ quarts ​1​ gallon =

FA M I LY M AT H ▸ Module 4 ▸ Topic E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 26

Name

26

Date

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

_5

1. Noah puts 2 ​ 0​quarts of soil equally into 6 ​ ​pots. The blue pot already has ​​ 6 ​​ quarts of soil in it.

How many quarts of soil are now in the blue pot?

20 20 ÷ 6 = ​__ ​ ​​ 6 5 __ 25 20 _ 1 __ ​​ 6 ​​ + ​6​ ​​ = ​​6 ​​ = 4 ​_​6​​

_1

There are now 4 ​ ​ 6 ​quarts of soil in the blue pot.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent a total of ​20​quarts of soil. I partition the total into 6 equal parts to represent the pots. The amount in each part is unknown.

20

?

I divide ​20​by ​6​to find the number of quarts of soil Noah puts in each pot.

20 Noah puts ​​ ___ ​​quarts of soil in each pot. The blue 6

pot already has __ ​​ 65 ​​ quarts of soil in it. I add ___ ​​ 20 ​​ to __ ​​ 65 ​​.

6

I rename ___ ​​ 25 ​​ as a mixed number because 4​​ __61 ​​ quarts 6 25 makes more sense than ​​ ___ ​​ quarts.

6

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155

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 26

_1

2. Lisa cuts ​3​feet of paper into pieces that are each ​​ 6 ​​ foot long. How many pieces of paper does Lisa have?

_1

Lisa has 1 ​ 8​pieces of paper.

​3 ÷ ​ 6 ​= 18​

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram to represent 3 ​ ​feet of 1 __ paper. I draw and label one part as ​​ 6 ​​ to represent the length of each piece of paper. The unknown is the total number of pieces of paper.

3 1 6

... ? pieces of paper

I divide to find the total number of pieces of paper. ​3 ÷ ​ __61 ​= 18​

156

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EUREKA MATH2 Tennessee Edition

Name

5 ▸ M4 ▸ TE ▸ Lesson 26

26

Date

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

1

1. Tyler puts 8 ​ ​cups of snack mix equally into 3 ​ ​bags. The blue bag already has _​​3​​ cup of snack mix in it. How many cups of snack mix are now in the blue bag?

_1

2. Julie cuts ​6​feet of plastic tubing into pieces that are each ​​ 4 ​foot long. How many pieces of plastic tubing does Julie have?

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157

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 27

Name

27

Date

Complete the tables.

1.

2.

Centimeters (cm) ​70​

Expression ​70 ×

Millimeters (mm)

Liters (L)

​ 700 ​

​3​

43

​7.2​

7.2 × 100

720

10 ​

Expression

3​ ×

Centiliters (cL)

100 ​

300

​4.3​

4.3 × 10

5​ .36​

5.36 × 10

53.6

​81.67​

​81.67 × 100 ​

8,167

​71.24​

71.24 × 10

712.4

​0.572​

0.572 × 100

57.2

​

​

There are 1​ 0​millimeters in ​1​ centimeter. So 1 centimeter is 10 times as long as 1 millimeter.

There are 100 centiliters in 1 liter. So 1 liter is 100 times as much as 1 centiliter.

To convert a measurement from centimeters to millimeters, I multiply by 10.​​​​​​​​​​​​​​​​

To convert a measurement from liters to centiliters, I multiply by 100.

​7 0 cm​ ​=​ ​___​ mm

​7.2 L​ ​= __ cL

70 cm =​7​ 0 × 1 cm​

7.2 L =​ ​7.2 × 1L

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= ​7 0 × 10 mm​

=​ ​7.2 × 100 cL

​=​ ​7 00 mm​

=​ ​7 20 cL​

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159

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 27

3.

Grams (g)

Expression

Milligrams (mg)

3

​3 × 1,000 ​

3,000

2.6

2.6 × 1,000

2,600

​0.8​

0.8 × 1,000

800

0.35

0.35 × 1,000

350

There are 1,000 milligrams in 1 gram. So 1 gram is 1,000 times as heavy as 1 milligram.

To convert a measurement from grams to milligrams, I multiply by 1,000. ​0.35 g​ ​=​ ​__​​ ​mg ​0.35 g​ ​=​ ​0.35 × 1 g =​ ​0.35 × 1,000 mg =​ ​350 mg​

Convert each measurement.

4. 3 ​ .7 km = 3 km

700

m​

I break apart ​3.7​kilometers into​ 3​kilometers and ​0.7​ kilometers. ​3 .7 km​

5. ​4​.007​ L = 4 L

7

mL​

I break apart 4.007 liters into 4 liters and 0.007 liters.

4.007 L

4L 3 km

0.7 km

Now, I convert 0 ​ .7​kilometers to meters. ​0.7 km​ ​=​ ​0.7 × 1 km​ ​=​ ​0.7 × 1,000 m​ ​ =​ ​7 00 m​ So ​3.7 km​ ​=​ ​3 km 700 m​.

160

P R ACT I C E PA R T N E R

0.007 L

Now I convert 0.007 liters to milliliters. ​0.007 liters​ ​=​ ​0.007 × 1 L =​ ​0.007 × 1,000 mL​ ​=​ ​7 mL​ So, ​4.007 L​ ​=​ ​4 L​ ​7 mL​.

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 27

REMEMBER 6. Draw a model to represent the division expression. Then complete the equation. ​2 ÷ 5​

The dividend is 2​ ​. I draw ​ 2​ rectangles.

The divisor is 5 ​ ​. I partition each rectangle into 5 ​ ​ equal parts.

2 2 ÷ 5 = ___ ​​ ​​ 5

7. Draw a model to represent the expression. Then divide.

_1​​ ​ ÷ 3 = ​1_​ 2 6 1 2

?

I think about ​​ __21 ​÷ 3​by asking myself, ​​ __21 ​​is ​3​groups of what?

I draw a tape diagram that represents 1​​. Then, I partition the tape diagram into ​2​equal parts. I label __2​​ 1 ​ ​, which represents the dividend.

1 2

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I color to show how the parts can be divided equally by 5 ​ ​. I color every ​ 2​parts a different color.

The color helps me see ​5​groups in the ​2​ rectangles.

Each group represents ​ 2​ fifths, or ​​ 5__2 ​ ​.

Next, I partition each half into ​3​equal parts because I need to divide __2​​ 1 ​​by ​3​.

I shade ​1​part and label the unknown.

1 2

?

I see the tape diagram has 6​ ​equal parts. The value of 1​ ​ part is ​​ __61 ​ ​. ​​ __21 ​÷ 3 = __6​ 1 ​​

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P R ACT I C E PA R T N E R

161

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 27

Name

27

Date

Complete the tables.

1.

2.

Centimeters (cm) ​20​

Millimeters (mm)

Expression

20 ×

Liters (L) ​4​

​6.5​

​8.5​

​5.72​

​25.87​

84​.​36

​0.384​

Expression

4​ ×

Centiliters (cL)

​

3.

Grams (g)

Expression

5

​5 ×

Milligrams (mg)

​

​1.4​ ​0.3​ ​0.26​

Convert each measurement.

4. 4 ​ .9 km = 4 km © Great Minds PBC •

m​

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5. ​8.005​ L = 8 L

mL​ 163

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 27

REMEMBER 6. Draw a model to represent the division expression. Then complete the equation. ​3 ÷ 4​

3 ÷ 4 = ___ ​​ ​​

7. Draw a model to represent the expression. Then divide.

_​​ 1​ ÷ 2 = ​ 6

164

P R ACT I C E

​

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 28

Name

28

Date

Use the tape diagram to help you convert each measurement.

1.

1 yard

1 foot

1 foot

a. ​2.5 yd = ​ 7.5

​ft​

b. ​1.1 yd = ​ 3.3

ft

c. 3.25 yd = ​ 9.75 ​ ft

30

d. 2.5​​​ ft =

1 inch

​ in​

To convert measurements from a larger unit to a smaller unit, I think about how many of the smaller units make up 1 of the larger unit.

1 yard = 3 feet

1 ft = 12 inches

To convert 2.5 yards to feet, I multiply by 3.

To convert 2.5 feet to inches, I multiply by 12.

2.5 yd = 2.5 × 1 yd

2.5 ft = 2.5 × 1 ft

= 2.5 × 3 ft

= 2.5 × 12 in

= 7.5 ft

= 30 in

2. ​4.75 lb ≈

Round to estimate the conversion.

80

​ oz

To estimate how many ounces are in 4.75 pounds, I first round to the nearest whole number.

4.75 pounds is about 5 pounds.

Then I convert 5 pounds to ounces. I know that 1 pound is equal to 16 ounces.

To convert, I multiply by 16.

5 lb = 5 × 1 lb = 5 × 16 oz = 80 oz

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165

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 28

​​Convert each measurement.

3. ​1.5 quarts =

3

​ pints​

4. ​1.75 pints = ​ 3.5

cups

​1​ pint​ = 2​cups​ ​1​ quart​ = 2​pints​ To convert ​1 .5​ quarts to pints, I multiply by 2.

To convert 1.75 pints to cups, I multiply by 2.

1.75 p = 1.75 × 1 p = 1.75 × 2 c

​​1 .5​qt​ = 1.5​ ​×​ 1 qt

= 3.5 c

​= 1.5​ ​×​ ​2​pt ​= 3 ​pt​

REMEMBER 5.​ ​​​5​​people equally share 3​ ​​ ​pounds of raisins.

How many pounds of raisins does each person get?

I draw 3​ ​​ rectangles to represent ​3​ pounds of raisins. I partition each rectangle into ​​ 5​ ​equal parts.

I color to show how the parts can be divided equally by ​5​. I color every ​3​ parts a different color.

The color helps me see ​5​ groups in the ​​3​​rectangles. Each group represents ​​ 3 fifths, or 5__​​ 3​​.

​3 ÷ 5 =​_​ 5 ​​ 3

_3 Each person gets ​​ ​​ pounds of raisins.

5

I write a division equation to represent the situation. ​​3 ÷ 5 = ​​ __53 ​​ Each person gets ​​ __53 ​​pounds of raisins.

My answer makes sense because there are more people than pounds of raisins.

So each person gets less than ​1​ pound of raisins.

166

P R ACT I C E PA R T N E R

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EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 28

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

6. Yuna rides her bike a total of ​52​ kilometers in ​5​​days. She rides the same number of kilometers each day. How many kilometers does Yuna ride her bike each day?

_ ​52 ÷ 5 = __ ​ ​5 ​= ​ ​10 ​ 5 ​ 52

2

_2

Yuna rides 1 ​ 0 ​ 5 ​​ kilometers each day.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with a total of ​52​ to represent the total number of kilometers Yuna rides her bike. I partition the tape diagram into 5​ ​​ parts to represent the ​​5​days. The unknown is the number of kilometers Yuna rides each day.

52

?

I divide to find the number of kilometers Yuna rides each day.

52 ​52 ÷ 5 = ​​ ___ ​​ 5 52 I rename ​​ ___ ​​as a mixed number because 1​ 0​​​ __52 ​​kilometers makes more 5 52 sense than ​​ ___ ​​ kilometers.

5

2 52 = 10 5 5 50 5

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2 5

P R ACT I C E PA R T N E R

167

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 28

Name

28

Date

Use the tape diagram to help you convert each measurement.

1.

1 yard

1 foot

1 foot

1 inch 2.

1 pound

1 ounce

a. ​3.5 yd =

ft

b. 1.6 yd =

ft​

c. 2.75 yd = d. 5.5 ft =

ft in​

a. ​2.25 lb =

oz​

b. 3.75 lb =

oz

c. 4.25 lb =

oz​

d. 4.5 lb =

oz​

Round to estimate the conversion.

3. ​6.25 lb ≈

oz

Convert each measurement.

4. ​7.5 quarts =

pints​

5. ​2.25 pints =

cups

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169

EUREKA MATH2 Tennessee Edition

5 ▸ M4 ▸ TE ▸ Lesson 28

REMEMBER 6. ​3​people equally share 2 ​ ​liters of lemonade. How many liters of lemonade does each person get?

Use the Read–Draw–Write process to solve the problem. ​ ​days. She runs the same number of miles each day. How many 7. Sasha runs a total of 2 ​ 8​miles in 6 miles does Sasha run each day?

170

P R ACT I C E

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EUREKA MATH2 Tennessee Edition

5 ▸ M4

Acknowledgments Kelly Alsup, Adam Baker, Agnes P. Bannigan, Christine Bell, Reshma P Bell, Joseph T. Brennan, Dawn Burns, Amanda H. Carter, David Choukalas, Mary Christensen-Cooper, Nicole Conforti, Cheri DeBusk, Lauren DelFavero, Jill Diniz, Mary Drayer, Christina Ducoing, Karen Eckberg, Melissa Elias, Danielle A Esposito, Janice Fan, Scott Farrar, Gail Fiddyment, Ryan Galloway, Krysta Gibbs, January Gordon, Torrie K. Guzzetta, Kimberly Hager, Jodi Hale, Karen Hall, Eddie Hampton, Andrea Hart, Stefanie Hassan, Tiffany Hill, Christine Hopkinson, Rachel Hylton, Travis Jones, Laura Khalil, Raena King, Jennifer Koepp Neeley, Emily Koesters, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Courtney Lowe, Sonia Mabry, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Ashley Meyer, Pat Mohr, Bruce Myers, Marya Myers, Kati O’Neill, Darion Pack, Geoff Patterson, Victoria Peacock, Maximilian Peiler-Burrows, Brian Petras, April Picard, Marlene Pineda, DesLey V. Plaisance, Lora Podgorny, Janae Pritchett, Elizabeth Re, Meri Robie-Craven, Deborah Schluben, Colleen Sheeron-Laurie, Michael Short, Erika Silva, Jessica Sims, Tara Stewart, Heidi Strate, Theresa Streeter, Mary Swanson, James Tanton, Cathy Terwilliger, Saffron VanGalder, Rafael Vélez, Allison Witcraft, Jim Wright, Jackie Wolford, Caroline Yang, Jill Zintsmaster Trevor Barnes, Brianna Bemel, Lisa Buckley, 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

Credits For a complete list of credits, visit http://eurmath.link/media-credits

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171

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 Multiplication and Division with Whole Numbers Module 2 Addition and Subtraction with Fractions Module 3 Multiplication and Division with Fractions Module 4 Place Value Concepts for Decimal Operations Module 5 Addition and Multiplication with Area and Volume Module 6 Foundations to Geometry in the Coordinate Plane

What does this painting have to do with math?

Color and music fascinated Wassily Kandinsky, an abstract painter and trained musician in piano and cello. Some of his paintings appear to be “composed” in a way that helps us see the art as a musical composition.

In math, we compose and decompose numbers to help us become more familiar with the number system. When you look at a number, can you see the parts that make up the total?

On the cover Thirteen Rectangles, 1930 Wassily Kandinsky, Russian, 1866–1944 Oil on cardboard Musée des Beaux-Arts, Nantes, France Wassily Kandinsky (1866–1944), Thirteen Rectangles, 1930. Oil on cardboard, 70 x 60 cm. Musée des Beaux-Arts, Nantes, France. © 2020 Artists Rights Society (ARS), New York. Image credit: © RMN-Grand Palais/Art Resource, NY

ISBN 978-1-63898-547-1

9

781638 985471