CHAPTER RESOURCES • Chapter 8elementary.dmschools.org/uploads/1/3/6/0/13604257/c8.pdfCHAPTER RESOURCES • Chapter 8 Multiply Fractions by Whole Numbers INCLUDES • School-Home

CHAPTER RESOURCES • Chapter 8Multiply Fractions by Whole Numbers

INCLUDES • School-Home Letter • Vocabulary Game Directions • Daily Enrichment Activities • Reteach Intervention for every lesson • Chapter 8 Test • Chapter 8 Performance Task • Answer Keys and Individual Record Forms

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

• Co

ver I

mag

e Cr

edits

: (Gr

ound

Squ

irrel

) ©D

on Jo

hnst

on/A

ll

Cana

da P

hoto

s/Ge

tty

Imag

es; (

Saw

toot

h Ra

nge.

Idah

o) ©

Ron

and

Patt

y Th

omas

Pho

togr

aphy

/E+

/Get

ty Im

ages

Copyright © by Houghton Mifflin Harcourt Publishing Company

All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any

form or by any means, electronic or mechanical, including photocopying, recording, broadcasting or by any

other information storage and retrieval system, without written permission of the copyright owner unless such

copying is expressly permitted by federal copyright law.

Only those pages that are specifically enabled by the program and indicated by the presence of the print

icon may be printed and reproduced in classroom quantities by individual teachers using the corresponding

student’s textbook or kit as the major vehicle for regular classroom instruction.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices

and Council of Chief State School Officers. All rights reserved.

This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National

Governors Association Center for Best Practices and the Council of Chief State School Officers.

HOUGHTON MIFFLIN HARCOURT and the HMH Logo are trademarks and service marks of Houghton

Mifflin Harcourt Publishing Company. You shall not display, disparage, dilute or taint Houghton Mifflin Harcourt

trademarks and service marks or use any confusingly similar marks, or use Houghton Mifflin Harcourt

marks in such a way that would misrepresent the identity of the owner. Any permitted use of Houghton

Mifflin Harcourt trademarks and service marks inures to the benefit of Houghton Mifflin Harcourt Publishing

Company.

All other trademarks, service marks or registered trademarks appearing on Houghton Mifflin Harcourt

Publishing Company websites are the trademarks or service marks of their respective owners.

ContentsChapter 8 School-Home Letter (English) .......................................................8-1

Chapter 8 School-Home Letter (Spanish) ......................................................8-2

Vocabulary Game ..........................................................................................8-3

8.1 Reteach ..................................................................................................8-5

8.1 Enrich ......................................................................................................8-6

8.2 Reteach ..................................................................................................8-7

8.2 Enrich ......................................................................................................8-8

8.3 Reteach ..................................................................................................8-9

8.3 Enrich .................................................................................................... 8-10

8.4 Reteach ................................................................................................ 8-11

8.4 Enrich ....................................................................................................8-12

8.5 Reteach ................................................................................................8-13

8.5 Enrich ....................................................................................................8-14

Chapter 8 Test .............................................................................................8-15

Chapter 8 Performance Task .......................................................................8-21

Answer Keys ................................................................................................8-26

Individual Record Forms ..............................................................................8-33

Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

iii

School-HomeSchool-Home

LetterChapter

Tips

14

24

34

44

54

64

74

84

94

104

0

8

ActivityUse everyday situations, such as cooking and measures to help your child practice fraction multiplication.

Renaming as a Mixed Number

When the numerator is greater than the denominator, the fraction can be renamed as a mixed number.

9 _ 4

= 4 _ 4

+ 4 _ 4

+ 1 _ 4

= 2 + 1 _ 4

= 2 1 _ 4

STEP 1

Start at 0. Draw jumps to find multiples of 3 __ 4 : 3 __ 4 , 6 __ 4 , 9 __ 4 .

STEP 2

Write the multiple as a product of a whole number and a unit fraction.

So, 3 × 3 __ 4 = 9 __ 4 = 9 × 1 __ 4 .

Write 3 3 3 _ 4

as the product of a whole number and a unit fraction.

Use a Number Line to Write Multiples of Fractions

Dear Family,

During the next few weeks, our math class will be learning how to multiply fractions and mixed numbers by whole numbers. We will learn to write a fraction as a product of a whole number and a unit fraction, and to find multiples of unit fractions.

You can expect to see homework that provides practice multiplying fractions and whole numbers with and without using models.

Here is a sample of how your child will be taught to use a number line to find multiples of a fraction.

mixed number A number represented by a whole number and a fraction

multiple A number that is the product of a given number and a counting number

unit fraction A fraction that has 1 as its top number or numerator

8-1Chapter Resources© Houghton Mifflin Harcourt Publishing Company

para la casaCartaCartaCapítulo

Pistas

14

24

34

44

54

64

74

84

94

104

0

8Querida familia,

Durante las próximas semanas, en la clase de matemáticas aprenderemos a multiplicar fracciones y números mixtos por números enteros. También aprenderemos a escribir fracciones como el producto de un número entero y una fracción unitaria y a hallar múltiplos de fracciones unitarias.

Llevaré a casa tareas para practicar la multiplicación de fracciones y números enteros usando modelos y sin modelos.

Este es un ejemplo de cómo vamos a usar una recta numérica para hallar los múltiplos de una fracción.

Expresarlo como un número mixto

Cuando el numerador es mayor que el denominador, la fracción se puede expresar como un número mixto.

9 _ 4

= 4 _ 4

+ 4 _ 4

+ 1 _ 4

= 2 + 1 _ 4

= 2 1 _ 4

fracción unitaria Una fracción que tiene al 1 como numerador, es decir, arriba de la barra

múltiplo Un número que es el producto de cierto número y un número positivo distinto de cero

número mixto Un número que se representa por un número entero y una fracción

Escribe 3 × 3 _ 4 como el producto de un número entero y una fracción unitaria.

PASO 2

Escribe el múltiplo como el producto de un número entero y una fracción unitaria.

Por lo tanto, 3 × 3 __ 4 = 9 __ 4 = 9 × 1 __ 4 .

PASO 1

Comienza en 0. Dibuja saltos para hallar los múltiplos de 3 __ 4 : 3 __ 4 , 6 __ 4 , 9 __ 4

Usar una recta numérica para escribir múltiplos de fracciones

ActividadUse situaciones de la vida diaria, como cocinar y medir para ayudar a su hijo o hija a practicar la multiplicación con fracciones.


GameGameGoing Places with Words©

Hou

ghto

n M

ifflin

Har

cour

t Pub

lishi

ng C

ompa

ny •

Imag

e Cr

edits

: (bg

) ©Ol

ena

Myk

hayl

ova/

Shut

ters

tock

Pick It Word Boxestimateexpanded forminverse operationsperiodroundstandard formthousandsword form

For 3 players

Materials

• 4 sets of word cards

How to Play

1. Each player is dealt 5 cards. Th e remaining cards are

a draw pile.

2. To take a turn, ask any player if he or she has a word

that matches one of your word cards.

3. If the player has the word, he or she gives you the word

card, and you must give the defi nition of the word.

• If you are correct, keep the card and put the matching pair

in front of you. Take another turn.

• If you are wrong, return the card. Your turn is over.

4. If the player does not have the word, he or she answers,

“Pick it.” Th en you take a card from the draw pile.

5. If the card you draw matches one of your word cards,

follow the directions for Step 3 above.

If it does not, your turn is over.

6. Th e game is over when one player

has no cards left. Th e player with

the most matches wins.

Chapter 8 454A

Chapter 8Vocabulary Game

8-3 Game DirectionsChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

5 _ 8

5 _ 8

4 _ 8

4 _ 8

3 _ 8

3 _ 8

2 _ 8

2 _ 8

1 __ 10

7

7

1 __ 10

1 __ 10

1 __ 10

1 __ 10

1 __ 10

1 __ 10

1 __ 10

A unit fraction is a fraction with a numerator of 1. You can write a fraction as the product of a whole number and a unit fraction.

Write 7 __ 10 as the product of a whole number and a unit fraction.

Write 7 __ 10 as the sum of unit fractions.

7 __ 10

5 1 1 1 1 1 1

Use multiplication to show repeated addition.

7 __ 10

5 3 1 __ 10

So, 7 __ 10

5 3 .

The product of a number and a counting number is a multiple of the number. You can find multiples of unit fractions.

List the next 4 multiples of 1 _ 8 .

Make a table and use repeated addition.

1 3 1 _ 8 2 3 1 _

8 3 3 1 _

8 4 3 1 _

8 5 3 1 _

8

1 _ 8 1 _

8 1 1 _

8 1 _

8 1 1 _

8 1 1 _

8 1 _

8 1 1 _

8 1 1 _

8 1 1 _

8 1 _

8 1 1 _

8 1 1 _

8 1 1 _

8 1 1 _

8

1 _ 8

The next 4 multiples of 1 _ 8 are , , , and .

Write the fraction as the product of a whole number and a unit fraction.

1. 2 __ 5

5 2. 5 ___ 12

5 3. 7 __ 2

5

List the next four multiples of the unit fraction.

4. 1 __ 4

, , , ,

5. 1 __ 6

, , , ,

Multiples of Unit Fractions

Lesson 8.1Reteach

8-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

1. 1 1 __ 3 2. 3 1 __ 2

3. 1 3 __ 5 4. 2 3 __ 8

5. 3 3 __ 4 6. 5 2 __ 3

7. 4 2 __ 5 8. 5 1 __ 5

9. Explain how you found the answer in Exercise 1.

Mixed Numbers and Unit Fractions

Write each mixed number as the product of a whole number and a unit fraction.

Lesson 8.1Enrich

8-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

10 __ 5

10 __ 5

8 _ 5

8 _ 5

6 _ 5

6 _ 5

4 _ 5

4 _ 5

6 3 1 _ 5

Multiples of Fractions

You have learned to write multiples of unit fractions. You can also write multiples of other fractions.

Write the next 4 multiples of 2 _ 5 .

Make a table.

1 3 2 _ 5 2 3 2 _

5 3 3 2 _

5 4 3 2 _

5 5 3 2 _

5

2 _ 5 2 _

5 1 2 _

5 2 _

5 1 2 _

5 1 2 _

5 2 _

5 1 2 _

5 1 2 _

5 1 2 _

5 2 _

5 1 2 _

5 1 2 _

5 1 2 _

5 1 2 _

5

2 _ 5

So, the next 4 multiples of 2 _ 5 are , , , and .

Write 3 3 2 _ 5 as the product of a whole number and a unit fraction.

Use a number line. Make three jumps of 2 _ 5 .

2 3 1_5

4 3 1_5

6 3 1_5

8 3 1_5

3 3 2_5

5 6_5

15

25

35

45

55

65

75

85

95

0

So, 3 3 2 _ 5

5 6 _ 5 , or .

List the next four multiples of the fraction.

1. 3 __ 4

, , , , 2. 5 __ 6

, , , ,

Write as the product of a whole number and a unit fraction.

3.

18

28

38

48

58

68

78

88

98

108

0

3 3 3 __ 8 5

4.

13

23

33

43

53

63

73

83

93

103

0

4 3 2 __ 3 5

Lesson 8.2Reteach


Name

1. 1 1 __ 8 2. 2 1 __ 2

3. 1 2 __ 3 4. 2 1 __ 3

5. 3 1 __ 5 6. 1 1 __ 4

7. 1 3 __ 5 8. 2 3 __ 4

9. Describe a method other than multiplication thatyou can use to find the next three multiples of the mixed number in Exercise 7.

Multiples of Mixed Numbers

List the next three multiples of the mixed number. Write each multiple as a mixed number or as a whole number.

Lesson 8.2Enrich


Name

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

15

Multiply a Fraction by a Whole Number Using Models

You can use a model to multiply a fraction by a whole number.

Find the product of 4 3 3 _ 5 .

Use fraction strips. Show 4 groups of 3 _ 5 each.

1 group of 3 _ 5 5 3 _

5

2 groups of 3 _ 5 5 6 _

5

3 groups of 3 _ 5 5 9 _

5

4 groups of 3 _ 5 5 12 __

5

So, 4 3 3 _ 5

5 12 __ 5 .

Multiply.

1.

2 3 5 __ 6 5

2. 18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

18

3 3 7 __ 8 5

3. 6 3 2 __ 3 5 4. 2 3 9 ___ 10 5 5. 5 3 3 __ 4 5

6. 4 3 5 __ 8 5 7. 7 3 2 __ 5 5 8. 8 3 4 __ 6 5

Lesson 8.3Reteach


Name

1. 1 __ 8

3 24 5 2. 2 __ 3

3 15 5

3. 3 __ 5

3 10 5 4. 4 __ 7

3 14 5

5. 5 __ 6

3 18 5 6. 3 __ 4

3 16 5

7. 2 __ 9

3 27 5 8. 7 __ 8

3 32 5

9. 9 ___ 10

3 50 5 10. 4 __ 5

3 45 5

11. 5 ___ 12

3 60 5 12. 8 __ 9

3 54 5

Lesson 8.3Enrich

Fraction of a Whole Number

Find the product. Write the product as a whole number.

13. Explain how you can tell if the product of a fraction and a whole number will be a whole number.


Name

4 1 _ 2

4 1 _ 2 4 2 _

4

1 _ 4 1 _

4 4

Multiply a Fraction or Mixed Number by a Whole Number

To multiply a fraction by a whole number, multiply the numerators. Then multiply the denominators.

A recipe for one loaf of bread calls for 2 1 _ 4 cups of flour. How many cups of flour will you need for 2 loaves of bread?

Step 1 Write and solve an equation.

2 3 2 1 _ 4 5 2 _

1 3 9 _

4 Write 2 as 2 _

1 . Write 2 1 _

4 as a fraction.

5 2 3 9 _____ 1 3 4

Multiply the numerators.Then multiply the denominators.

5 18 __ 4 Simplify.

Step 2 Write the product as a mixed number.

18 __ 4 5 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4 1 1 _

4

5 5 5 5 1 1 1 1 1 1 1 1

1 _ 4 1 1 _ 4

5 + + Combine the wholes. Then combine the remaining parts.

5 , or Add. Write the sum as a mixed number.

So, you will need cups of flour.

Multiply. Write the product as a mixed number.

1. 3 3 2 __ 5 5 2. 4 3 3 __ 8 5 3. 5 3 1 __ 3 5

4. 2 3 1 3 ___ 10 5 5. 4 3 1 2 __ 3 5 6. 7 3 1 1 __ 6 5

Lesson 8.4Reteach


Name

1. 3 3 __ 4 5 2 1 __ 4 2. 4 3 __ 5 5 1 3 __ 5

3. 7 3 5 1 5 __ 9 4. 2 3 1 __ 3 5 6 2 __ 3

5. 3 1 5 __ 6 5 9 1 __ 6 6. 3 2 2 __ 7 5 13 5 __ 7

7. Explain how you found the unknown number in Exercise 3.

Unknown Numbers

Find the unknown number that makes each equation true.

Lesson 8.4Enrich


Name

2 2 _ 5

4 _ 5 4 _

5 4 _

5

4 _ 5

4 _ 5

3

3

sea level Lake Titicaca is.

2 2 _ 5

Lake Titicaca

Lake Titicaca

Great Salt Lake

12 __ 5

draw a diagram

about how high above

5

Problem Solving • Comparison Problems with Fractions

The Great Salt Lake in Utah is about 4 _ 5 mile above sea level. Lake Titicaca in South America is about 3 times as high above sea level as the Great Salt Lake. About how high above sea level is Lake Titicaca?

Read the Problem Solve the ProblemWhat do I need to find?

I need to find

Draw a comparison model. Compare the heights above sea level of the Great Salt Lake and Lake Titicaca, in miles.

4 _ 5

tWrite an equation and solve.

t is the height above sea level of , in miles.

t 5 3 Write an equation.

t 5 Multiply.

t 5 Write the fraction as a mixed number.

What information do I need to use?

The Great Salt Lake is about mile above sea level. Lake Titicaca is about

times as high above sea level.

How will I use the information?

I can to compare the heights.

So, Lake Titicaca is about miles above sea level.

1. Amelia is training for a triathlon. She

swims 3 _ 5 mile. Then she runs about 6

times farther than she swims. About

how far does Amelia run?

2. Last week, Meg bought 1 3 _ 4 pounds of

fruit at the market. This week, she buys

4 times as many pounds of fruit as last

week. In pounds, how much fruit does

Meg buy this week?

Lesson 8.5Reteach


Name

1. The depth of Lake Carl is about 1 1 _ 8 miles. Lake Susan is 3 times as

deep as Lake Carl. Lake Wayne is 2 times as deep as Lake Susan.

How much deeper is Lake Wayne than Lake Susan?

2. Mount Rogers rises 1 _ 4 mile above sea level. Mount Taylor rises

6 times as high as Mount Rogers. Mount Sullivan rises 2 times as

high as Mount Rogers. What is the difference in the elevation of

Mount Taylor and the elevation of Mount Sullivan?

3. A certain tree was 5 1 _ 3 feet tall when it was first planted. A few

years later, the tree is 4 times as tall as it was when it was first

planted. How much has the tree grown since it was first planted?

4. Explain how you solved Problem 3.

Heights and Depths

Solve each problem. You may find it helpful to draw a diagram.

Lesson 8.5Enrich


Chapter 8 TestPage 1

1. What are the next four multiples of 1 __ 7 ?

2. Sarah is making 4 batches of granola bars. She adds 7 _ 8 cup peanuts to each batch. Her measuring cup holds 1 _ 8 cup. How many times must Sarah measure 1 _ 8 cup of peanuts to have enough for the granola bars? Shade the models to show your answer.

Sarah must measure 1 _ 8 cup times.

3. Alice walks 6 __ 10 mile every day. How many miles does she walk in 5 days?

miles

Chapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

8-15 Chapter 8 Test


4. Hannah is baking 3 batches of health bars. She needs

1 2 _ 3 cups of carob chips for each batch of bars.

Part A

Hannah completed the multiplication below and said she

needed 6 cups of carob chips for 3 batches of bars. What is

Hannah’s error?

3 × 1 2 __ 3 = 3 ×

6 __

3 =

18 ___

3 = 6

Part B

What is the correct number of cups Hannah needs for

3 batches of bars? Explain how you found your answer.

5. Which fraction is a multiple of 1 __ 8 ? Mark all that apply.

A 3 __

8 C 2 __

8 E

8 ___

10

B 8 ___

12 D 4 __

8 F

8 __

8

6. Bo recorded a basketball game that lasted 2 1 _ 2 hours.

Bo watched the game 4 times last week. How many

hours did Bo spend watching the game? Show your work.

7. Rudi is comparing shark lengths. She

reads that a sandbar shark is 4 1 _ 2 feet

long. A thresher shark is 3 times as

long as a sandbar shark. Complete

the model. Then find the length of a

thresher shark.

A thresher shark is feet long.

Sandbar Shark

Thresher Shark

4 12


Name

Chapter 8 Test


8. Phil made a number line showing the multiples of 3 _ 6 .

16

26

36

46

56

66

76

86

96

106

116

0

The product 2 × 3 __ 6

is shown by the fraction on the number line.

8

+

8 3 __

8

6 3 __

8

3

×

9. Tara has softball practice Tuesday, Wednesday, Thursday,

and Sunday. Each practice is 1 1_3

hours. Tara says she will

have practice for 3 hours this week.

Part A

Without multiplying, explain how you know Tara is incorrect.

Part B

How long will Tara have softball practice this week? Write

your answer as a mixed number. Show your work.

10. Look at the number line. Write the

missing fractions.

11. Trevor‘s pet goat weighed 6 3 _ 8 pounds when it was

born. By age 3, the goat weighed 8 times as much.

Fill each box with a number or symbol from the list

to show how to find the weight of Trevor‘s goat at

age 3. Not all numbers and symbols may be used.

weight =

15

25

35

45

55

65

75

0 1 2


Name

8-17 Chapter 8 Test


12. Oleg made a fraction number line to help him find 4 × 2 __ 5 .

15

25

35

45

55

65

75

85

95

105

0

Select a way to write 4 × 2 __ 5 as the product of a whole number and a unit fraction.

4 × 2 __ 5 =

6 × 1 __ 5

2 × 4 __ 5

8 × 1 __ 5

13. Malik wanted to give 1 _ 5 of his bag of balloons to each of 3 of his friends. How many of his balloons will he give away?

14. Select the correct product for the equation.

488

812

128

248

4 × 6 __ 8 = 4 × 3 __ 8 =


Name

Chapter 8 Test


15. The lengths of different types of snakes at

a zoo are shown in the table.

Snake’s Name Type of Snake Length

Sherman Kenyan Sand Boa 1 1 __ 4 feet

Thomas Ball Python 3 3 __ 4 feet

Sam Blood Python 6 1 __ 4 feet

For numbers 15a–15d, select True or False for the statement.

15a. Thomas is 3 times as long as Sherman.

15b. Thomas is 2 times as long as Sherman.

15c. Sam is 5 times as long as Sherman.

15d. Sam is 2 times as long as Thomas.

16. Violet used 1 3 _ 4 gallons of paint on her kitchen walls. She used

4 times as much paint for her living room and bedroom

walls. How much paint did Violet use for the living room and

bedroom walls?

gallons

17. Maddie made a batch of popcorn balls. She used 1 1 _ 4 cups

of raisins. She used 5 times as much popcorn.

Part A

Draw a model to show the problem.

Part B

Use your model to write an equation. Then solve the equation

to find the amount of popcorn Maddie needs.

True False

True False

True False

True False


Name

8-19 Chapter 8 Test


18. Mrs. McGlashan is making paint for her class. She needs 3 _ 4 cup

of warm water for each batch.

Part A

Mrs. McGlashan has a 1-cup measure that has no other

markings. Can she make 8 batches of paint using only the

1-cup measure? Describe two ways you can find the answer.

Part B

The paint recipe also calls for 1 _ 4 cup of food coloring. Tyler says

Mrs. McGlashan will also need 6 cups of food coloring. Do you

agree or disagree? Explain.

19. Sandi buys some fabric to make a quilt. She needs 1 _ 6 yard of

each type of fabric. She has 7 different types of fabrics to make

her design. Use the following equation. Write the number in the

box to make the statement true.

7 __ 6 = × 1 __

6

20. Mrs. Tokala uses 9 __ 10

of a can of coffee beans each week.

How many cans of coffee beans does Mrs. Tokala use in

6 weeks? Write your answer two different ways.

Mrs. Tokala uses or cans of coffee beans.

21. Alma is making 3 batches of tortillas. Each batch needs 3 _ 4 cup of

water. She only has a 1 _ 4 -cup measure. How many times must Alma

measure 1 _ 4 cup of water to have enough for all of the tortillas?

times


Name

Chapter 8 Test

Name Chapter 8

Dollar Days

Mr. Asfour owns a small grocery store. The store is very popular for its fresh fruit and vegetables. On Tuesdays, he offers special deals for $1.00.

2. Deshi paid $5.00 for two different fruits. His grocery bag weighed between 1 1 _ 2 and 2 1 _ 2 pounds. Which combinations of fruit could he have purchased? Show your work.

__ $3 worth of pears and $2 worth of apples



1. Elaine bought $4 worth of apples and $3 worth of lemons. Did her grocery bag weigh more than or less than 5 1 _ 4 pounds? Use a model to support your answer.

Only $1.00 Tuesday DOLLAR DAYS! Only $1.00

Apples – 3 _ 4 lb Oranges – 1 _ 4 lb Peaches – 2 _ 5 lb

Pears – 3 _ 8 lb Bananas – 1 _ 5 lb Peppers – 4 _ 6 lb

Limes – 4 _ 5 lb Peanuts – 3 __ 10 lb Lemons – 7 _ 8 lb

8-21 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company

3. Mrs. Nazari bought 2 1 _ 4 pounds of apples, 1 3 _ 5 pounds of peaches, and 1 1 _ 5 pounds of bananas. She paid with a $20 bill. How much change did she receive? Show your work.

4. Ming paid $8 for every item except peppers. Was her bag lighter than or heavier than 4 pounds? Show the addition using as few steps as you can.


Chapter 8Multiply Fractions by Whole Numbers

Dollar DaysCOMMON CORE STANDARDS

4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.B.4a Understand a fraction a/b as a multiple of 1/b.

4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Also MP2, MP7

PURPOSETo assess the ability to multiply a fraction by a whole number

TIME25–30 minutes

GROUPINGIndividuals

MATERIALS• Performance Task, paper, pencil

• Fraction circles (optional)

PREPARATION HINTS• Review multiplication of fractions and whole numbers with students before assigning the task.

• Review multiplication of mixed numbers and whole numbers with students before assigning the task.

• Review vocabulary, including multiple, numerator, denominator, mixed number, and simplest form.

IMPLEMENTATION NOTES • Read the task aloud to students and make sure that all students have a clear understanding of

the task.

• Students may use manipulatives to complete the task.

• Allow students as much paper as they need to complete the task.

• Allow as much time as students need to complete the task.

• Students must complete the task individually, without collaboration.

• Collect all student work when the task is complete.


TASK SUMMARYStudents apply multiplication of a fraction by a whole number to solve word problems involving weight. Students compare fractional weights.

REPRESENTATION In this task, teachers can…

• Assist students in listing what they know, what they don’t know, and what is being asked to help them determine how to arrive at the solution.

• Provide a word wall that features pertinent vocabulary words and symbols.

ACTION and EXPRESSION In this task, teachers can…

• Provide fraction circles or fraction bars for kinesthetic learners, or those who need a visual reminder while completing the task.

ENGAGEMENT In this task, teachers can…

• Engage interest by discussing personal experiences related to the task with students.

• Increase mastery by providing specific feedback that encourages perseverance.

EXPECTED STUDENT OUTCOMES• Complete the task within the time allowed

• Reflect engagement in a productive struggle

• Multiply fractions by whole numbers

SCORING Use the associated Rubric to evaluate each student’s work.


Performance Task Rubric

DOLLAR DAYS

A level 3 response • Demonstrates that the student has reasoned abstractly and qualitatively

• Shows appropriate use of multiplication to solve word problems

• Indicates a solid understanding of multiplying both fractions and mixed numbers

• Shows a complete understanding of the relationship between addition and multiplication

A level 2 response • Demonstrates that the student has reasoned abstractly and qualitatively

• Shows appropriate use of multiplication to solve word problems

• Indicates an understanding of multiplying both fractions and mixed numbers

• Shows an understanding of the relationship between addition and multiplication

• May include a computational error derived from a correct procedure

A level 1 response • Demonstrates that the student has made an effort to reason abstractly and qualitatively

• Shows some understanding of the use of multiplication in solving word problems

• May show some confusion about multiplying fractions or mixed numbers

• May indicate that the student has relied exclusively on repeated addition to solve problems

• Errors may reflect a lack of understanding of the process or procedure

A level 0 response • Shows little evidence that the student has reasoned abstractly or qualitatively

• Reflects a lack of understanding of the process of multiplying fractions and mixed numbers

• Shows little evidence of addressing the components of the task


Chap

ter 8

Tes

tPa

ge 2

4

. H

annah is

bakin

g 3

batc

hes

of

health b

ars

. She n

eeds

1 2

_

3 c

ups

of

caro

b c

hip

s fo

r each b

atc

h o

f bars

.

Par

t A

Hannah c

om

ple

ted t

he m

ultip

lication b

elo

w a

nd s

aid

she

needed 6

cups

of

caro

b c

hip

s fo

r 3

batc

hes

of

bars

. W

hat

is

Hannah’s

err

or?

3 ×

1 2

__

3 =

3 ×

6

__

3 =

18

___

3 =

6

Po

ssib

le e

xpla

nat

ion

: Han

nah

did

no

t w

rite

th

e m

ixed

nu

mb

er, 1

2 _ 3 , as

a fr

acti

on

co

rrec

tly.

1 2 _ 3 i

s n

ot

equ

al to

6 _ 3 .

Par

t B

What

is t

he c

orr

ect

num

ber

of

cups

Hannah n

eeds

for

3 b

atc

hes

of

bars

? E

xpla

in h

ow

you f

ound y

our

answ

er.

5 cu

ps;

po

ssib

le e

xpla

nat

ion

: firs

t I w

rote

1 2 _ 3 a

s a

frac

tion

. 1 2 _ 3 5

3 _ 3 1 2 _ 3 5

5 _ 3 ; th

en, I

mu

ltip

lied

3 3

5 _ 3 5 15

__

3

5 5

.

5

. W

hic

h f

raction is

a m

ultip

le o

f 1

__

8 ?

Mark

all

that

apply

.

A

3

__

8

C

2

__

8

E

8

___

10

B

8

___

12

D

4

__

8

F

8

__

8

6

. B

o r

ecord

ed a

bask

etb

all

gam

e t

hat

last

ed 2

1

_

2 h

ours

.

Bo w

atc

hed t

he g

am

e 4

tim

es

last

week. H

ow

many

hours

did

Bo s

pend w

atc

hin

g t

he g

am

e?

Show

your

work

.

10 h

ou

rs; 2

1 _ 2 × 4

= 5 _ 2 ×

4 =

20

__

2 = 1

0

7

. R

udi is

com

pari

ng s

hark

length

s. S

he

reads

that

a s

andbar

shark

is

4 1

_

2 f

eet

long. A

thre

sher

shark

is

3 t

imes

as

long a

s a s

andbar

shark

. C

om

ple

te

the m

odel.

Then f

ind t

he length

of

a

thre

sher

shark

.

A t

hre

sher

shark

is

feet

long.

13 1 _ 2

Sand

bar S

hark

Thre

sher

Sha

rk

41 2 41 2

41 2

41 2

8-16

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 8

Tes

t

Chap

ter 8

Tes

tPa

ge 1

1

. W

hat

are

th

e n

ext

fou

r m

ultip

les

of

1

__

7 ?

2 _ 7 , 3 _ 7 , 4 _ 7 , 5 _ 7

2

. S

ara

h is

makin

g 4

batc

hes

of

gra

nola

bars

. S

he a

dd

s

7

_

8 c

up

pean

uts

to e

ach

batc

h. H

er

measu

rin

g c

up

hold

s 1

_

8 c

up

. H

ow

man

y tim

es

mu

st S

ara

h m

easu

re 1

_

8 c

up

of

pean

uts

to h

ave

en

ou

gh

for

the g

ran

ola

bars

?

Sh

ad

e t

he m

od

els

to s

how

you

r an

swer.

Sara

h m

ust

measu

re 1

_

8 c

up

t

imes.

3

. A

lice w

alk

s 6

__

10 m

ile e

very

day.

How

man

y m

iles

does

she w

alk

in

5 d

ays

?

mile

s

28

3

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

8-15

Chap

ter 8

Tes

t

8-26 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company

Chap

ter 8

Tes

tPa

ge 4

12

. O

leg

mad

e a

frac

tion

num

ber

line

to h

elp

him

find

4 ×

2 __ 5 .

1 52 5

3 54 5

5 56 5

7 58 5

9 510 5

0

Sele

ct a

way

to w

rite

4 ×

2 __ 5 as

the

prod

uct o

f a w

hole

num

ber

and

a un

it fr

actio

n.

4 ×

2 __ 5 =

6 ×

1 __ 5

2 ×

4 __ 5

8 ×

1 __ 5

13

. M

alik

wan

ted

to g

ive

1 _ 5 o

f his

bag

of b

allo

ons

to e

ach

of 3

of

his

frie

nds.

How

man

y of

his

bal

loon

s w

ill h

e gi

ve a

way

?

3 _ 5

14

. Se

lect

the

corr

ect p

rodu

ct fo

r th

e eq

uatio

n.

48 88 12

12 824 8

4 ×

6 __ 8 =

24

__

8

4 ×

3 __ 8 =

12

__

8

8-18

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 8

Tes

t

Chap

ter 8

Tes

tPa

ge 3

8.

Phil

mad

e a

num

ber

line

show

ing

the

mul

tiple

s of

3 _ 6 .

1 62 6

3 64 6

5 66 6

7 68 6

9 610 6

11 60

The

prod

uct 2

× 3 __

6 is s

how

n by

the

frac

tion

on

the

num

ber

line.

6 _ 6

8 +

8 3 __ 8

6 3 __ 8

3 ×

9.

Tara

has

sof

tbal

l pra

ctic

e Tu

esda

y,W

edne

sday

, Thu

rsda

y,

and

Sund

ay. E

ach

prac

tice

is 1

1 _ 3ho

urs.

Tar

a sa

ys s

he w

ill

have

pra

ctic

e fo

r 3

hour

s th

is w

eek.

Par

t A

With

out m

ultip

lyin

g, e

xpla

in h

ow y

ou k

now

Tar

a is

inco

rrec

t.

Po

ssib

le e

xpla

nat

ion

: Tar

a n

eed

s to

fi n

d 4

3 1

1 _ 3 . I

f sh

e es

tim

ates

4 3

1 h

ou

r, sh

e fi

nd

s th

at p

ract

ice

is a

t le

ast

4 h

ou

rs; 4

is g

reat

er t

han

3, s

o T

ara

is in

corr

ect.

Par

t B

How

long

will

Tar

a ha

ve s

oftb

all p

ract

ice

this

wee

k? W

rite

your

ans

wer

as

a m

ixed

num

ber.

Show

you

r w

ork.

5 1 _ 3 ho

urs

; 4 ×

1 1 _ 3 =

4 ×

4 _ 3 = 16

__

3 =

5 1 _ 3

10

.Lo

ok a

t the

num

ber

line.

Writ

e th

e m

issi

ng fr

actio

ns.

11

.Tr

evor

‘s p

et g

oat w

eigh

ed 6

3 _ 8 p

ound

s w

hen

it w

as

born

. By

age

3, th

e go

at w

eigh

ed 8

tim

es a

s m

uch.

Fi

ll ea

ch b

ox w

ith a

num

ber

or s

ymbo

l fro

m th

e lis

t to

sho

w h

ow to

find

the

wei

ght o

f Tre

vor‘s

goa

t at

age

3. N

ot a

ll nu

mbe

rs a

nd s

ymbo

ls m

ay b

e us

ed.

wei

ght =

8

×6

3 _ 8

1 52 5

3 54 5

5 56 5

7 5

01

28 5

9 510 5

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

8-17

Chap

ter 8

Tes

t


Chap

ter 8

Tes

tPa

ge 6

18

. M

rs. M

cG

lash

an

is

makin

g p

ain

t fo

r h

er

cla

ss. S

he n

eed

s 3

_

4 c

up

of

warm

wate

r fo

r each

batc

h.

Par

t A

Mrs

. M

cG

lash

an

has

a 1

-cu

p m

easu

re t

hat

has

no o

ther

mark

ing

s. C

an

sh

e m

ake 8

batc

hes

of

pain

t u

sin

g o

nly

th

e

1-c

up

measu

re?

Desc

rib

e t

wo w

ays

you

can

fin

d t

he a

nsw

er.

Yes;

po

ssib

le e

xpla

nat

ion

: sh

e n

eed

s 8

× 3 _ 4 c

up

s o

f w

ater

.

I can

use

a n

um

ber

lin

e to

mak

e 8

jum

ps

of

3 _ 4 .

Th

e la

st ju

mp

en

ds

at 24

__

4 o

r 6.

I co

uld

als

o li

st t

he

firs

t 8

mu

ltip

les

of

3 _ 4 : 3 _ 4 ,

6 _ 4 , 9 _ 4 ,

12

__

4 , 15

__

4 ,

18

__

4 , 21

__

4 ,

24

__

4 . T

he

sixt

h m

ult

iple

is 24

__

4 ,

wh

ich

is 6

wh

ole

cu

ps.

Sh

e ca

n u

se t

he

1-cu

p

mea

sure

6 t

imes

to m

ake

8 b

atch

es.

Par

t B

Th

e p

ain

t re

cip

e a

lso c

alls

for

1

_

4 c

up

of

food

colo

rin

g. Tyl

er

says

Mrs

. M

cG

lash

an

will

als

o n

eed

6 c

up

s of

food

colo

rin

g. D

o y

ou

ag

ree o

r d

isag

ree?

Exp

lain

.

I dis

agre

e; p

oss

ible

exp

lan

atio

n: 8

× 1 _ 4 =

8 _ 4 or

2.

Sh

e n

eed

s 2

cup

s o

f fo

od

co

lori

ng

, no

t 6.

19

. S

an

di b

uys

som

e f

ab

ric t

o m

ake a

qu

ilt. S

he n

eed

s 1

_

6 y

ard

of

each

typ

e o

f fa

bri

c. S

he h

as

7 d

iffe

ren

t ty

pes

of

fab

rics

to m

ake

her

desi

gn

. U

se t

he f

ollo

win

g e

qu

ation

. W

rite

th

e n

um

ber

in t

he

box

to m

ake t

he s

tate

men

t tr

ue.

7

__

6 =

7

× 1

__

6

20

. M

rs. Tokala

use

s 9

__

10 o

f a c

an

of

coff

ee b

ean

s each

week.

How

man

y can

s of

coff

ee b

ean

s d

oes

Mrs

. Tokala

use

in

6 w

eeks?

Wri

te y

ou

r an

swer

two d

iffe

ren

t w

ays

.

Mrs

. Tokala

use

s o

r c

an

s of

coff

ee b

ean

s.

21

. A

lma is

makin

g 3

batc

hes

of to

rtill

as.

Each b

atc

h n

eeds

3

_

4 c

up o

f

wate

r. S

he o

nly

has

a 1

_

4 -c

up m

easu

re. H

ow

many

tim

es

must

Alm

a

measu

re 1

_

4 c

up o

f w

ate

r to

have

enough for

all

of th

e tort

illas?

tim

es

54

__

10

5 4 __

10

9

8-20

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 8

Tes

t

Chap

ter 8

Tes

tPa

ge 5

15

. Th

e len

gth

s of

diffe

ren

t ty

pes

of

snakes

at

a z

oo a

re s

how

n in

th

e t

ab

le.

Sn

ak

e’s

Na

me

Typ

e o

f S

na

ke

Le

ng

th

She

rman

Ken

yan

San

d B

oa1 1

__ 4 fe

et

Tho

mas

Bal

l Pyt

hon

3 3 __

4 feet

Sam

Blo

od P

ytho

n6 1

__ 4 fe

et

For

nu

mb

ers

15

a–1

5d

, se

lect

Tru

e o

r Fals

e f

or

the s

tate

men

t.

15a.

Th

om

as

is 3

tim

es

as

lon

g a

s S

herm

an

.

15b.

Th

om

as

is 2

tim

es

as

lon

g a

s S

herm

an

.

15c.

S

am

is

5 t

imes

as

lon

g a

s S

herm

an

.

15d.

S

am

is

2 t

imes

as

lon

g a

s Th

om

as.

16

. V

iole

t u

sed

1 3

_

4 g

allo

ns

of

pain

t on

her

kitch

en

walls

. S

he u

sed

4 t

imes

as

mu

ch

pain

t fo

r h

er

livin

g r

oom

an

d b

ed

room

walls

. H

ow

mu

ch

pain

t d

id V

iole

t u

se f

or

the liv

ing

room

an

d

bed

room

walls

?

gallo

ns

17

. M

ad

die

mad

e a

batc

h o

f p

op

corn

balls

. S

he u

sed

1 1

_

4 c

up

s

of

rais

ins.

Sh

e u

sed

5 t

imes

as

mu

ch

pop

corn

.

Par

t A

Dra

w a

mod

el to

sh

ow

th

e p

rob

lem

.

po

pco

rn1

1 _ 4 1

1 _ 4 1

1 _ 4 1

1 _ 4 1

1 _ 4

rais

ins

1 1 _ 4

Par

t B

Use

you

r m

od

el to

wri

te a

n e

qu

ation

. Th

en

solv

e t

he e

qu

ation

to f

ind

th

e a

mou

nt

of

pop

corn

Mad

die

need

s.

r =

5 ×

1 1 _ 4 =

5 ×

5 _ 4 = 25

__

4 =

6 1 _ 4

So

, Mad

die

nee

ds

6 1 _ 4 c

up

s o

f p

op

corn

.

Tru

e

Fals

e

Tru

e

Fals

e

Tru

e

Fals

e

Tru

e

Fals

e

7

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

8-19

Chap

ter 8

Tes

t


Sample Level 3 Response








8-33© Houghton Mifflin Harcourt Publishing Company

Chapter Resources Individual Record Form

Student’s Name Date

Chapter 8 Test

Item Lesson Standard Content Focus Intervene with

Personal Math Trainer

1, 5, 10 8.1 4.NF.B.4a Identify multiples of unit fractions. R—8.1 4.NF.4a

19, 21 8.2 4.NF.B.4b Understand a fraction a _ b as a multiple of 1 _ b . R—8.2 4.NF.4b

3, 4, 6, 9, 11, 14, 16, 18, 20

8.4 4.NF.B.4c Multiply a fraction or mixed number by a whole number. R—8.4 4.NF.4c

7, 17 8.5 4.NF.B.4c Draw a diagram to solve comparison problems with fractions. R—8.5 4.NF.4c

2, 8, 12 8.3 4.NF.B.4b Use a visual model to multiply a fraction by a whole number. R—8.3 4.NF.4b

13 8.4 4.NF.B.4c Decompose a fraction into a sum of fractions. R—8.4 4.NF.4c

Key: R—Reteach

Documents

CHAPTER RESOURCES • Chapter 8elementary.dmschools.org/uploads/1/3/6/0/13604257/c8.pdfCHAPTER RESOURCES • Chapter 8 Multiply Fractions by Whole Numbers INCLUDES • School-Home