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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
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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
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School-HomeSchool-Home
LetterChapter
Tips
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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
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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.
8-2Chapter Resources© Houghton Mifflin Harcourt Publishing Company
GameGameGoing Places with Words©
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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
8-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
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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
8-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
8-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
Chapter 8 TestPage 2
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
8-16Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 3
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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8-17 Chapter 8 Test
Chapter 8 TestPage 4
12. Oleg made a fraction number line to help him find 4 × 2 __ 5 .
15
25
35
45
55
65
75
85
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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 =
8-18Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 8 Test
Chapter 8 TestPage 5
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
8-19 Chapter 8 Test
Chapter 8 TestPage 6
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
8-20Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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
__ $4 worth of pears and $1 worth of apples
__ $2 worth of pears and $3 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.
8-22 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
8-23 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
8-24 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-25 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
8-27 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
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pany
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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
8-28 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 3 Response
8-29 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 2 Response
8-30 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 1 Response
8-31 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 0 Response
8-32 Chapter 8 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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