www.everydaymathonline.com

Lesson 8�6 649

Key Concepts and Skills• Use an area model to find fractions of

fractions. [Operations and Computation Goal 5]

• Write number models for fraction

multiplication problems shown with

an area model. 

[Operations and Computation Goal 7]

• Describe the patterns in the area model

for fraction multiplication. 

[Patterns, Functions, and Algebra Goal 1]

• Recognize the patterns in products when a

number is multiplied by a fraction that is

less than or equal to 1.

[P atterns, Functions, and Algebra Goal 1]

Key ActivitiesStudents solve problems using an area

model for fraction multiplication. They use

the area model and fraction multiplication

patterns to derive the standard algorithm.

Ongoing Assessment: Informing Instruction See page 651.

Ongoing Assessment: Recognizing Student Achievement Use journal page 265. [Operations and Computation Goal 5]

Key Vocabularyarea model

MaterialsMath Journal 2, pp. 264–266

Student Reference Book, p. 76

Study Link 8�5; transparency of

Math Masters, p. 231 (optional) � slate

Math Boxes 8�6Math Journal 2, p. 267

Geometry Template

Students practice and maintain skills

through Math Box problems.

Study Link 8�6Math Masters, p. 232

Students practice and maintain skills

through Study Link activities.

READINESS

Supporting Fraction Multiplication ConceptsMath Masters, p. 233

Students compare area models to reinforce

the use of the word of to indicate

multiplication.

EXTRA PRACTICE

Fraction ProblemsMath Masters, p. 234

Students solve real-world number stories

involving fractions.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

An Area Model for Fraction Multiplication

Objective To develop a fraction multiplication algorithm.

��������

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Advance PreparationFor Part 1, make a transparency of Math Masters, page 231 for use in the discussion of journal page 265.

The master is identical to the journal page.

Teacher’s Reference Manual, Grades 4–6 pp. 143, 144, 220, 221

649_EMCS_T_TLG2_G5_U08_L06_576914.indd 649649_EMCS_T_TLG2_G5_U08_L06_576914.indd 649 3/17/11 9:04 AM3/17/11 9:04 AM

Fraction MultiplicationLESSON

8 �6

Date Time

Math Message

1. Use the rectangle at the right to sketch how you would fold paper to help you find �

13� of �

23�.

What is �13� of �

23�?

2. Use the rectangle at the right to sketch how you would fold paper to help you find �

14� of �

35�.

What is �14� of �

35�?

3. Rewrite �23� of �

34� using the multiplication symbol �.

4. Rewrite the following fraction-of-fraction problems using the multiplication symbol �.

a. �14� of �

13� b. �

45� of �

23�

c. �16� of �

14� d. �

37� of �

25�

�37� � �

25��

16� � �

14�

�45� � �

23��

14� � �

13�

�23� � �

34�

�230�

�29�

Math Journal 2, p. 264

Student Page

650 Unit 8 Fractions and Ratios

Getting Started

Math MessageComplete Problem 1 on journal page 264.

Mental Math and Reflexes Have students solve multiplication problems.

3 sets of 4 coins. How many coins in all? 12

8 rows of 8 stamps. How many stamps in all? 64

3 bags of 12 oranges for each of 3 classrooms. How many oranges in all? 108

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 264)

Ask a volunteer to demonstrate how to fold and shade a sheet of paper to solve the Math Message problem. Reinforce the demonstration by sketching the folds on the board or a transparency. The folded paper and sketch should show the paper folded into thirds in both directions. The whole has 9 parts, 2 of them shaded twice, so the answer is 2 _ 9 . Have students complete Problem 2.

▶ Introducing the Word of

WHOLE-CLASS ACTIVITY

to Mean Multiply(Math Journal 2, p. 264)

Ask students what operation they used to solve the Mental Math and Reflexes problems. multiplication Point out that the number of coins in 3 sets of 4 coins is equal to 3 times 4. Similarly, 2 _ 3 of 3 _ 4 is equal to 2 _ 3 times 3 _ 4 . Students should record this as the answer to Problem 3 on the journal page. Have students complete the rest of the page and then compare answers with a partner.

▶ Using the Area Model for PARTNER ACTIVITY

Fraction Multiplication(Math Journal 2, p. 265)

On the board or a transparency, demonstrate how to solve 2 _ 3 ∗ 3 _ 4 from Problem 1 on journal page 265. Partition and shade a rectangle. Students should reproduce the shading in the rectangle at the top of the journal page.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMMOOOOOOOOOOBBBBBBLBLBLBBBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROOOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEELELEELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBLELEELEMMMMMMMOOOOOOOOOBLBLBLBLBLBBLLOOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINNNNVINVINVINNVINVINVINVINVINVV GGGGGGGGGGGOLOOOOLOOLOLOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLOLOOO VVVLLLLLLLLLLVVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS NNNNNNNNNNNNNNNNNNNNNNNNNNNVVVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVVLLVVVVVVVVIIIIIIIIIIIIIIIIIIILLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGSOLVING

Study Link 8�5 Follow-UpDiscuss students’ solution strategies for Problem 5.

650-653_EMCS_T_TLG1_G5_U08_L06_576914.indd 650650-653_EMCS_T_TLG1_G5_U08_L06_576914.indd 650 2/12/11 9:47 AM2/12/11 9:47 AM

Date Time

1. Use the rectangle at the right to find �23� � �

34�.

�23� � �

34� �

Your completed drawing in Problem 1 is called an area model.Use area models to complete the remaining problems.

2. 3. 4.

�23� � �

15� � �

34� � �

25� � �

14� � �

56� �

5. 6. 7.

�38� � �

35� � �

12� � �

58� � �

56� � �

45� �

Explain how you sketched and shaded the rectangle to solve Problem 7.

�23

00�, or �

23��1

56��4

90�

�254��2

60�, or �1

30��1

25�

�162�, or �

12�

shaded equal �23

00� or �

23�, which is the answer.

of those sections. The 20 parts that are doubly rectangle into 6 sections horizontally and shaded 5 and shaded 4 of those sections. Then I divided the I divided the rectangle into 5 sections vertically

LESSON

8 �6 �An Area Model for Fraction Multiplication

Math Journal 2, p. 265

Student Page

An Algorithm for Fraction MultiplicationLESSON

8 �6

Date Time

1. Look carefully at the fractions on journal page 265. What is the relationship between the numerators and the denominators of the two fractions being multiplied and the numerator and the denominator of their product?

2. Describe a way to multiply two fractions.

3. Multiply the following fractions using the algorithm discussed in class.

a. �13� � �

15� � b. �

23� � �

13� �

c. �130� � �1

70� � d. �

58� � �

14� �

e. �38� � �

56� � f. �

25� � �1

52� �

g. �45� � �

25� � h. �

49� � �

37� �

i. �24� � �

48� � j. �

37� � �

59� �

k. �79� � �

26� � l. �

27� � �1

90� �

4. Girls are one-half of the fifth-grade class. Two-tenths of these girls have red hair. Red-haired girls are what fraction of the fifth-grade class?

�220�, or �1

10� of the fifth-grade class

as the product denominator.Multiply the denominators and record the product and record the product as the product numerator.

Multiply the numerators,

is equal to the product denominator.product numerator. The product of the two denominatorsThe product of the two numerators is equal to the

�115�

�12010� �3

52�

�1458�, or �1

56� �

1600�, or �

16�

�285�

�382�, or �

14�

�1544�, or �2

77� �

1780�, or �3

95�

�1653�, or �2

51�

�1623�, or �2

41�

�29�

Math Journal 2, p. 266

Student Page

Lesson 8�6 651

Figure 1 Figure 2

1. Note that the denominator of the second fraction is 4.

2. Divide the rectangle into fourths vertically. (See Figure 1.)

3. Shade the left 3 _ 4 of the interior of the rectangle.

4. Note that the denominator of the first fraction is 3.

5. Divide the rectangle into thirds horizontally. (See Figure 2.)

6. Use a different shading to shade the bottom 2 _ 3 of the interior.

7. Note the parts that have been shaded twice.

Ongoing Assessment: Informing Instruction

Watch for students who have difficulty sketching the area models for the

problems on the journal page. Have them first use the folded-paper method and

then copy the results to the journal page.

Discuss the results:

● How does the diagram show the answer to 2 _ 3 ∗ 3 _ 4 ? The parts of the rectangle that were shaded first represent 3 _ 4 of the rectangle. The parts that were shaded second represent 2 _ 3 of the rectangle. The parts that have both shadings represent 2 _ 3 of 3 _ 4 of the rectangle. 6 parts out of 12 are shaded twice, so 2 _ 3 of 3 _ 4 , or 2 _ 3 ∗ 3 _ 4 , equals 6 _ 12 , or 1 _ 2 .

● How is this model similar to paper folding? The lines that divide the rectangle into fractional parts are just like the folds that divide the paper into fractional parts.

● Why would either of these models be called an area model for fraction multiplication? The doubly shaded part represents a fraction. The area of the doubly shaded part of the rectangle is a fraction of the area of the whole rectangle.

Have partners complete the journal page. Circulate and assist. When most students have finished, briefly review the answers.

Ongoing Assessment:Recognizing Student Achievement

Journal

Page 265 �

Use journal page 265 to assess students’ understanding of the area model for

fraction multiplication. Students are making adequate progress if their sketches

accurately reflect the correct answers.

[Operations and Computation Goal 5]

650-653_EMCS_T_TLG1_G5_U08_L06_576914.indd 651650-653_EMCS_T_TLG1_G5_U08_L06_576914.indd 651 2/12/11 9:47 AM2/12/11 9:47 AM

Math Boxes LESSON

8 �6

Date Time

1. The digit in the hundreds place is a square number, and it is odd.

The digit in the tens place is 1 more than the square root of 16.

The digit in the hundredths place is 0.1 larger than 1 _ 10 of the digit in the hundreds place.

The digit in the thousandths place is equivalent to 30

_ 5 .

The other digits are all 2s. 9 5

2

. 2

1

6

Write this number in expanded notation. 900 + 50 + 2 + 0.2 + 0.01 + 0.006

3. Jon spent 24 1 _ 4 hours reading in March and

15 1 _ 2 hours reading in April. How many more

hours did he spend reading in March?

Number model:

Answer:

2. Write 3 equivalent fractions for each number.

a. 2 _ 5 =

b. 4 _ 7 =

c. 1 _ 2 =

d. 40

_ 50 =

e. 25

_ 75 =

h = 8 3 _ 4 hours

24 1

_ 4 - 15

1

_ 2 = h

4. Complete.

a. 10

_ 100 =

b. 8

_ 100 =

c. 5

_ 20 =

d. 10

_ 12 =

5. Use your Geometry Template to draw

a trapezoid.

How does the trapezoid you’ve drawn

differ from other quadrangles on the

Geometry Template?

The sides are not all

the same length.

4

71 7259

108 109 134–136

Sample answers:

1

5

10

25

4 _ 10 , 6

_ 15 , 8 _ 20

8 _ 14 , 12

_ 21 , 16

_ 28

2 _ 4 , 3

_ 6 , 4 _ 8

4 _ 5 , 8

_ 10 , 80

_ 100

1 _ 3 , 2

_ 6 , 50

_ 150

1

2

4

6

248-287_EMCS_S_MJ2_U08_576434.indd 267 2/15/11 9:39 AM

Math Journal 2, p. 267

Student Page

652 Unit 8 Fractions and Ratios

After briefly reviewing answers, pose a few fraction multiplication number stories. Suggestions:

● Laura and her brother will paint 3 _ 4 of a wall. How much of the entire wall will each paint if they share the work equally? 3 _ 8 of the wall

● A tube of blue oil paint holds 5 _ 6 of an ounce of paint. It takes 3 _ 4 of the tube to paint the background of a sign. How many ounces of blue paint does it take to paint the background? 15 _ 24 , or 5 _ 8 oz

▶ Deriving a Fraction PARTNER ACTIVITY

Multiplication Algorithm(Math Journal 2, p. 266; Student Reference Book, p. 76)

Have students work on Problems 1 and 2 on journal page 266. Discuss their answers. Students should notice that the product of the numerators is equal to the numerator of the product and that the product of the denominators is equal to the denominator of the product.

Ask volunteers to share their descriptions of a fraction multiplication algorithm from Problem 2. Explain that the relationships and descriptions are examples of the following general pattern: To multiply fractions, simply multiply the numerators and multiply the denominators. This pattern can be expressed as a _ b ∗ c _ d = a ∗ c _ b ∗ d . Remind students that b and d cannot be 0. Ask students to complete the journal page using this algorithm for fraction multiplication. Ask students to refer to Student Reference Book, page 76 as needed.

Circulate and assist. When most students have finished, have partners share answers and resolve differences.

NOTE Fraction multiplication is deceptively easy. One can easily learn by rote

that to multiply fractions, one simply multiplies the numerators and multiplies the

denominators. However, through modeling fractions by folding paper and shading

rectangles students internalize concepts necessary to understand the meaning of

expressions like 3

_ 4 ∗ 2 _ 3 .

When students do not understand the reasons behind the fraction multiplication

algorithm, they are more likely to add (or subtract or divide) numerators and

denominators when they add (or subtract or divide) fractions. Students who

understand what to do and why they are doing it will be better able to apply their

knowledge in problem solving.

650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652 4/1/11 2:11 PM4/1/11 2:11 PM

Lesson 8�6 652A

▶ Multiplying a Fraction by 1 WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 265)

Ask students to revisit Problem 1 on journal page 265. Remind them that they began by dividing the rectangle into fourths vertically and shading three of those four parts to show 3 _ 4 of the rectangle shaded. Then they divided the rectangle into thirds horizontally. Ask:

● How does dividing the rectangle into thirds (before applying the second round of shading) affect the number of parts in the rectangle and the number of parts that were shaded initially? Sample answer: Dividing the rectangle into thirds resulted in 3 times as many parts in all and 3 times as many parts shaded.

● Did this change how much of the rectangle was shaded? Explain. Sample answer: No, because the resulting fraction, 9 _ 12 , is equivalent to the original fraction, 3 _ 4 ; the shaded amount of the rectangle remained the same.

Repeat the above discussion for Problem 5 ( 3 _ 8 ∗ 3 _ 5 ) on journal page 265. Students should conclude that after the rectangle was divided into eighths horizontally, there were now 8 times as many parts in all and 8 times as many parts shaded. So, the 3 _ 5 of the

rectangle that was initially shaded became 24 _ 40 . Because 3 _ 5 = 24 _ 40 , the fractional part of the rectangle that was initially shaded did not change.

Help students conclude that when they divide rectangles into equal parts horizontally (or vertically if they began with horizontal partitions), they are in essence multiplying the numerator and the denominator of the original fraction by the same (nonzero) number.

Explain that this pattern can be expressed as a _ b = n ∗ a _ n ∗ b , where b ≠ 0 and n ≠ 0. Multiplying by n _ n does not change the value of the original fraction because it is equivalent to multiplying the fraction by 1. Ask students to try out this pattern on Problem 6.

Pose the following problems to provide additional practice multiplying by a fraction that has a value of 1.

● 1 ∗ 3 _ 4 = _ 3 _ 4

● 4 _ 9 = ∗ 4 _ 5 ∗ 9 5

● 5 _ 8 ∗ _ = 15 _ 24 3 _ 3

● 4 ∗ 7 _ 4 ∗ 10 = _ 10 7

650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652A650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652A 4/1/11 2:11 PM4/1/11 2:11 PM

STUDY LINK

8�6 Multiplying Fractions

74 76

Name Date Time

Write a number model for each area model.

Example:

1.

2. 3.

Multiply.

4. 3_7 º 2_

10= 5. 5_

6 º 2_3= 6. 1_

2 º 1_4=

7.4_5

º3_5= 8. 2_

3 º3_8= 9. 1_

7 º5_9=

10. Matt is making cookies for the school fund-raiser. The recipe calls

for 2_3 cup of chocolate chips. He decides to triple the recipe.

How many cups of chocolate chips does he need? cups

11. The total number of goals scored by both teams in the field-hockey

game was 15. Julie’s team scored 3_5 of the goals. Julie scored 1_3 of

her team’s goals. How many goals did Julie’s team score? goals

How many goals did Julie score? goals

1_4 º 2_

5 =2_20 , or 1_

101_3

º 2_5= 2_

15

3_4

º 1_4=

3_16

7_8

º 1_3=

7_24

Reminder: a_b º

c_d=

a ºa c_b ºb d

6_70, or

3_35

10_18 , or

5_9

1_8

12

_ 25 6 _ 24 , or 1 _

4 5 _ 63

2

9

3

221-253_EMCS_B_MM_G5_U08_576973.indd 232 3/25/11 2:00 PM

Math Masters, p. 232

Study Link Master

652B Unit 8 Fractions and Ratios

▶ Multiplying by a Fraction WHOLE-CLASSDISCUSSION

Less than 1(Math Journal 2, pp. 265 and 266)

Have students examine the drawings and the results in Problems 1–7 on journal page 265. Ask the following questions:

● In each problem, does the fractional part of the rectangle you shaded first represent the first fraction or the second fraction of the problem? It represents the second fraction.

● In each problem, how does the first fraction compare to 1? The first fraction in each problem is less than 1.

● In each problem, how would you compare the fractional part of the rectangle with double shading to the fractional part you shaded first? Sample answer: In each case, the fractional part with double shading is a portion of what I shaded first. So it is less than what I shaded first.

● In each problem, how does the product compare to the second fraction? Explain why that is the case. Sample answer: Each product is less than the second fraction. In each problem, we multiplied the second fraction by a fraction that is less than 1. So we were finding a portion of the second fraction.

Ask students to examine the results in Problem 3 on journal page 266. Ask: Do the results support what we said about a fraction being multiplied by a number less than 1? yes Ask students to describe the size of the product when you multiply a number by a fraction that is less than 1. Sample answer: When you multiply a number by a fraction that is less than 1, the product is less than the original number. For example, in Problem 3a, the product is a fraction, 1 _ 15 , that is less than the original fraction, 1 _ 5 .

2 Ongoing Learning & Practice

▶ Math Boxes 8�6

INDEPENDENT ACTIVITY

(Math Journal 2, p. 267)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-8. The skill in Problem 5 previews Unit 9 content.

▶ Study Link 8�6

INDEPENDENT ACTIVITY

(Math Masters, p. 232)

Home Connection Students solve fraction multiplication problems. They use the area model and the fraction multiplication algorithm.

650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652B650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 652B 4/1/11 2:11 PM4/1/11 2:11 PM

LESSON

8�6

Name Date Time

Fraction Multiplication

Problem 1

a. How many squares are in this grid?

b. How many squares represent 1_3 of 1_2 of the grid.

Shade these squares.

c. Think of the total number of squares in the grid

as the denominator and the shaded squares as

the numerator, and write the fraction. 1_3 of 1_2 =

d. Write the number model you would use to find the area of this rectangle.

Reminder: Area : = length º width

Area =

e. The number model to find the fractional part of the rectangle

is the same as the number model to find the area of the

rectangle. Write the number model you would use to find

the fractional part of the rectangle.

Problem 2

Linda bakes a peach pie. She serves 1_2 of the pie for dessert.

She saves 1_3 of what is left for her mom.

a. Shade the circle to represent the piece of the pie that

should be saved.

b. Think of the total number of pie pieces as the denominator

and the shaded piece as the numerator, and write the fraction.

c. Write a number sentence to show how you could find the fractional

part of the pie that was saved without counting pie pieces.

To find a fraction of a fraction, multiply.

4

3

12

1 3

Try This

Write and solve a number model to find the fractional part of the pie left

after subtracting dessert and the piece saved for Linda’s mom.

2_12, or

1_6

Sample answer:g

1 - (1_2 + 1_

6) = m; m =2_6, or 1_

3

1_3 º

1_2

12 squares

3 º 4

1_6

1_3 º

1_2

= p

2 squares

221-253_434_EMCS_B_MM_G5_U08_576973.indd 233 2/22/11 4:08 PM

Math Masters, p. 233

Teaching Master

Name Date Time

LESSON

8�6 Fraction Problems

1. Ailene is baking corn bread. She will cover 3

_ 4 of the cornbread

with cheese. Then she plans to give 2

_ 3 of the cornbread with cheese

to her friend Alex.

a. Use the rectangle to show an area model for the problem.

b. Write an open number model for the problem. Choose a letter to

stand for the portion that will be given to Alex. 2 _ 3 ∗ 3 _ 4 = a

c. Ailene will give 1 _ 2 of the cornbread to Alex.

2. A recipe for granola bars calls for 1

_ 2 cup almonds. Cy is making

3

_ 4 of

the recipe.

a. Write an open number model to show how many ounces of almonds

Cy will use. 3 _ 4 ∗ 1 _ 2 = a

b. Cy will use 3 _ 8 cup of almonds.

3. An ant weighs 1

_ 10

the weight of a crumb that it is carrying. Suppose the crumb

weighs 3

_ 100

gram.

a. Write an open number model to show the weight of the ant in grams.

1 _ 10 ∗ 3

_ 100 = a

b. The ant weighs 3

_ 1,000 gram.

4. Walker plans to hike a trail that is 8

_ 10

of a mile long. So far, he has walked 1

_ 4

that distance.

a. Write an open number model for the problem. 1 _ 4 ∗ 8 _ 10 = w

b. So far, Walker has walked 1 _ 5 mi.

5. In Mrs. Ortiz’s class, 9

_ 22

of the students are boys. Of the boys, 1

_ 9 are

left-handed.

a. Write an open number model to show how to find what fraction of the class

are left-handed boys. 1 _ 9 ∗ 9 _ 22 = b

b. 1 _ 22 of the class are left-handed boys.

221-253_EMCS_B_MM_G5_U08_576973.indd 234 3/16/11 1:24 PM

Math Masters, p. 234

Teaching Master

Lesson 8�6 653

3 Differentiation Options

READINESS

SMALL-GROUP ACTIVITY

▶ Supporting Fraction 5–15 Min

Multiplication Concepts(Math Masters, p. 233)

To provide an additional model for the connection between the word of and multiplication, guide students through the activity on the Math Masters page.

Problem 1 Students review using multiplication to find the area of a rectangle and an area that is a fractional part of the rectangle. Point out that the numerators represent the length and width of the part of the rectangle that is shaded. Remind students that 1 _ 2 is equivalent to 2 _ 4 . The denominators represent the length and width of the entire rectangle. The product of the fractions names the twice-shaded area of the rectangle.

Problem 2 Students find and shade a similar fractional part of a circle.

Review both problems by emphasizing that finding 1 _ 3 of 1 _ 2 of the rectangle is the same as finding 1 _ 3 of 1 _ 2 of the circle. Both problems can be solved using multiplication.

Pose several problems for students to solve using multiplication, and have them write the number sentences.

● 1 _ 5 of 1 _ 4 1 _ 5 ∗ 1 _ 4 = 1 _ 20

● 3 _ 5 of 1 _ 4 3 _ 5 ∗ 1 _ 4 = 3 _ 20

● 2 _ 5 of 3 _ 4 2 _ 5 ∗ 3 _ 4 = 6 _ 20 , or 3 _ 10

EXTRA PRACTICE

INDEPENDENT ACTIVITY

▶ Fraction Problems 5–15 Min

(Math Masters, p. 234)

Students solve real-world number stories involving fractions. They are asked to first write an open number model for each problem.

650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 653650-653_EMCS_T_TLG2_G5_U08_L06_576914.indd 653 4/1/11 2:11 PM4/1/11 2:11 PM

234

Name Date Time

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

LESSON

8�6 Fraction Problems

1. Ailene is baking corn bread. She will cover 3

_ 4 of the cornbread

with cheese. Then she plans to give 2

_ 3 of the cornbread with cheese

to her friend Alex.

a. Use the rectangle to show an area model for the problem.

b. Write an open number model for the problem. Choose a letter to

stand for the portion that will be given to Alex.

c. Ailene will give of the cornbread to Alex.

2. A recipe for granola bars calls for 1

_ 2 cup almonds. Cy is making

3

_ 4 of

the recipe.

a. Write an open number model to show how many ounces of almonds

Cy will use.

b. Cy will use cup of almonds.

3. An ant weighs 1

_ 10

the weight of a crumb that it is carrying. Suppose the crumb

weighs 3

_ 100

gram.

a. Write an open number model to show the weight of the ant in grams.

b. The ant weighs gram.

4. Walker plans to hike a trail that is 8

_ 10

of a mile long. So far, he has walked 1

_ 4

that distance.

a. Write an open number model for the problem.

b. So far, Walker has walked mi.

5. In Mrs. Ortiz’s class, 9

_ 22

of the students are boys. Of the boys, 1

_ 9 are

left-handed.

a. Write an open number model to show how to find what fraction of the class

are left-handed boys.

b. of the class are left-handed boys.

221-253_EMCS_B_MM_G5_U08_576973.indd 234221-253_EMCS_B_MM_G5_U08_576973.indd 234 3/16/11 1:24 PM3/16/11 1:24 PM