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CurriculumFocal Points

Common Core State Standards

637A Unit 7 Fractions and Their Uses; Chance and Probability

Advance Preparation

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

Multiplying Fractions by Whole Numbers

Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number.o

Key Concepts and Skills• Use a number line to represent a fraction.

[Number and Numeration Goal 2]

• Understand a fraction a _ b as a multiple of 1 _ b .[Number and Numeration Goal 3]

• Determine between which two whole numbers a fraction lies.[Number and Numeration Goal 6]

• Solve number stories involving multiplication of a fraction by a whole number.[Operations and Computation Goal 7]

• Write equations to model number stories.[Patterns, Functions, and Algebra Goal 2]

Key ActivitiesStudents use a number line as a visual fraction model to represent a fraction a _ b multiplied by a whole number n as the product n ∗ ( a _ b ) or (n ∗ a)

_ b . They solve number stories involving multiplication of a fraction by a whole number by using visual fraction models and equations to represent the problems.

Ongoing Assessment: Informing Instruction See page 637D.

Key Vocabularymultiple � equation

MaterialsMath Journal 2, pp. 217A–217EStudy Link 7 �12half-sheets of paper � calculator (optional)

Math Boxes 7�12aMath Journal 2, p. 217FStudents practice and maintain skills through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Operations and Computation Goal 5]

Study Link 7�12aMath Masters, p. 242AStudents practice and maintain skillsthrough Study Link activities.

READINESS

Skip Counting to Show Multiples of Unit FractionsMath Masters, p. 242BcalculatorStudents use calculators to skip count by unit fractions.

ENRICHMENTVisual Models for Multiplying a Fraction by a Whole NumberStudent Reference Book, p. 58Math Masters, pp. 242C and 242DStudents explore alternative visual fraction models for multiplying a fraction by a whole number.

EXTRA PRACTICE 5-Minute Math5-Minute Math™, pp. 22 and 23Students practice multiplying fractions by whole numbers.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

��

637A_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637A 3/3/11 2:51 PM

Lesson 7�12a 637B

Adjusting the Activity Provide students with calculators to assist with skip counting. See the Part 3 Readiness activity for additional information.AUDITORY � KINESTHETIC � TACTILE � VISUAL

NOTE In Third Grade Everyday Mathematics children participated in skip-counting activities to help them memorize the multiplication facts. While completing these activities, they were finding multiples. A multiple of a number is the product of a counting number and the number itself.

Date Time

Multiples of Unit FractionsLESSON

7�12a

For Problems 1–3, fill in the blanks to complete an equation describing the number line.

1. 18

28

38

48

58

68

780 1

Equation: 5 ∗ 1 _ 8 = 5 _ 8

2. 16

26

36

46

560 1

Equation: 3 ∗ 1 _ 6 = 3 _ 6 , or 1 _ 2

3. 13

23

33

43

53

630

Equation: 4 ∗ 1 _ 3 = For Problems 4–6, use the number line to help you multiply the fraction by the whole number.

4. 14

24

340 1

Equation: 2 ∗ 1 _ 4 = 2

_ 4 , or 1 _ 2

5. 110

210

310

410

510

610

710

810

910

10100

Equation: 6 ∗ 1 _ 10 =

6. 15

25

35

45

55

65

75

85

95

1050

Equation: 7 ∗ 1 _ 5 =

58

4 _ 3 , or 1 1 _ 3

6 __ 10 , or 3 _ 5

7 _ 5 , or 1 2 _ 5

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217A 3/24/11 9:28 AM

Math Journal 2, p. 217A

Student Page

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Ask students how they determined the next three multiples in each sequence. Possible strategies:

� Think of the problem as skip counting by 1 _ 10 s. To get the next multiple, add 1 _ 10 to the previous fraction. For example,

1 _ 10 + 1 _ 10 = 2 _ 10 ; 2 _ 10 + 1 _ 10 = 3 _ 10 ; 3 _ 10 + 1 _ 10 = 4 _ 10 ; and so on.

� Think in terms of equal groups. For example, 1 group of 1 _ 4 is 1 _ 4 ; 2 groups of 1 _ 4 is 2 __ 4 ; 3 groups of 1 _ 4 is 3 _ 4 ; 4 groups of 1 _ 4 is 4 _ 4 ; and so on.

Tell students that in this lesson they will use their understanding of multiples to multiply fractions by whole numbers.

� Using a Visual Fraction Model to PARTNER ACTIVITY

Multiply a Unit Fraction by a Whole Number(Math Journal 2, pp. 217A)

Draw the number line below on the board or overhead.

12

22

32

42

52

620

Have volunteers explain how they could use the number line and their understanding of multiples to help them solve the problem 3 ∗ 1 __ 2 .

Getting Started

Mental Math and Reflexes Have students name the next three multiples in a sequence. Suggestions:

8, 16, 24, ... 32, 40, 48 50, 60, 70, ... 80, 90, 100 25, 50, 75, ... 100, 125, 150 82, 84, 86, ... 88, 90, 92 56, 60, 64, ... 68, 72, 76 18, 27, 36, ... 45, 54, 63 70, 140, 210, ... 280, 350, 420 600; 1,200; 1,800; ... 2,400; 3,000; 3,600 125, 250, 375, ... 500, 625, 750

Math MessageName the next three multiples in each sequence.

1 __ 10 , 2 __ 10 , 3 __ 10 , … 4 __ 10 , 5 __ 10 , 6 __ 10

1 __ 4 , 2 __ 4 , 3 __ 4 , … 4 _ 4 , 5 _ 4 , 6 _ 4

Study Link 7�12 Follow-UpHave small groups compare the results of the penny toss experiment. Ask volunteers to share their answers for Problem 5. Have students indicate thumbs-up if they agree.

Mathematical PracticesSMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8Content Standards4.OA.4, 4.NF.4a, 4.NF.4b, 4.NF.4c

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637B 3/1/12 2:16 PM

637C Unit 7 Fractions and Their Uses; Chance and Probability

217C

Date Time

Multiplying Fractions by Whole NumbersLESSON

7�12a 58

Use number lines to help you solve the problems.

1. 5 ∗ 1 _ 6 = 5 _ 6

66

16

0

16

16

16

16

2. 6 ∗ 1 _ 3 = 6 _ 3 , or 2

93

63

33

13

0

13

13

13

13

13

3. 3 _ 8 = 3 ∗ 1 _ 8

88

48

18

0

Sample answer:18

18

4. 2 ∗ 4 _ 3 = 8 _ 3 , or 2 2 _ 3

93

63

33

43

0

43

5. 12 __ 8 , or 1 4 _ 8 , or 1 1 _ 2 = 4 ∗ 3 _ 8

88

168

48

1280

38

38

38

38

6. 6 __ 10 , or 3 _ 5 = 3 ∗ 2 _ 10

1010

510

210

210

210

0

Sample answer:

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217C 3/3/11 12:39 PM

Math Journal 2, p. 217C

Student Page

217B

Date Time

An Algorithm for Multiplying a Fraction by a Whole NumberLESSON

7�12a

Example 1: Equation: 6 ∗ 1 _ 5 = 6 _ 5

55

15

1050

15

15

15

15

15

Example 2: Equation: 3 ∗ 2 _ 5 = 6 _ 5

55

25

1050

25

25

Write an equation to describe each number line.

1. a. 44

840

14

14

14

14

14

14

6 ∗ 1 _ 4 = 6 _ 4

b . 44

840

34

34

2 ∗ 3 _ 4 = 6 _ 4

2. a. 93

63

330

13

13

13

13

13

13

13

13

8 ∗ 1 _ 3 = 8 _ 3

b . 93

63

330

23

23

23

23

4 ∗ 2 _ 3 = 8 _ 3

3. Study the pairs of number lines above. Use the patterns you see to describe a way to multiply a fraction by a whole number.

Sample answer: If I take the whole number, multiply it by

the numerator of the fraction and then write the product over the denominator, that is my answer.

58

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217B 3/3/11 12:39 PMMath Journal 2, p. 217B

Student PageOne way is to visualize jumps or hops on the number line, starting at 0. The fraction tells the size of the jump; the whole number tells the number of jumps. Thus, 3 ∗ 1 _ 2 is 3 jumps, each 1 _ 2 unit long. You end up at 3 _ 2 . So, 3 ∗ 1 _ 2 = 3 _ 2 , or 1 1 _ 2 .

12

22

32

42

52

620

12

12

12

Partners complete journal page 217A. Tell students that an equation is a number sentence with an equals sign, such as 3 ∗ 1 _ 2 = 3 _ 2 . As you circulate and assist, pose questions such as the following:

● Which number in the equation tells you the size of the jump? The first fraction

● Which number in the equation tells you the number of jumps? The whole number

● Can you name the products in Problems 3 and 6 as mixed numbers? 4 _ 3 = 1 1 _ 3 ; 7 _ 5 = 1 2 _ 5

� Using a Visual Fraction Model WHOLE-CLASS ACTIVITY

to Multiply Any Fraction by a Whole Number(Math Journal 2, pp. 217B and 217C)

Have partners study the examples at the top of journal page 217B. On a half-sheet of paper, students should record any similarities and differences they see between the equations modeled on the number lines.

Expect students to share observations such as the following:

� Both equations involve multiplication of a fraction by a whole number.

� Both equations have the same product.

� The factors in the equations are different, but 2 _ 5 is a multiple of 1 _ 5 and 6 is a multiple of 3.

� It takes more jumps of 1 _ 5 to get to 6 _ 5 than it does jumps of 2 _ 5 because the jumps of 1 _ 5 are smaller than the jumps of 2 _ 5 .

� The whole number factor in 6 ∗ 1 _ 5 = 6 _ 5 is twice as much as the whole number factor in 3 ∗ 2 _ 5 = 6 _ 5 . The fraction factor in 6 ∗ 1 _ 5 = 6 _ 5 is half as much as the fraction factor in 3 ∗ 2 _ 5 = 6 _ 5 .

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637C 3/3/11 2:51 PM

Lesson 7�12a 637D

Date Time

Solving Number StoriesLESSON

7�12a

Suma and her sister Puja are making 12 blueberry-wheat muffins for breakfast. The recipe lists the following ingredients:

1 cup flour 1 egg1 _ 2 cup whole-wheat flour 1 _ 2 cup skim milk2 teaspoons baking powder 2 _ 3 cup honey3 _ 4 cup blueberries 1 _ 4 cup cooking oil1 _ 4 teaspoon salt 3 _ 8 teaspoon cinnamon

Use the list of recipe ingredients to help you solve the number stories below. For each problem, write an equation to show what you did.

1. The sisters decided to double the recipe.

a. How many cups of whole-wheat flour do they need now?

2 _ 2 , or 1 cup(s) Equation: 2 ∗ 1 _ 2 = 2 _ 2

b. How many cups of blueberries do they need now?

6 _ 4 , or 1 2 _ 4 , or 1 1 _ 2 cup(s) Equation: 2 ∗ 3 _ 4 = 6 _ 4

c. How many cups of honey do they need now?

4 _ 3 , or 1 1 _ 3 cup(s) Equation: 2 ∗ 2 _ 3 = 4 _ 3

2. Suma and Puja decide to make 48 muffins instead of 12.

a. How many teaspoons of salt do they need now?

4 _ 4 , or 1 teaspoon(s) Equation: 4 ∗ 1 _ 4 = 4 _ 4 b. How many teaspoons of cinnamon do they need now?

12 __ 8 , or 1 4 _ 8 , or 1 1 _ 2 teaspoon(s) Equation: 4 ∗ 3 _ 8 = 12 __ 8

c. How many cups of skim milk do they need now?

4 _ 2 , or 2 cup(s) Equation: 4 ∗ 1 _ 2 = 4 _ 2

58

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217D 3/3/11 12:39 PM

Math Journal 2, p. 217D

Student Page

NOTE In Lesson 3-8, students used number models to model number stories. A number model is a number sentence or part of a number sentence. A number model can include an equal sign, but it is not required. An equation is a number sentence with an equal sign. See Section 10.2 in the Teacher’s Reference Manual for more information.

Have partners complete Problems 1 and 2 on journal page 217B by writing a multiplication equation to describe each number line. When students have completed Problem 3, bring the class together to discuss the algorithm for multiplication of a fraction by a whole number. The pattern can be expressed as: n ∗ a __

b = (n ∗ a)

_ b .

Have students complete journal page 217C for additional practice multiplying fractions by whole numbers. Encourage students to use the pattern they discovered on journal page 217B to check their answers.

� Solving Number Stories PARTNER ACTIVITY

(Math Journal 2, pp. 217D and 217E)

Pose the following number story:

When Carlos goes to the gym, he exercises for 3 _ 4 of an hour and burns about 200 calories. Last week he went to the gym 5 times. How many hours did Carlos spend at the gym last week?

Ongoing Assessment: Informing InstructionWatch for students who are distracted by the “extra” 200 in the number story. Encourage them to eliminate irrelevant information by determining exactly what they want to find out, what information they already know, and what they might need to know in order to solve the problem.

On a half-sheet of paper, have students draw a visual fraction model to represent the number story. Expect drawings such as the following:

0 44

84

124

164

204

34

34

34

34

34

Then have students write a multiplication equation to represent the problem. 5 ∗ 3 _ 4 = 15 __ 4

Ask students to determine between which two whole numbers of hours the product lies. 3 and 4 hours Have them explain their strategy for finding the answer. Possible strategies:

� Use the number line drawn to represent the number story. Note that the product lies between 12 _ 4 , or 3, and 16 _ 4 , or 4.

� The fraction 15 _ 4 can be renamed as the mixed number 3 3 _ 4 by dividing the numerator, 15, by the denominator, 4: 15 � 4 → 3 R3. The quotient, 3, is the whole number part of the mixed number. The remainder, 3, is the numerator of the fraction part of the mixed number. It tells how many fourths are left over after making as many wholes as possible.

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637D 3/3/11 2:52 PM

637E Unit 7 Fractions and Their Uses; Chance and Probability

Date Time

Solving Number Stories continuedLESSON

7�12a

The Hillside Elementary School walking club meets every Monday after school. The table below shows how far some students walked at their last meeting.

Student

Miles 1 _ 3 9 _

10 5 _

4 5 _

2 4 _

3 5 _

6

Katie Mahpara Nikhil Cole Maria Jack

Use the information in the table to solve the number stories.

3. a. If Katie walks the same distance at every meeting, how far will she walk after 2 meetings? miles

b. After 7 meetings? 7 _ 3 , or 2 1 _ 3 miles

c. After 7 meetings, Katie will have walked between . Circle the best answer.

1 and 2 miles 2 and 3 miles 3 and 4 miles

4. a. If Jack walks the same distance at every meeting, how far will he walk after 3 meetings? miles

b. After 3 meetings, Jack will have walked between . Circle the best answer.


5. a. If Mahpara walks the same distance at every meeting, how far will she walk after 4 meetings? miles

b. After 4 meetings, Mahpara will have walked between . Circle the best answer.


6. If Cole walks the same distance at every meeting and wants to walk a total of 15 _ 2 miles, how many meetings will he need to attend? 3 meetings

7. Make up your own multiplication number story about Nikhil or Maria.

Answers vary.

Try This

2 _ 3

15 __ 6 , or 2 3 _ 6 , or 2 1 _ 2

36 __ 10 , or 3 6 __ 10 , or 3 3 _ 5

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217E 3/24/11 9:28 AM

Math Journal 2, p. 217E

Student Page

Have partners complete journal pages 217D and 217E. Encourage students to use visual fraction models, such as number lines, to help them solve the problems. When reviewing answers, pose questions such as the following:

● Which of the products on journal page 217D can you rename as whole numbers? Problem 1a: 2 _ 2 = 1; Problem 2a: 4 _ 4 = 1; Problem 2c: 4 _ 2 = 2

● Between which two whole numbers does the product in Problem 2b lie? 1 and 2

● In Problem 2, how did you decide which whole number you would multiply the recipe ingredients by? Sample answer: The recipe makes 12 muffins. If the sisters want 48 muffins they will need to quadruple the recipe because 12 ∗ 4 = 48.

● How did you solve Problem 6? Sample answer: Let the letter a stand for the number of meetings Cole would need to attend and write the equation a ∗ 5 _ 2 = 15 _ 2 . Use the algorithm for multiplying a fraction by a whole number and think: What number times 5 will give me 15? 3 ∗ 5 = 15, so 3 ∗ 5 _ 2 = 15 _ 2 . Cole will need to attend 3 meetings.

● In Problem 6, between which two whole-number distances does the distance 15 _ 2 miles lie? Between 7 and 8 miles

Allow time for students to share and solve the number stories they wrote for Problem 7. For each problem, pose questions such as the following:

● Between which two whole numbers does the answer lie?

● Can you use a visual fraction model or an equation to represent the problem?

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637E 3/24/11 2:40 PM

Lesson 7�12a 637F

Date Time

Math BoxesLESSON

7�12a

4. Write an equivalent fraction, decimal, or whole number.

Decimal Fraction

a. 0.60 b. 0.65

65 _ 100

c. 1.0 50 _

50

d. 0.9

1. Karen used 60 square feet of her back yard for a garden. Vegetables fill 3 _ 5 of her garden space. Tomato plants fill 1 _ 6 of the space taken up by vegetables. How many square feet are used for tomatoes?

6 square feet

2. Multiply. Use a paper-and-pencil algorithm.

3,741 = 87 ∗ 43

3. a. Lukasz drew a line segment that was 2 2 _ 8 inches long. Then he extended it another 2 3 _ 8 inches. How long is the line segment now?

4 5 _ 8 inches

b. Sybil drew a line segment 3 1 _ 8 inches long. Then she extended it another 2 3 _ 4 inches. How long is the line segment now?

5 7 _ 8 inches

18 1959

55–57

162–166 129

61 62

60 ___ 100

6. Complete.

a. 42 in.= 3 ft 6 in.

b. 16 ft = 192 in.

c. 67 in. = 5 ft 7 in.

d. 22 ft = 7 yd 1 ft

e. 1 1 _ 2 yd = 4 ft 6 in.

5. Complete the table and write the rule.

Rule: -3.49 in out

104.16 100.67

87.35 83.86

45.72 42.23 55.41 51.92 77.69 74.20

9 __ 10

�

185-218_EMCS_S_MJ2_G4_U07_576426.indd 217F 3/3/11 12:39 PM

Math Journal 2, p. 217F

Student Page

242A

Name Date Time

58


7�12a

Use the number lines to help you solve the problems.

1. 5 ∗ 1 _ 5 = 5

_ 5 , or 1

105

15

25

35

45

55

65

75

85

950

15

15

15

15

15

2. 3 ∗ 4 _ 9 =

189

990

49

49

49

3. 6 ∗ 3 _ 6 = 18

_ 6 , or 3

186

126

660

36

36

36

36

36

36

Write a multiplication equation to represent the problem and then solve.

4. Rahsaan needs to make 5 batches of granola bars. A batch calls for 1 _ 2 cup of honey.

How much honey does he need? Equation: 5 ∗ 1 _ 2 = 5 _ 2 , or 2 1 _ 2 cups 5. Joe swims 6 _ 10 of a mile 5 days a week. How far does he swim every week?

Equation: 5 ∗ 6 _ 10 = 30

_ 10 , or 3 miles

How far would he swim if he swam every day of the week?

Equation: 7 ∗ 6 _ 10 = 42

_ 10 , or 4 2 _ 10 , or 4 1 _ 5 milesPractice

6. a. List the factor pairs of 5. 1 and 5 b. Is 5 a prime number? yes 7. a. List the factor pairs of 21. 1 and 21; 3 and 7

b. Is 21 a prime number? no

12

_ 9 , or 1 3 _ 9 , or 1 1 _ 3

242A-242D_EMCS_B_MM_G4_U07_576965.indd 242A 3/23/11 12:43 PM

Math Masters, p. 242A

Study Link Master

2 Ongoing Learning & Practice

� Math Boxes 7�12a INDEPENDENTACTIVITY

(Math Journal 2, p. 217F)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 7-9 and 7-11. The skill in Problem 6 previews Unit 8 content.

Ongoing Assessment: Math Boxes Problem 3 �

Recognizing Student AchievementUse Math Boxes, Problem 3 to assess students’ ability to solve mixed-number addition problems. Students are making adequate progress if they are able to solve Problem 3a, which involves mixed numbers with like denominators. Some students may be able to solve Problem 3b, which involves mixed numbers with unlike denominators, by using equivalent mixed numbers with like denominators, using manipulatives, or drawing pictures. [Operations and Computation Goal 5]

� Study Link 7�12a INDEPENDENTACTIVITY

(Math Masters, p. 242A)

Home Connection Students use number lines to multiply fractions by whole numbers.

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637F 3/24/11 2:40 PM

637G Unit 7 Fractions and Their Uses; Chance and Probability

Name Date Time

Skip Counting by a Unit FractionLESSON

7�12a

1. Use your calculator to count by 1 _ 2 s. Complete the table below.

One 1 _ 2

Two 1 _ 2 s

Three 1 _ 2 s

Four 1 _ 2 s

Five 1 _ 2 s

Six 1 _ 2 s

Seven 1 _ 2 s

Eight 1 _ 2 s

Nine 1 _ 2 s

Ten 1 _ 2 s

1 _ 2 2 _ 2 3 _ 2 4 _ 2 5 _ 2

6 _ 2

7 _ 2

8 _ 2

9 _ 2

10 _ 2


One 1 _ 3

Two 1 _ 3 s

Three 1 _ 3 s

Four 1 _ 3 s

Five 1 _ 3 s

Six 1 _ 3 s

Seven 1 _ 3 s

Eight 1 _ 3 s

Nine 1 _ 3 s

Ten 1 _ 3 s

1 _ 3 2 _ 3 3 _ 3 4 _ 3 5 _ 3

6 _ 3

7 _ 3

8 _ 3

9 _ 3

10 _ 3


One 1 _ 5

Two 1 _ 5 s

Three 1 _ 5 s

Four 1 _ 5 s

Five 1 _ 5 s

Six 1 _ 5 s

Seven 1 _ 5 s

Eight 1 _ 5 s

Nine 1 _ 5 s

Ten 1 _ 5 s

1 _ 5 2 _ 5 3 _ 5

4 _ 5

5 _ 5

6 _ 5

7 _ 5

8 _ 5

9 _ 5

10 _ 5


One 1 _ 8

Two 1 _ 8 s

Three 1 _ 8 s

Four 1 _ 8 s

Five 1 _ 8 s

Six 1 _ 8 s

Seven 1 _ 8 s

Eight 1 _ 8 s

Nine 1 _ 8 s

Ten 1 _ 8 s

1 _ 8 2 _ 8

3 _ 8

4 _ 8

5 _ 8

6 _ 8

7 _ 8

8 _ 8

9 _ 8

10 _ 8


One 1 _ 10

Two 1 _ 10 s

Three 1 _ 10 s

Four 1 _ 10 s

Five 1 _ 10 s

Six 1 _ 10 s

Seven 1 _ 10 s

Eight 1 _ 10 s

Nine 1 _ 10 s

Ten 1 _ 10 s

1 _ 10

2 _ 10

3 _ 10

4 _ 10

5 _ 10

6 _ 10

7 _ 10

8 _ 10

9 _ 10

10 _ 10

6. How is skip counting by 1 _ 3 s on your calculator from 0 to nine 1 _ 3 s the same as finding the product 9 ∗ 1 _ 3 ?

Sample answer: When you skip count by 1

_ 3 from 0 nine

times, you are finding nine groups of 1

_ 3 . This is the same

as 9 ∗ 1

_ 3 .

242A-242D_EMCS_B_MM_G4_U07_576965.indd 242B 3/3/11 10:44 AM

Math Masters, p. 242B

Teaching Master

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Skip Counting to Show 15–30 Min

Multiples of Unit Fractions(Math Masters, p. 242B)

To explore multiples of unit fractions, have students skip count on the calculator. Remind students that when you skip count by a number, your counts are the multiples of that number.

Review the steps for counting by 5s on the calculator. Students can program their calculator using the following steps:

TI-15:

1. Press On/Off and Clear simultaneously. This clears your calculator display and memory.

2. Press Op1 + 5 Op1 . This tells the calculator to count up by 5s.

3. Press 0. This is the starting number.

Casio fx-55:

1. Press . This clears your calculator display and memory.

2. Press 5. This tells the calculator to count by 5s.

3. Press . This tells the calculator to count up.

4. Press 0. This is the starting number.

Now the calculator is ready to count by 5s. Without clearing their calculators, have students press the Op1 key or the key. Press the Op1 key or the key repeatedly as the students count together by 5s.

Next have students skip count by the unit fraction 1 _ 4 . You may first need to remind students of the steps to enter a fraction on their calculators.

To enter 1 _ 4 :

� On a TI-15: 1 n 4 d .

� On a Casio fx-55: 1 4.

Have students skip count by unit fractions to complete the tables on Math Masters, page 242B. Afterward, discuss how Problem 6 highlights the concept that a fraction such as 9 _ 3 means the same thing as 9 ∗ ( 1 _ 3 ). In general, a _ b = a ∗ ( 1 _ b ).

637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637G 3/28/11 4:34 PM

Lesson 7�12a 637H

Name Date Time

LESSON

7�12a Addition Model for Multiplying

Draw models for each product. Then add the fractions to find the product.

1. 2 ∗ 1 _ 3 = 1 _ 3 + 1 _ 3 = 2 _ 3

2. 3 ∗ 1 _ 2 = 1 _ 2 + 1 _ 2 + 1 _ 2 = 3 _ 2

3. 2 ∗ 2 _ 5 = 2 _ 5 + 2 _ 5 = 4 _ 5

4. 4 ∗ 2 _ 3 =

Sample shading is given in models.

58

2 _ 3 + 2 _ 3 + 2 _ 3 + 2 _ 3 = 8 _ 3

242A-242D_EMCS_B_MM_G4_U07_576965.indd 242C 3/23/11 12:43 PM

Math Masters, p. 242C

Teaching Master

Name Date Time

Area Model for MultiplyingLESSON

7�12a

58

For each problem, divide the model into strips, and then shade a fraction of the area to find the product.

1. 1 _ 3 of 2 square units = 2 _ 3 square unit(s)

So, 1 _ 3 ∗ 2 = 2 _ 3 .


So, 1 _ 4 ∗ 4 = 4 _ 4 .


So, 2 _ 3 ∗ 3 = 6 _ 3 .

4. 3 _ 4 of 5 square units = 15

_ 4 square unit(s)

So, 3 _ 4 ∗ 5 = 15

_ 4 .

Sample shading is given in models.

242A-242D_EMCS_B_MM_G4_U07_576965.indd 242D 3/3/11 10:44 AM

Math Masters, p. 242D

Teaching Master

ENRICHMENT SMALL-GROUP ACTIVITY

� Visual Models for Multiplying 15–30 Min

a Fraction by a Whole Number(Student Reference Book, p. 58; Math Masters, pp. 242C and 242D)

To extend students’ understanding of fraction multiplication, have them explore two different models: addition and area. Begin by having students read Student Reference Book, page 58. Discuss the example provided for each model as a group.

Have students complete Math Masters, pages 242C and 242D. For page 242C, encourage the groups to discuss how each number in the problem was represented in the model. The whole number is the number of rectangles drawn. The denominator of the fraction is the number of equal parts each rectangle is divided into. The numerator of the fraction is the number of parts of each rectangle that are shaded.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

▶ 5-Minute Math 5–15 Min

To offer students more experience with multiplying fractions by whole numbers, see 5-Minute Math, pages 22 and 23.

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7�12a

Use the number lines to help you solve the problems.

1. 5 ∗ 1 _ 5 =

105

15

25

35

45

55

65

75

85

950

2. 3 ∗ 4 _ 9 =

189

990

3. 6 ∗ 3 _ 6 =

186

126

660

Write a multiplication equation to represent the problem and then solve.

4. Rahsaan needs to make 5 batches of granola bars. A batch calls for 1 _ 2 cup of honey.

How much honey does he need? Equation:

5. Joe swims 6 _ 10 of a mile 5 days a week. How far does he swim every week?

Equation:

How far would he swim if he swam every day of the week?

Equation:

Practice

6. a. List the factor pairs of 5. b. Is 5 a prime number?

7. a. List the factor pairs of 21.

b. Is 21 a prime number?

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Skip Counting by a Unit FractionLESSON

7�12a


One 1 _ 2

Two 1 _ 2 s

Three 1 _ 2 s

Four 1 _ 2 s

Five 1 _ 2 s

Six 1 _ 2 s

Seven 1 _ 2 s

Eight 1 _ 2 s

Nine 1 _ 2 s

Ten 1 _ 2 s

1 _ 2 2 _ 2 3 _ 2 4 _ 2


One 1 _ 3

Two 1 _ 3 s

Three 1 _ 3 s

Four 1 _ 3 s

Five 1 _ 3 s

Six 1 _ 3 s

Seven 1 _ 3 s

Eight 1 _ 3 s

Nine 1 _ 3 s

Ten 1 _ 3 s

1 _ 3 2 _ 3 3 _ 3 4 _ 3


One 1 _ 5

Two 1 _ 5 s

Three 1 _ 5 s

Four 1 _ 5 s

Five 1 _ 5 s

Six 1 _ 5 s

Seven 1 _ 5 s

Eight 1 _ 5 s

Nine 1 _ 5 s

Ten 1 _ 5 s

1 _ 5 2 _ 5


One 1 _ 8

Two 1 _ 8 s

Three 1 _ 8 s

Four 1 _ 8 s

Five 1 _ 8 s

Six 1 _ 8 s

Seven 1 _ 8 s

Eight 1 _ 8 s

Nine 1 _ 8 s

Ten 1 _ 8 s

1 _ 8


One 1 _ 10

Two 1 _ 10 s

Three 1 _ 10 s

Four 1 _ 10 s

Five 1 _ 10 s

Six 1 _ 10 s

Seven 1 _ 10 s

Eight 1 _ 10 s

Nine 1 _ 10 s

Ten 1 _ 10 s

6. How is skip counting by 1 _ 3 s on your calculator from 0 to nine 1 _ 3 s the same as finding the product 9 ∗ 1 _ 3 ?

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LESSON

7�12a Addition Model for Multiplying

Draw models for each product. Then add the fractions to find the product.

1. 2 ∗ 1 _ 3 =

2. 3 ∗ 1 _ 2 =

3. 2 ∗ 2 _ 5 =

4. 4 ∗ 2 _ 3 =

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Area Model for MultiplyingLESSON

7�12a

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For each problem, divide the model into strips, and then shade a fraction of the area to find the product.

1. 1 _ 3 of 2 square units = square unit(s)

So, 1 _ 3 ∗ 2 = .


So, 1 _ 4 ∗ 4 = .


So, 2 _ 3 ∗ 3 = .


So, 3 _ 4 ∗ 5 = .

multiplying fractions by whole numbers - mcgraw-hill ... epresentations etoolkit interactive...

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