Download Multiplying Fractions by Whole Numbers

Multiplying Fractions
by Whole Numbers
Objective To apply and extend previous understandings
of multiplication to multiply a fraction by a whole number.
o
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Use a number line to represent a fraction.
[Number and Numeration Goal 2]
• Understand a fraction _ab as a multiple of _1b .
[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.
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Math Boxes 7 12a
Math Journal 2, p. 217F
Students 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 12a
Math Masters, p. 242A
Students practice and maintain skills
through Study Link activities.
[Patterns, Functions, and Algebra Goal 2]
Key Activities
Students use a number line as a visual
a
fraction model to represent a fraction _b
multiplied by a whole number n as the
(n ∗ a)
a
product n ∗ (_b ) or _
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.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Skip Counting to Show Multiples
of Unit Fractions
Math Masters, p. 242B
calculator
Students use calculators to skip count by
unit fractions.
ENRICHMENT
Visual Models for Multiplying a Fraction
by a Whole Number
Student Reference Book, p. 58
Math Masters, pp. 242C and 242D
Students explore alternative visual fraction
models for multiplying a fraction by a whole
number.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 22 and 23
Students practice multiplying fractions by
whole numbers.
Ongoing Assessment:
Informing Instruction See page 637D.
Key Vocabulary
multiple equation
Materials
Math Journal 2, pp. 217A–217E
Study Link 7 12
half-sheets of paper calculator (optional)
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 143, 144
637A Unit 7
Fractions and Their Uses; Chance and Probability
637A_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637A
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Getting Started
Mental Math and Reflexes
Math Message
Have students name the next three multiples in
a sequence. Suggestions:
Name the next three multiples in each sequence.
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
3
1 __
2 __
__
10 , 10 , 10 ,
__ __ __
… 10
, 10 , 10
3
1 __
2 __
__
4 5 6
4, 4, 4,
4
5
6
… _4 , _4 , _4
Study Link 712 Follow-Up
Have 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.
600; 1,200; 1,800; ... 2,400; 3,000; 3,600
125, 250, 375, ... 500, 625, 750
1 Teaching the Lesson
Adjusting the Activity
Math Message Follow-Up
Provide students with calculators
to assist with skip counting. See the Part 3
Readiness activity for additional information.
WHOLE-CLASS
DISCUSSION
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Ask students how they determined the next three multiples in
each sequence. Possible strategies:
NOTE In Third Grade Everyday Mathematics
1
Think of the problem as skip counting by _
s. To get the
10
1
_
next multiple, add 10 to the previous fraction. For example,
3 _
1 + _
1 = _
2 _
1 = _
1 = _
4
_
; 2 +_
; 3 +_
; and so on.
10
10
10 10
10
10 10
10
10
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.
Think in terms of equal groups. For example, 1 group of _14 is _14 ;
2 groups of _14 is __24 ; 3 groups of _14 is _34 ; 4 groups of _14 is _44 ; and so on.
Tell students that in this lesson they will use their understanding
of multiples to multiply fractions by whole numbers.
Student Page
Date
Time
LESSON
7 12a
Multiples of Unit Fractions
58
For Problems 1–3, fill in the blanks to complete an equation describing the number line.
Using a Visual Fraction Model to
PARTNER
ACTIVITY
Multiply a Unit Fraction by a
Whole Number
1.
1
8
0
2
8
_1
8
Equation: 5 ∗
3
8
4
8
_5
5
8
6
8
7
8
1
8
=
2.
1
6
0
3
Equation:
(Math Journal 2, pp. 217A)
2
6
_3 or _1
6,
2
1
∗_
6 =
3
6
4
6
5
6
1
3
3
4
3
5
3
6
3
3.
1
3
0
Draw the number line below on the board or overhead.
2
3
Equation:
_4
_1
4
3
∗
=
3,
or 1_13
For Problems 4–6, use the number line to help you multiply the fraction by the whole number.
0
1
2
2
2
3
2
4
2
5
2
6
2
Have volunteers explain how they could use the number line and
their understanding of multiples to help them solve the problem
3 ∗ __12 .
4.
1
4
0
_2
4,
1
Equation: 2 ∗ _
4 =
5.
0
1
10
or
2
10
1
Equation: 6 ∗ _
10 =
2
4
3
4
1
_1
2
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
4
5
5
5
6
5
7
5
8
5
9
5
10
5
6
__
_3
10 , or 5
6.
0
1
5
1
Equation: 7 ∗ _
5 =
2
5
_7
5,
3
5
_2
or 15
Math Journal 2, p. 217A
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Lesson 7 12a
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Student Page
Date
Time
LESSON
One 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 ∗ _12 is 3 jumps, each _12 unit long. You
end up at _32 . So, 3 ∗ _12 = _32 , or 1_12 .
An Algorithm for Multiplying a Fraction by a Whole Number
7 12a
6
1
_
Example 1: Equation: 6 ∗ _
5 = 5
1
5
1
5
1
5
1
5
1
5
1
5
58
5
5
0
2
_
5
Example 2: Equation: 3 ∗
=
2
5
10
5
6
_
5
2
5
2
5
5
5
0
1
2
10
5
1
2
1
2
Write an equation to describe each number line.
1
4
1
4
1
4
1
4
1
4
1
4
1. a.
_1
0
6
4
4
_6
4
∗
8
4
0
4
=
3
4
3
4
1
2
2
2
3
2
4
2
5
2
6
2
b.
_3
0
2
_6
4
∗
1
3
1
3
4
4
4
=
1
3
1
3
8
4
1
3
1
3
1
3
Partners complete journal page 217A. Tell students that an
equation is a number sentence with an equals sign, such as
3 ∗ _12 = _32 . As you circulate and assist, pose questions such as
the following:
1
3
2. a.
3
3
_1
0
8
3
∗
2
3
6
3
_8
9
3
3
=
2
3
2
3
2
3
b.
4
3.
3
3
_2
0
3
∗
6
3
_8
9
3
3
=
●
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? _43 = 1_13 ; _75 = 1_25
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.
217B
Math Journal 2, p. 217B
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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.
Student Page
Date
Time
LESSON
7 12a
Multiplying Fractions by Whole Numbers
Expect students to share observations such as the following:
58
Both equations involve multiplication of a fraction by a
whole number.
Use number lines to help you solve the problems.
_5
1
_
1. 5 ∗ 6 =
6
1
6
1
6
1
3
1
3
0
1
3
1
8
1
8
0
_8
3,
1
8
3
8
6.
217C
6
3
_3
10 , or 5
2
10
0
9
3
It takes more jumps of _15 to get to _65 than it does jumps of _25
because the jumps of _15 are smaller than the jumps of _25 .
Sample answer:
4
8
8
8
The whole number factor in 6 ∗ _15 = _65 is twice as much
as the whole number factor in 3 ∗ _25 = _65 . The fraction factor
in 6 ∗ _15 = _65 is half as much as the fraction factor in 3 ∗ _25 = _65 .
4
3
, or 1_48, or 1_12
6
__
The factors in the equations are different, but _25 is a multiple
of _15 and 6 is a multiple of 3.
1
3
4
3
0
0
Both equations have the same product.
1
=3∗_
8
or 2_23
12
__
8
1
3
3
3
_3
4
_
4. 2 ∗ 3 =
5.
1
6
6
6
1
3
8
3.
1
6
6
_
3 , or 2
0
1
_
2. 6 ∗ 3 =
1
6
3
3
3
8
6
3
3
=4∗_
8
4
8
3
8
3
8
8
8
2
10
2
=3∗_
10
9
3
2
10
12
8
16
8
Sample answer:
5
10
10
10
Math Journal 2, p. 217C
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637C Unit 7 Fractions and Their Uses; Chance and Probability
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Student Page
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
(n ∗ a)
a = _
number. The pattern can be expressed as: n ∗ __
.
b
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.
Date
Time
LESSON
Solving Number Stories
7 12a
1 cup flour
1
_
2 cup whole-wheat flour
1.
The sisters decided to double the recipe.
a.
How many cups of whole-wheat flour do they need now?
_2
2,
c.
cup(s)
Equation:
_6
or 1_24, or 1_12
cup(s)
Equation:
How many cups of honey do they need now?
_4
or 1_13
cup(s)
Equation:
2 ∗ _12 = _22
2 ∗ _34 = _64
2 ∗ _23 = _43
Suma and Puja decide to make 48 muffins instead of 12.
a.
How many teaspoons of salt do they need now?
_4
4,
b.
When Carlos goes to the gym, he exercises for 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?
or 1
How many cups of blueberries do they need now?
3,
2.
3
_
4
8
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.
PARTNER
ACTIVITY
Pose the following number story:
3
1
_
4 cup cooking oil
3
_
teaspoon cinnamon
4
1
_
4 teaspoon salt
4,
(Math Journal 2, pp. 217D and 217E)
1 egg
1
_
2 cup skim milk
2
_
cup honey
2 teaspoons baking powder
3
_
cup blueberries
b.
Solving Number Stories
58
Suma and her sister Puja are making 12 blueberry-wheat muffins for breakfast. The
recipe lists the following ingredients:
teaspoon(s)
Equation:
How many teaspoons of cinnamon do they need now?
12
__
8
c.
or 1
, or 1_48, or 1_12 teaspoon(s)
Equation:
4 ∗ _14 = _44
12
4 ∗ _38 = __
8
How many cups of skim milk do they need now?
_4
2,
or 2
cup(s)
Equation:
4 ∗ _12 = _42
Math Journal 2, p. 217D
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3/3/11 12:39 PM
Ongoing Assessment: Informing Instruction
Watch 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:
3
4
0
3
4
3
4
4
4
3
4
8
4
3
4
12
4
16
4
20
4
Then have students write a multiplication equation to represent
15
the problem. 5 ∗ _34 = __
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
16
12
that the product lies between _
, or 3, and _
, or 4.
4
4
15
The fraction _
can be renamed as the mixed number 3_34 by
4
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.
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.
Lesson 7 12a
637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637D
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3/3/11 2:52 PM
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: _22 = 1; Problem 2a: _44 = 1;
Problem 2c: _42 = 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
15
and write the equation a ∗ _52 = _
. Use the algorithm for
2
multiplying a fraction by a whole number and think: What
15
number times 5 will give me 15? 3 ∗ 5 = 15, so 3 ∗ _52 = _
. Cole
2
will need to attend 3 meetings.
●
In Problem 6, between which two whole-number distances does
15
the distance _
miles lie? Between 7 and 8 miles
2
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?
Student Page
Date
Time
LESSON
Solving Number Stories
7 12a
continued
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
Katie
Mahpara
Nikhil
Cole
Maria
Jack
1
_
9
_
5
_
5
_
4
_
5
_
3
10
4
2
3
6
Use the information in the table to solve the number stories.
3. a.
_2
If Katie walks the same distance at every
meeting, how far will she walk after 2 meetings?
_7
3,
3
_1
or 23
b.
After 7 meetings?
c.
After 7 meetings, Katie will have walked between
Circle the best answer.
1 and 2 miles
4. a.
2 and 3 miles
.
3 and 4 miles
15
__
, or 2_36, or 2_12
If Jack walks the same distance at every
6
meeting, how far will he walk after 3 meetings?
b.
After 3 meetings, Jack will have walked between
Circle the best answer.
5. a.
If Mahpara walks the same distance at every 10
meeting, how far will she walk after 4 meetings?
1 and 2 miles
b.
miles
miles
miles
.
2 and 3 miles
3 and 4 miles
36
__
6
_3
, or 3__
10 , or 3 5
miles
.
After 4 meetings, Mahpara will have walked between
Circle the best answer.
1 and 2 miles
2 and 3 miles
3 and 4 miles
Try This
6.
If Cole walks the same distance at every meeting and wants to
15
walk a total of _
2 miles, how many meetings will he need to attend?
7.
Make up your own multiplication number story about Nikhil or Maria.
3
meetings
Answers vary.
Math Journal 2, p. 217E
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Unit 7 Fractions and Their Uses; Chance and Probability
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Student Page
2 Ongoing Learning & Practice
Math Boxes 7 12a
Date
Math Boxes
7 12a
1.
INDEPENDENT
ACTIVITY
Time
LESSON
Karen used 60 square feet of her back
3
yard for a garden. Vegetables fill _
5 of
1
her garden space. Tomato plants fill _
6 of
the space taken up by vegetables. How
many square feet are used for tomatoes?
6
2.
Multiply. Use a paper-and-pencil algorithm.
3,741
= 87 ∗ 43
square feet
(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.
b.
Ongoing Assessment:
Recognizing Student Achievement
Lukasz drew a line segment that was
2
2_
8 inches long. Then he extended it
3
another 2_
8 inches. How long is the line
segment now?
4_58
[Operations and Computation Goal 5]
Write an equivalent fraction, decimal, or
whole number.
Decimal
a.
inches
1
Sybil drew a line segment 3_
8 inches
3
long. Then she extended it another 2_
4
inches. How long is the line segment now?
58
5.
inches
-3.49
in
104.16
100.67
83.86
45.72
55.41
42.23
51.92
77.69
74.20
60
___
100
d.
0.9
_
65
100
_
50
50
9
__
10
61 62
6.
Complete.
a.
b.
out
87.35
c.
0.65
1.0
b.
Fraction
0.60
55–57
Complete the table and write the rule.
Rule:
Use 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.
4.
_7
Math Boxes
Problem 3
18 19
59
3. a.
c.
d.
e.
3
192
5
67 in. =
7
22 ft =
1
4
1_
yd =
2
42 in.=
ft
16 ft =
in.
ft
yd
ft
162–166
7
1
6
in.
in.
ft
in.
129
Math Journal 2, p. 217F
185-218_EMCS_S_MJ2_G4_U07_576426.indd 217F
Study Link 7 12a
6
3/3/11 12:39 PM
INDEPENDENT
ACTIVITY
(Math Masters, p. 242A)
Home Connection Students use number lines to multiply
fractions by whole numbers.
Study Link Master
Name
Date
Time
LESSON
7 12a Multiplying Fractions by Whole Numbers
Use the number lines to help you solve the problems.
5
_1
1. 5 ∗ = 5
_, or 1
5
1
5
1
5
1
5
0
2.
1
5
2
5
1
5
3
5
4
5
12
_
_3
_1
3 ∗ _ = 9 , or 1 9 , or 1 3
4
9
0
4
9
3
6
5
5
4
9
6
5
3
6
8
5
9
5
10
5
4
9
18
9
3
6
3
6
6
6
0
7
5
9
9
18
_
, or 3
_3
3. 6 ∗ 6 = 6
58
1
5
3
6
3
6
12
6
18
6
Write a multiplication equation to represent the problem and then solve.
_1
4. Rahsaan needs to make 5 batches of granola bars. A batch calls for 2 cup of honey.
How much honey does he need? Equation:
5 ∗ _12 = _52 , or 2_12 cups
6
_
5. Joe swims 10 of a mile 5 days a week. How far does he swim every week?
Equation:
6
30
_
5∗_
10 = 10 , or 3 miles
How far would he swim if he swam every day of the week?
6
42
2
1
5
10
10
10
Equation:
7 ∗ _ = _, or 4_, or 4_ miles
Practice
1 and 5 b. Is 5 a prime number?
1 and 21; 3 and 7
no
b. Is 21 a prime number?
6. a. List the factor pairs of 5.
yes
7. a. List the factor pairs of 21.
242A
Math Masters, p. 242A
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Lesson 7 12a
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3/24/11 2:40 PM
Teaching Master
Name
Date
Time
3 Differentiation Options
LESSON
7 12a Skip Counting by a Unit Fraction
1
1. Use your calculator to count by _2 s. Complete the table below.
One
_1
2.
2
Two
_1 s
2
Three
_1 s
2
Four
_1 s
2
Five
_1 s
2
Six
_1 s
2
Seven
_1 s
2
Eight
_1 s
2
Nine
_1 s
2
Ten
_1 s
2
_1
_2
_3
_4
2
2
2
2
5
_
2
6
_
2
7
_
2
8
_
2
9
_
2
10
_
2
One
_1
3.
3
Two
_1 s
3
Three
_1 s
3
Four
_1 s
3
Five
_1 s
3
Six
_1 s
3
Seven
_1 s
3
Eight
_1 s
3
Nine
_1 s
3
Ten
_1 s
3
_1
_2
_3
_4
3
3
3
3
5
_
3
6
_
3
7
_
3
8
_
3
9
_
3
10
_
3
5
Two
_1 s
5
Three
_1 s
5
Four
_1 s
5
Five
_1 s
5
Six
_1 s
5
Seven
_1 s
5
Eight
_1 s
5
Nine
_1 s
5
Ten
_1 s
5
_1
_2
5
5
3
_
5
4
_
5
5
_
5
6
_
5
7
_
5
8
_
5
9
_
5
10
_
5
8
_1
8
Three
_1 s
8
Four
_1 s
8
Five
_1 s
8
Six
_1 s
8
Seven
_1 s
8
Eight
_1 s
8
Nine
_1 s
8
Ten
_1 s
8
2
_
8
3
_
8
4
_
8
5
_
8
6
_
8
7
_
8
8
_
8
9
_
8
10
_
8
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
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:
1
1
How is skip counting by _3 s on your calculator from 0 to nine _3 s the same as
1
finding the product 9 ∗ _?
TI-15:
3
Sample answer: When you skip count by _13 from 0 nine
times, you are finding nine groups of _1 . This is the same
as 9 ∗ _31 .
1. Press On/Off and Clear simultaneously. This clears your
calculator display and memory.
3
Math Masters, p. 242B
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242B
15–30 Min
(Math Masters, p. 242B)
1
Use your calculator to count by _
10 s. Complete the table below.
One
1
_
6.
Two
_1 s
8
SMALL-GROUP
ACTIVITY
Multiples of Unit Fractions
1
Use your calculator to count by _8 s. Complete the table below.
One
_1
5.
Skip Counting to Show
1
Use your calculator to count by _5 s. Complete the table below.
One
_1
4.
READINESS
1
Use your calculator to count by _3 s. Complete the table below.
2. Press Op1 + 5 Op1 . This tells the calculator to count up by 5s.
3/3/11 10:44 AM
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 _14 . You may first
need to remind students of the steps to enter a fraction on their
calculators.
To enter _14 :
On a TI-15: 1
n
4
On a Casio fx-55: 1
d
.
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 _93 means the same
thing as 9 ∗ (_13 ). In general, _ab = a ∗ (_1b ).
637G Unit 7 Fractions and Their Uses; Chance and Probability
637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637G
3/28/11 4:34 PM
Teaching Master
ENRICHMENT
Visual Models for Multiplying
SMALL-GROUP
ACTIVITY
Name
Date
Time
LESSON
7 12a Addition Model for Multiplying
Draw models for each product. Then add the fractions to find the product.
15–30 Min
_1 + _1 = _2
3
3
3
1.
1
2 ∗ _3 =
2.
1
3 ∗ _2 =
_1 + _1 + _1 = _3
2
2
2
2
3.
2
2 ∗ _5 =
_2 + _2 = _4
5
5
5
4.
2
4 ∗ _3 =
Sample shading is
given in models.
58
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.
_2 + _2 + _2 + _2 = _8
3
3
3
3
3
Math Masters, p. 242C
EXTRA PRACTICE
▶ 5-Minute Math
SMALL-GROUP
ACTIVITY
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242C
3/23/11 12:43 PM
5–15 Min
To offer students more experience with multiplying fractions by
whole numbers, see 5-Minute Math, pages 22 and 23.
Teaching Master
Name
Date
Time
LESSON
7 12a Area Model for Multiplying
For each problem, divide the model into strips, and then shade a fraction
of the area to find the product.
_2
_1
1. 3 of 2 square units =
1
So, _3 ∗ 2 =
_1
2. 4
square unit(s)
.
_4
4
_4
4
square unit(s)
.
_6
3
of 3 square units =
2
So, _3 ∗ 3 =
_3
4. 4
3
of 4 square units =
1
So, _4 ∗ 4 =
_2
3. 3
3
_2
58
Sample shading is
given in models.
_6
3
square unit(s)
.
15
_
4
of 5 square units =
3
So, _4 ∗ 5 =
15
_
4
square unit(s)
.
Math Masters, p. 242D
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242D
3/3/11 10:44 AM
Lesson 7 12a
637B-637H_EMCS_T_TLG2_G4_U07_L12a_576906.indd 637H
637H
3/28/11 4:34 PM
Name
Date
Time
LESSON
7 12a Multiplying Fractions by Whole Numbers
Use the number lines to help you solve the problems.
58
1.
5∗
_1
5
=
0
2.
1
5
2
5
3
5
4
5
6
5
7
5
8
5
9
5
10
5
4
3 ∗ _9 =
9
9
0
3.
5
5
18
9
3
6 ∗ _6 =
0
6
6
12
6
18
6
Write a multiplication equation to represent the problem and then solve.
Copyright © Wright Group/McGraw-Hill
4.
1
Rahsaan needs to make 5 batches of granola bars. A batch calls for _2 cup of honey.
How much honey does he need? Equation:
5.
6
Joe swims _
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.
7.
a. List the factor pairs of 21.
b. Is 21 a prime number?
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242A
b. Is 5 a prime number?
242A
3/23/11 12:43 PM
Name
Date
Time
LESSON
7 12a Skip Counting by a Unit Fraction
1
1. Use your calculator to count by _2 s. Complete the table below.
One
_1
2.
2
Two
_1 s
2
Three
_1 s
2
Four
_1 s
2
_1
_2
_3
_4
2
2
2
2
3
Two
_1 s
3
Three
_1 s
3
Four
_1 s
3
_1
_2
_3
_4
3
3
3
3
Seven
_1 s
2
Eight
_1 s
2
Nine
_1 s
2
Ten
_1 s
2
Five
_1 s
3
Six
_1 s
3
Seven
_1 s
3
Eight
_1 s
3
Nine
_1 s
3
Ten
_1 s
3
Eight
_1 s
5
Nine
_1 s
5
Ten
_1 s
5
Eight
_1 s
8
Nine
_1 s
8
Ten
_1 s
8
Eight
1
_
10 s
Nine
1
_
10 s
Ten
1
_
10 s
1
Use your calculator to count by _5 s. Complete the table below.
One
_1
4.
Six
_1 s
2
1
Use your calculator to count by _3 s. Complete the table below.
One
_1
3.
Five
_1 s
2
5
Two
_1 s
5
_1
_2
5
5
Three
_1 s
5
Four
_1 s
5
Five
_1 s
5
Six
_1 s
5
Seven
_1 s
5
1
Use your calculator to count by _8 s. Complete the table below.
One
_1
8
Two
_1 s
8
Three
_1 s
8
Four
_1 s
8
Five
_1 s
8
Six
_1 s
8
Seven
_1 s
8
_1
8
1
Use your calculator to count by _
10 s. Complete the table below.
One
1
_
10
6.
Two
1
_
10 s
Three
1
_
10 s
Four
1
_
10 s
Five
1
_
10 s
Six
1
_
10 s
Seven
1
_
10 s
1
1
How is skip counting by _3 s on your calculator from 0 to nine _3 s the same as
1
finding the product 9 ∗ _?
3
Copyright © Wright Group/McGraw-Hill
5.
242B
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242B
3/3/11 10:44 AM
Name
Date
Time
LESSON
7 12a Addition Model for Multiplying
Draw models for each product. Then add the fractions to find the product.
Copyright © Wright Group/McGraw-Hill
58
_1
3
1.
2∗
2.
1
3 ∗ _2 =
3.
2
2 ∗ _5 =
4.
2
4 ∗ _3 =
=
242C
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242C
3/23/11 12:43 PM
Name
Date
Time
LESSON
7 12a Area Model for Multiplying
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 =
1
So, _3 ∗ 2 =
_1
2. 4
_2
3. 3
.
square unit(s)
.
of 3 square units =
2
So, _3 ∗ 3 =
square unit(s)
.
of 5 square units =
3
So, _4 ∗ 5 =
square unit(s)
.
Copyright © Wright Group/McGraw-Hill
_3
4. 4
square unit(s)
of 4 square units =
1
So, _4 ∗ 4 =
58
242D
242A-242D_EMCS_B_MM_G4_U07_576965.indd 242D
3/3/11 10:44 AM