Objectives
To reinforce renaming fractions as percents using
a calculator; and to introduce solving number stories involving
discounts expressed as percents.
1
materials
Teaching the Lesson
Key Activities
Students use the percent key on a calculator to rename fractions as percents. They rename
fractions as decimals by dividing, and they are shown that a decimal can be easily renamed
as a percent by multiplying it by 100. Students solve number stories involving discounts
expressed as percents.
calculator
overhead calculator (optional)
slate
Key Concepts and Skills
•
•
•
•
Math Journal 2, pp. 256 and 257
Study Link 9 3
Solve number stories involving discounts. [Number and Numeration Goal 2]
Name the whole, or the ONE. [Number and Numeration Goal 2]
Use a calculator to rename fractions as percents. [Number and Numeration Goal 5]
Rename any decimal as a percent. [Number and Numeration Goal 5]
Key Vocabulary regular price • list price • discount • percent of discount • fraction of discount
• sale price • discounted price
Ongoing Assessment: Informing Instruction See page 740.
2
materials
Ongoing Learning & Practice
Students create a bar graph using cellular-telephone-use data.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Recognizing Student Achievement Use journal page 259.
Math Journal 2, pp. 258 and 259
Student Reference Book, p. 302
Study Link Master (Math Masters,
p. 285)
[Number and Numeration Goal 2]
3
materials
Differentiation Options
READINESS
Students use
counters to solve
“percent-of”
problems.
ENRICHMENT
Students solve
number stories in
which they compare
discounts for two
items.
EXTRA PRACTICE
Students practice
solving problems
involving percents.
ELL SUPPORT
Students discuss
vocabulary used in
discount number
stories.
Teaching Masters (Math Masters,
pp. 286 and 287)
5-Minute Math, pp. 103, 176, 187,
and 196
counters
store catalogs or advertisements
Technology
Assessment Management System
Math Boxes, Problem 4
See the iTLG.
Lesson 9 4
739
Getting Started
Mental Math and Reflexes
Math Message
Pose “percent-of ” problems. Have students explain their
strategies. Suggestions:
Experiment with the percent key on your calculator.
1
Find a way to rename 4 as a percent. Write your
method on a half sheet of paper.
25% of 40 10
75% of 40 30
25% of 32 8
75% of 32 24
50% of 60 30
100% of 60 60
10% of 60 6
20% of 60 12
20% of 150 30
40% of 110 44
5% of 20 1
15% of 10 1.5
Study Link 9 3 Follow-Up
Have students compare answers. Ask volunteers to
share some of the problems they made up.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Ask a volunteer to use an overhead calculator (if available) to
demonstrate how to use the percent key to rename fractions as
percents. Write the keystrokes on the board to support English
language learners. Then have students practice with a few
“easy” fractions.
TI-15: 1 ÷ 4
Casio fx-55:
1
1. A store is offering a discount of 10% on all items. This means that you save of
10
the regular price. Find the sale price of each item below. The sale price is the
amount you pay after subtracting the discount from the regular price.
Item
Regular Price
CD player
Giant screen TV
Radio
DVD player
38
(Subtract:
regular price – discount)
$140
$14
$1,200
$80
$120
$8
$30
$3
$126
$1,080
$72
$27
Sample picture:
$80
found the discount and sale price for the radio.
1
. Cut $80 into 10
10
9
parts. 10% of $80 is $8. 10 is left. 9 $8 $72.
Sample answer: 10% is
3. An airline offers a 25% discount on the regular airfare for tickets
90% 10%
purchased at least 1 month in advance. Find the sale price of
each ticket below.
Discount
(25% of regular airfare)
$400
$100
$240
$60
$300
$75
39
Sale Price
Discount
(10% of regular price)
2. Use a drawing and number models to explain how you
Regular Airfare
Sale Price
(Subtract:
regular airfare – discount)
33
To rename 7
5 as a percent, divide 33 by 75 to get 0.44.
44
This is 100 , or 44%.
You can use this rule to rename any decimal as a percent:
To convert a decimal to a percent, multiply the decimal by 100.
Decimal
100 decimal
Percent
0.67
67
67%
0.375
37.5
37.5%
0.1666
16.66
16.66%
$300
$180
$225
4. Use a drawing and number models to explain how you found the
regular airfare when you knew $75 was 25% of the regular airfare.
1
1
Sample answer: 25% 4. If 4 $75,
4
then 4 4 $75, or $300.
Sample picture:
25%
$75
256
Math Journal 2, p. 256
740
Display: 25
1
Discount Number Stories
9 4
4
To rename 4 as a percent, divide 1 by 4 to get 0.25.
25
This is 100 , or 25%.
Time
LESSON
1
The percent key does NOT have to be used to rename fractions as
percents. Remind students that they can convert any fraction to a
decimal by dividing the numerator by the denominator. Once they
have the decimal name, it is easy to write the percent name.
Student Page
Date
Display: 25
Unit 9 Fractions, Decimals, and Percents
Ongoing Assessment: Informing Instruction
Watch for students who notice a pattern when multiplying a decimal by 100.
Ask them to explain why the decimal moves two places to the right.
Student Page
Solving Number Stories
PARTNER
ACTIVITY
Involving Discounts
Date
Time
LESSON
Discount Number Stories
9 4
continued
5. The regular price of a swing set is $400. Mrs. Lefevre received a
30% discount because she ordered it during the Big Spring Sale.
(Math Journal 2, pp. 256 and 257)
a. How much did she save?
$120
$280
b. How much did she pay?
c. Explain how you solved the problem.
Consumer Link Tell students that in this lesson they
will use their calculators and mental arithmetic to solve
discount number stories. Have students work in partnerships
to complete journal pages 256 and 257.
Sample answer:
If the discount is 10%, then 10%, or
1
10,
of $400 is $40. A 30%
discount is 3 times as much as a 10% discount, so 3 $40 $120.
Then I subtracted $120 from $400 and got $280.
Try This
6. You can pay for a refrigerator by making 12 payments of $50 each.
Or you can save 25% if you pay for it all at once.
a. How much will the refrigerator cost if you pay for it all at once?
b. Explain how you solved the problem.
$450
Sample answer:
If I make payments, it will cost 12 $50, which is $600.
Adjusting the Activity
Paying for it all at once, I’ll get a 25% discount. 25% is
1
4
of
$600, or $150. Then I subtracted $150 from $600 and got $450.
Rephrase or illustrate the last rows in the tables in Problems 1 and 2
as follows:
10
1
Problem 1: If $3 is 1
0 of the whole, what is the whole? The whole is 10 , which is
1
10 times as much as 10. So 10 $3 $30.
1
Problem 2: If $75 is 25%, or 4 of the whole, what is the whole? The whole
4
1
is 4, which is 4 times as much as 4. So 4 $75 $300.
7. Write your own discount number story. Ask a partner to solve it.
Answers vary.
257
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Math Journal 2, p. 257
When students have completed journal pages 256 and 257, use
Problem 5 to demonstrate how to use the percent key to find the
discount and the sale price.
TI-15:
Discount: 400
Æ
30
Display: 120
Sale price: 400 – 400 Æ 30
Display: 280
Casio fx-55:
Discount: 400
Sale price: 400
30
Display: 120
30
Display: 280
Student Page
Date
Time
LESSON
Cellular Telephone Use
9 4
Links to the Future
1. Use the “Subscriptions per 100 People” data in the Cellular Telephone Use table
at the bottom of Student Reference Book, page 302 to complete the bar graph.
Round each decimal to the nearest whole number.
Solving problems involving percents and discounts is a Grade 5 Goal.
Cellular Telephone Use
112
110
108
Subscriptions per 100 People
106
2 Ongoing Learning & Practice
104
102
100
98
96
94
Creating a Bar Graph
INDEPENDENT
ACTIVITY
92
90
(Math Journal 2, p. 258; Student Reference Book, p. 302)
Taiwan
Luxembourg
Italy
Iceland
Israel
Spain
Countries
2. Write a question that can be answered by looking at the data displayed
Students create a bar graph to display cellular-telephone-use data.
in the bar graph. Answer the question.
Answers vary.
2 8
Math Journal 2, p. 258
Lesson 9 4
741
Student Page
Date
Math Boxes 9 4
Time
LESSON
1. Complete the table with equivalent names.
Fraction
Decimal
Percent
3
4
0.75
6
10
0.6
75%
60%
10%
1
10
0.1
0.5
50
100
INDEPENDENT
ACTIVITY
Math Boxes
9 4
2. About 1.96% of the words on the Internet
are a, and about 0.81% of the words are it.
What percent of all words on the Internet
are either a or it? Show your work.
2.77%
50%
61
62
(Math Journal 2, p. 259)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-2. The skill in Problem 6
previews Unit 10 content.
34–37
3. 2 ft 7 in. __ in. Choose the best answer.
4. Three girls cut a pizza into 12 equal slices
and plan to share the pizza equally.
14
a. What fraction of the
pizza should each girl get?
24
b. How many slices
27
should each girl get?
4
1
3
c. Suppose 2 more girls arrive. How many
slices should each of the 5 girls get?
2 25 slices
44
129
6. What temperature is it?
3
rectangle. Include the correct units.
°C
20
6"
Math Boxes
Problem 4
slices
31
5. Find the area and perimeter of the
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 4 to assess students’ ability to solve “fraction-of”
problems. Students are making adequate progress if they are able to identify the
fraction of the pizza each girl gets and the number of slices. Some students may
be able to determine the number of slices each girl would get if two more girls
arrived and explain how they got their answers.
°C
[Number and Numeration Goal 2]
10
2"
12 in2
Perimeter 16 in.
0
Area –10
131 133
139
259
Math Journal 2, p. 259
Study Link 9 4
INDEPENDENT
ACTIVITY
(Math Masters, p. 285)
Home Connection Students rename fractions as percents
with and without a calculator. Note that in Problems 9,
12, and 17, students will have to write the percent using
a decimal.
3 Differentiation Options
READINESS
Study Link Master
Name
Date
STUDY LINK
Fractions and Decimals to Percents
9 4
Do NOT use a calculator to convert these fractions to percents.
On the back of this page, show your work for Problems 3–6.
34
1. 100
42
3. 50
17
5. 20
Solving “Percent-of” Problems
Time
34 %
84 %
85 %
67
2. 100
13
4. 25
25
6. 125
25 %
62.5%
60
15
%
400
(Math Masters, p. 286)
67 %
52 %
20 %
30 %
70 %
21
37.5
%
56
12
8. 40
20
9. 32
49
10. 70
11.
13.
12.
Describe how you used your calculator to convert the fractions
in Problems 7–12 to percents.
I divided the numerator by the denominator
and then multiplied by 100.
Do NOT use a calculator to convert these decimals to percents.
14.
0.86 16.
0.140 86 %
14 %
15.
0.03 17.
0.835 3 %
83.5%
Practice
Order the fractions from smallest to largest.
7 7 7 7
18. , , , 16 8 12 9
7 3 8 4
19. , , , 15 15 15 15
5 15 1 9
20. , , , 9 16 4 10
7 7 7 7
16 12 9 8
3 4 7 8
15 15 15 15
1
15
5 9 4 9 10 16
, , ,
, , ,
, , ,
Math Masters, p. 285
742
5–15 Min
62
206 207
Use a calculator to convert these fractions to percents.
23
7. 92
PARTNER
ACTIVITY
Unit 9 Fractions, Decimals, and Percents
To explore “percent- of” situations using a concrete model, have
students use counters to solve problems. Encourage students to
rename the percents as fractions and solve the problems as
“fraction-of” problems.
Teaching Master
Name
ENRICHMENT
Solving Discount Number Stories
PARTNER
ACTIVITY
38 39
5–15 Min
1.
Building Background for
If
is 100%, draw 50%.
50% of 10 3.
If
5.
SMALL-GROUP
ACTIVITY
5–15 Min
7.
2.
5
is 100%, draw 10%.
10% of 20 To offer students more experience with percents, see 5-Minute
Math, pages 103, 176, 187, and 196.
ELL SUPPORT
“Percent-of” Problems
9 4
To apply students’ understanding of “percent-of”
situations, have them solve number stories for which they
compare the discounts of two items. In one story, students
compare the percents of discount; in a second story, they compare
the actual discounts.
5-Minute Math
Time
Use counters to solve the problems on this page.
(Math Masters, p. 287)
EXTRA PRACTICE
Date
LESSON
is 75%, draw 100%.
75% of
12
is 100%, draw 25%.
25% of 16 4.
2
If
If
6.
9
4
If
is 50%, draw 100%.
50% of
12
If
6
is 40%, draw 100%.
40% of
20
8
Pick one of the problems from above and explain how you got your answer.
3 Sample answer:
I know that 10% is another name for
1
of 20 is 2, so 10% of 20 is 2.
10
Problem
SMALL-GROUP
ACTIVITY
1
10
.
Math Masters, p. 286
15–30 Min
Mathematics Words
To provide language support for percents, have students look at
store catalogs or advertisements and discuss the following:
The regular price (sometimes called the list price) of an
item is the price without a discount.
The discount is the amount you save. It is given in dollars
and cents.
The percent of discount or the fraction of discount is a
percent or fraction that tells what part of the regular price
you save.
Teaching Master
Name
The sale price (or discounted price) is the amount you pay
after subtracting the discount from the regular price.
LESSON
9 4
1.
Date
Time
Discount Number Stories
A store is having a sale on gym shoes.
38 39
The regular price of the High Flyers is $50. Now they are on sale for $38.
Example:
The Zingers are $15 off the regular price. When not on sale, the Zingers
cost $75 a pair.
The regular price of a bird feeder is $15. It is on sale at a 20%
discount. What is the sale price?
20
Which pair has the greater “percent-of” discount? Explain your answer.
The High Flyers pair has a greater percent-of
4
discount. $50–$38 $12. 1520 120
0 , so the
discount is 24%. The Zingers’ discount is
20
15
1
75 5 100 , or 20%.
1
The percent of discount is 20% of the regular price. 20% is 100 , or 5 .
One-fifth of $15 is $3, so you save $3. This is the discount. To
find the sale price, subtract $3 from $15. The sale price is $12.
2.
The same store is also having a sale on tennis rackets.
The regular price of the Smasher is $54.00. It is on sale for 25% off
the regular price.
The regular price of the Fast Flight is $75.00. It is on sale for 20% off
the regular price.
For which tennis racket are you getting more money taken off the regular price?
Explain your answer.
The Fast Flight has a greater percent-of
$75
discount. 20% off $75.00 5 $15.00.
The Smasher’s discount is 25% off $54.00 $54
$13.50.
4
Math Masters, p. 287
Lesson 9 4
743