# 1 materials Objective Teaching the Lesson

```Objective
To broaden students’ understanding of calculating
percents to include discounts.
1
materials
Teaching the Lesson
Key Activities
Students estimate and then calculate the percent of a number using fractions and decimals.
They identify and calculate percent discounts and explore the percent key on their calculators.
Math Journal 2, pp. 277 and 278
Student Reference Book,
pp. 263–265
Study Link 8 8
Key Concepts and Skills
• Calculate percents and discounts, and describe strategies used.
[Number and Numeration Goal 2]
• Convert between fractions, decimals, and percents.
[Number and Numeration Goal 5]
• Use ratios expressed as percents to solve problems.
slates
calculator
[Operations and Computation Goal 7]
Key Vocabulary
discount
Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes.
[Number and Numeration Goal 5]
2
Ongoing Learning & Practice
Students practice and maintain skills through Math Boxes and Study Link activities.
3
Students review finding the percent
of a number.
ENRICHMENT
Students explore a variety of situations
involving discounts.
Advance Preparation Many calculators have a percent key, but not all calculators work the
same. For Part 1, familiarize yourself with the use of the percent key on the calculators used
by your class. Directions for the TI-15 and Casio fx-55 have been provided.
664
Unit 8 Fractions and Ratios
Math Journal 2, p. 279
Study Link Master (Math Masters,
p. 238)
materials
Differentiation Options
materials
Teaching Masters (Math Masters,
pp. 239 and 240)
calculator (optional)
Technology
Assessment Management System
Mental Math and Reflexes
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message
Have students write each percent as a decimal and as a fraction in
simplest form. Suggestions:
1
20% 0.20, or 0.2; 5
1
29% 0.29; 100
50% 0.50, or 0.5; 2
10% 0.10, or 0.1; 10
1
100% 1.00; 1
1
9
45% 0.45; 20
It would cost \$150,000 to rent a large
amusement park for a private party. Would you
rather have this price reduced by \$35,000 or
discounted 25%?
7
29
35% 0.35; 20
3
110% 1.10; 10
11
12% 0.12; 25
Study Link 8 8 Follow-Up
Have partners compare answers and
resolve differences.
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and
Reflexes
Use the Mental Math and Reflexes problems to assess students’ facility with
converting between fractions, decimals, and percents and expressing fractions
in simplest form. Students are making adequate progress if they have correctly
written both the decimal and the fraction.
[Number and Numeration Goal 5]
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Have small groups share their solution strategies and then choose
one strategy to represent the group. Ask volunteers to present the
group strategies. A 25% discount is \$37,500; therefore, it is a
better deal than a \$35,000 discount.
Finding the Percent of
WHOLE-CLASS
DISCUSSION
a Number
Pose the following percent-of-a-number problem: The flu hit
Roosevelt School hard. 40% of the 480 students were absent at
least one day last week. How many students were absent at least
one day?
Write 40% of 480 students absent at least one day on the board
or a transparency. Ask students to share their solution
strategies for this problem. Expect a variety of responses such as
the following:
The unit-percent approach. 480 is 100%, or the whole.
1% of 480 is 4.8.
40% of 480 is 40 4.8, or 192.
Lesson 8 9
665
Student Page
Date
Time
LESSON
Remind students that to find 1%, they could divide the whole
by 100 or think: What times 100 equals the whole?
Finding a Percent of a Number
8 9
1. The Madison Middle School boys’
basketball team has played 5 games.
The table at the right shows the number
of shots taken by each player and the
percent of shots that were baskets.
Study the example. Then calculate the
number of baskets made by each player.
Example:
Bill took 15 shots.
of these shots.
40
Shots
Taken
Percent
Bill
15
40%
6
Amit
40
30%
Josh
25
60%
Kevin
8
75%
Mike
60
25%
Zheng
44
25%
Player
4
, or 40% 100
10
4 º 15
4
4
15
60
of 15 6
10 º 1
10
10
1
10
2. On the basis of shooting ability,
André
50
10%
David
25
20%
Bob
18
50%
Lars
15
20%
Justin
28
25%
The 10-percent approach. 480 is 100%, or the whole.
12
15
6
15
11
5
5
9
3
7
10% of 480 is 48.
40% of 480 is 4 48, or 192.
Remind students that to find 10%, they could divide the
whole by 10 or think: What times 10 equals 480?
2
The equivalent-fraction approach. 40% is equal to 5.
which five players would you
select as the starting lineup for
the next basketball game?
2
2
40% of 480 is the same as 5 of 480, or 5 480, which is 192.
Bill, Amit, Josh, Kevin, and Bob
The equivalent-decimal approach. 40% is equal to 0.40.
They have the highest percent of
40% of 480 is the same as 0.40 of 480, or 0.40 480,
which is 192.
Kevin
Why? Of the few shots taken, he has made
baskets 75% of the time.
3. Which player(s) would you encourage to shoot more often?
André
Of the many shots taken, he has
made baskets only 10% of the time.
4. Which player(s) would you encourage to pass more often?
Links to the Future
Why?
277
This lesson stresses the use of equivalent fractions and equivalent decimals.
Lesson 8-10 will address unit percents.
Math Journal 2, p. 277
Using Fractions to Find the
PARTNER
ACTIVITY
Percent of a Number
(Math Journal 2, p. 277)
Work through the example at the top of the journal page as a
class. Emphasize the following points:
A percent can be thought of as a fraction with a denominator
of 100.
43
Student Page
Date
Time
LESSON
8 9
Calculating a Discount
Example: The list price for a toaster is \$45. The toaster is sold at a 12% discount
12
(12% off the list price). What are the savings? (Reminder: 12% = 100 0.12)
Paper and pencil:
12% of \$45
540
12 45 100
100 1
\$5.40
Æ
Calculator B: Enter 0.12
45
45
and interpret the answer of 5.4 as \$5.40.
Then use your calculator or paper and pencil to calculate the discount.
(If necessary, round to the nearest cent.)
Estimated
Discount
Item
List
Price
Percent of
Discount
\$33.00
20%
\$6.00
\$6.60
Calculator
\$60.00
7%
Sweater
\$20.00
42%
\$4.00
\$8.00
\$4.20
\$8.40
Calculated
Discount
\$54.00
Tent
\$180.00
30%
\$54.00
Bicycle
\$200.00
17%
\$30.00
\$34.00
Computer
\$980.00
25%
\$250.00
\$245.00
Skis
\$325.00
18%
\$65.00
\$58.50
\$29.99
15%
\$4.50
\$4.50
\$110.00
55%
\$55.00
\$60.50
278
Math Journal 2, p. 278
666
Unit 8 Fractions and Ratios
1
1
Example: 50% of 18 is 100 or 2 of 18, or 2 18; and 25% of 28
1
1
is 4 of 28, or 4 28.
NOTE Some students might write number models in the form 60% 25, rather
Jacket
100
Many commonly used percents are equivalent to easy fractions:
1
1
25% 4, 50% 2, and so on.
50
and interpret the answer of 5.4 as \$5.40.
First use your percent sense to estimate the discount for each item in the table below.
The discount is the amount by which the list price of an item is reduced. It is the
amount the customer saves.
Double CD
7
Finding the percent of a number can be thought of as finding a
fraction of that number.
12
12
45
45 100
100
1
Calculator A: Enter 0.12
99
Example: 43% is 100 ; 99% is 100 ; 7% is 100; and 100% is 100,
or 1.
60
6
than 100 25, 10 25, or 0.6 25. All of these notations are acceptable.
Assign the journal page. Circulate and assist.
Calculating a Percent Discount
PARTNER
ACTIVITY
(Math Journal 2, p. 278)
Refer students to journal page 278. As a class, work through the
example at the top of the page. Remind students that a discount
Student Page
is the amount to be subtracted from a given whole. In this case, it
is by how much the list price is reduced.
Date
Time
LESSON
Math Boxes
8 9
1. Rename each fraction as a mixed number
Ask students to complete the Estimated Discount column of the
table on journal page 278. When most students have finished,
have volunteers share their solution strategies. For example:
20% is equal to
1
.
5
79
a. 8
45
b. 9
7
8
9
5
37
21
2135
111
c. 3
126
d. 6
Clock radio: 20% of \$33
108
e. 5
One-fifth of \$33 is between \$6 and \$7.
2. Find the area of the rectangle.
or a whole number.
6
3
6 (3 5) A,
(6 3) (6 5) A,
or 6 8 A
62
3. Sam has 8 pounds of oats. A cup of oats
is about 1 a pound. How many cups of
2
\$980 is about \$1,000. So 25% of \$980 is about
or \$250.
Yes. If Amy does the dishes
on 6 nights, she will make
more than Julie: 6 0.75 6
6
3
18
75
1
4,
1
1
4
4
100
2
of \$1,000,
or 4.5 \$4.50.
79 80
Jacket: 55% of \$110
189
dishes. She pays her sister Amy \$0.75
each time Amy does the dishes for her.
Is that fair? Explain.
16 c
1
4
48 units2
4. Julie makes \$4.00 per week for washing
oats does Sam have?
Computer: 25% of \$980
5
Number model:
42
5. a. Plot the following points on the grid:
(4,2); (2,4); (2,7); (6,7)
1
55% is about 2. So 55% of \$110 is about \$55.
8
7
b. Connect the points with line
6
segments in the order given above.
Then connect (6,7) and (4,2). What
shape have you drawn?
Ask students to calculate and record the actual discount using any
method they choose. Encourage them to try calculator and
paper-and-pencil calculations.
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
208
279
Math Journal 2, p. 279
Exploring the Percent Key
PARTNER
ACTIVITY
on a Calculator
(Student Reference Book, pp. 263–265)
Refer students to Student Reference Book, pages 263–265. As a
class, discuss the examples for using the percent key
to solve
percent-of problems and to display percents as decimals and as
fractions in simplest form. If your class calculators differ from the
Student Reference Book examples, demonstrate the key sequences
using an overhead calculator or by drawing the key sequences on
the board.
Ask students to use the percent key
on their calculators to
find 25% of 180. 45 Have volunteers share the key sequences they
entered. Partners then make up percent-of problems for each other
to solve.
Name
Date
89
1.
Complete the table so each number is shown as a fraction, decimal,
and percent.
Fraction
45
,
100
Math Boxes 8 9
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 279)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-11. The skill in Problem 5
previews Unit 9 content.
or 9
20
2
10
15
,
100
2.
Decimal
3
10
2 Ongoing Learning & Practice
Time
Fractions, Decimals, and Percents
or
3
20
26 48
51 83 89
Percent
0.45
45%
0.3
30%
0.2
20%
0.15
15%
Use your percent sense to estimate the discount for each item. Then calculate
the discount for each item. (If necessary, round to the nearest cent.) Sample
Item
List
Price
Percent of
Discount
Estimated
Discount
Calculated
Discount
Saguaro cactus
with arms
\$400.00
25%
\$100.00
\$100.00
Life-size wax
figure of yourself
\$1,500.00 \$1,600.00
\$10,000.00
16%
Manhole cover
\$78.35
10%
\$8.00
\$7.84
Live scorpion
\$14.98
5%
\$0.75
\$0.75
10,000
honeybees
\$29.00
30%
\$9.00
\$8.70
Dinner for one on
the Eiffel Tower
\$88.00
6%
\$4.50
\$5.28
Magician’s box
for sawing a
person in half
\$4,500.00
18%
\$900.00
\$810.00
Fire hydrant
\$1,100.00
35%
\$350.00
\$385.00
Source: Everything Has Its Price
Math Masters, p. 238
Lesson 8 9
667
Teaching Master
Name
Date
LESSON
89
Time
Finding the Percent of a Number
The unit percent is 1% or 0.01.
For example, the unit percent of
100 is 1; the unit percent of
200 is 2; the unit percent of
10 is 0.1.
20
10
1% of 100
1% of 200
1 mm
0
cm
1
2
3
4
5
6
7
8
9
10
1% of 10 cm
Another way to think of the unit percent of a number is to think: What number times 100
equals the whole? For example, 1 100 100; 2 100 200; 0.1 100 10
1
100
Writing/Reasoning Have students write a response to the
following: Explain how to rename an improper fraction as
a mixed number. Use Problem 1a as an example. Sample
79
answer: To rename 8 as a mixed number, first find how many
groups of 8 are in 79. There are 9 groups of 8 because 9 8 72.
Then subtract 72 from 79. The difference is the fraction part of
79
72
7
the mixed number. It tells how many eighths are left: 8 8 8.
79
7
7
So 8 9 8, or 98.
To find the unit percent of a whole, multiply by 0.01 or .
Solve.
1.
1% of 84 0.84
2.
0.35
1% of 35 3.
6.28
1% of 628 The unit percent can be used to find other percents of a whole. For example, if you want to
find 8% of 200:
Calculate the unit percent: 1% of 200 200 0.01 2
Study Link 8 9
INDEPENDENT
ACTIVITY
(Math Masters, p. 238)
Multiply your answer by the percent you are finding: 2 8 16; 8% of 200 16
Solve.
15.96
25.2
19% of 84 7.
Think about the steps you followed in Problems 4–6. First you multiplied the unit
percent by 0.01, and then you multiplied the product by the number of percents. How
can you find the percent of a number by multiplying only once? Provide an example.
5.
72% of 35 6.
37% of 628 232.36
4.
Home Connection Students convert between fractions,
decimals, and percents. Then they estimate and calculate
discounts for various items.
I can change the percent to a fraction and
multiply the number by that fraction.
19
19
84
1,596
19% of 84: 100 84 100 1 10
0 15.96
Math Masters, p. 239
3 Differentiation Options
Finding the Percent of
SMALL-GROUP
ACTIVITY
15–30 Min
a Number
(Math Masters, p. 239)
Teaching Master
Name
LESSON
89
Date
Time
Calculating Discounts
There are 2 steps to finding a discounted total:
Calculate the amount that represents the percent of discount.
Subtract the calculated discount from the original total. This is the discounted total.
Calculate the discounted total for the following problems. Show your work on the
back of this sheet.
1.
A computer store has an Internet special for their customers. If Carla spends \$50.00 or
more, she gets 10% off her order. The shipping and handling charge is 4% of the original
total. Carla buys \$68.00 in software. What is her total charge?
To review finding the percent of a number, have students use
unit fractions. Ask students to describe a unit fraction. Sample
answer: A unit fraction has a 1 as its numerator and names
one of the equal parts that make the whole. Have a volunteer
use counters to demonstrate how to use the unit fraction to
3
1
3
find 4 of 20. 4 of 20 is 5 because 20 divided by 4 equals 5. So, 4 of
20 is 5 3, or 15.
Explain that the unit percent is similar to a unit fraction. You
can find the percent of a whole by finding the unit percent and
multiplying. Have students use mental math, paper and pencil,
and/or calculators to complete the Math Masters page.
\$63.92; Discount: 68 0.10 6.80; shipping and handling:
68 0.04 2.72; total charge: 68.00 2.72 6.80 63.92
2.
The Hartfield School District wants to get the government discount for telephone service.
The discount is based on the percent of students qualifying for the National School Lunch
Program. 32% of students in this urban district qualify. The district pays about \$3,500 per
month for telephone service. Use the table below to find how much the district would save.
Percent of Students
Urban Discount
Rural Discount
Less than 1%
20%
25%
1% to 19%
40%
50%
20% to 34%
50%
60%
35% to 49%
60%
70%
50% to 74%
80%
80%
75% to 100%
90%
90%
50% discount. The district will save
The Hartfield School District is eligible for a
about \$1,750.00 per month for its telephone service. With the government discount,
the district will pay about \$1,750.00 per month.
3.
At the Goose Island Family Restaurant, if the original bill is \$75.00 or more, the kids’
meals are discounted 3%. If the original bill is \$95.70, with \$23.00 for kids’ meals, what is
\$0.69 What is the discounted total? \$95.01
the discounted amount?
Math Masters, p. 240
668
Unit 8 Fractions and Ratios
ENRICHMENT
Calculating Discounts
PARTNER
ACTIVITY
15–30 Min
(Math Masters, p. 240)
To apply students’ understanding of calculating percents,
have them find and calculate the discounts for a variety of
situations. Students solve number stories by calculating
the percent discount and the discounted total.
```