Objectives
To guide the use of percents in describing
real-life situations; and to reinforce naming equivalencies
among fractions, decimals, and percents.
1
materials
Teaching the Lesson
Key Activities
Students discuss uses of percents in everyday life. They represent various percent situations
by shading 10-by-10 grid squares, and they restate each percent situation using a fraction
name and a decimal name.
Math Journal 2, pp. 248–250
Study Link 8 6 (Math Masters,
p. 262)
slate
Key Concepts and Skills
•
•
•
•
Name the “whole” or the ONE. [Number and Numeration Goal 2]
Solve “percent-of” problems. [Number and Numeration Goal 2]
Rename fractions with denominators of 100 as decimals. [Number and Numeration Goal 5]
Find equivalent names for percents. [Number and Numeration Goal 5]
Key Vocabulary
percent • 100% box
Ongoing Assessment: Informing Instruction See page 724.
2
materials
Ongoing Learning & Practice
Students play Fraction Match to practice naming equivalent fractions.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Recognizing Student Achievement Use Math Masters,
page 278. [Number and Numeration Goal 5]
3
Students shade 50% of a square in
different ways.
Study Link Masters (Math Masters,
pp. 279 and 280)
Teaching Master (Math Masters,
p. 278)
Fraction Match Cards (Math
Masters, pp. 473–476)
materials
Differentiation Options
READINESS
Math Journal 2, p. 251
Student Reference Book, p. 243
ELL SUPPORT
Students collect examples of percents
and display them in a Percents All
Around Museum.
Study Link 8 6 (Math Masters,
p. 262)
Teaching Master (Math Masters,
p. 281)
Technology
Assessment Management System
Math Masters, page 278
Problems 1 and 2
See the iTLG.
722
Unit 9 Fractions, Decimals, and Percents
Getting Started
Mental Math and Reflexes
Math Message
Write fractions on the board. For each fraction, students write the equivalent
decimal and percent on their slates. Suggestions:
Be ready to discuss the
examples of percents you
collected for Study Link 8-6.
15
0.15, 15%
100
55
0.55, 55%
100
29
0.29, 29%
100
3
0.03, 3%
100
1
0.1, 10%
10
7
0.7, 70%
10
2
1, 100%
2
1
0.20, 20%
5
3
0.75, 75%
4
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Masters, p. 262)
Have students share the examples they collected of uses of
percents. Encourage students to restate each percent situation
in a variety of ways.
Example:
Candidate Reed got 50% of the votes.
This can be restated as
“For every 100 votes cast, Reed got 50 votes.”
“If 100 people voted, then Reed got 50 votes.”
“Reed got 50 out of every 100 votes cast.”
Study Link Master
50
“Reed got 100 of the votes cast.”
Emphasize that “50 out of 100” does not mean that exactly 100
votes were cast but that Reed got 50 votes for every 100 votes that
1
50
were cast. (Since 100 equals 2 , Reed got half the votes cast.) If it
were a club election with only 60 votes cast, then Reed would have
gotten 50% of 60 votes, or 30 votes. If it were an election for
mayor with 30,000 votes cast, then Reed would have gotten 50%
of 30,000 votes, or 15,000 votes.
Name
STUDY LINK
86
Date
Time
Percents in My World
1
100
Percent means “per hundred” or “out of a hundred.” 1 percent means or 0.01.
40
“48 percent of the students in our school are boys” means that out of every
100 students in the school, 48 are boys.
Percents are written in two ways: with the word percent, as in the sentence above,
and with the symbol %.
Collect examples of percents. Look in newspapers, magazines, books, almanacs, and
encyclopedias. Ask people at home to help. Write the examples below. Also tell where
you found them. If an adult says you may, cut out examples and bring them to school.
Encyclopedia: 91% of the area of New Jersey is land,
and 9% is covered by water.
Newspaper: 76 percent of the seniors in Southport
High School say they plan to attend college next year.
Answers vary.
Math Masters, p. 262
Lesson 9 1
723
Remind students that, just as with fractions, a percent always
represents a percent of something. The “something” is the whole
100%, which is the entire object, or the entire collection of objects,
or the entire quantity being considered. In the example, the whole,
or the ONE, is the total number of votes cast. The total number of
votes cast is 100 percent of the votes. The 100% box serves the
same purpose for percents as the whole box does for fractions: It
helps focus students’ attention on the whole, or 100%.
Language Arts Link The word percent comes from the
Latin per centum: Per means “for,” and centum means “one
hundred.” Ask students if they can think of other words that
1
begin with cent-. Sample answers: Cent (
100 of a dollar), century
(100 years), centennial (100th anniversary), centipede (looks like
1
it has 100 legs), centimeter (
100 of a meter)
Making Up Equivalent
WHOLE-CLASS
ACTIVITY
Names for Percents
(Math Journal 2, p. 248)
Tell students that in this lesson they will represent percents on
a 10-by-10 square grid. Discuss the example on journal page 248:
“Last season, Duncan made 62 percent of his basketball shots.”
The 10-by-10 grid represents the whole (100%)—in this case,
all of the shots Duncan attempted.
The 10-by-10 grid is made up of 100 small squares. Each
1
small square is 100 , or 1%, of the whole. A decimal name
1
for 100 is 0.01.
Sixty-two small squares are shaded. These shaded squares
represent the number of shots Duncan made out of every
100 shots he took.
Student Page
Date
Had Duncan taken 100 shots, he would have made 62 shots.
62
This can also be stated as a fraction, 100 of his shots, or as a
decimal, 0.62 of his shots.
Time
LESSON
9 1
Many Names for Percents
Your teacher will tell you how to fill in the percent examples.
Answers vary.
Fill in the “100% box” for each example. Show the percent by shading the
10-by-10 grid. Then write other names for the percent next to the grid.
38
39
Example: Last season, Duncan made 62 percent of his basketball shots.
62
100%
That is
all of
Duncan’s shots
out of every 100.
Fraction name:
62
Decimal name:
0.62
100
1. Percent Example:
That is
out of every 100.
100%
Fraction name:
100
Decimal name:
2. Percent Example:
100%
That is
out of every 100.
Fraction name:
100
Decimal name:
248
Math Journal 2, p. 248
724
Unit 9 Fractions, Decimals, and Percents
Ongoing Assessment: Informing Instruction
Watch for students who mistakenly think Duncan took exactly 100 shots and
made exactly 62 of them. Explain, for example, that he might have taken only
50 shots and made 31 of them or taken 200 shots and made 124 of them.
Now select two of the examples of percents that students collected
and discussed during the Math Message Follow-Up. Work as a
class to complete Problems 1 and 2 on journal page 248. Have
students write a brief description for each percent example. Then
fill in the 100% box, shade the grid to show the percent, and write
the fraction and decimal names for the percent.
Adjusting the Activity
Journal pages 248–250 prompt students to provide an equivalent
hundredths-fraction for the percent example. Students may wonder why they
25
need to write a fraction such as 100 when it can be written in simplest form
1
as 4. Encourage students to write both forms whenever possible to emphasize
the connection between percents and fractions with 100 in the denominator.
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
Finding Equivalent Names
V I S U A L
PARTNER
ACTIVITY
for Percents
(Math Journal 2, pp. 249 and 250)
Students complete journal pages 249 and 250.
For Problems 3–5, ask: Which percent is the largest? 80%
Did you look at the grid, the fraction, the decimal, or the percent to
decide? For Problems 5–7, students may have difficulty deciding
what the “whole” is and how to fill in the 100% box.
Problem 5: The example does not mention a specific time
period. The whole (100%) could logically be “1 day” or any
longer period (week, month, year). Any period shorter than
1 day could pose a problem. For example, cats are much more
likely to be active at night and to sleep a lot during the day.
Problem 6: 40% will be deducted from the original price of
any item sold, so the whole (100%) is the “original price.”
Problem 7: The buyer must pay 20% of the cost of the carpet
at the time of purchase, so the whole (100%) is the “cost of
carpet.”
Student Page
Date
LESSON
9 1
Student Page
Time
Date
Many Names for Percents
LESSON
9 1
continued
Fill in the “100% box” for each example. (Problem 3 is done for you.)
Show the percent by shading the 10-by-10 grid. Then write other names
for the percent next to the grid.
Time
Many Names for Percents
continued
Fill in the “100% box” for each example. Show the percent by shading
the 10-by-10 grid. Write other names for the percent next to the grid.
Then answer the question.
3. Example: 12% of the students in Marshall School are left-handed.
100%
all students at
Marshall School
That is
12
6. Example:
Sale—40% Off
Everything Must Go!
out of every 100.
Fraction name:
12
Decimal name:
0.12
original
price
80
Decimal name:
0.40
out of every 100.
Fraction name:
80
Decimal name:
0.80
“Pay 20% when you order. Take 1 full year to pay the rest.”
That is
cost of
carpet
5. Example: Cats sleep about 58% of the time.
That is
58
100%
Fraction name:
$180
7. Example: A carpet store ran a TV commercial that said:
100
100%
all minutes
in 1 day
Fraction name:
What would Mr. Thompson pay for a bicycle that had been selling for $300?
100%
all words on
the test
out of every 100.
40
100
4. Example: Sarah spelled 80% of the words correctly on her last test.
That is
40
That is
100%
100
20
out of every 100.
Fraction name:
20
Decimal name:
0.20
100
out of every 100.
58
100
Decimal name:
0.58
Mrs. Shields wants to order a $1,200 carpet. How much must she pay
when she orders it?
249
Math Journal 2, p. 249
$240
250
Math Journal 2, p. 250
Lesson 9 1
725
2 Ongoing Learning & Practice
Playing Fraction Match
SMALL-GROUP
ACTIVITY
(Student Reference Book, p. 243; Math Masters,
pp. 278 and 473–476)
Students play Fraction Match to practice naming equivalent
fractions. See Lesson 7-7 for additional information.
Name
LESSON
9 1
1.
Playing Fraction Match
1
2
1
2
Suppose she had
a WILD card in her
hand. Write a
different fraction,
equivalent to
3
9
, that she
4
could name. 12
2
3
2
3
4
5
2
3
WILD
WILD
WILD
Name an equivalent
fraction with a
denominator of
2, 3, 4, 5, 6, 8, 9,
10, or 12.
4
5
6
8
4
5
3.
After students have had a chance to play several rounds, ask them
to complete Math Masters, page 278.
Time
Katrina is playing Fraction Match. The target card is 34. She has the following
cards in her hand. Circle the card she may play.
1
2
2.
Date
6
8
3
9
6
8
3
9
3
9
Imagine that a WILD card allowed
Katrina to name any fraction
equivalent to 34. Write two fractions
that she could name.
12
16
75
100
Sample
answers:
Ongoing Assessment:
Recognizing Student Achievement
Math Masters
Page 278
Problems 1 and 2
Use Math Masters, page 278, Problems 1 and 2 to assess students’ ability to
find equivalent fractions. Students are making adequate progress if they indicate
6
3
9
that 8 and 1
2 are equivalent to 4 . Some students may be able to name additional
3
fractions that are equivalent to 4 in Problem 3.
[Number and Numeration Goal 5]
Math Masters, page 278
Math Boxes 9 1
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 251)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-3. The skill in Problem 6
previews Unit 10 content.
Study Link 9 1
Student Page
Date
Time
LESSON
9 1
(Math Masters, pp. 279 and 280)
Math Boxes
1. In which situation below do you need to
2. Complete.
know the area? Choose the best answer.
Rule:
finding the distance around a pool
2
1
10, or 5
buying a wallpaper border for your
bedroom
carpeting the living room
fencing a yard
in
out
2
5
1
10
3
5
3
10
4
5
5
,
5
7
10
3
10
9
10
1
2
131 133
3. Multiply. Use a paper-and-pencil algorithm.
or 1
162–166
4. Find the approximate latitude and longitude
of these Region 2 cities.
4,408
58 76
a. Dublin, Ireland
b. Rome, Italy
18
53 N
W
longitude 7
N
latitude 42
E
longitude 12
latitude
19
5. Angle RST is an obtuse (acute or
272 273
6. Use a straightedge to draw the line
obtuse) angle.
of symmetry.
R
S
The measure of RST is
T
127 .
141–143
109
251
Math Journal 2, p. 251
726
INDEPENDENT
ACTIVITY
Unit 9 Fractions, Decimals, and Percents
Home Connection Students name equivalent fractions,
decimals, and percents and shade grids to represent them.
Students complete the survey on the second page of the
Study Link to collect data for an activity in Lesson 9-6.
Study Link Master
Name
3 Differentiation Options
Date
STUDY LINK
Time
Fractions, Decimals, and Percents
9 1
61 62
Rename each decimal as a fraction and a percent.
0.90 1.
PARTNER
ACTIVITY
READINESS
Finding 50% of a Square
90
—
100
60
60% — 4.
100
50
7. 100
0 . 60
0 . 50 50 %
53
0.53 — 100
53 %
3.
0.04 — 0 . 25
6.
7% — 4
100
4
%
5.
25
25% — 100
7
100
0 . 07
10
Decimal:
Percent:
11.
SMALL-GROUP
ACTIVITY
Creating a Percents All
12.
0 . 75 75 %
6
9. 100
0 . 06 6 %
30
Sample answers
0.20
20%
Shade more than 25% and less than 60% of the grid.
Write the value of the shaded part as a decimal and a percent.
Percent:
ELL SUPPORT
75
8. 100
Shade more than and less than of the grid.
100
100
Write the value of the shaded part as a decimal and a percent.
Decimal:
0.40
40%
Sample answers
Shade more than 0.65 and less than 0.85 of the grid.
Write the value of the shaded part as a decimal and a percent.
Decimal:
Percent:
0.70
70%
Sample answers
15–30 Min
Around Museum
Practice
Order the fractions from smallest to largest.
(Math Masters, p. 262)
3 3 3 3
13. , , , 6 3 5 7
To provide language support for percents, have students display
the examples of percents collected for Study Link 8-6 in a Percents
All Around Museum. Ask students to describe the numbers they
see in the museum. If several English language learners speak
the same language, have them discuss the museum in their
own language first and then share what they can in English.
Date
3 3 3 3
, , , 7 6 5 3
2 6 1 19
14. , , , 3 7 2 20
1 2 6 19
, , , 2 3 7 20
Math Masters, p. 279
Teaching Master
Name
2.
Rename each percent as a fraction and a decimal.
10.
To explore equivalent names for percents, have students shade
50% of grids in different ways and explain how they know the
shaded portions represent 50%.
9 1
90 %
Rename each fraction as a decimal and a percent.
5–15 Min
(Math Masters, p. 281)
LESSON
Study Link Master
Name
Time
STUDY LINK
50% of a Square
9 1
Date
Time
Trivia Survey
Conduct the survey below. The results will be used in Lesson 9-6.
Benito and Silvia each shaded 50% of a grid.
70
Find at least five people to answer the following survey questions. You can
ask family members, relatives, neighbors, and friends.
BE CAREFUL! You will not ask every person every question. Pay attention to the
instructions that go with each question.
Record each answer with a tally mark in the Yes or No column.
1.
Do you think they shaded the grids correctly? Explain your reasoning.
Question
50
Sample answer: Yes. Both grids have 100 squares. Half, or 100 ,
are shaded, which is 50%.
2.
Shade 50% of the grids below in different ways. Explain how you know
you have shaded 50%.
p
Sample answers:
a.
b.
Answers vary.
Yes
No
1. Is Monday your favorite day?
(Ask everyone younger than 20.)
2. Have you gone to the movies in the last month?
(Ask everyone older than 8.)
3. Did you eat breakfast today?
(Ask everyone over 25.)
4. Do you keep a map in your car?
(Ask everyone who owns a car.)
5. Did you eat at a fast-food restaurant yesterday?
(Ask everyone.)
I divided the grid into 8 equal
parts and then shaded 4 of
50
4
them. 8 100 50%.
Half, or 50%, of 100 is 50.
I shaded 10 groups of
5 squares for a total of
50 squares.
6. Did you read a book during the last month?
(Ask everyone over 20.)
7. Are you more than 1 meter tall?
(Ask everyone over 20.)
8. Do you like liver?
(Ask everyone.)
Try This
3.
Shade 50% of the grid. Explain how you know you have shaded 50%.
Sample answers:
There are 50 squares in the grid.
1
25
25 are shaded. 100 2 50%.
Math Masters, p. 281
Math Masters, p. 280
Lesson 9 1
727