Lesson 17
For use before Module 9 Ratio, Proportion, and
Percent Lesson 7 Understanding Percents
Texas Edition: For use before Module 7 Ratio,
Proportion, and Percent Lesson 8 Fractions,
Decimals, and Percents
Objective
To use decimal grid paper to model fractions,
decimals, and percents
Materials
•
•
Copy Master: Decimal Grid Paper
colored pencils or crayons
Lesson Notes
Before beginning the lesson, be sure each student has
a Student Book, a copy of the Copy Master: Decimal
Grid Paper, and colored pencils or crayons.
By coloring 10 × 10 decimal grids as models, students
will see the relationship between fractions and
decimals. Because percent means hundredths, any
fraction in hundredths is expressed easily as a decimal
and as a percent.
Problem 1 How many congruent parts is the rectangle
divided into in problem 1? (5) Because there are
5 congruent parts, each part is called a fifth. How
many fifths are shaded? (3) What fraction of the
3
rectangle is shaded? ( 5 )
Problem 2 In problem 2, how many congruent parts
is the rectangle divided into? (10) Because there are
10 congruent parts, what is each part called? (tenth)
How many tenths are shaded? (6) What fraction of the
6
6
rectangle is shaded? ( 10 ) What is 10 written in simplest
3
form? ( 5 ) What is noticeable about the shaded parts
in problems 1 and 2? (They are both the same size. The
6
3
fractions 10 and 5 are equivalent.)
Problem 3 How many congruent parts is the grid divided into
in problem 3? (100) Because there are 100 congruent parts,
what is each part called? (hundredth) How many hundredths are
70
shaded? (70) What fraction of the grid is shaded? (100) What is the
numerator of the fraction? (70) What is the denominator of the
fraction? (100) Because the denominator is 100, the fraction can
be written as a decimal in hundredths. What is the decimal?
(0.70) The word percent means hundredths. This is the symbol
for percent. Write % on the board. Because 70 out of 100, or
70
100 , or 0.70 of the grid is shaded, we can say that 70% of the
grid is shaded.
Problem 4 How many congruent parts is the square divided into
in problem 4? (10) Because there are 10 congruent parts, what
is each part called? (tenth) How many tenths are shaded? (7)
7
What fraction of the grid is shaded? ( 10 ) What is the numerator
of the fraction? (7) What is the denominator of the fraction? (10)
Because the denominator is 10, you can write the fraction as a
decimal in tenths. What is the decimal? (0.7) To write a percent,
the denominator of a fraction must be 100 or a decimal must be
in hundredths. What decimal in hundredths is equivalent to 0.7?
(0.70) Why? (The model of 0.7 is the same size as the model for
0.70. Writing 0 to the right of the tenths place does not change the
value.) What percent of the grid is shaded? (70%) Now look back
at problem 3. How are these problems similar? (Both represent
70%.) What does one column on a decimal grid represent?
(1 tenth)
Hands-On Lesson 17 • Modeling Fractions, Decimals, and Percents Using Decimal Grid Paper
37
Lesson 17
Model 50% on the decimal grid. How many parts did you
50
shade? (50) How can you write 100 as a decimal? (0.50)
How many tenths are shaded? (5 tenths) How can you
write 5 tenths as a decimal? (0.5) What fractional part of
1
1
the grid is shaded? ( 2 ) So, 50%, 2 , and 0.5 all represent
the same amount.
Problems 7–10 Now that students have used decimal
grid paper to understand the relationship between
fractions, decimals, and percents, have them complete
problems 7–10. For problem 9, remind students to use 0 as
a placeholder when writing 4 hundredths as a decimal. For
problem 10, point out that the denominator of the fraction
is 10 and that each column on a decimal grid represents
1 tenth.
Lesson Adaptations
for Module 9
Problem 5 Look at problem 5. Take out your copy of Decimal Grid
Paper and your crayons or colored pencils. How many parts is the
decimal grid divided into? (100) Shade 9 out of 100 parts. Does it
matter which 9 parts you shade? (no) What fraction of the grid is
9
9
shaded? (100) How is the fraction 100 written as a decimal? (0.09)
What percent of the grid is shaded? (9%)
Problem 6 Look at problem 6. Shade 45 out of 100 parts on a
decimal grid. Does it matter which 45 parts you shade? (no) What
45
45
fraction of the grid is shaded? (100) How is the fraction 100 written
as a decimal? (0.45) What percent of the grid is shaded? (45%)
38
Level H Module 9 • Ratio, Proportion, and Percent
Lesson 9.7
In Lesson 9.7 students explore the meaning of
percent. You may want to have students model some
of the problems on a decimal grid.
Lesson 8
Lesson 8
Decimals and Percents
Objective
Name _______________________________________ Class __________________________ Date _________________
To write percents as decimals and decimals
as percents
16 out of 100
1
a.
Preskills
Understanding Percents
Transparency
H.7.7
16
0._______
b.
2
1.0 5 .
0.08
8% _______
3
.0 8 .
Materials
• transparency H.7.8
4
a.
68
0.68 _______%
b.
Order the numbers from least to greatest: 0.09, 75%, 0.57, 20%
20%
75%
0%
Student Book pXX
Problem 1
What is the ratio in problem 1? (16 out of 100) What
is 16 out of 100 written as a decimal? (0.16) What is
16 out of 100 written as a percent? (16%)
©Voyager Expanded Learning, Inc.
0
REVIEW PRESKILLS
Problem 2
The percent in problem 2 is greater than 100%.
How many total small squares are shaded in the
model shown in problem 2? (105) The model
represents 105%.
How many whole grids are shaded? (1) In the grid
on the right, 5 out of 100 squares are shaded. What
is 5 out of 100 written as a decimal? (0.05)
To write a percent as a decimal, move the decimal
point two places to the left and drop the percent
symbol. Where is the decimal point in 105%? (to
the right of 5) Move the decimal point two places
to the left and drop the percent symbol. What is
105% written as a decimal? (1.05)
Problem 3
The percent in problem 3 is less than 100% because
less than one whole grid is shaded. Where is the
decimal point in 8%? (to the right of the 8) To write
the percent as a decimal, move the decimal point
two places to the left and drop the percent symbol.
Level H Module 7 • Ratio, Proportion, and Percent
0.1
0.2
0.09
0.75
75% _______
.7 5 .
0.3
0.4
0.5
0.6
0.57
0.7
0.8
0.9
100%
BUILD
THE
CONCEPT
1
0.20
20% _______
.2 0 .
0.09 _______,
20% _______,
0.57 and _______.
75%
The numbers from least to greatest are _______,
Level H Module 7 • Ratio, Proportion, and Percent
Vmath H Mod7_SE_v3.indd 5
MODEL NEW SKILLS
7.5
0.075 _______%
0 . 0 7.5
0.68.
32
16
_______%
1.05
105% _______
5
4/3/08 3:32:17 PM
Since there is only one digit, 8, write a 0 to the left of 8 as
a placeholder when moving the decimal point. What is
8% written as a decimal? (0.08)
Problem 4
In problem 4a, the model represents 0.68. How many small
squares are shaded in the model shown in problem 4? (68)
What is 68 out of 100 written as a percent? (68%)
To write a decimal as a percent, which way does the
decimal point move? (to the right) How many places does
the decimal point move? (two) So, to write a decimal as a
percent, move the decimal point two places to the right
and write the percent symbol.
In problem 4b, the decimal is 0.075. To write the decimal as
a percent, move the decimal point two places to the right
and write the percent symbol. Where is the decimal point
in 0.075? (to the right of the first 0 from left to right) What is
0.075 written as a percent? (7.5%)
Lesson 8
Lesson 8
Student Book pXX
Write each percent as a decimal.
22%
5
6
0.22
_______
3%
7
0.03
_______
118%
SCAFFOLD INSTRUCTION
1.18
_______
Problem 5
How is a percent written as a decimal? (by moving
the decimal point in the percent two places to the
left and dropping the percent symbol) What is
22% written as a decimal? (0.22)
Write each decimal as a percent.
1.08
8
9
108
_______%
0.49
49
_______%
10
0.07
7
_______%
Write a Percent as a Decimal
Using Symbols
Using Words
58% 0.58.
Move the decimal point two places to the left and drop
the percent symbol.
HOW
TO
58% 0.58
Write a Decimal as a Percent
Using Symbols
Using Words
0.25 25.%
Move the decimal point two places to the right and write
the percent symbol.
Problem 6
How is a percent written as a decimal? (by moving
the decimal point in the percent two places to the
left and dropping the percent symbol) To write
3% as a decimal, what needs to be added? (a 0 as a
placeholder) What is 3% written as a decimal? (0.03)
0.25 25%
©Voyager Expanded Learning, Inc.
Problem 7
How is a percent written as a decimal? (by moving
the decimal point in the percent two places to the
left and dropping the percent symbol) What is
118% written as a decimal? (1.18)
6
Lesson 8 • Decimals and Percents
Vmath H Mod7_SE_v3.indd 6
4/3/08 3:32:26 PM
To "5),$
order the numbers
0.09, 75%,
0.57, and 20%,
02/",%-
72)4%
"5),$
(/7
4(% they should either all be written as decimals
4/
-!4(
3+),,3
#/.#%04 or all be
3/,6).' For this
written as percents.
problem,
change the percents
to decimals. To write 75% as a decimal,
#2)4)#!,
!,'%'2!)#
move the decimal
point two places to the left and drop
4().+).'
4().+).'
the percent symbol. Where is the decimal point in 75%?
(to the right of 5) Move the decimal point two places to the
left and drop the percent symbol. What is 75% written as a
decimal? (0.75)
Where is the decimal point in 20%? (to the right of 0) Move
the decimal point two places to the left and drop the
percent symbol. What is 20% written as a decimal? (0.20)
The decimal 0.20 is the same as 0.2. Graph the decimals on
the number line and label the original numbers. Read the
numbers off the number line from left to right. What are
the numbers written in order from least to greatest? (0.09,
20%, 0.57, 75%)
Problem 8
How is a decimal written as a percent? (by moving
the decimal point in the decimal two places to the
right and writing the percent symbol) What is
1.08 written as a percent? (108%)
Problem 9
How is a decimal written as a percent? (by moving
the decimal point in the decimal two places to the
right and writing the percent symbol) What is
0.49 written as a percent? (49%)
Problem 10
How is a decimal written as a percent? (by moving
the decimal point in the decimal two places to the
right and writing the percent symbol) What is
0.07 written as a percent? (7%)
Lesson 8 • Decimals and Percents
33
Lesson 8
Go to
VmathLive.com
USE CORRECTION PROCEDURES
Lesson 8
Module Ratio, Proportion, and Percent
Activity Percents and Decimals
SKILL BUILDING:
NEW AND REVIEW
Preskills
Correct errors by reviewing or reteaching how to
understand decimals. Use the HOW TO process from
the lesson transparency listed in the preskills box on
page XX.
Write each percent as a decimal.
11
17%
44.5%
12
0.17
13
0.445
125%
1.25
Write each decimal as a percent.
14
1.22
0.98
15
122%
16
98%
0.274
27.4%
Write each ratio as a decimal and as a percent.
New Skills
For reteaching:
• Review the Support examples shown in VmathLive
in the Percents and Decimals activity in the Ratio,
Proportion, and Percent module.
• Use Reteach Copy Master H.7.8 and the modeled
teacher text to show students an alternative
method for writing percents as decimals and
decimals as percents. Have students complete the
Copy Master.
14 out of 100
77 out of 100
18
0.14; 14%
19
0.77; 77%
3 out of 100
0.03; 3%
PROBLEM-SOLVING:
NEW AND REVIEW
Solve each problem.
20
Alicia spent 3% of her money at the bookstore.
How is this percent written as a decimal? 0.03
21
Seven tenths of Martin’s marbles are red. How is
this decimal written as a percent? 70%
22
A bakery sells 87 out of 100 sticky buns that they made for the day. What percent of the
sticky buns did not get sold? 87% were sold; 100% ⴚ 87% ⴝ 13%;
23
Of the books on a store shelf, 67 out of 100 are paperbacks. Write the ratio of paperbacks to
total books as a ratio three different ways.
13% did not get sold
67 to 100; 67:100; 67
100
©Voyager Expanded Learning, Inc.
For additional practice:
• Assign the VmathLive Percents and Decimals
activity in the Ratio, Proportion, and Percent
module.
• Have students complete the Extra Practice
problems on Student Book page XX.
17
Level H Module 7 • Ratio, Proportion, and Percent
Vmath H Mod7_SE_v3.indd 7
7
4/3/08 3:32:49 PM
Student Book pXX
Student Book pXX
MONITOR INDEPENDENT WORK
Before students begin independent work, review the
HOW TO process example. As you review,
HOW emphasize the words of mathematics by
TO
having students read aloud the words
shown at the right for each process step.
Problems 11–23
Have students work independently. Check work and
have students total the number correct and record
results. Instruct students to record a 6 if they got
12 or 13 correct, a 5 for 11 correct, a 4 for 10 correct,
a 3 for 8 or 9 correct, a 2 for 7 correct, and a 1 for
1–6 correct. Use Correction Procedures as needed.
34
Level H Module 7 • Ratio, Proportion, and Percent
ASSESS INFORMALLY
Error Analysis
Check work and record results. Use the error analysis below
to determine which skills need review, reteaching, or extra
practice.
WRITE If student answered problem 3 incorrectly:
MATH Remind the student to write each answer
choice as a decimal, then compare it to 0.042.
As you review the Explain It problem together,
understand that the correct answer is only part
)4 of the solution. Appropriate math vocabulary, a
logical method for solving the problem, and the justification
of a reasonable answer complete the student response.
Explain It problem answers can be used as part of a daily
math journal.
%80,!).
Lesson 8
Lesson 8
DIFFERENTIATION
Additional Resources
Answer each question.
1
3
Which of the following is equal to
0.042?
2
Jay wrote 75% of a paper for school.
Which decimal represents this amount?
a. 42%
b. 4.2%
a. 75
b. 7.5
c.
d. 0.042%
c.
d. 0.075
420%
0.75
Change each
How can the answer choices to problem 1 be checked? _______________
answer choice to a decimal and see which one is equal
______________________________________________________________
to 0.042.
______________________________________________________________
VmathLive
Module: Ratio, Proportion, and Percent
Activity: Percents and Decimals
WRITE
MATH
______________________________________________________________
%80,!).
A percent is written as a decimal. If the percent is greater than 100%, what is
known about the number in the decimal that is to the left of the decimal point?
One hundred percent written as a decimal is 1. The number
Explain. __________________________________________________________________
)4
to
the left of the decimal point will be 1 or greater.
_________________________________________________________________________
_________________________________________________________________________
4
decimal point is moved to the right. So, the decimal
____________________________________________________________
with the greatest first digit to the right of the decimal
____________________________________________________________
point will be the decimal that is the greatest percent.
____________________________________________________________
Eight is the greatest digit in the tenths place.
____________________________________________________________
Lesson 8 • Decimals and Percents
Vmath H Mod7_SE_v3.indd 8
Extra Practice
Student Book page XX
English Language Learners
CRITICAL
THINKING
0.88; When a decimal is converted to a percent, the
____________________________________________________________
©Voyager Expanded Learning, Inc.
8
Without converting the decimals to percents, which percent will be
the greatest? Explain.
0.095, 0.88, 0.102
Vmath Reteach
Copy Master H.7.8 page XX
Instructional Support page XX
4/3/08 3:32:55 PM
To familiarize students with percent, have them
shade different figures according to a given
percent. For example, have them shade a heart
to show about 38% shaded. Have students
compare their drawings with those of other
students. Then, have students vote for the most
accurate representation.
Students with Special Needs
Write several percents on an index card or sticky
note. Allow students to use a counter or a coin to
represent the decimal point. Remind students to
move the decimal point two places to the left to
show the number as a decimal.
Now, ask students to move the decimal
point (counter or coin) in order to show the
number as a decimal. Students will become
more proficient with renaming decimals and
percents if they practice physically manipulating
the decimal point. Repeat this activity, using
different numbers or using decimal numbers
that students make into percents by moving the
decimal two places to the right.
Lesson 8 • Decimals and Percents
35
Lesson 18
For use before Module 9 Ratio, Proportion, and
Percent Lesson 13 Applications of Percent
Texas Edition: For use before Module 7 Ratio,
Proportion, and Percent Lesson 12 Applications
of Percents
Objective
To use a model to explore markup and discount
as percents of change
Materials
•
Gizmo: Percent of Change
ons
Gizmos Log In Instructi
using the Username
e
Liv
• Log in to Vmath
in VPORT.
and Password provided
.
• Select the Gizmos tab
of Change Gizmo link.
t
cen
Per
the
on
ck
Cli
•
Lesson Notes
amount of increase by the original amount. What is the
division problem? (8 ⫼ 40) What is 8 divided by 40? (0.2)
What is 0.2 written as a percent? (20%) So, the percent
change from 40 to 48 is 20%.
Before beginning the lesson, be sure students have
their Student Books and are ready to work at the
computers.
Complete problem 1 before students log in to the
Percent of Change Gizmo.
If students have additional time, have them answer
Assessment Questions 1−3 in the Gizmo. They can
click on the Check Your Answers button to see how
well they did on the assessment.
Problem 1 In problem 1, 40 is changing to 48. Is the
change an increase or a decrease? (increase) The first
step in finding a percent increase is to find the amount of
increase. How is the amount of increase found? (Subtract
the original amount from the amount after the increase.)
What is the original amount? (40) What is the amount
after the increase? (48) What is 48 minus 40? (8) So, the
amount of increase is 8. The next step is to divide the
Problem 2 Have students log in to the Percent of Change Gizmo
using the instructions in the box. Look at problem 2. A store
charges more for an item than the store paid for it. This is how a
store makes money. A store sells a sweater for $45. The sweater
cost the store $30. To model this situation, drag the Selling price
handle to $45 in the Markup portion of the Gizmo. Then drag the
Original cost handle to $30. Look at the model. The selling price is
the sum of what two amounts? (the original cost and the markup)
The amount of increase from the original cost to the selling price
is the markup. The increments on the ruler are labeled every
$5. According to the model, what is the amount of the markup?
($15) Compare the length of the Markup bar to the length of the
1
Original cost bar. The length of the Markup bar is 2 the length of
the Original cost bar. One-half can be written as what percent?
(50%) So, the length of the Markup bar is 50% of the length of the
Original cost bar. So, the markup is 50% of the original cost. The
selling price can be written as a percent of the original cost. Look
at the Selling price bar and the Original cost bar. The Selling price
1
bar is 1 2 times the length of the Original cost bar. One and onehalf can be written as what percent? (150%) So, the selling price is
150% of the original cost.
Gizmo Lesson 18 • Percent of Change
39
Lesson 18
Problem 3 Look at problem 3. A shirt costs a store $20.
The store wants to mark up the price by 25%. To model
this situation, drag the Original cost handle to $20 in
the Markup portion of the Gizmo. What is the percent
increase? (25%) So, the length of the Markup bar should
be 25% of the length of the Original cost bar. What is 25%
1
written as a fraction? ( 4 ) So, the length of the Markup bar
1
should be 4 of the length of the Original cost bar. Look
1
at the length of the Original cost bar. What length is 4
the length of the Original cost bar? ($5) Drag the Markup
bar handle so that the selling price is $5 more than
the original cost. The percent below the model is 25%.
According to the model, what is the selling price? ($25)
Problem 4 Look at problem 4. Stores often have sales in
which they reduce their prices. The difference between
the original price and the sale price is the discount. A
book that originally sold for $40 is put on sale for $30.
To model this situation, drag the Original price handle
to $40 in the Discount portion of the Gizmo. Then drag
the Sale price handle to $30. Look at the model. The sale
price is the difference of what two amounts? (the original
price and the discount) The amount of decrease from the
original price to the sale price is the discount. According
to the model, what is the amount of the discount? ($10)
Compare the length of the Discount bar to the length
of the Original price bar. The length of the Discount bar
1
is 4 the length of the Original price bar. One-fourth can
be written as what percent? (25%) So, the length of the
Discount bar is 25% of the length of the Original price
bar. The discount is 25% of the original price. The sale
price can be written as a percent of the original price.
Look at the Sale price bar and the Original price bar.
3
The Sale price bar is 4 the length of the Original price bar.
Three-quarters can be written as what percent? (75%)
The sale price is 75% of the original price.
Problem 5 Look at problem 5. A store is currently selling
a DVD for $30. The store wants to discount the price by
50%. To model this situation, drag the Original price
handle to $30 in the Discount portion of the Gizmo. What
is the percent decrease? (50%) The length of the Discount
bar should be 50% of the length of the Original price bar.
1
What is 50% written as a fraction? ( 2 ) So, the length of
1
the Discount bar should be 2 of the length of the Original
price bar. Look at the length of the Original price bar.
1
What length is 2 the length of the Original price bar? ($15)
Drag the Discount bar handle so that the sale price is $15
less than the original price. The percent below the model
is 50%. According to the model, what is the sale price?
($15)
40
Level H Module 9 • Ratio, Proportion, and Percent
Lesson 18
Look at the percents in the Markup portion of the screen.
Which bar lines up with 100%? (Original cost) If the selling
price were equal to the original cost, the selling price
would be what percent of the original cost? (100%) Is
the selling price usually greater or less than the original
cost? (greater) If the selling price were written as a
percent of the original cost, the percent should be greater
than 100% because the selling price is greater than the
original cost. Look at the percents in the Discount portion
of the screen. The sale price and discount can be written
as percents of the original price. If the sale price were
equal to the original price, the sale price would be what
percent of the original price? (100%) Is the sale price
usually greater or less than the original cost? (less)
If the sale price or discount were written as a percent
of the original price, the percent should be less than
100% because the sale price or discount is less than
the original price.
Problems 6–8 Have students work individually. Students
will use the Gizmo to find percents of change.
Gizmo Lesson 18 • Percent of Change
41