Converting “Easy” Fractions
to Decimals and Percents
Objectives To reinforce renaming fourths, fifths, and tenths as
decimals
and percents; and to introduce solving percent
d
problems by using equivalent fractions.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Find the fraction and percent of a collection
and a region. Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
[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 Activities
Students name shaded parts of 10-by-10
grids as fractions, decimals, and percents.
The shaded parts are all “easy” fractions:
fourths, fifths, and tenths.
Playing Rugs and Fences
Student Reference Book, pp. 260
and 261
Math Masters, p. 502
Rugs and Fences Cards (Math
Masters, pp. 498–501)
Students practice finding the areas
and perimeters of polygons.
Math Boxes 9 2
Math Journal 2, p. 254
Students practice and maintain skills
through Math Box problems.
Study Link 9 2
Math Masters, p. 282
Students practice and maintain skills
through Study Link activities.
Students solve percent problems by
substituting “easy” equivalent fractions
for percents.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 253. [Number and Numeration Goal 5]
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Exploring Percent Patterns
Math Masters, p. 283
Students identify and use patterns to solve
percent problems.
ENRICHMENT
Writing and Solving “Percent-of”
Number Stories
Students write and solve “percent-of”
number stories.
EXTRA PRACTICE
Adding Tenths and Hundredths
Math Masters, pp. 283A and 283B;
p. 426 (optional)
base-10 blocks (optional)
Students add fractions with 10 and 100 in the
denominator.
EXTRA PRACTICE
Finding Equivalent Names for Fractions
Math Masters, p. 445
Students name a fraction and a percent for
the shaded part of a 10-by-10 grid.
Materials
Math Journal 2, pp. 252, 253, 342, and 343
Study Link 9 1
slate
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 62, 63, 153, 154
728
Unit 9
Fractions, Decimals, and Percents
728_EMCS_T_TLG1_U09_L02_576906.indd 728
2/3/11 12:47 PM
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.
problems.
Have students explain their strategies for the
Suggestions:
Complete Problem 1 on journal page 252.
36 0.36, 36%
_
100
87
_
0.87, 87%
100
19
_
0.19, 19%
100
3 0.3, 30%
_
10
1
_
0.5, 50%
2
4
_
0.8, 80%
5
Study Link 9 1 Follow-Up
7 0.35, 35%
_
Have partners compare answers. Ask volunteers
to share different solutions for Problems 10–12.
20
3
_
0.12, 12%
25
14
_
7.0, 700%
2
For Problems 13 and 14, you might have students draw
number lines and identify the positions of the fractions.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 252)
Remind students that it is easy to rename a fraction as a percent
32
when the denominator is 100. For example, another name for _
100
is 32%.
1
There are other fractions, such as _12 , _14 , _15 , and _
, that can be
10
renamed as percents fairly easily. Knowing such equivalencies
often makes percent problems easier to solve. In Problem 1,
Alfred missed 50% of 20 problems. To find how many problems
he missed, students may think of 50% as _12 and ask themselves,
“What is _12 of 20?”
Some students may reason: _12 of the 10-by-10 grid is shaded.
50
That is 50 small squares, or _
, or 0.50, or 50% of the
100
10-by-10 grid. 50% of 20 is the same as _12 of 20, or 10.
Use the shaded 10-by-10 grid in Problem 1 to help you illustrate
equivalent fraction, decimal, and percent names. Point out the
following:
Student Page
Date
LESSON
92
Time
“Percent-of” Number Stories
Alfred, Nadine, Kyla, and Jackson each took the
same math test. There were 20 problems on the test.
1.
How many problems did he miss?
10
38
39
problems
10
10
1
_
of 20 =
2
The whole is the 20-problem test—100% of the test.
100%
Rule
20-problem test
1
Alfred missed _
of the problems. He missed
2
0.50 of the problems. That is 50% of the problems.
50% of 20 =
1
_
, or 50% is shaded.
2
The whole test is represented by the 10-by-10 grid.
2.
The 10-by-10 grid can be divided into 20 equal parts
(rectangles), each representing 1 problem on the test.
1
Nadine missed _
of the problems. She missed
4
0.25 of the problems. That is 25% of the problems.
How many problems did she miss?
1
How many problems did she miss?
10% of 20 =
The 10-by-10 grid is also divided into 100 small squares;
1
each small square is _
, or 1%, of the 10-by-10 grid.
100
Have students solve Problems 2–4 with a partner.
4.
1
_
, or 25% is shaded.
4
Kyla missed _
of the problems. She missed
10
0.10 of the problems. That is 10% of the problems.
1
_
of 20 =
10
Each rectangle, consisting of 5 small squares, represents 1 problem on the test.
problems
5
25% of 20 =
3.
5
5
1
_
of 20 =
4
2
problems
2
2
1
_
, or 10% is shaded.
10
1
Jackson missed _
of the problems. He missed
5
0.20 of the problems. That is 20% of the problems.
How many problems did he miss?
1
_
of 20 =
5
4
problems
4
20% of 20 =
4
1
_
, or 20% is shaded.
5
Math Journal 2, p. 252
248-273_EMCS_S_MJ2_G4_U09_576426.indd 252
2/1/11 1:49 PM
Lesson 9 2
729-733_EMCS_T_TLG1_U09_L02_576906.indd 729
729
2/3/11 4:54 PM
Student Page
Date
Time
LESSON
Links to the Future
Fractions, Decimals, and Percents
92
_2
3
_
1.
Fill in the missing numbers.
Problem 1 has been done
for you.
4
Ways of showing
:
2.
5
Ways of showing
:
100%
Rule
large square
3
— is
4
75
shaded.
3
—
5
0.
5
Ways of showing
is shaded.
60
—
100
60
60
3
Ways of showing _
:
10
5
is shaded.
0.
40
5.
Ways of showing
40
—
100
40
_5
_4
:
4.
4
—
5
% 0.
7.
5
Ways of showing
is shaded.
80
Shade the grid. Then fill in the missing numbers.
6.
—
100
75 %
_3
3.
2
—
0. 75
80
—
100
:
5
—
5
is shaded.
5
%
:
100
—
100
100 %
80 % 1
Sample answers:
7
Ways of showing _
:
10
8.
9
Ways of showing _
:
10
The ability to use fractions and percents interchangeably will prove useful in later
grades when students learn to estimate with percents that are not equivalent to
“easy” fractions. For example, by the end of sixth grade, most students should
be able to apply the following kind of reasoning: The population of Colombia is
about 40 million. About 23% of the population lives in rural areas. Because 23%
is equivalent to a little less than _14 , and _14 of 40 million is 10 million, about
10 million Colombians live in rural areas.
Finding Equivalent Names for
INDEPENDENT
ACTIVITY
Other “Easy” Fractions
(Math Journal 2, p. 253)
30
—
100
0.
70
—
is shaded.
30
30
100
% 0.
90
is shaded.
70
—
70
100
% 0.
Students find equivalent names for several more “easy” fractions
on journal page 253.
is shaded.
90
90
%
Math Journal 2, p. 253
248-273_EMCS_S_MJ2_G4_U09_576426.indd 253
2/1/11 1:49 PM
Ongoing Assessment:
Recognizing Student Achievement
Journal
page 253
Use journal page 253 to assess students’ ability to rename fourths, fifths,
tenths, and hundredths as decimals and percents. Students are making
adequate progress if they are able to fill in the missing numbers and shade the
grids. Some students may use shading that involves full and partial squares.
[Number and Numeration Goal 5]
“Easy”
Fractions
1
_
2
1
_
4
3
_
4
1
_
5
2
_
5
3
_
5
4
_
5
1
_
10
3
_
10
7
_
10
9
_
10
730
Decimals
Percents
0.50
50%
0.25
25%
0.75
75%
0.20
20%
0.40
40%
0.60
60%
0.80
80%
0.10
10%
0.30
30%
0.70
70%
0.90
90%
Completing the Table of
INDEPENDENT
ACTIVITY
Equivalent Names for Fractions
(Math Journal 2, pp. 252, 253, 342, and 343)
Ask students to copy the decimal and percent names for the
fractions on journal pages 252 and 253 to the table of Equivalent
Names for Fractions on journal pages 342 and 343. Students may
want to check their answers against the chart on the inside front
cover of their journals.
When students have completed this activity, they should have
recorded the equivalencies shown in the chart in the margin.
Unit 9 Fractions, Decimals, and Percents
729-733_EMCS_T_TLG1_U09_L02_576906.indd 730
2/3/11 4:54 PM
Student Page
2 Ongoing Learning & Practice
Games
Rugs and Fences
Materials □ 1 Rugs and Fences Polygon Deck A, B, or C
(Math Masters, page 499, 500, or 501)
□ 1 Rugs and Fences Area and Perimeter Deck
(Math Masters, page 498)
Playing Rugs and Fences
PARTNER
ACTIVITY
(Student Reference Book, pp. 260 and 261; Math Masters, pp. 498–502)
□ 1 Rugs and Fences Record Sheet for each
player (Math Masters, page 502)
Players
2
Skill
Calculating area and perimeter
Object of the game To score more points by finding the
perimeters and areas of polygons.
Directions
Students play Rugs and Fences to practice finding the area and
perimeter of a polygon. Note that area is reported in square units
and perimeter in units. When using Polygon Deck C, students
should assume that sides that appear to be the same length are
the same length and angles that appear to be right angles are
right angles.
1. Select one of the Polygon Decks—A, B, or C. Shuffle
the deck and place it picture-side down on the table.
(Variation: Combine 2 or 3 Polygon decks.)
2. Shuffle the deck of Area and Perimeter cards and place
it word-side down next to the Polygon Deck.
3. Players take turns. At each turn, a player draws 1 card from
each deck and places them faceup on the table.
The player finds the area (A) or the perimeter (P) of the
polygon, as directed by the Area and Perimeter card.
Examples from Polygon
Decks A, B, and C
♦ If a “Player’s Choice” card is drawn, the player may choose
to find either the area or the perimeter of the polygon.
♦ If an “Opponent’s Choice” card is drawn, the opposing
player chooses whether the area or the perimeter of the
polygon will be found.
Polygon Deck A
.
Polygon Deck B
Polygon Deck C
Card
A
P
Card
A
P
Card
A
P
1
48
28
17
35
24
33
48
28
2
40
26
18
36
26
34
22
20
3
20
24
19
14
18
35
48
36
4
16
20
20
60
32
36
17
20
5
27
24
21
64
32
37
28
28
6
49
28
22
8
18
38
40
36
7
56
30
23
36
24
39
28
32
8
9
20
24
54
30
40
24
24
9
24
20
25
48
32
41
23
26
10
72
34
26
6
12
42
28
32
11
42
26
27
54
36
43
86
54
12
63
32
28
192
64
44
48
32
13
25
20
29
32
26
45
22
30
4. A player records a turn on his or her Record Sheet. The
player records the polygon card number, circles A (area) or
P (perimeter), and writes a number model used to calculate
the area or perimeter. The solution is the player’s score for
the round.
5. The player with the higher total score at the end of
8 rounds is the winner.
Student Reference Book, p. 260
Student Page
Date
Time
LESSON
Math Boxes
92
14
15
16
16
16
28
22
18
18
30
31
32
64
36
20
25
216
66
46
48
47
60
48
160
52
1.
32
Fraction
Decimal
Percent
1
_
5
0.20
20%
80%
30%
_4
0.80
5
3
_
10
0.30
0.90
9
_
10
Have students use the following:
Polygon Deck A to practice counting unit squares and sides of squares
to find the area and perimeter of rectangles.
Polygon Deck B to practice using formulas to find the area and perimeter
of rectangles, triangles, and parallelograms.
3 yd 2 ft =
11
ft
6 yd 1 ft =
19
ft
c.
72
in. = 2 yd
d.
17
ft = 5 yd 2 ft
f.
25 ft =
8
yd
570%
2
6
in. = 30 in.
K I N E S T H E T I C
T A C T I L E
V I S U A L
ft
1
34–37
57%
ft
Zena earned $12. She spent $8.
What fraction of her
earnings did she spend?
b.
What fraction did 4
, or 13
she have left? 12
c.
The amount she spent is how
many times as much as the
amount she saved?
_
6.
12
3
_
2 times
129
_8 , or _2
a.
44
What temperature is it?
− 10
°F
7"
10
4"
Area =
62
Find the area and perimeter of the
rectangle. Include the correct units.
Polygon Deck C to practice using combinations of formulas to find the area
and perimeter of irregular shapes.
A U D I T O R Y
5.7%
4.
a.
e.
5.
5.71%
Complete.
b.
About 4.02% of the words on the Internet
are the, and about 1.68% of the words are
and. About what percent of all words on
the Internet are either the or and? Choose
the best answer.
90%
61
3.
2.
Complete the table with equivalent names.
70
Adjusting the Activity
There are 4 kinds of Area
and Perimeter cards.
28 in
Perimeter =
°F
0
2
–10
22 in.
–20
131 133
139
Math Journal 2, p. 254
248-273_EMCS_S_MJ2_G4_U09_576426.indd 254
2/1/11 1:49 PM
Lesson 9 2
729-733_EMCS_T_TLG1_U09_L02_576906.indd 731
731
2/3/11 12:47 PM
Study Link Master
Name
Date
STUDY LINK
9 2
1.
Time
Coins as Percents of $1
How many pennies in $1?
2.
How many nickels in $1?
100
3.
How many dimes in $1?
20
100
What fraction of $1 is 1 penny?
1
%
5
_, or _
100
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-4. The skill in Problem 6
previews Unit 10 content.
1
What fraction of $1 is 1 nickel? 20
_, or _
10
100
1
What fraction of $1 is 1 dime? 10
Write the decimal that shows what part of $1 is 1 dime.
0.10
Writing/Reasoning Have students write a response to the
following: Suppose you tripled the lengths of the sides of the
rectangle in Problem 5. What would happen to the area of the
rectangle? Sample answer: The area of the new rectangle would be
252 in2. It would be 9 times as large as the area of the original
rectangle.
10 %
25
_1
_
4
How many quarters in $1?
What fraction of $1 is 1 quarter? 4 , or 100
Write the decimal that shows what part of $1 is 1 quarter. 0.25
What percent of $1 is 1 quarter? 25 %
50
1
2 What fraction of $1 is 1 half-dollar? _2 , or _
100
How many half-dollars in $1?
0.50
Write the decimal that shows what part of $1 is 1 half-dollar.
What percent of $1 is 1 half-dollar? 50 %
What percent of $1 is 1 dime?
4.
5.
Three quarters (75¢) is _4 of $1.
3
6.
Write the decimal.
7.
0.75
2
Two dimes (20¢) is _
10 of $1.
Write the decimal.
0.20
What percent of $1 is
What percent of $1 is
3 quarters?
2 dimes?
75
%
20
Study Link 9 2
%
Practice
4,488
8.
= 748 º 6 9. 51 º 90 =
4,590
25,284 = 28 º 903
10.
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 254)
0.01
Write the decimal that shows what part of $1 is 1 nickel. 0.05
5 %
What percent of $1 is 1 nickel?
10
1
_
Write the decimal that shows what part of $1 is 1 penny.
What percent of $1 is 1 penny?
Math Boxes 9 2
38 39
(Math Masters, p. 282)
Math Masters, p. 282
278-303_EMCS_B_MM_G4_U09_576965.indd 282
INDEPENDENT
ACTIVITY
2/1/11 2:36 PM
Home Connection For each of several coins, students
identify what fraction of $1, decimal part of $1, and
percent of $1 that coin represents.
3 Differentiation Options
READINESS
Exploring Percent Patterns
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 283)
To explore the relationship between fractions and percents, have
students identify and use patterns to solve percent problems. Ask
students to describe how they used the patterns. For example:
Teaching Master
Name
Date
LESSON
Time
Percent Patterns
9 2
If there are 20 per 100, then there are
Complete each set of statements. Use grids or base -10 blocks,
or draw pictures to help you. Look for patterns in your answers.
Example:
1
1
2 per 10. 10 is _
of 100. _
of 20 is 2, so 20 per 100 is the
10
10
same as 2 per 10.
50% is the same as 50 per 100.
If there are 50 per 100, then there are
1.
5
per 10.
500
per 1,000.
10
per 20.
100
per 200.
20% is the same as 20 per 100.
2.
If there are 20 per 100, then there are
2
4
3.
per 10.
per 20.
If there are 30 per 100, then there are
3
6
200 per 1,000.
40 per 200.
80% is the same as 80 per 100.
4.
If there are 80 per 100, then there are
8
16
per 10.
per 20.
30% is the same as 30 per 100.
per 10.
per 20.
300 per 1,000.
60 per 200.
60% is the same as 60 per 100.
200 per 1,000. 1,000 is 10 times as much as 100. 10 times 20
is 200, so 20 per 100 is the same as 200 per 1,000.
200
2 _
4 per 20. _
, 20 , _
are all names for _15 . 4 is _15 of 20, so 4 per
10 100 1,000
20 is the same as 20 per 100.
If there are 60 per 100, then there are
800 per 1,000.
160 per 200.
6
12
per 10.
per 20.
600 per 1,000.
120 per 200.
40
40 per 200. _
= _15
200
p
Try This
5.
75% is the same as 75 per 100.
If there are 75 per 100, then there are
py g
g
7.5
15
per 10.
per 20.
750 per 1,000.
150 per 200.
6.
120% is the same as 120 per 100.
If there are 120 per 100, then there are
12
24
1,200 per 1,000.
240 per 200.
per 10.
per 20.
Math Masters, p. 283
278-303_EMCS_B_MM_G4_U09_576965.indd 283
732
2/1/11 2:36 PM
Unit 9 Fractions, Decimals, and Percents
729-733_EMCS_T_TLG1_U09_L02_576906.indd 732
2/3/11 12:47 PM
Teaching Master
ENRICHMENT
Writing and Solving
“Percent-of” Number Stories
PARTNER
ACTIVITY
Name
Date
LESSON
Time
Adding Tenths and Hundredths
92
You can use base-10 blocks to model adding fractions with 10 and 100 in the denominator.
15–30 Min
ELL
Use a long
1
to represent _
10 .
Use a cube
1
to represent _
100 .
53
_
3
23
+_
=
Example: _
10
100
100
+
To apply students’ understanding of fraction and percent
equivalencies, have them write, illustrate, and solve
“percent-of” number stories. Ask students to exchange
stories with a partner, revise if necessary, and solve.
To support English language learners, provide an opportunity for
students to share and revise their writing. For example:
Read problems aloud or have students read their own
problems aloud.
Have students read and comment on each other’s drafts.
Model the problems with longs and cubes. Record your answer.
5
16
_
+_
=
10
100
1.
Adding Tenths and Hundredths
PARTNER
ACTIVITY
100
+
8
2
+_
=
2. _
100
10
82
_
100
+
3.
Write your own problem. Have your partner solve it and record the answer.
Solve. You may use base-10 blocks or any other method.
34
17
_
+_
=
100
100
4.
55
25
+_
=
5. _
100
100
EXTRA PRACTICE
66
_
6.
33
4
_
+_
=
100
10
7.
9
7
_
+_
=
100
10
51
_
100
80
_
100
73
_
100
79
_
100
Math Masters, p. 283A
5–15 Min
283A-283B_EMCS_B_MM_G4_U09_576965.indd 283A
3/6/11 8:18 AM
(Math Masters, pp. 283A, 283B, and 426)
To practice adding fractions with 10 and 100 in the denominator,
have students shade grids or use base-10 blocks to find the sums.
Students may want to use longs and cubes to model the problem.
EXTRA PRACTICE
Finding Equivalent Names
INDEPENDENT
ACTIVITY
5–15 Min
for Fractions
(Math Masters, p. 445)
Teaching Master
To practice finding equivalent decimals and percents for fractions,
have students shade grids and fill in the missing numbers. Use
Math Masters, page 445 to create problems to meet the needs of
individual students, or have students create and solve their
own problems.
Name
LESSON
92
Date
Time
Adding Tenths and Hundredths
continued
You can also model adding tenths and hundredths by shading a grid.
Example:
3
27
57
_
+_
=_
10
100
100
Shade the grid to help find the sum.
8.
9.
5
36
_
+_
=
10
100
86
_
19
4
_
=
+_
100
10
100
10.
59
_
100
11.
6
14
_
+_
=
10
100
74
_
30
3
_
+_
=
100
10
100
12.
6
60
_
_
10 , or 100
13.
64
2
_
+_
=
10
100
84
_
100
9
9
_
+_
=
100
10
99
_
100
Math Masters, p. 283B
283A-283B_EMCS_B_MM_G4_U09_576965.indd 283B
4/11/11 12:17 PM
Lesson 9 2
729-733_EMCS_T_TLG1_U09_L02_576906.indd 733
733
4/11/11 3:19 PM
Name
LESSON
92
Date
Time
Adding Tenths and Hundredths
You can use base-10 blocks to model adding fractions with 10 and 100 in the denominator.
Use a long
1
to represent _
10 .
Use a cube
1
to represent _
100 .
3
23
+_
=
Example: _
10
100
53
_
100
+
Model the problems with longs and cubes. Record your answer.
1.
5
16
_
+_
=
10
100
2.
8
2
_
+_
=
100
10
3.
Write your own problem. Have your partner solve it and record the answer.
4.
34
17
_
+_
=
100
100
5.
55
25
_
+_
=
100
100
6.
33
4
_
+_
=
100
10
7.
9
7
_
+_
=
100
10
Copyright © Wright Group/McGraw-Hill
Solve. You may use base-10 blocks or any other method.
283A
283A-283B_EMCS_B_MM_G4_U09_576965.indd 283A
4/12/11 11:28 AM
Name
LESSON
92
Date
Time
Adding Tenths and Hundredths continued
You can also model adding tenths and hundredths by shading a grid.
Example:
3
27
57
_
+_
=_
10
100
100
Shade the grid to help find the sum.
8.
9.
19
4
_
+_
=
100
10
5
36
_
+_
=
10
100
Copyright © Wright Group/McGraw-Hill
10.
11.
30
3
_
+_
=
100
10
6
14
_
+_
=
10
100
12.
13.
64
2
_
+_
=
10
100
9
9
_
+_
=
100
10
283B
283A-283B_EMCS_B_MM_G4_U09_576965.indd 283B
4/12/11 11:28 AM