Converting “Easy” Fractions to Decimals and Percents€¢ Find the fraction and percent of a collection and a region. [Number and Numeration Goal 2] • Solve “percent-of”

$Page 1: Converting “Easy” Fractions to Decimals and Percents€¢ Find the fraction and percent of a collection and a region. [Number and Numeration Goal 2] • Solve “percent-of”$
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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

728 Unit 9 Fractions, Decimals, and Percents

��

Converting “Easy” Fractions to Decimals and Percents

Objectives To reinforce renaming fourths, fifths, and tenths as

decimals and percents; and to introduce solving percent

problems by using equivalent fractions.

d

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 62, 63, 153, 154

Key Concepts and Skills• Find the fraction and percent of a collection

and a region.

[Number and Numeration Goal 2]

• Solve “percent-of” problems.


• Rename fractions with denominators of 100

as decimals.


• Find equivalent names for percents.


Key ActivitiesStudents name shaded parts of 10-by-10

grids as fractions, decimals, and percents.

The shaded parts are all “easy” fractions:

fourths, fifths, and tenths.

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]

MaterialsMath Journal 2, pp. 252, 253, 342, and 343

Study Link 9�1

slate

Playing Rugs and FencesStudent 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�2Math Journal 2, p. 254

Students practice and maintain skills

through Math Box problems.

Study Link 9�2Math Masters, p. 282

Students practice and maintain skills

through Study Link activities.

READINESS

Exploring Percent PatternsMath Masters, p. 283

Students identify and use patterns to solve

percent problems.

ENRICHMENTWriting and Solving “Percent-of” Number StoriesStudents write and solve “percent-of”

number stories.

EXTRA PRACTICEAdding Tenths and HundredthsMath 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 FractionsMath Masters, p. 445

Students name a fraction and a percent for

the shaded part of a 10-by-10 grid.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

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Alfred, Nadine, Kyla, and Jackson each took the

same math test. There were 20 problems on the test.

1. Alfred missed 1

_

2 of the problems. He missed

0.50 of the problems. That is 50% of the problems.

How many problems did he miss? problems

1

_

2 of 20 =

50% of 20 =

2. Nadine missed 1

_

4 of the problems. She missed


How many problems did she miss? problems

1

_

4 of 20 =

25% of 20 =

3. Kyla missed 1

_

10 of the problems. She missed


How many problems did she miss? problems

1

_

10 of 20 =

10% of 20 =

4. Jackson missed 1

_

5 of the problems. He missed


How many problems did he miss? problems

1

_

5 of 20 =

20% of 20 =

“Percent-of” Number StoriesLESSON

9�2

Date Time

1

_ 4 , or 25% is shaded.

1


1


Rule

20-problem test

100%

1


10

10

10

5

5

5

2

2

2

4

4

4

38 39

248-273_EMCS_S_MJ2_G4_U09_576426.indd 252 2/1/11 1:49 PM

Math Journal 2, p. 252

Student Page

Lesson 9�2 729

Getting Started

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 252)

Remind students that it is easy to rename a fraction as a percent when the denominator is 100. For example, another name for 32 _ 100 is 32%.

There are other fractions, such as 1 _ 2 , 1 _ 4 , 1 _ 5 , and 1 _ 10 , that can be 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 1 _ 2 and ask themselves, “What is 1 _ 2 of 20?”

Some students may reason: 1 _ 2 of the 10-by-10 grid is shaded. That is 50 small squares, or 50 _ 100 , or 0.50, or 50% of the 10-by-10 grid. 50% of 20 is the same as 1 _ 2 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:

� The whole is the 20-problem test—100% of the test.

� The whole test is represented by the 10-by-10 grid.

� The 10-by-10 grid can be divided into 20 equal parts (rectangles), each representing 1 problem on the test.

Each rectangle, consisting of 5 small squares, represents 1 problem on the test.

� The 10-by-10 grid is also divided into 100 small squares; each small square is 1 _ 100 , or 1%, of the 10-by-10 grid.

Have students solve Problems 2–4 with a partner.

Math MessageComplete Problem 1 on journal page 252.

Study Link 9�1 Follow-UpHave partners compare answers. Ask volunteers to share different solutions for Problems 10–12.

For Problems 13 and 14, you might have students draw number lines and identify the positions of the fractions.

Mental Math and ReflexesWrite fractions on the board. For each fraction, students write the equivalent decimal and percent on their slates. Have students explain their strategies for the problems. Suggestions:

36 _ 100

0.36, 36%

87 _

100 0.87, 87%

19 _

100 0.19, 19%

3 _ 10

0.3, 30%

1 _ 2 0.5, 50%

4 _ 5 0.8, 80%

7 _ 20

0.35, 35%

3 _

25 0.12, 12%

14 _

2 7.0, 700%

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Fractions, Decimals, and PercentsLESSON

9�2

Date Time

Fill in the missing numbers.

Problem 1 has been done

for you.

6. Ways of showing 3

_

10 :

—100

is shaded.

0. 30

30 %


_

10 :

—100

is shaded.

0. 70

70 %


_

10 :

—100

is shaded.

0. 90

90 %

1. Ways of showing :

—4 is shaded. —

100

0. 75 75 %

3 _

4

3 75


—5 is shaded. —

100

0. 40

40 %

2 _ 5

2 40

3


—5 is shaded. —

100

1

100%

5 _ 5

5 100


—5 is shaded. —

100

0. 60

60 %

3 _ 5

60


—5 is shaded. —

100

0. 80

80 %

4 _ 5

4 80

Shade the grid. Then fill in the missing numbers.

30 70 90

Rule100%

�

Sample answers:

large square



Student Page

Links to the Future

“Easy” Fractions Decimals Percents

1

_ 2 0.50 50%

1 _ 4 0.25 25%

3 _

4 0.75 75%

1 _ 5 0.20 20%

2 _ 5 0.40 40%

3 _

5 0.60 60%

4 _ 5 0.80 80%

1 _ 10

0.10 10%

3 _

10 0.30 30%

7 _ 10

0.70 70%

9 _

10 0.90 90%

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 1

_ 4 , and

1

_ 4 of 40 million is 10 million, about

10 million Colombians live in rural areas.

� Finding Equivalent Names for INDEPENDENTACTIVITY

Other “Easy” Fractions(Math Journal 2, p. 253)

Students find equivalent names for several more “easy” fractions on journal page 253.

Ongoing Assessment: Journal

page 253 �Recognizing Student Achievement

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.


� Completing the Table of INDEPENDENTACTIVITY

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.


Lesson 9�2 731

Adjusting the Activity

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)

□ 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 theperimeters and areas of polygons.

Directions

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.

♦ 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.

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.

Examples from Polygon Decks A, B, and C

There are 4 kinds of Area and Perimeter cards.

Student Reference Book, p. 260

Student Page

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

14 16 16 30 64 36 46 48 52

15 28 22 31 20 25 47 60 32

16 18 18 32 216 66 48 160 70

Fraction Decimal Percent

0.80

Math Boxes LESSON

9�2

Date Time

5. Find the area and perimeter of the

rectangle. Include the correct units.

Area =

Perimeter = 22 in.

6. What temperature is it?

− 10 °F

1. Complete the table with equivalent names.

3. Complete.

a. 3 yd 2 ft = 11 ft

b. 6 yd 1 ft = 19 ft

c. 72 in. = 2 yd

d. 17 ft = 5 yd 2 ft

e. 25 ft = 8 yd 1 ft

f. 2 ft 6 in. = 30 in.

4. Zena earned $12. She spent $8.

a. What fraction of her

earnings did she spend?

b. What fraction did

she have left?

c. The amount she spent is how

many times as much as the

amount she saved?

2 times

34–37

44

139

129

131 133

2. 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.

5.71%

5.7%

570%

57%61 62

0.20

0.30

0.90 90%

20%

80%

30% 3

_

10

1

_

5

28 in2

–10

0

10

–20

°F

8

_ 12 , or

2

_ 3

4

_ 12 , or

1

_ 3

7"

4"

4

_ 5

9

_ 10



Student Page

2 Ongoing Learning & Practice

� Playing Rugs and Fences PARTNER ACTIVITY

(Student Reference Book, pp. 260 and 261; Math Masters, pp. 498–502)

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.

.

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.

� 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 � K I N E S T H E T I C � T A C T I L E � V I S U A L



STUDY LINK

9 �2 Coins as Percents of $1 38 39

Name Date Time

1. How many pennies in $1? 100 What fraction of $1 is 1 penny?

Write the decimal that shows what part of $1 is 1 penny. 0.01 What percent of $1 is 1 penny? 1 %

2. How many nickels in $1? 20 What fraction of $1 is 1 nickel?

Write the decimal that shows what part of $1 is 1 nickel. 0.05 What percent of $1 is 1 nickel? 5 %

3. How many dimes in $1? 10 What fraction of $1 is 1 dime?

Write the decimal that shows what part of $1 is 1 dime. 0.10 What percent of $1 is 1 dime? 10 %

4. How many quarters in $1? 4 What fraction of $1 is 1 quarter?

Write the decimal that shows what part of $1 is 1 quarter. 0.25 What percent of $1 is 1 quarter? 25 %

5. How many half-dollars in $1? 2 What fraction of $1 is 1 half-dollar?

Write the decimal that shows what part of $1 is 1 half-dollar. 0.50 What percent of $1 is 1 half-dollar? 50 %

6. Three quarters (75¢) is 3

_ 4 of $1. 7. Two dimes (20¢) is

2

_ 10

of $1.

Write the decimal. 0.75 Write the decimal. 0.20 What percent of $1 is What percent of $1 is

3 quarters? 75 % 2 dimes? 20 %

8. = 748 º 6 9. 51 º 90 = 10. = 28 º 9034,488 4,590 25,284

Practice

1

_ 100

1 _ 20 , or 5

_ 100

1

_ 10 , or 10

_ 100

1 _ 4 , or 25

_ 100

1 _ 2 , or 50

_ 100

278-303_EMCS_B_MM_G4_U09_576965.indd 282 2/1/11 2:36 PM


Study Link Master

LESSON

9 �2

Name Date Time

Percent Patterns

py

gg

p

Complete each set of statements. Use grids or base -10 blocks,

or draw pictures to help you. Look for patterns in your answers.

Example:

50% is the same as 50 per 100.

If there are 50 per 100, then there are

5 per 10. 500 per 1,000.

10 per 20. 100 per 200.

1. 20% is the same as 20 per 100. 2. 30% is the same as 30 per 100.

If there are 20 per 100, then there are If there are 30 per 100, then there are

2 per 10. 200 per 1,000. 3 per 10. 300 per 1,000.

4 per 20. 40 per 200. 6 per 20. 60 per 200.



8 per 10. 800 per 1,000. 6 per 10. 600 per 1,000.

16 per 20. 160 per 200. 12 per 20. 120 per 200.

Try This



7.5 per 10. 750 per 1,000. 12 per 10.1,200 per 1,000.

15 per 20. 150 per 200. 24 per 20. 240 per 200.

278-303_EMCS_B_MM_G4_U09_576965.indd 283 2/1/11 2:36 PM


Teaching Master

� Math Boxes 9�2 INDEPENDENTACTIVITY

(Math Journal 2, p. 254)

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.

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.

� Study Link 9�2 INDEPENDENTACTIVITY

(Math Masters, p. 282)

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 PARTNER ACTIVITY

� Exploring Percent Patterns 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:

If there are 20 per 100, then there are

� 2 per 10. 10 is 1 _ 10 of 100. 1 _ 10 of 20 is 2, so 20 per 100 is the same as 2 per 10.

� 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.

� 4 per 20. 2 _ 10 , 20 _ 100 , 200 _ 1,000 are all names for 1 _ 5 . 4 is 1 _ 5 of 20, so 4 per 20 is the same as 20 per 100.

� 40 per 200. 40 _ 200 = 1 _ 5


Lesson 9�2 733

Name Date Time

Adding Tenths and HundredthsLESSON

9�2

You can use base-10 blocks to model adding fractions with 10 and 100 in the denominator.

Use a long to represent 1 _ 10 .

Use a cube to represent 1 _ 100 .

Example: 3 _ 10 + 23 _ 100 =

+

Model the problems with longs and cubes. Record your answer.

1. 5 _ 10 + 16 _ 100 = 66

_ 100 +

2. 2 _ 100 + 8 _ 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.

4. 34 _ 100 + 17

_ 100 = 51 _ 100

5. 55 _ 100 + 25

_ 100 = 80 _ 100

6. 33 _ 100 + 4 _ 10 = 73

_ 100 7. 9

_ 100 + 7 _ 10 = 79 _ 100

53 _ 100

283A-283B_EMCS_B_MM_G4_U09_576965.indd 283A 3/6/11 8:18 AM

Math Masters, p. 283A

Teaching Master

Name Date Time

Adding Tenths and Hundredths continuedLESSON

9�2

You can also model adding tenths and hundredths by shading a grid.

Example:

3 _ 10 + 27 _ 100 = 57

_ 100

Shade the grid to help find the sum.

8. 9.

5 _ 10 + 36 _ 100 = 86

_ 100 19 _ 100 + 4 _ 10 = 59 _ 100

10. 11.

6 _ 10 + 14 _ 100 = 74

_ 100 30 _ 100 + 3 _ 10 = 6 _ 10 , or 60

_ 100 12. 13.

2 _ 10 + 64 _ 100 = 84

_ 100 9 _ 100 + 9 _ 10 = 99 _ 100

283A-283B_EMCS_B_MM_G4_U09_576965.indd 283B 4/11/11 12:17 PM

Math Masters, p. 283B

Teaching Master

ENRICHMENT PARTNER ACTIVITY

� Writing and Solving 15–30 Min

“Percent-of” Number Stories 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.

EXTRA PRACTICE PARTNER ACTIVITY

� Adding Tenths and Hundredths (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 INDEPENDENTACTIVITY

� Finding Equivalent Names 5–15 Min

for Fractions(Math Masters, p. 445)

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.

ELL

5–15 Min


Name Date Time

283A

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

Adding Tenths and HundredthsLESSON

9�2

You can use base-10 blocks to model adding fractions with 10 and 100 in the denominator.

Use a long to represent 1

_ 10

.

Use a cube to represent 1

_ 100

.

Example: 3

_ 10

+ 23

_ 100

=

+

Model the problems with longs and cubes. Record your answer.

1. 5

_ 10

+ 16

_ 100

=

2. 2

_ 100

+ 8

_ 10

=

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.

4. 34

_ 100

+ 17

_ 100

=

5. 55

_ 100

+ 25

_ 100

=

6. 33

_ 100

+ 4

_ 10

=

7. 9

_ 100

+ 7

_ 10

=

53 _ 100

283A-283B_EMCS_B_MM_G4_U09_576965.indd 283A283A-283B_EMCS_B_MM_G4_U09_576965.indd 283A 4/12/11 11:28 AM4/12/11 11:28 AM

Name Date Time

283B

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

Adding Tenths and Hundredths continuedLESSON

9�2

You can also model adding tenths and hundredths by shading a grid.

Example:

3

_ 10

+ 27

_ 100

= 57

_ 100

Shade the grid to help find the sum.

8. 9.

5

_ 10

+ 36

_ 100

= 19 _ 100 +

4

_ 10

=

10. 11.

6

_ 10

+ 14

_ 100

= 30 _ 100

+ 3

_ 10

=

12. 13.

2

_ 10

+ 64

_ 100

= 9 _ 100 +

9

_ 10

=

283A-283B_EMCS_B_MM_G4_U09_576965.indd 283B283A-283B_EMCS_B_MM_G4_U09_576965.indd 283B 4/12/11 11:28 AM4/12/11 11:28 AM

Documents

Converting “Easy” Fractions to Decimals and Percents€¢ Find the fraction and percent of a collection and a region. [Number and Numeration Goal 2] • Solve “percent-of”