lesson 9.2 converting 'easy' fractions to decimals …ellis2020.org/itlg/itlg grade...

Technology Assessment Management System

Journal page 253See the iTLG.

728 Unit 9 Fractions, Decimals, and Percents

Teaching the Lesson materials

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.

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

[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]

Ongoing Assessment: Recognizing Student Achievement Use journal page 253.[Number and Numeration Goal 5]

Ongoing Learning & Practice materialsStudents play Rugs and Fences to practice finding the area and perimeter of a polygon.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students identify and usepatterns to solve percentproblems.

Students write and solve“percent-of” number stories.

Students name a fractionand a percent for the shadedpart of a 10-by-10 grid.

� Teaching Master (Math Masters,p. 283)

� Teaching Aid Master (Math Masters,p. 445)

EXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 2, p. 254� Student Reference Book,

pp. 260 and 261� Study Link Master (Math Masters,

p. 282)� Game Master (Math Masters,

p. 502)� Rugs and Fences Cards

(Math Masters, pp. 498–501)

2

� Math Journal 2, pp. 252, 253, 342,and 343

� Study Link 9 �1 � slate

1

Objectives To reinforce renaming fourths, fifths, and tenths as

decimals and percents; and to introduce solving percent problems

by using equivalent fractions.

� Math Message Follow-Up(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 �1

3020�

is 32%.

There are other fractions, such as �12�, �

14�, �

15�, and �1

10�, that can be

renamed as percents fairly easily. Knowing such equivalenciesoften 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.

That is 50 small squares, or �15000�, or 0.50, or 50% of the

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 illustrateequivalent fraction, decimal, and percent names. Point out thefollowing:

� 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 is 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.

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

252

“Percent-of” Number StoriesLESSON

9 � 2

Date Time

�14�, or 25% is shaded.



Rule

20-problem test

100%


1010

10

55

5

222

44

4

38 39

Alfred, Nadine, Kyla, and Jackson each took thesame math test. There were 20 problems on the test.

1. Alfred missed �12� of the problems. He missed

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

How many problems did he miss? problems

�12� of 20 �

50% of 20 �

2. Nadine missed �14� of the problems. She missed


How many problems did she miss? problems

�14� of 20 �

25% of 20 �

3. Kyla missed �110� of the problems. She missed


How many problems did she miss? problems

�110� of 20 �

10% of 20 �

4. Jackson missed �15� of the problems. He missed


How many problems did he miss? problems

�15� of 20 �

20% of 20 �

Math Journal 2, p. 252

Student Page

Lesson 9�2 729

Getting Started

Math MessageComplete Problem 1 on journal page 252.

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

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

�13060� 0.36, 36%

�18070� 0.87, 87%

�11090� 0.19, 19%

�130� 0.3, 30%

�12� 0.5, 50%

�45� 0.8, 80%

�270� 0.35, 35%

�235� 0.12, 12%

�124� 7.0, 700%


253

Fractions, Decimals, and PercentsLESSON

9 � 2

Date Time

Fill in the missing numbers.Problem 1 has been done for you.

1. Ways of showing :

—4 is shaded. —100

0. %7575



0. %4040



0. %6060



0. %8080



%1001

6. Ways of showing �130�:

—100 is shaded.

0. %3030


—100 is shaded.

0. %7070


—100 is shaded.

0. %9090

�34� �

25�

�35� �

45� �

55�

3 75 2 40

3 4 5 10060 80

Shade the grid. Then fill in the missing numbers.

30 70 90

Rule100%

�

Sample answers:

large square


Student Page

Links to the FutureThe ability to use fractions and percents interchangeably will prove useful in latergrades when students learn to estimate with percents that are not equivalent to“easy” fractions. For example, by the end of sixth grade, most students shouldbe able to apply the following kind of reasoning: The population of Colombia isabout 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 Other “Easy” Fractions(Math Journal 2, p. 253)

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

Ongoing Assessment: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 thegrids. Some students may use shading that involves full and partial squares.

[Number and Numeration Goal 5]

� Completing the Table of 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 EquivalentNames for Fractions on journal pages 342 and 343. Students maywant to check their answers against the chart on the inside frontcover of their journals.

When students have completed this activity, they should haverecorded the equivalencies shown in the chart in the margin.

INDEPENDENT

ACTIVITY

Journal

page 253 �

INDEPENDENT

ACTIVITY

“Easy”Fractions Decimals Percents

�12� 0.50 50%

�14� 0.25 25%

�34� 0.75 75%

�15� 0.20 20%

�25� 0.40 40%

�35� 0.60 60%

�45� 0.80 80%

�110� 0.10 10%

�130� 0.30 30%

�170� 0.70 70%

�190� 0.90 90%

ExamplesExamples

Games

Ama draws the two cards shown here. Ama may chooseto calculate the area or the perimeter.

♦ Ama counts unit squares to find the area. Area � 20 square units.

♦ Ama counts unit lengths around the polygon to find the perimeter. Perimeter � 24 units.

Ama records card number 3 and circles P on her record sheet. She writes the number model 10 � 10 � 2 � 2 � 24, and earns 24 points.

Parker draws the 2 cards shown here.

He finds the area of the polygon by using the formula A � b * h. He records card number 17 and circles A on hisrecord sheet. He writes the number model 5 * 7 � 35, andearns 35 points.

The rug covers an area. The fence goes aroundthe perimeter.

3

Player’sChoice

A or P

17

7

5

Find the area ofthe polygon.

A

Name Date Time

Rugs and Fences Record Sheet

Round Record Circle A Write a Recordthe card (area) or P number model yournumber (perimeter) score

Sample 3 A or P 10 + 10 + 2 + 2 = 24 24

1 A or P

2 A or P

3 A or P

4 A or P

5 A or P

6 A or P

7 A or P

8 A or P

Total Score

132

4

Student Reference Book, p. 261

Student Page

Lesson 9�2 731

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

Adjusting the Activity

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

Students play Rugs and Fences to practice finding the area andperimeter of a polygon. Note that area is reported in square unitsand perimeter in units. When using Polygon Deck C, studentsshould assume that sides that appear to be the same length arethe same length and angles that appear to be right angles areright 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 areaand 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

PARTNER

ACTIVITY

2 Ongoing Learning & Practice 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 2Skill 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 cardfrom each deck and places them faceup on the table. The player finds the area (A) or the perimeter (P) of thepolygon, as directed by the Area and Perimeter card.

♦ If a “Player’s Choice” card is drawn, the player may chooseto 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 thepolygon will be found.

4. A player records a turn on his or her Record Sheet. Theplayer records the polygon card number, circles A (area) or P (perimeter), and writes a number model used to calculatethe area or perimeter. The solution is the player's score forthe round.

5. The player with the higher total score at the end of8 rounds is the winner.

Games

1 2

25 26

10 8 10

12

54

3

39

6

2

2

2

6

4

41

4.5

4.5

8

6

1 1

1

Find the area ofthe polygon.

Player’sChoice

Opponent’sChoice

Find the perimeterof the polygon.

A

A or P A or P

P

Examples from PolygonDecks A, B, and C

There are 4 kinds of Areaand Perimeter cards.

Student Reference Book, p. 260

Student Page


STUDY LINK

9 �2 Coins as Percents of $1 38 39

Name Date Time

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

Write the decimal that shows what part of $1 is 1 penny.

What percent of $1 is 1 penny? %

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

Write the decimal that shows what part of $1 is 1 nickel.

What percent of $1 is 1 nickel? %

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

Write the decimal that shows what part of $1 is 1 dime.

What percent of $1 is 1 dime? %

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

Write the decimal that shows what part of $1 is 1 quarter.

What percent of $1 is 1 quarter? %

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

Write the decimal that shows what part of $1 is 1 half-dollar.

What percent of $1 is 1 half-dollar? %

6. Three quarters (75¢) is �34� of $1. 7. Two dimes (20¢) is �1

20� of $1.

Write the decimal. Write the decimal.

What percent of $1 is What percent of $1 is

3 quarters? % 2 dimes? %2075

50

225

410

105

201

100 �1100�

�110�, or �1

1000�

�14�, or �1

2050�

�12�, or �1

5000�

8. � 748 º 6 9. 51 º 90 � 10. � 28 º 90325,2844,5904,488Practice

�210�, or �1

500�

0.01

0.05

0.10

0.25

0.50

0.75 0.20

Math Masters, p. 282

Study Link Master

Math Boxes LESSON

9 � 2

Date Time

5. Find the area and perimeter of therectangle. Include the correct units.

Area �

Perimeter � 22 in.

6. What temperature is it?

°F�10

1. Complete the table with equivalent names.

3. Complete.

a. 3 yd 2 ft � ft

b. 6 yd 1 ft � ft

c. in. � 2 yd

d. ft � 5 yd 2 ft

e. 25 ft � yd ft

f. ft in. � 30 in.6218

1772

1911

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 Internetare the, and about 1.68% of the words areand. About what percent of all words onthe Internet are either the or and? Choosethe best answer.

5.71%

5.7%

570%

57%61 62

0.20

0.300.90�1

90�

�45�

90%

20%80%30%�1

30�

Fraction Decimal Percent

0.80

�15�

28 in2

–10

0

10

–20

°F

�182�, or �23�

�142�, or �13�

7"

4"


Student Page

� Math Boxes 9�2(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 be252 in2. It would be 9 times as large as the area of the originalrectangle.

� Study Link 9�2(Math Masters, p. 282)

Home Connection For each of several coins, studentsidentify what fraction of $1, decimal part of $1, and percent of $1 that coin represents.

� Exploring Percent Patterns(Math Masters, p. 283)

To explore the relationship between fractions and percents, havestudents identify and use patterns to solve percent problems. Askstudents to describe how they used the patterns. For example:

If there are 20 per 100, then there are

� 2 per 10. 10 is �110� 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 20is 200, so 20 per 100 is the same as 200 per 1,000.

� 4 per 20. �120�, �1

2000�, �1

2,00000� are all names for �

15�. 4 is �

15� of 20, so 4 per

20 is the same as 20 per 100.

� 40 per 200. �24000� � �

15�

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

� Writing and Solving “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 forstudents 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.

� Finding Equivalent Names 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. UseMath Masters, page 445 to create problems to meet the needs ofindividual students, or have students create and solve their own problems.

5–15 Min

INDEPENDENT

ACTIVITYEXTRA PRACTICE

15–30 Min

PARTNER

ACTIVITYENRICHMENT LESSON

9 �2

Name Date Time

Percent Patterns

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

per 10. per 1,000.

per 20. 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

per 10. per 1,000. per 10. per 1,000.

per 20. per 200. per 20. per 200.



per 10. per 1,000. per 10. per 1,000.

per 20. per 200. per 20. per 200.120121601660068008

60640430032002

10010

5005

Try This



per 10. per 1,000. per 10. per 1,000.

per 20. per 200. per 20. per 200.2402415015127507.5 1,200


Teaching Master

Lesson 9�2 733

Name Date Time

Fractions, Decimals, and Percents

Fill in the missingnumbers. If the grid is not shaded, thenshade the grid.


0. %


0. %

is shaded.4 100


0. %


0. %


0. %


0. %


0. %


0. %

large square

100%

is shaded.5 100

is shaded.5 100

is shaded.5 100

is shaded.5 100

is shaded.10 100

is shaded.10 100

is shaded.10 100


Teaching Aid Master

lesson 9.2 converting 'easy' fractions to decimals …ellis2020.org/itlg/itlg grade...

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