722 Unit 9 Fractions, Decimals, and Percents

Teaching the Lesson materials

Key ActivitiesStudents 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 fractionname and a decimal name.

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 Vocabularypercent • 100% box

Ongoing Assessment: Informing Instruction See page 724.

Ongoing Learning & Practice materialsStudents 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]

Differentiation Options materials

Students shade 50% of a square in different ways.

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)

ELL SUPPORTREADINESS

3

� Math Journal 2, p. 251� Student Reference Book, p. 243� Study Link Masters (Math Masters,

pp. 279 and 280)� Teaching Master (Math Masters,

p. 278)� Fraction Match Cards (Math

Masters, pp. 473–476)

2

� Math Journal 2, pp. 248–250 � Study Link 8�6 (Math Masters,

p. 262)� slate

1

Objectives To guide the use of percents in describing

real-life situations; and to reinforce naming equivalencies

among fractions, decimals, and percents.

Technology Assessment Management System

Math Masters, page 278 Problems 1 and 2See the iTLG.

� Math Message Follow-Up(Math Masters, p. 262)

Have students share the examples they collected of uses ofpercents. 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.”

� “Reed got �15000� 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 were cast. (Since �1

5000� equals �

12�, Reed got half the votes cast.) If it

were a club election with only 60 votes cast, then Reed would havegotten 50% of 60 votes, or 30 votes. If it were an election formayor with 30,000 votes cast, then Reed would have gotten 50%of 30,000 votes, or 15,000 votes.

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

STUDY LINK

8�6 Percents in My World

40

Name Date Time

Percent means “per hundred” or “out of a hundred.” 1 percent means �1100� or 0.01.

“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, andencyclopedias. Ask people at home to help. Write the examples below. Also tell whereyou 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 SouthportHigh School say they plan to attend college next year.

Answers vary.

Math Masters, p. 262

Study Link Master

Lesson 9�1 723

Getting Started

Math MessageBe ready to discuss theexamples of percents you collected for Study Link 8-6.

Mental Math and ReflexesWrite fractions on the board. For each fraction, students write the equivalentdecimal and percent on their slates. Suggestions:

�11050� 0.15, 15%

�15050� 0.55, 55%

�12090� 0.29, 29%

�1300� 0.03, 3%

�110� 0.1, 10%

�170� 0.7, 70%

�22� 1, 100%

�15� 0.20, 20%

�34� 0.75, 75%

724 Unit 9 Fractions, Decimals, and Percents

248

Many Names for PercentsLESSON

9 �1

Date Time

Your teacher will tell you how to fill in the percent examples.

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.

Example: Last season, Duncan made 62 percent of his basketball shots.

That is out of every 100.

Fraction name:

Decimal name:

1. Percent Example:

That is out of every 100.

Fraction name:

Decimal name:

2. Percent Example:

That is out of every 100.

Fraction name:

Decimal name:

0.62

62

62

100

100

100

Answers vary.38 39

all ofDuncan’s shots

100%

100%

100%

Math Journal 2, p. 248

Student Page

Remind students that, just as with fractions, a percent alwaysrepresents a percent of something. The “something” is the whole100%, 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 ofvotes cast is 100 percent of the votes. The 100% box serves thesame purpose for percents as the whole box does for fractions: Ithelps focus students’ attention on the whole, or 100%.

Language Arts Link The word percent comes from theLatin per centum: Per means “for,” and centum means “one

hundred.” Ask students if they can think of other words that begin with cent-. Sample answers: Cent (�1

100� of a dollar), century

(100 years), centennial (100th anniversary), centipede (looks like it has 100 legs), centimeter (�1

100� of a meter)

� Making Up Equivalent 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 small square is �1

100�, or 1%, of the whole. A decimal name

for �1100� 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.

� Had Duncan taken 100 shots, he would have made 62 shots. This can also be stated as a fraction, �1

6020� of his shots, or as a

decimal, 0.62 of his shots.

Ongoing Assessment: Informing InstructionWatch for students who mistakenly think Duncan took exactly 100 shots andmade 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 collectedand discussed during the Math Message Follow-Up. Work as aclass to complete Problems 1 and 2 on journal page 248. Havestudents write a brief description for each percent example. Thenfill in the 100% box, shade the grid to show the percent, and writethe fraction and decimal names for the percent.

WHOLE-CLASS

ACTIVITY

250

Many Names for Percents continuedLESSON

9 �1

Date Time

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.

6. Example:

That is out of every 100.

Fraction name:

Decimal name:

What would Mr. Thompson pay for a bicycle that had been selling for $300?

7. Example: A carpet store ran a TV commercial that said:“Pay 20% when you order. Take 1 full year to pay the rest.”

That is out of every 100.

Fraction name:

Decimal name:

Mrs. Shields wants to order a $1,200 carpet. How much must she pay

when she orders it? $240

0.20

2020

$180

0.40

4040

100

100

Sale—40% OffEverything Must Go!

original price

100%

cost of carpet

100%

Math Journal 2, p. 250

Student Page

249

Many Names for Percents continuedLESSON

9 �1

Date Time

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.

3. Example: 12% of the students in Marshall School are left-handed.

That is out of every 100.

Fraction name:

Decimal name:

4. Example: Sarah spelled 80% of the words correctly on her last test.

That is out of every 100.

Fraction name:

Decimal name:

5. Example: Cats sleep about 58% of the time.

That is out of every 100.

Fraction name:

Decimal name: 0.58

5858

0.80

8080

0.12

1212

100

100

100

all students atMarshall School

100%

all minutesin 1 day

100%

100%

all words onthe test

Math Journal 2, p. 249

Student Page

Lesson 9�1 725

Adjusting the ActivityJournal pages 248–250 prompt students to provide an equivalent

hundredths-fraction for the percent example. Students may wonder why they need to write a fraction such as �1

2050� when it can be written in simplest form

as �14�. 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 � V I S U A L

� Finding Equivalent Names 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 todecide? For Problems 5–7, students may have difficulty decidingwhat 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 anylonger period (week, month, year). Any period shorter than 1 day could pose a problem. For example, cats are much morelikely 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.”

PARTNER

ACTIVITY

726 Unit 9 Fractions, Decimals, and Percents

251

Math Boxes LESSON

9 �1

Date Time

5. Angle RST is an (acute orobtuse) angle.

The measure of �RST is .�127

6. Use a straightedge to draw the line of symmetry.

1. In which situation below do you need toknow the area? Choose the best answer.

finding the distance around a pool

buying a wallpaper border for yourbedroom

carpeting the living room

fencing a yard

3. Multiply. Use a paper-and-pencil algorithm.

� 58 � 764,4084. Find the approximate latitude and longitude

of these Region 2 cities.

a. Dublin, Ireland latitude �

longitude �

b. Rome, Italy latitude�

longitude� E12N42W7

N53

162–166

272 273

109

18 19

141–143

2. Complete.

131 133

in out

�170�

�110�

�190�

�12

�

�45

�

�25

�

�130�

�35

�

�130�

�55�, or 1

R

S T

obtuse

Rule:

��120�, or��

15�

Math Journal 2, p. 251

Student Page

� Playing Fraction Match(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.

After students have had a chance to play several rounds, ask themto complete Math Masters, page 278.

Ongoing Assessment:Recognizing Student Achievement

Use Math Masters, page 278, Problems 1 and 2 to assess students’ ability tofind equivalent fractions. Students are making adequate progress if they indicate that �

68� and �1

92� are equivalent to �

34�. Some students may be able to name additional

fractions that are equivalent to �34� in Problem 3.

[Number and Numeration Goal 5]

� Math Boxes 9�1(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(Math Masters, pp. 279 and 280)

Home Connection Students name equivalent fractions,decimals, and percents and shade grids to represent them.Students complete the survey on the second page of theStudy Link to collect data for an activity in Lesson 9-6.

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

Math MastersPage 278 �Problems 1 and 2

SMALL-GROUP

ACTIVITY

2 Ongoing Learning & Practice

LESSON

9 �1

Name Date Time

Playing Fraction Match

1. Katrina is playing Fraction Match. The target card is �34�. She has the following

cards in her hand. Circle the card she may play.

2. Suppose she had 3. Imagine that a WILD card allowed a WILD card in her Katrina to name any fraction hand. Write a equivalent to �

34�. Write two fractions

different fraction, that she could name. Sampleequivalent to answers:�34�, that she could name.

�17050��

1126�

1�2 1

�2

1�2

2�3 2

�3

2�3

4�5 4

�5

4�5

6�8 6

�8

6�8

3�9 3

�9

3�9

WILDName an equivalent

fraction with a denominator of

2, 3, 4, 5, 6, 8, 9,10, or 12.

WILD WILD

�

��192�

Math Masters, page 278

� Finding 50% of a Square(Math Masters, p. 281)

To explore equivalent names for percents, have students shade50% of grids in different ways and explain how they know theshaded portions represent 50%.

� Creating a Percents All Around Museum(Math Masters, p. 262)

To provide language support for percents, have students displaythe examples of percents collected for Study Link 8-6 in a PercentsAll Around Museum. Ask students to describe the numbers theysee 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.

15–30 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

10. Shade more than �11000� and less than �1

3000� of the grid.

Write the value of the shaded part as a decimal and a percent.

Decimal:

Percent:

11. Shade more than 25% and less than 60% of the grid. Write the value of the shaded part as a decimal and a percent.

Decimal:

Percent:

12. 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: 70%0.70

40%0.40

20%0.20

STUDY LINK

9 �1 Fractions, Decimals, and Percents

Name Date Time

Rename each decimal as a fraction and a percent.

1. 0.90 � —100 � % 2. 0.53 � —100 � % 3. 0.04 � —100 � %

Rename each percent as a fraction and a decimal.

4. 60% � —100 � . 5. 25% � —100 � . 6. 7% � —100 � .

Rename each fraction as a decimal and a percent.

7. �15000� � . � % 8. �1

7050� � . � % 9. �1

600� � . � %60607575050500

07072502560060

445353909061 62

Practice

Order the fractions from smallest to largest.

13. �36�, �

33�, �

35�, �

37� 14. �

23�, �

67�, �

12�, �

1290�

�12�, �

23�, �

67�, �

1290��

37�, �

36�, �

35�, �

33�

Sample answers

Sample answers

Sample answers

Math Masters, p. 279

Study Link Master

STUDY LINK

9 �1 Trivia Survey

70

Name Date Time

Conduct the survey below. The results will be used in Lesson 9-6.

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.

Question 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.)

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.)

Answers vary.

Math Masters, p. 280

Study Link Master

Lesson 9�1 727

LESSON

9 �1

Name Date Time

50% of a Square

Benito and Silvia each shaded 50% of a grid.

1. Do you think they shaded the grids correctly? Explain your reasoning.

Sample answer: Yes. Both grids have 100 squares. Half, or �15000�,

are shaded, which is 50%.

2. Shade 50% of the grids below in different ways. Explain how you knowyou have shaded 50%. Sample answers:a. b.

I divided the grid into 8 equal parts and then shaded 4 of them. �

48� � �1

5000� � 50%.

p

3. Shade 50% of the grid. Explain how you know you have shaded 50%.

Sample answers:

Try This

Half, or 50%, of 100 is 50. I shaded 10 groups of 5 squares for a total of 50 squares.

There are 50 squares in the grid. 25 are shaded. �1

2050� � �

12� � 50%.

Math Masters, p. 281

Teaching Master