Technology Assessment Management System

Math Boxes, Problem 4See the iTLG.

Teaching the Lesson materials

Key ActivitiesStudents use the percent key on a calculator to rename fractions as percents. They rename fractions as decimals by dividing, and they are shown that a decimal can be easily renamed as a percent by multiplying it by 100. Students solve number stories involving discountsexpressed as percents.

Key Concepts and Skills• Solve number stories involving discounts. [Number and Numeration Goal 2]• Name the whole, or the ONE. [Number and Numeration Goal 2]• Use a calculator to rename fractions as percents. [Number and Numeration Goal 5]• Rename any decimal as a percent. [Number and Numeration Goal 5]

Key Vocabulary regular price • list price • discount • percent of discount • fraction of discount • sale price • discounted price

Ongoing Assessment: Informing Instruction See page 740.

Ongoing Learning & Practice materialsStudents create a bar graph using cellular-telephone-use data.

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

Ongoing Assessment: Recognizing Student Achievement Use journal page 259. [Number and Numeration Goal 2]

Differentiation Options materials

Students use counters to solve“percent-of” problems.

Students solve number stories inwhich they comparediscounts for twoitems.

Students practicesolving problemsinvolving percents.

Students discussvocabulary used indiscount number stories.

� Teaching Masters (Math Masters,pp. 286 and 287)

� 5-Minute Math, pp. 103, 176, 187,and 196

� counters� store catalogs or advertisements

ELL SUPPORTEXTRA PRACTICEENRICHMENTREADINESS

3

� Math Journal 2, pp. 258 and 259� Student Reference Book, p. 302� Study Link Master (Math Masters,

p. 285)

2

� Math Journal 2, pp. 256 and 257� Study Link 9�3 � calculator� overhead calculator (optional)� slate

1

Objectives To reinforce renaming fractions as percents using

a calculator; and to introduce solving number stories involving

discounts expressed as percents.

Lesson 9�4 739

740 Unit 9 Fractions, Decimals, and Percents

Getting Started

Math MessageExperiment with the percent key on your calculator. Find a way to rename �

14� as a percent. Write your

method on a half sheet of paper.

Study Link 9�3 Follow-Up Have students compare answers. Ask volunteers toshare some of the problems they made up.

Mental Math and ReflexesPose “percent-of ” problems. Have students explain theirstrategies. Suggestions:

50% of 60 30100% of 60 6010% of 60 620% of 60 12

25% of 40 1075% of 40 3025% of 32 875% of 32 24

20% of 150 3040% of 110 445% of 20 115% of 10 1.5

Decimal 100 � decimal Percent

0.67 67 67%

0.375 37.5 37.5%

0.1666 16.66 16.66%

4. Use a drawing and number models to explain how you found theregular airfare when you knew $75 was 25% of the regular airfare.

256

Discount Number StoriesLESSON

9 �4

Date Time

1. A store is offering a discount of 10% on all items. This means that you save �110� of

the regular price. Find the sale price of each item below. The sale price is theamount you pay after subtracting the discount from the regular price.

Sale PriceItem Regular Price

Discount(Subtract:(10% of regular price)

regular price – discount)

CD player $140 $14 $126Giant screen TV $1,200 $120 $1,080Radio $80 $8 $72DVD player $30 $3 $27

2. Use a drawing and number models to explain how youfound the discount and sale price for the radio.

$80Sample picture:

10%90%

Sample answer: 10% is �110�. Cut $80 into 10

parts.10% of $80 is $8. �190� is left. 9� $8 � $72.

Sample answer: 25% � �14�. If �

14� � $75,

then �44� � 4 � $75, or $300.

3. An airline offers a 25% discount on the regular airfare for ticketspurchased at least 1 month in advance. Find the sale price ofeach ticket below.

Sale PriceRegular Airfare Discount (Subtract:

(25% of regular airfare)regular airfare – discount)

$400 $100

$240

$75$300$60 $180

$300

$225

$7525%

Sample picture:

38 39

Math Journal 2, p. 256

Student Page

� Math Message Follow-UpAsk a volunteer to use an overhead calculator (if available) todemonstrate how to use the percent key to rename fractions aspercents. Write the keystrokes on the board to support Englishlanguage learners. Then have students practice with a few “easy” fractions.

TI-15: 1 4 Display: 25

Casio fx-55: 1 4 Display: 25

The percent key does NOT have to be used to rename fractions aspercents. Remind students that they can convert any fraction to adecimal by dividing the numerator by the denominator. Once theyhave the decimal name, it is easy to write the percent name.

� To rename �14� as a percent, divide 1 by 4 to get 0.25.

This is �12050�, or 25%.

� To rename �37

35� as a percent, divide 33 by 75 to get 0.44.

This is �14040�, or 44%.

You can use this rule to rename any decimal as a percent: To convert a decimal to a percent, multiply the decimal by 100.

Ongoing Assessment: Informing InstructionWatch for students who notice a pattern when multiplying a decimal by 100. Ask them to explain why the decimal moves two places to the right.

÷

WHOLE-CLASS

ACTIVITY

1 Teaching the Lesson

257

Discount Number Stories continuedLESSON

9 �4

Date Time

5. The regular price of a swing set is $400. Mrs. Lefevre received a 30% discount because she ordered it during the Big Spring Sale.

a. How much did she save?

b. How much did she pay?

c. Explain how you solved the problem.

6. You can pay for a refrigerator by making 12 payments of $50 each. Or you can save 25% if you pay for it all at once.

a. How much will the refrigerator cost if you pay for it all at once?

b. Explain how you solved the problem.

7. Write your own discount number story. Ask a partner to solve it.

Answers vary.

$450

$280$120

If the discount is 10%, then 10%, or �110�, of $400 is $40. A 30%

discount is 3 times as much as a 10% discount, so 3 � $40 � $120.Then I subtracted $120 from $400 and got $280.

If I make payments, it will cost 12 � $50, which is $600.

$600, or $150. Then I subtracted $150 from $600 and got $450.

Try This

Paying for it all at once, I’ll get a 25% discount. 25% is �14� of

Sample answer:

Sample answer:

Math Journal 2, p. 257

Student Page

Lesson 9�4 741

Adjusting the Activity

2 8

Cellular Telephone UseLESSON

9 �4

Date Time

1. Use the “Subscriptions per 100 People” data in the Cellular Telephone Use table at the bottom of Student Reference Book, page 302 to complete the bar graph. Round each decimal to the nearest whole number.

2. Write a question that can be answered by looking at the data displayed in the bar graph. Answer the question.

90

92

94

96

98

100

102

104

106

108

110

112

Subs

crip

tions

per

100

Peo

ple

Cellular Telephone Use

CountriesTaiwan Luxembourg Italy Iceland Israel Spain

Answers vary.

Math Journal 2, p. 258

Student Page

Links to the Future

� Solving Number Stories Involving Discounts(Math Journal 2, pp. 256 and 257)

Consumer Link Tell students that in this lesson they will use their calculators and mental arithmetic to solve

discount number stories. Have students work in partnerships to complete journal pages 256 and 257.

Rephrase or illustrate the last rows in the tables in Problems 1 and 2 as follows:

Problem 1: If $3 is �110� of the whole, what is the whole? The whole is �

1100�, which is

10 times as much as �110�. So 10 � $3 � $30.

Problem 2: If $75 is 25%, or �14� of the whole, what is the whole? The whole

is �44�, which is 4 times as much as �

14�. So 4 � $75 � $300.

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

When students have completed journal pages 256 and 257, useProblem 5 to demonstrate how to use the percent key to find thediscount and the sale price.

TI-15:

Discount: 400 30 Display: 120

Sale price: 400 400 30 Display: 280

Casio fx-55:

Discount: 400 30 Display: 120

Sale price: 400 30 Display: 280

Solving problems involving percents and discounts is a Grade 5 Goal.

� Creating a Bar Graph(Math Journal 2, p. 258; Student Reference Book, p. 302)

Students create a bar graph to display cellular-telephone-use data.

INDEPENDENT

ACTIVITY

2 Ongoing Learning & Practice

Æ–

Æ

PARTNER

ACTIVITY

742 Unit 9 Fractions, Decimals, and Percents

�

259

Math Boxes LESSON

9�4

Date Time

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

Area �

Perimeter �

6. What temperature is it?

°C�3

1. Complete the table with equivalent names.

4. Three girls cut a pizza into 12 equal slicesand plan to share the pizza equally.

a. What fraction of the pizza should each girl get?

b. How many slices should each girl get? slices

c. Suppose 2 more girls arrive. How manyslices should each of the 5 girls get?

slices

4

34–37

44

139

129

131 133

2. About 1.96% of the words on the Internetare a, and about 0.81% of the words are it.What percent of all words on the Internetare either a or it? Show your work.

2.77%

61 62

0.75

0.10.5 50%

75%60%10%

�160�

�110�

�15000�

Fraction Decimal Percent

0.6

�34�

3. 2 ft 7 in. � __ in. Choose the best answer.

14

24

27

31

�13�

2 �25�

6"

2"

12 in2

16 in.0

10

20

–10

°C

Math Journal 2, p. 259

Student Page

STUDY LINK

9 � 4 Fractions and Decimals to Percents

62206 207

Name Date Time

Do NOT use a calculator to convert these fractions to percents.On the back of this page, show your work for Problems 3–6.

1.�13040

� � % 2.�16070

� � %

3.�4520� � % 4.

�1235� � %

5.�1270� � % 6.

�12255

� � %

Use a calculator to convert these fractions to percents.

7.�2932� � % 8.

�1420� � %

9.�2302� � % 10.

�4790� � %

11.�46000

� � % 12.�2516� � %

13. Describe how you used your calculator to convert the fractions in Problems 7–12 to percents.

I divided the numerator by the denominator and then multiplied by 100.

Do NOT use a calculator to convert these decimals to percents.

14. 0.86 � % 15. 0.03 � %

16. 0.140 � % 17. 0.835 � %83.514386

37.5157062.53025

208552846734

Order the fractions from smallest to largest.

18. �176�, �

78�, �1

72�, �

79�

19. �175�, �1

35�, �1

85�, �1

45�

20. �59�, �

1156�, �

14�, �1

90�

Practice

�176�, �1

72�, �79�, �78�

�135�, �1

45�, �1

75�, �1

85�

�14�, �59�, �190�, �11

56�

Math Masters, p. 285

Study Link Master

� Math Boxes 9�4(Math Journal 2, p. 259)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-2. The skill in Problem 6 previews Unit 10 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 4 to assess students’ ability to solve “fraction-of”problems. Students are making adequate progress if they are able to identify thefraction of the pizza each girl gets and the number of slices. Some students maybe able to determine the number of slices each girl would get if two more girlsarrived and explain how they got their answers.

[Number and Numeration Goal 2]

� Study Link 9�4(Math Masters, p. 285)

Home Connection Students rename fractions as percentswith and without a calculator. Note that in Problems 9,12, and 17, students will have to write the percent usinga decimal.

� Solving “Percent-of” Problems(Math Masters, p. 286)

To explore “percent- of” situations using a concrete model, havestudents use counters to solve problems. Encourage students torename the percents as fractions and solve the problems as “fraction-of” problems.

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENT

ACTIVITY

Math Boxes

Problem 4 �

INDEPENDENT

ACTIVITY

� Solving Discount Number Stories(Math Masters, p. 287)

To apply students’ understanding of “percent-of” situations, have them solve number stories for which theycompare the discounts of two items. In one story, students

compare the percents of discount; in a second story, they comparethe actual discounts.

� 5-Minute MathTo offer students more experience with percents, see 5-MinuteMath, pages 103, 176, 187, and 196.

� Building Background for Mathematics WordsTo provide language support for percents, have students look atstore catalogs or advertisements and discuss the following:

� The regular price (sometimes called the list price) of an item is the price without a discount.

� The discount is the amount you save. It is given in dollars and cents.

� The percent of discount or the fraction of discount is apercent or fraction that tells what part of the regular price you save.

� The sale price (or discounted price) is the amount you payafter subtracting the discount from the regular price.

Example:

The regular price of a bird feeder is $15. It is on sale at a 20%discount. What is the sale price?

The percent of discount is 20% of the regular price. 20% is �12000�, or �

15�.

One-fifth of $15 is $3, so you save $3. This is the discount. To find the sale price, subtract $3 from $15. The sale price is $12.

15–30 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

5–15 Min

SMALL-GROUP

ACTIVITYEXTRA PRACTICE

5–15 Min

PARTNER

ACTIVITYENRICHMENT LESSON

9 � 4

Name Date Time

“Percent-of” Problems

Use counters to solve the problems on this page.

1. If is 100%, draw 50%. 2. If is 100%, draw 25%.

50% of 10 � 25% of 16 �

3. If is 100%, draw 10%. 4. If is 50%, draw 100%.

10% of 20 � 50% of � 6

5. If is 75%, draw 100%. 6. If is 40%, draw 100%.

75% of � 9 40% of � 8

7. Pick one of the problems from above and explain how you got your answer.

Problem

I know that 10% is another name for �110�.

�110� of 20 is 2, so 10% of 20 is 2.

3

2012

122

45

38 39

Sample answer:

Math Masters, p. 286

Teaching Master

Lesson 9�4 743

LESSON

9 � 4

Name Date Time

Discount Number Stories

1. A store is having a sale on gym shoes.

� The regular price of the High Flyers is $50. Now they are on sale for $38.

� The Zingers are $15 off the regular price. When not on sale, the Zingerscost $75 a pair.

Which pair has the greater “percent-of” discount? Explain your answer.

The High Flyers pair has a greater percent-ofdiscount. $50–$38 � $12. �

1520� � �1

2040�, so the

discount is 24%. The Zingers’ discount is

2. The same store is also having a sale on tennis rackets.

� The regular price of the Smasher is $54.00. It is on sale for 25% off the regular price.

� The regular price of the Fast Flight is $75.00. It is on sale for 20% off the regular price.

For which tennis racket are you getting more money taken off the regular price?Explain your answer.

The Fast Flight has a greater percent-ofdiscount. 20% off $75.00 � �

$755

� � $15.00.The Smasher’s discount is 25% off $54.00 ��$544

� � $13.50.

38 39

�1755� � �

15� � �1

2000�, or 20%.

Math Masters, p. 287

Teaching Master