744 Unit 9 Fractions, Decimals, and Percents

Teaching the Lesson materials

Key ActivitiesStudents look up country population and land area data and convert these to percents of the world population and land area. Students complete the percent column of the Equivalent Names for Fractions table on journal pages 342 and 343.

Key Concepts and Skills• Read and use large numbers.

[Numbers and Numeration Goal 1]• Explore repeating and terminating decimals.

[Number and Numeration Goal 5]• Use a calculator to rename fractions as percents; rename decimals as percents by

multiplying by 100; round to the nearest whole-number percent. [Number and Numeration Goal 5]

• Compare two quantities with like units using division. [Operations and Computation Goal 4]

• Use a data table. [Data and Chance Goal 2]

Ongoing Assessment: Informing Instruction See page 746.

Ongoing Learning & Practice materials

Students continue the World Tour.

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

Ongoing Assessment: Recognizing Student Achievement Use journal page 260.[Operations and Computation Goal 4]

Differentiation Options materials

Students use a curved number-linemodel to round percents.

Students practice conversions among fractions, decimals, and percents.

� Teaching Master (Math Masters, p. 289)� 5-Minute Math, pp. 93 and 181 � calculator

EXTRA PRACTICEREADINESS

3

� Math Journal 2, pp. 260, 329–331, 336,and 337

� Student Reference Book� Study Link Master (Math Masters, p. 288)� Teaching Aid Masters (Math Masters,

pp. 419 and 420; optional)� calculator

2

� Math Journal 2, pp. 342 and 343� Student Reference Book, pp. 271 and 281� Study Link 9�4 � calculator� classroom world map� slate

1

Objectives To reinforce the use of a data table; and to reinforce

renaming fractions as percents using a calculator and renaming

decimals as percents.

Technology Assessment Management System

Math Boxes, Problem 4 See the iTLG.

Lesson 9�5 745

Getting Started

Math MessageUse your calculator to rename these fractions as percents: �

18�, �

38�, �

58�, �

78�.

Study Link 9�4 Follow-Up Review answers. Have students share the strategies they used to solveProblems 3–6. For example:

� Problem 3: �4520� � �1

8040� (multiply numerator and denominator by 2); �1

8040� � 84%

� Problem 6: �12255� � �

15� (divide numerator and denominator by 25); �

15� � 20%

Ask if any student can describe a solution strategy to solve Problems 7 and 8 without a calculator. For example:

� Problem 7: �2932� � �

14� (divide numerator and denominator by 23); �

14� � 25%

� Problem 8: �1420� � �1

30� (divide numerator and denominator by 4); �1

30� � 30%

Mental Math and Reflexes Write fractions on the board. For eachfraction, students write the equivalentdecimal and percent on their slates.Have students explain their strategies for the problems. Suggestions:

Adjusting the Activity

� Math Message Follow-UpGo over the answers: �

18� � 12.5%; �

38� � 37.5%; �

58� � 62.5%;

�78� � 87.5%. Students may have renamed the fractions as percentsin one of two ways.

� Use the percent key. For example, to rename �38� as a percent,

TI-15: 3 8 Display: 37.5

Casio fx-55: 3 8 Display: 37.5

� Divide numerator by denominator, and multiply by 100. Forexample, divide 3 by 8 (� 0.375) and multiply by 100 (� 37.5).Remind students that multiplying a decimal by 100 can bedone by moving the decimal point two digits to the right.

Students may use either method, but they should be able to use both.

ELL

Ask students to explain how �18�, �

38�, �

58�, and �

78� could be renamed as

percents without using a calculator. Record the steps on the board.

� �18� is half of �

14�. Because �

14� � 25% and half of 25% is 12.5%, �

18� � 12.5%.

� �38� equals �

14� � �

18�, which is 25% � 12.5%, or 37.5%.

� �58� and �

78� are renamed in the same way.

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

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WHOLE-CLASS

ACTIVITY

1 Teaching the Lesson

�15050� 0.55, 55% �2

20� 0.10, 10%

�17010� 0.71, 71% �

1225� 0.48, 48%

�16070� 0.67, 67% �

135� 5, 500%

�1500� 0.05, 5%

�150� 0.5, 50%

�14� 0.25, 25%

� Renaming Fractions as Percents(Student Reference Book, pp. 271 and 281)

Social Studies Link Use the classroom world map to identify Russia and China. Russia has the largest land area

of any country in the world. China has the largest population ofany country in the world. Tell students that in this lesson theywill investigate population and land area data and use their calculators to convert these to percents of the world populationand land area.

Ask students to use the Student Reference Book to find the population of China and the total world population.

Write these populations on the board. Point out that the worldpopulation has been rounded to the nearest million.

� Ask students to round China’s population to the nearest million.Record this estimate on the board.

� Ask students what fraction of the world’s population lives inChina. Write this fraction on the board.

Have students use their calculators to rename this fraction as apercent. They should use both methods and get the same answer:

� Use the percent key.

TI-15: 1299000000 6378000000 Display willshow 20.36688617.

Casio fx-55: 1299 6378 Display will show20.366886.

� Divide numerator by denominator, and multiply by 100.

1299000000 6378000000 Display will show 0.2036688617.

0.2036688617 100 Display will show 20.36688617.

Ongoing Assessment: Informing InstructionWatch for students who notice that, because both numbers are in millions, it issufficient to divide 1,299 by 6,378. If students’ calculators, such as the Casio fx-55, cannot display these large numbers, encourage them to use this strategy.

Help students summarize. Round percent answers to the nearestwhole-number percent. In 20.366886179, the digit in the tenthsplace is less than 5, so the number is rounded down to 20%. About20 of every 100 people in the world live in China. Because 20%equals �

15�, about 1 of every 5 people in the world live in China.

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WHOLE-CLASS

ACTIVITY

746 Unit 9 Fractions, Decimals, and Percents

Facts About the World

Continents are large land masses. There areseven continents on the Earth, although Europeand Asia are sometimes thought of as onecontinent. Most continents contain manycountries, but there are no countries at allin Antarctica.

A country is a territory and the people who livethere under one government. The number ofcountries in the world often changes as countriessplit apart or join with other countries. At thistime, there are about 200 countries in the world.

Population is the number of people who live in a certain region. Population growth is the change in the population every year after all births and deaths are accounted for. The population growth rate is the increase(or decrease) in population per year, written asa percent.

The world’s population is now increasing by about 200,000 people per day, or about 75 million people per year. Over the last 40 years, the world’s population has about doubled. It reached the 6 billion mark in 1999. World population is expected to reachabout 9 billion people by the year 2050.

World Tour

North America 509,000,000 8.0% 8,300,000 14.8%South America 367,000,000 5.8 6,800,000 12.1Europe 799,000,000 12.5 4,100,000 7.3Asia 3,797,000,000 59.5 16,700,000 29.8Africa 874,000,000 13.7 11,500,000 20.5Australia 32,000,000 0.5 3,300,000 5.9Antarctica 0 0.0 5,400,000 9.6

World Totals 6,378,000,000 100.0% 56,100,000 100.0%(about 6.4 billion)

The Continents

Continent Population*

Percent of WorldPopulation

Area (sq miles)

Percent ofLand Area

*Data are for the year 2004. World population growth rate for the year 2004: about 1.2% per year

Dimensions of the EarthEquatorial circumference*:about 24,900 miles (40,000 kilometers)Equatorial diameter**:about 7,930 miles (12,760 kilometers)Volume: 2.6 x 1011 cubic miles (1.1 x 1012 cubic kilometers)Weight (mass): 6.6 x 1021 tons (6.0 x 1021 metric tons)Total world water area:about 139,433,000 square miles (361,129,000 square kilometers)*Circumference is the distance around a circle or sphere.

**Diameter is the distance measured by a straight line passing from one side of a circle or sphere, through the center, to the other side.

Student Reference Book, p. 271

Student Page

REGION 5 North America

Canada

Area: 3,851,800 sq miPopulation: 32,508,000Capital: Ottawa (Pop. 1,093,000)Languages: English, French

Monetary unit: DollarCosta Rica

Area: 19,700 sq miPopulation: 3,957,000Capital: San José (Pop. 1,085,000)Language: Spanish

Monetary unit: ColonCuba

Area: 42,800 sq miPopulation: 11,309,000Capital: Havana (Pop. 2,189,000)Language: Spanish

Monetary unit: PesoEl Salvador

Area: 8,100 sq miPopulation: 6,588,000Capital: San Salvador (Pop. 1,424,000)

Language: Spanish

Monetary unit: ColonGuatemala

Area: 42,000 sq miPopulation: 14,281,000Capital: Guatemala City (Pop. 951,000)Languages: Spanish, MayanlanguagesMonetary unit: QuetzalHaiti

Area: 10,700 sq miPopulation: 7,656,000Capital: Port-au-Prince (Pop. 1,961,000)Languages: French, HaitianCreole

Monetary unit: GourdeJamaica

Area: 4,200 sq miPopulation: 2,713,000Capital: Kingston (Pop. 575,000)Languages: English, JamaicanCreoleMonetary unit: Jamaican Dollar

Mexico

Area: 761,600 sq miPopulation: 104,960,000Capital: Mexico City (Pop. 18,660,000)Languages: Spanish, MayandialectsMonetary unit: New PesoPanama

Area: 30,200 sq miPopulation: 3,000,000Capital: Panama City (Pop. 930,000)Languages: Spanish, EnglishMonetary unit: BalboaUnited States of America

Area: 3,717,800 sq miPopulation: 293,028,000Capital: Washington, D.C. (Pop. 563,000)Languages: English, SpanishMonetary unit: Dollar

World Tour

REGION 4 Asia and Australia

Australia

Area: 2,967,900 sq miPopulation: 19,913,000Capital: Canberra (Pop. 373,000)Languages: English, aboriginallanguagesMonetary unit: Australian DollarBangladesh

Area: 55,600 sq miPopulation: 141,340,000Capital: Dhaka (Pop. 11,560,000)Languages: Bangla, EnglishMonetary unit: TakaChina

Area: 3,705,400 sq miPopulation: 1,298,848,000Capital: Beijing (Pop. 10,848,000)Languages: Mandarin, Gan, Wu,Haka, Yue, Minbei, Xiang, MinnanMonetary unit: Renminbi (Yuan)India

Area: 1,269,300 sq miPopulation: 1,065,071,000Capital: New Delhi (Pop. 12,441,000)

Languages: Hindi, English, 14 regional languages

Monetary unit: RupeeIran

Area: 636,000 sq miPopulation: 67,503,000Capital: Tehran (Pop. 7,190,000)Languages: Farsi, Kurdish,Turkic, LuriMonetary unit: RialJapan

Area: 145,900 sq miPopulation: 127,333,000Capital: Tokyo (Pop. 34,997,000)Language: Japanese

Monetary unit: YenRussia

Area: 6,592,800 sq miPopulation: 143,782,000Capital: Moscow (Pop. 6,468,000)Languages: Russian, manyothersMonetary unit: Ruble

Thailand

Area: 198,500 sq miPopulation: 64,866,000Capital: Bangkok (Pop. 6,486,000)Languages: Thai, EnglishMonetary unit: BahtTurkey

Area: 301,400 sq miPopulation: 68,894,000Capital: Ankara (Pop. 3,428,000)Languages: Turkish, Arabic,KurdishMonetary unit: LiraVietnam

Area: 127,200 sq miPopulation: 82,690,000Capital: Hanoi (Pop. 3,977,000)Languages: Vietnamese,Chinese, French, EnglishMonetary unit: Dong

Student Reference Book, p. 281

Student Page

China

World

Population

1,298,848,000

6,378,000,000

PopulationRounded

1,299,000,000

6,378,000,000

Fraction

�16,,239798,,000000,,000000

�

Repeat this last routine to calculate the percent of the world’s landarea that is in Russia. Russia’s area is about 6,592,800 squaremiles. The world’s land area is about 57,900,000 square miles.The fraction of the world’s area that belongs to Russia is about6,593,000 � 57,900,000 � 0.1138687392. Multiply 0.11 � 100 �11%. So about 11% of the world’s area belongs to Russia.

� Completing the Equivalent Names for Fraction Table(Math Journal 2, pp. 342 and 343)

Students should already have filled in the equivalent fractions anddecimals columns of the table on journal pages 342 and 343. Nowthey will fill in the percents column.

� On the first page of the table, students find the percents byusing the percent key. If the calculator display shows ananswer with more than 3 digits, they record only the first 3 digits. For example, for the fraction �

56�, the percent answer will

be displayed on the calculator as 83.33333333, but only 83.3should be recorded in the table.

� On the second page of the table, students can find the percentswithout using a calculator and without making any actual computations. The decimal names are already recorded in thetable. Students need only multiply the decimal by 100 (movethe decimal point two digits to the right) to rename the decimalas a percent. As before, ask students to record only the first 3 digits for any percent name.

INDEPENDENT

ACTIVITY

342

Equivalent Names for Fractions

Date Time

Fraction Equivalent Fractions Decimal Percent

�20� 0 0%

�12� �24�, �

36�

�22� 1 100%

�13�

�23�

�14�

�34�

�15�

�25�

�35�

�45�

�16�

�56�

�18�

�38�

�58�

�78�

Math Journal 2, p. 342

Student Page

343

Equivalent Names for Fractions continued

Date Time

Fraction Equivalent Fractions Decimal Percent

�19�

�29�

�49�

�59�

�79�

�89�

�110�

�130�

�170�

�190�

�112�

�152�

�172�

�1112�

Math Journal 2, p. 343

Student Page

Lesson 9�5 747

748 Unit 9 Fractions, Decimals, and Percents

STUDY LINK

9 �5 Renaming Fractions as Percents

Name Date Time

In 2001, there were about 2,317,000 marriages in the United States. The table below shows the approximate number of marriages each month.

1. Use a calculator to find the percent of the total number of marriages that occurred each month. Round the answers to the nearest whole-number percent.

2. According to the table, what is the most popular month for a wedding?

What is the least popular month for a wedding?

3. Describe how you used your calculator to find the percent for each month.

month by the total then multiplied by 100 and rounded.Sample answer: I divided the number of marriages for each

JanuaryJuly

Name all the factors of each number.

4. 63 5. 28 1, 2, 4, 7, 14, 281, 3, 7, 9, 21, 63

Practice

Approximate Approximate Month Number of Percent of

Marriages Total Marriages

January 147,000 6%February 159,000 7%March 166,000 7%April 166,000 7%May 189,000 8%June 237,000 10%July 244,000 11%August 225,000 10%September 224,000 10%October 217,000 9%November 191,000 8%December 152,000 7%

Source: U.S. Department of Health and Human Services

62 207

Math Masters, p. 288

Study Link Master

260

Math Boxes LESSON

9 � 5

Date Time

5. What is the height of the parallelogram?Include the correct unit.

Area � 27 in2

Number model:

Height:

?

9 in.

6. Draw the mirror image of the figure shownon the left of the vertical line.

3. Complete the table with equivalent names. 4. Divide. Use a paper-and-pencil algorithm.

897 � 6 �

22 23

106 109

61 62

135

2. Insert parentheses to make each numbersentence true.

a. 6 � 2 � 4 � 32

b. 5 � 7 � 3 � 36

c. 1 � 8 � 8 � 2 � 90

d. 1 � 7 � 8 � 2 � 8038 39

( ))))

(( )

)(

( (

0.5

0.7�12000�

0.4 40%

50%20%

70%

�25�

Fraction Decimal Percent

0.20

�150� �

149 R3,or 149�

12�

27 / 9 � 33 in.

150

1. Calculate.

a. 10% of 70 �

b. 5% of 60 �

c. 25% of � 7

d. % of 48 � 24

e. % of 25 � 208050

2837

�170�

Math Journal 2, p. 260

Student Page

� Updating the World Tour(Math Journal 2, pp. 329–331, 336, and 337; Student Reference Book;Math Masters, pp. 419 and 420)

Social Studies Link Students follow the established WorldTour routine.

� They update the Route Map by drawing a line segment to connect Brasília, Brazil, and Beijing, China.

� They use the World Tour section of the Student Reference Bookto locate facts about China and Beijing, and they fill in theCountry Notes pages for this country and capital.

� Students who are also keeping a Route Log update that as well.

� Math Boxes 9�5(Math Journal 2, p. 260)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 9-7 and 9-9. The skill inProblem 6 previews Unit 10 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 4 to assess students’ ability to divide a multidigitwhole number by a 1-digit divisor. Students are making adequate progress ifthey express the quotient as a whole number with a whole-number remainder.Some students may be able to express the remainder as a fraction.

[Operations and Computation Goal 4]

� Study Link 9�5(Math Masters, p. 288)

Home Connection Students use a table of data to calculate the approximate percentage of marriages that occurred each month in 2001.

INDEPENDENT

ACTIVITY

Math Boxes

Problem 4 �

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

2 Ongoing Learning & Practice

� Rounding Percents(Math Masters, p. 289)

To explore rounding percents to the nearest whole number, have students plot numbers on a curved number line to see whichway the percent will “slide.” Ask students to describe how theyrounded their numbers. Encourage vocabulary such as top, bottom,endpoint, middle, closer, and farther.

� 5-Minute MathTo offer students more experience with conversions among fractions,decimals, and percents, see 5-Minute Math, pages 93 and 181.

Planning Ahead

Remind students to bring to school the second page of Study Link 9-1 (Trivia Survey). Their survey results will be used inLesson 9-6.

5–15 Min

SMALL-GROUP

ACTIVITYEXTRA PRACTICE

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

LESSON

9 �5

Name Date Time

Rounding Percents

The number lines below are curved like hills. You can use them to help youround percents to the nearest whole-number percent.

Example:

Round 89.7% to the nearest whole-number percent.

� Think: Which whole-number percents are nearest to 89.7%?

� If I look at the number line, 89% is the whole-number percent to the left of 89.7%.

� If I look at the number line, 90% is the whole-number percent to the right of 89.7%.

� What number would be exactly halfway between 89% and 90%?

Mark 89.7% on the curved number line.

Would 89.7% slide down to 89% or 90%?

89.7% rounded to the nearest whole-number percent is 90%.

1. Round 23.6% to the nearest whole-number percent.

Label the curved number line. Mark 23.6%.

23.6% would slide down to .

23.6% rounded to the nearest whole-number percent is .

2. Round 92.1% to the nearest whole-number percent.

Label the curved number line. Mark 92.1%.

92.1% would slide down to .

92.1% rounded to the nearest whole-number percent is .92%

92%

24%

24%

92.1%

92.5%

92% 93%

23.6%23.5%

23% 24%

89.5%

89.7%

89% 90%

Math Masters, p. 289

Teaching Master

Lesson 9�5 749