problem solving book

Problem Solvingand

Reading StrategiesWorkbookP U P I L E D I T I O N

Grade 6

Orlando • Boston • Dallas • Chicago • San Diegowww.harcourtschool.com

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Unit 1: NUMBER SENSE ANDOPERATIONS

Chapter 1: Whole Number Applications1.1 Estimate with Whole Numbers . . . . 11.2 Use Addition and Subtraction . . . . 21.3 Use Multiplication and Division . . . 31.4 Reading Strategy: Compare . . . . . . . 41.5 Algebra: Use Expressions . . . . . . . . . 51.6 Algebra: Mental Math and

Equations . . . . . . . . . . . . . . . . . . . . . . 6

Chapter 2: Operation Sense2.1 Mental Math: Use the Properties . . 72.2 Algebra: Exponents . . . . . . . . . . . . . . 82.4 Algebra: Order of Operations . . . . . 92.5 Reading Strategy: Sequence . . . . . 10

Chapter 3: Decimal Concepts3.1 Represent, Compare, and Order

Decimals . . . . . . . . . . . . . . . . . . . . . . . 113.2 Reading Strategy: Use

Graphic Aids . . . . . . . . . . . . . . . . . . . 123.3 Estimate with Decimals . . . . . . . . . 133.4 Decimals and Percents . . . . . . . . . . 14

Chapter 4: Decimal Operations4.1 Add and Subtract Decimals . . . . . . 154.2 Multiply Decimals . . . . . . . . . . . . . . 164.4 Divide with Decimals . . . . . . . . . . . 174.5 Reading Strategy: Use Context . . . 184.6 Algebra: Decimal Expressions

and Equations . . . . . . . . . . . . . . . . . . 19

Unit 2: STATISTICS AND GRAPHING

Chapter 5: Collect and Organize Data5.1 Samples . . . . . . . . . . . . . . . . . . . . . . 205.2 Bias in Surveys . . . . . . . . . . . . . . . . . 215.3 Reading Strategy: Use

Graphic Aids . . . . . . . . . . . . . . . . . . . 22

5.4 Frequency Tables and Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.5 Measures of Central Tendency . . . 245.6 Outliers and Additional Data . . . . 255.7 Data and Conclusions . . . . . . . . . . 26

Chapter 6: Graph Data6.1 Make and Analyze Graphs . . . . . . . 276.2 Find Unknown Values . . . . . . . . . . . 286.3 Stem-and-Leaf Plots and

Histograms . . . . . . . . . . . . . . . . . . . . 296.5 Box-and-Whisker Graphs . . . . . . . . 306.6 Analyze Graphs . . . . . . . . . . . . . . . . 31

Unit 3: FRACTION CONCEPTS ANDOPERATIONS

Chapter 7: Number Theory7.1 Divisibility . . . . . . . . . . . . . . . . . . . . . 327.2 Prime Factorization . . . . . . . . . . . . . 337.3 Least Common Multiple and

Greatest Common Factor . . . . . . . 347.4 Reading Strategy: Synthesize

Information . . . . . . . . . . . . . . . . . . . . 35

Chapter 8: Fraction Concepts8.1 Equivalent Fractions and

Simplest Form . . . . . . . . . . . . . . . . . 368.2 Mixed Numbers and Fractions . . . 378.3 Compare and Order Fractions . . . 388.5 Fractions, Decimals, and

Percents . . . . . . . . . . . . . . . . . . . . . . . 39

Chapter 9: Add and Subtract Fractionsand Mixed Numbers9.1 Estimate Sums and

Differences . . . . . . . . . . . . . . . . . . . . 409.3 Add and Subtract Fractions . . . . . . 419.4 Add and Subtract Mixed

Numbers . . . . . . . . . . . . . . . . . . . . . . 429.6 Subtract Mixed Numbers . . . . . . . . 439.7 Reading Strategy: Summarize . . . . 44

CONTENTS

Chapter 10: Multiply and DivideFractions and Mixed Numbers10.1 Estimate Products and

Quotients . . . . . . . . . . . . . . . . . . . . . 4510.2 Multiply Fractions . . . . . . . . . . . . . 4610.3 Multiply Mixed Numbers . . . . . . . 4710.5 Divide Fractions and Mixed

Numbers . . . . . . . . . . . . . . . . . . . . . . 4810.6 Reading Strategy:

Multiple-Meaning Words . . . . . . . 4910.7 Algebra: Fraction Expressions

and Equations . . . . . . . . . . . . . . . . . 50

Unit 4: ALGEBRA: INTEGERS

Chapter 11: Number Relationships11.1 Understand Integers . . . . . . . . . . . . 5111.2 Rational Numbers . . . . . . . . . . . . . . 5211.3 Compare and Order Rational

Numbers . . . . . . . . . . . . . . . . . . . . . . 5311.4 Reading Strategy: Analyze

Information . . . . . . . . . . . . . . . . . . . 54

Chapter 12: Add and Subtractwith Integers12.2 Algebra: Add Integers . . . . . . . . . . . 5512.4 Algebra: Subtract Integers . . . . . . . 56

Chapter 13: Multiply and Dividewith Integers13.2 Algebra: Multiply Integers . . . . . . . 5713.3 Algebra: Divide Integers . . . . . . . . . 5813.4 Combine Operations with

Integers . . . . . . . . . . . . . . . . . . . . . . . 59

Unit 5: ALGEBRA: EXPRESSIONS ANDEQUATIONS

Chapter 14: Expressions14.1 Write Expressions . . . . . . . . . . . . . . 6014.2 Evaluate Expressions . . . . . . . . . . . . 6114.4 Expressions with Squares and

Square Roots . . . . . . . . . . . . . . . . . . 62

Chapter 15: Addition and SubtractionEquations15.1 Connect Words and Equations . . . 63

15.3 Solve Addition Equations . . . . . . . 6415.4 Solve Subtraction Equations . . . . . 65

Chapter 16: Multiplication andDivision Equations16.2 Solve Multiplication and

Division Equations . . . . . . . . . . . . . 6616.3 Use Formulas . . . . . . . . . . . . . . . . . . 6716.5 Reading Strategy: Draw

Conclusions . . . . . . . . . . . . . . . . . . . 68

Unit 6: GEOMETRY AND SPATIALREASONING

Chapter 17: Geometric Figures17.1 Points, Lines, and Planes . . . . . . . . 6917.3 Angle Relationships . . . . . . . . . . . . 7017.4 Classify Lines . . . . . . . . . . . . . . . . . . 71

Chapter 18: Plane Figures18.1 Triangles . . . . . . . . . . . . . . . . . . . . . . 7218.2 Reading Strategy: Make

Inferences . . . . . . . . . . . . . . . . . . . . . 7318.3 Quadrilaterals . . . . . . . . . . . . . . . . . 7418.4 Draw Two-Dimensional Figures . . 7518.5 Circles . . . . . . . . . . . . . . . . . . . . . . . . 76

Chapter 19: Solid Figures19.1 Types of Solid Figures . . . . . . . . . . 7719.2 Different Views of Solid Figures . . 7819.4 Reading Strategy: Paraphrase . . . . 79

Unit 7: RATIO, PROPORTION,PERCENT, AND PROBABILITY

Chapter 20: Ratio and Proportion20.1 Ratios and Rates . . . . . . . . . . . . . . . 8020.3 Reading Strategy: Follow

Directions . . . . . . . . . . . . . . . . . . . . . 8120.4 Algebra: Ratios and Similar

Figures . . . . . . . . . . . . . . . . . . . . . . . . 8220.5 Algebra: Proportions and

Similar Figures . . . . . . . . . . . . . . . . . 8320.6 Algebra: Scale Drawings . . . . . . . . . 8420.7 Algebra: Maps . . . . . . . . . . . . . . . . . 85

Chapter 21: Percent and Change21.1 Percent . . . . . . . . . . . . . . . . . . . . . . . 8621.2 Percents, Decimals, and

Fractions . . . . . . . . . . . . . . . . . . . . . . 8721.3 Estimate and Find Percent of a

Number . . . . . . . . . . . . . . . . . . . . . . . 8821.5 Discount and Sales Tax . . . . . . . . . 8921.6 Simple Interest . . . . . . . . . . . . . . . . 90

Chapter 22: Probability of Simple Events22.1 Theoretical Probability . . . . . . . . . . 9122.2 Reading Strategy: Choose

Relevant Information . . . . . . . . . . . 9222.4 Experimental Probability . . . . . . . . 93

Chapter 23: Probability ofCompound Events23.1 Reading Strategy: Classify

and Categorize . . . . . . . . . . . . . . . . 9423.2 Compound Events . . . . . . . . . . . . . . 9523.3 Independent and Dependent

Events . . . . . . . . . . . . . . . . . . . . . . . . 9623.4 Make Predictions . . . . . . . . . . . . . . 97

Unit 8: MEASUREMENT

Chapter 24: Units of Measure24.1 Algebra: Customary

Measurements . . . . . . . . . . . . . . . . . 9824.2 Algebra: Metric

Measurements . . . . . . . . . . . . . . . . . 9924.3 Relate Customary and

Metric . . . . . . . . . . . . . . . . . . . . . . . 10024.4 Appropriate Tools and Units . . . . 10124.5 Reading Strategy: Make

Predictions . . . . . . . . . . . . . . . . . . . 102

Chapter 25: Length and Perimeter25.2 Perimeter . . . . . . . . . . . . . . . . . . . . . 10325.3 Reading Strategy: Use

Graphic Aids . . . . . . . . . . . . . . . . . . 10425.5 Circumference . . . . . . . . . . . . . . . . 105

Chapter 26: Area26.1 Estimate and Find Area . . . . . . . . 10626.2 Algebra: Areas of Parallelograms

and Trapezoids . . . . . . . . . . . . . . . . 107

26.4 Algebra: Areas of Circles . . . . . . . 10826.5 Algebra: Surface Areas of

Prisms and Pyramids . . . . . . . . . . . 109

Chapter 27: Volume27.1 Estimate and Find Volume . . . . . . 11027.2 Reading Strategy: Activate

Prior Knowledge . . . . . . . . . . . . . . . 11127.3 Algebra: Volumes of Pyramids . . . 11227.5 Volumes of Cylinders . . . . . . . . . . . 113

Unit 9: ALGEBRA: PATTERNS ANDRELATIONSHIPS

Chapter 28: Patterns28.1 Reading Strategy: Cause and

Effect . . . . . . . . . . . . . . . . . . . . . . . . 11428.2 Patterns in Sequences . . . . . . . . . . 11528.3 Number Patterns and

Functions . . . . . . . . . . . . . . . . . . . . . 11628.4 Geometric Patterns . . . . . . . . . . . . 117

Chapter 29: Geometry and Motion29.1 Transformations of Plane

Figures . . . . . . . . . . . . . . . . . . . . . . . 11829.2 Tessellations . . . . . . . . . . . . . . . . . . 11929.3 Reading Strategy: Form Mental

Images . . . . . . . . . . . . . . . . . . . . . . . 12029.4 Transformations of Solid

Figures . . . . . . . . . . . . . . . . . . . . . . . 12129.5 Symmetry . . . . . . . . . . . . . . . . . . . . 122

Chapter 30: Graph Relationships30.1 Inequalities on a Number Line . . 12330.2 Graph on the Coordinate

Plane . . . . . . . . . . . . . . . . . . . . . . . . 12430.3 Graph Functions . . . . . . . . . . . . . . . 12530.4 Reading Strategy: Make

Generalizations . . . . . . . . . . . . . . . 12630.6 Graph Transformations . . . . . . . . . 127

NameLESSON 1.1

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Problem Solving PS1

Estimate with Whole NumbersWrite the correct answer.

1. Use clustering to estimate the sum.

7,843 8,213

� 8,107

3. The local museum estimates that about5,475 people visited the museum in thelast 9 days. About how many peoplevisited the museum each day?

Choose the letter for the best answer.

5. What is the place value of theunderlined digit?

1,345.835A hundredthsB tenthsC tensD hundreds

7. The Rockwells traveled 4,476 miles in11 days. Each day they traveled aboutthe same number of miles. What is agood estimate of how many miles theytraveled each day? A 200 mi C 400 miB 300 mi D 500 mi

2. Use rounding to estimate the product.

33 � 21

4. Ruby made a quilt using 588 squares.There were 28 rows of squares in thequilt. About how many squares were ineach row?

6. What is 2,768 rounded to the nearesthundred? F 3,000G 2,800H 2,770J 2,700

8. June gets paid about $1,550 eachmonth. What is a reasonable estimateof how much she makes in a year? F Less than $10,000G Between $10,000 and $15,000H Between $15,000 and $20,000J More than $20,000

9. Write About It Explain how to use clustering to estimate the sum of385 � 408 � 396 � 411.

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PS2 Problem Solving

Use Addition and SubtractionSolve.

1. In 1995, there were about 58,000 farmsin North Carolina and about 22,000farms in South Carolina. There wereabout 100,000 farms in Iowa in 1995.About how many more farms werethere in Iowa than in North Carolinaand South Carolina combined in 1995?

3. Give the value represented by the digit8 in the number 258,034,199.


5. In 1999, a world record for the largestgathering of twins was set in Taipei,Taiwan, with 3,961 pairs of twins inattendance. The number of twinsshattered the previous record of 2,900pairs set in Twinsburg, Ohio, in 1998.What is a reasonable estimate of theincrease in the number of pairs of twins?A 60 pairsB 160 pairsC 900 pairsD 1,100 pairs

7. What 2 numbers have a sum of 4,949and a difference of 1,963? A 1,999 and 2,950B 1,493 and 3,456C 1,358 and 3,591D 1,078 and 3,871

2. Carrie participated in a bird censusduring three days last week. Shecounted 435 birds on Monday, 206birds on Tuesday, and 359 birds onWednesday. How many birds did shecount in all during these three days?

4. Use clustering to estimate the sum.65 � 57 � 62 � 54

6. When a children’s museum openednear Roberto’s home, he was among14,756 children who visited it duringthe first month it was open. The nextmonth, 18,355 children visited, while27,982 children visited during the thirdmonth. What is a reasonable estimateof the number of children who visitedthe museum during the first threemonths it was open? F 40,000 children H 60,000 childrenG 50,000 children J 70,000 children

8. Which is the greatest number of thefour shown below?

23,887; 32,109; 24,999; 32,190 F 23,887G 32,109H 24,999J 32,190

NameLESSON 1.2

9. Write About It Which operation would you use to solve a problemin which you are asked to find an amount of increase? Explain.

NameLESSON 1.3

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Problem Solving PS3

8. Sam has 9 friends in the gardeningclub. He orders 340 tomato seeds forhis friends to share. What is a goodestimate of how many seeds eachperson would get if they share theseeds equally? F 40 seedsG 25 seedsH 20 seedsJ 15 seeds

9. Write About It Which operation would you use to solve a problemin which objects are being shared equally? Explain your choice.

Use Multiplication and DivisionWrite the correct answer.

1. Larry washed 58 windows. He charged$4 for every window he washed. Howmuch money did he make washingwindows?

2. Claire had 108 balloons that shewanted to give to her 6 friends. If eachperson got the same number, howmany balloons did each person get?


3. Write the numbers in order from leastto greatest. Use �.

80,808, 80,080, 80,088

4. What is the value of the 2 in 3,927,648?

5. What is the difference between2,403,615 and 1,417,528? A 1,096,133B 1,086,197C 986,087D 985,987

6. What is the product of 1,010 and 100? F 1,010,000G 110,101H 101,000J 100,110

7. Pauline rides to and from school onher bike every day. Each round-trip is6 miles. What is a good estimate forthe number of miles she rides in180 school days? A 1,000 miB 1,500 miC 2,000 miD 2,500 mi

NameLESSON 1.4

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PS4 Reading Strategy

CompareWhen you compare two or more things, you examine how theyare alike. It can be helpful to compare information in aproblem. Read the following problem.

Ralph has some chickens and some pigs. Together, theanimals have 38 legs. They have 15 heads. How many of eachkind of animal does he have?

This is a problem for which you might want to use the predict and teststrategy. When you use this strategy, you think of possible solutions.Then you compare to see whether your solution fits the informationgiven in the problem. You can use a table to compare information.

3. The Ping-Pong Paddlers table-tennisteam played 15 games. They lost 4fewer games than they won. They tied2 more games than they lost. What wasthe team’s record?

1. Complete the table. Compare the information about heads andlegs in the chart with the information given in the problem.

2. Solve the problem.

4. Janine bought 20 pieces of fruit. Tencan be eaten without peeling. Eight areyellow and 6 are orange. She has 2more pears than bananas. She boughtgrapefruit, lemons, bananas, apples,yellow pears, and oranges. How manyof each fruit did she buy?

Predict TestNumber of Chickens Number of Pigs Number of Legs Number of Heads

7 8 46

9 6

Make a table to compare the facts. Solve.

VOCABULARYcompare

NameLESSON 1.5

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Problem Solving PS5

Algebra: Use ExpressionsWrite the correct answer.

1. Write an algebraic expression for theword expression.

15 less than a number, a

3. Fred scored 8 points more than Daleduring the game. If together theyscored 32 points, determine thenumber of points Dale scored.


5. Which algebraic expression representsthe word expression?

the sum of 9 and a number, a, squaredA 9 � a2 C 9 � a2

B 9 � a2 D 9 � a2

7. What 2 numbers have a product of 48and a quotient of 48? A 8 and 6B 12 and 4C 48 and 1D 96 and 2

2. Write a numerical expression for theword expression.

24 times 8

4. Patricia wants to share her package of36 pretzels equally among her 5 friendsand herself. How many pretzels willeach person receive?

6. Which word expression represents thenumerical expression?

24 � 6F 24 decreased by 6G the sum of 24 and 6H 24 increased by 6J the quotient of 24 and 6

8. Joan bought 5 yards of fabric for $2.85a yard, including tax. Which equationcould be used to find the change Joanreceived, a, if she gave the cashier $50? F a � 50 � (5 � 2.85)G a � 50 � (5 � 2.85)H a � 50 � (5 � 2.85)J a � 50 � 5 � 2.85

9. Write About It Give examples of phrases that can usually betranslated into subtraction expressions.

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PS6 Problem Solving

Algebra: Mental Math and EquationsWrite the correct answer.

1. Shania is saving $25 each week for abicycle. When she began saving, sheused the equation 25y � 200 to find outhow many weeks she needed to savethe money for the bike. How manyweeks will it take her to save enoughfor the bike?

3. Write the number 86,003 in words.


5. Determine which of the values is asolution of the equation 5x � 55. A 5B 10C 11D 55

7. It is 12 blocks from Hiro’s house to thestore. He uses the equation 12 � b � 24to find out how much farther he needsto walk to get to the library, which is24 blocks from his house. How far doeshe have to walk?A 2 blocksB 12 blocksC 36 blocksD 268 blocks

2. An average of 2 million people visited anew encyclopedia web site each dayduring the first 5 days it was open. Youcan use the equation n � 2 � 5 todetermine how many millions ofpeople visited the site during the5 days. How many visitors were there?

4. Write 40,610 in expanded form.

6. Which of the following numbers isdivisible by 3, 4, and 9? F 9,164G 6,372H 4,581J 3,762

8. A video costs $16.48. Sondra has saved$7.95. Which equation could she use tofind how much more money she needsto buy the video? F $16.48 � n � $7.95G $7.95 � n � $16.48H $7.95 � $16.48 � nJ n � $16.48 � $7.95

NameLESSON 1.6

9. Write About It How would you use mental math to solve theequation z � 8 � 9?

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Problem Solving PS7

NameLESSON 2.1

Use the PropertiesWrite the correct answer.

1. Use compensation to add.

48 � 35

2. Use mental math to find the value of

(13 � 12) � 7.

3. In the auditorium, there are 32 rows ofseats. Each row has 24 chairs. Howmany students can the auditoriumseat?


4. Brock sorted his toy cars into fivegroups. The groups contained 18, 22,16, 7, and 14 cars. Use mental math tofind the total number of cars.

5. Which expression shows how to usecompensation to subtract 22 from 47?

A (47 � 2) � (22 � 2)B (47 � 3) � (22 � 2)C (47 � 20) � (22 � 2)D 47 � 22

6. What is the value of the underlineddigit in 9,987.6532?

F 5 tensG 5 onesH 5 tenthsJ 5 hundredths

7. If you swim between 35 and 45minutes a day, what is a reasonableestimate of the number of minutes youswim in 15 days? A Less than 300B Between 300 and 500C Between 500 and 700D More than 700

8. Which equation illustrates theCommutative Property?

F (2 � 3) � 4 � (2 � 3) � 4G 2 � (3 � 4) � (2 � 3) � 4H (2 � 3) � 4 � (3 � 2) � 4J (2 � 3) � 4 � 6 � 4

9. Write About It Explain how to use the Distributive Property tomultiply 48 and 17.

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PS8 Problem Solving

NameLESSON 2.2

ExponentsWrite the correct answer.

1. Write in exponent form.

5 � 5 � 5 � 5 � 5 � 5 � 5 � 5

2. Compare the fractions �34

� and �78

�.Use � or �.

3. Claire is working on her readingassignment for school. On Monday sheread three pages. Then, on each dayafter the first day, she read triple theamount of the previous day. Usingexponent form, write the number ofpages she will read on the fifth day.


4. Bill needs to know the decimalequivalent of �1

36� to solve a problem in

his math homework. He changes thefraction to a decimal by dividing thenumerator by the denominator. Whatdecimal does he get?

5. Find the value of 73. A 73B 343C 21D 10

6. Which is the exponent form of n � n � n � n � n? F n5 H 5nG 5n J 5n5

7. Which group of numbers is listed fromgreatest to least? A 3.045, 3.04, 3.05B 4.2, 4.013, 4.01C 2.7, 2.86, 2.68D 5.10, 5.010, 5.02

8. A salesman travels 517 miles a week tocover his territory. Which is a goodestimate for the number of miles hetravels in 4 weeks? F 500 miG 1,000 miH 1,500 miJ 2,000 mi

9. Write About It Explain how you can tell which is greater, 86 or 126,without finding their values.

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Problem Solving PS9

NameLESSON 2.4

Order of OperationsFor Problems 1–2, write and evaluate an expression to solve each problem.

1. Rita and Ken worked as volunteers ina fund-raising effort for a candidate inthe Georgia primary. Rita stuffed132 envelopes per hour for 4 hoursand Ken stuffed 116 per hour for 6hours. How many envelopes did theyget done?

2. The Academy School District filled 21buses to capacity when it announced itwould transport students to the statechampionship football game. If eachbus holds 52 students and 145 morestudents went by car, how manyattended the championship game?

3. Use mental math to find the value of 234 w, for w � 6.


4. Give two numbers between 4.8 and4.9.

5. Maureen plans to walk 2 miles a dayfor the first week in her exercise planand 3 miles a day for the next 12 daysafter that. Which of the followingexpressions shows how far she plansto walk? A (2 � 7) � (3 � 12)B (2 � 7) � (3 � 12)C (2 � 3) � (7 � 12)D (2 � 3) � 12

6. Denzel bought 14 boxes of cups for aparty. Each box of cups cost $1.99. Healso bought 5 bottles of juice that cost$2.39 each and paid $1.99 in sales tax.How much did he spend in all? F $6.37G $31.69H $39.81J $41.80

7. Which of the following is the value of 54? A 20B 125C 625D 1,024

8. Evaluate the expression 42 � 7 � 8 � (15 � 2). F 51G 59H 85J 167

9. Write About It Explain the steps you would use in finding thevalue of 82 � 3 � 7 � 21 � (5 � 8).

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NameLESSON 2.5

Sequence

Whether you are reading a story or a math problem, putting eventsin order, or in sequence, can help you understand it better. To putevents in sequence, you prioritize the order of the events. You canuse clues in the text and common sense. Read this problem.

Albert gets home at 5:15 P.M. Dinner is at 5:30. Albert has fourtasks to do tonight. In what order should he do them?

ALBERT’S EVENING SCHEDULE

1. Next to each task in the chart above, write the factors that will helpyou sequence the events.

2. Using the information from the table and common sense, write apossible sequence for Albert’s tasks.

Use the schedule below. Each event lasts 50 minutes. Sequence the events to solve.

CHITTENDEN COUNTY FAIR

3. Antoine and Penny get to the countyfair at 9:45 A.M. They both want to go toas many activities as possible, with nobreaks. What is the best schedule forAntoine and Penny?

4. Helen and Raoul want to see at least onejudged event and they want to eat lunchat noon. They want to see the jugglingshow right after the tractor pull event.What is the best schedule for them?

Event Times OfferedPie Judging 10:00 A.M.Dog Judging 11:00 A.M.Pig Races 10:00 A.M., 12 noon, 2:00 P.M.Juggling Show 9:00 A.M., 10:00 A.M., 11:00 A.M., 12 noonTractor Pull 9:00 A.M., 11:00 A.M., 1:00 P.M.Trained Bear Show 9:00 A.M., 1:00 P.M., 3:00 P.M.

Task Time It Takes Factors That Affect Sequence

Do homework 2 hr

Pack up backpack for the next day �43

� hr

Wash the dinner dishes �21

� hr

Make a salad for the family dinner �41

� hr

VOCABULARYsequence

NameLESSON 3.1

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Problem Solving PS11

Represent, Compare, and Order DecimalsWrite the correct answer.

1. Write the numbers in order from leastto greatest.

6.2; 6.002; 6.02

2. Write the value of the digit 3 in thenumber 145.36.

3. Kirk ran 2.6 miles on Monday, 4.2 mileson Tuesday, 1.8 miles on Wednesday,and 5.1 miles on Thursday. Estimatehow many miles he ran in the 4 days.


4. Morgan carries between 4 and 6 logs ata time. At this rate, what is areasonable number of trips it will takeher to move a pile of 118 logs?

5. Which group of decimals is listed inorder from least to greatest? A 1.010, 1.001, 1.100B 2.10, 2.200, 2.3C 1.400, 1.040, 1.44D 2.03, 2.33, 2.003

6. Jill went to the store with $20. Shebought 6 cans of soup, 3 gallons ofmilk, and 2 packages of spaghetti.What else do you need to know to findhow much change Jill received? F The brand of milk Jill boughtG The size of a can of soupH The weight of a package of

spaghettiJ The cost of each item

7. What is the value of the underlineddigit in 34.17? A 1 tenB 1 oneC 1 tenthD 1 hundredth

8. Simeon played the piano between 2and 3 hours. What is a reasonableestimate of the number of minutes heplayed? F Less than 60 minutesG Between 60 and 120 minutesH Between 120 and 180 minutesJ More than 180 minutes

9. Write About It Explain how you would compare 4.08 and 4.3.

NameLESSON 3.2

Use Graphic AidsYou have used graphic aids such as tables to find information. You canmake a table to organize data with numbers to help you solve problems.Read the following problem.

Five friends have saved different amounts of money. Bob has $18.94;Dot, $25.37; Carol, $9.59; Ruth, $34.75; and Ann, $12.38. Who has savedthe second greatest amount of money? the second least amount?

1. Order the data in the table below to make the problem easier to solve.


3. Explain the strategy you used to solve the problem.

Reorder the data in the table to solve.

Name Amount Saved

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4. Mr. French is buying new officeequipment. The store requires him topay for the least and most expensiveitems in advance. How much does hehave to pay now?

5. There are five girls’ basketball teams inthe district. Which team is in secondplace?

MR. FRENCH’S OFFICEEquipment Price

scanner $299copy machine $1,769

printer $995phone system $488

computer $2,500

fax machine $547

GIRLS’ BASKETBALLTeam Games Won and Lost

Diamonds 1 win, 3 losses

Tigers 0 wins, 4 losses

Hawks 3 wins, 1 loss

Astros 2 wins, 2 losses

Rubies 1 win, 3 losses

VOCABULARYgraphic aids

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Estimate with DecimalsWrite the correct answer.

1. Is 18 or 24 a better estimate for theproduct 3.98 � 6.02?

2. Use estimation to determine which isgreater, 209.4 � 81.6 or 241.54 � 3.

3. The owner of a computer store had 12copies of a popular software programin stock. She ordered 8 more cartons,each of which contained 20 copies ofthe program. She used the expression12 � 8 � 20 to determine how manycopies she would have. What total didshe find?


4. Malik wants to read a 210-page bookduring his 12-day vacation. Heestimates that he can read 20 pagesper day in his free time. If Malik keepsto his estimate, will he be able to finishthe book in the 12 days? If so, on whichday will he finish?

5. Kaitlin spent $39.95, $17.80, $42.30,and $59.89 on gifts for her family.Which is the best estimate for the totalamount that she spent? A $150B $160C $170D $180

6. Collin drove 79.9 miles in the morningand 121.1 miles after lunch. What isthe best estimate of the differencebetween the two distances? F 20 milesG 30 milesH 40 milesJ 50 miles

7. On a bar graph comparing how studentsget to school, the bar representing thosewho ride bikes was half as tall as the barrepresenting those who ride a bus. Thebar for those who walk was twice theheight of the one for the students whoride a bus. If 40 students ride bikes toschool, how many students walk? A 80 studentsB 120 studentsC 140 studentsD 160 students

8. The Master Disk Company had sales of$2,800,000 in 1998. Creative CDs hadsales of $1,900,000 in 1998. If Master’ssales grow by $100,000 per year andCreative’s grow by $200,000, in howmany years will the sales of the twocompanies be equal? F 9 yearsG 10 yearsH 11 yearsJ 12 years

9. Write About It Explain two different ways to estimate the product47.92 � 8.7.

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Decimals and PercentsWrite the correct answer.

1. Carl paid for a $0.25 box of crackersand a $0.55 drink with a one-dollarbill. What percent of the dollar did hereceive in change?

2. There are 26 students in class 6-A, 24in class 6-B, 23 in class 6-C, and 27 inclass 6-D. What percent of the sixthgraders are in classes 6-A and 6-B?

3. Rama’s bus ride to or from school takes9 minutes. How long is she on the busin a 5-day school week?


4. A rectangular array of dots has 6 rows.There are a total of 216 dots in thearray. How many columns of dots arethere?

5. A computer in the school library has100 web sites bookmarked. Of these, 68are educational and 16 are travel-related. What percent of the sites arenot related to either education or travel?A 16% C 52%B 18% D 84%

6. Carlos is 7 years older than his sister.The sum of their ages is 13 less thantheir mother’s age. If their mother is 30years old, how old is Carlos? F 7 years old H 12 years oldG 10 years old J 17 years old

7. Using one possible route, the drivingdistance from New York City toPhiladelphia is 100 miles. If you drive1 hour at 50 miles per hour and onehour at 45 miles per hour, whatpercent of the trip will you still haveleft? A 95%B 50%C 10%D 5%

8. During a sale on film, a store charges$4.99 for a roll of 36 exposures. Youneed enough film to take individualpictures of all 100 students in the sixthgrade. If your budget for film is $25.00,how much extra money do you have? F $10.03G $14.97H $15.02J $20.01

9. Write About It Explain how you would find an unknown percentif you know that a figure consists of two regions and you knowthe percent represented by one region.

PS14 Problem Solving

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NameLESSON 4.1

Add and Subtract DecimalsWrite the correct answer.

1. Round 38.75 to the nearest wholenumber.

2. Paul has a balance in his checkbook of$268.53. He writes a check to the storefor $35.78. What is the new balance inhis checkbook?

3. Michael bought a CD for $11.87 and abook for $8.76. How much money didhe spend on the purchases?


4. The wall is covered with 27 rows ofcolorful tiles. If there are 43 tiles ineach row, how many tiles are on thewall?

5. Which list of numbers is in order fromgreatest to least? A 0.034, 0.03, 0.8B 0.065, 0.05, 0.012C 0.008, 0.07, 0.3D 0.12, 0.21, 0.030

6. Which expression shows one way touse compensation to add 58 � 43? F (58 � 3) � (43 � 3)G (58 � 3) � (43 � 3)H (58 � 2) � (43 � 2)J (58 � 2) � (58 � 2)

7. Philip and George ran a race. Philip’stime was 38.45 seconds and George’stime was 34.76 seconds. Whichexpression can be used to find out howmany seconds George finished beforePhilip?A 38.45 � 34.76B 38.45 � 34.76C 38.45 � 34.76D 38.45 � 34.76

8. Daniel has ridden a total of 58 miles onhis skateboard so far this month. Herides it about the same distance eachday. What else do you need to know tofind how many miles he rides eachday?

F The number of days in the monthG The length of the skateboardH What time he starts riding each dayJ How many days this month he has

ridden

9. Write About It Why is it important to align the decimal pointswhen you add decimals?

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NameLESSON 4.2

Multiply DecimalsWrite the correct answer.

1. Which is greater, 0.108 or 0.091? Use � or �.

2. Sonia wrote a check for $27.86. What isthe number of dollars written inwords?


3. Walter grew a pumpkin that weighed38.73 pounds. Bill grew a pumpkin thatweighed 42.1 pounds. How many morepounds did Bill’s pumpkin weigh thanWalter’s pumpkin? A 4.67 more poundsB 4.63 more poundsC 3.67 more poundsD 3.37 more pounds

4. Ted wants to use a special wallpaperborder in his living room. He has threepieces of border that are 11.7 meters,6.05 meters, and 24.75 meters long.How many meters of border does hehave in all? F 24.75 metersG 31.97 metersH 42.5 metersJ 641.45 meters

5. A pencil costs $0.85 and a pen costs$1.76. Wayne buys 12 pencils and 8 pens.Which expression can be used to findthe total cost of Wayne’s purchases? A (12 � 0.85) � (8 � 1.76)B (12 � 0.85) � (8 � 1.76)C (12 � 0.85) � (8 � 1.76)D (12 � 0.85) � (8 � 1.76)

6. A grocery store needs to stock a newcereal on the shelf. There are 8 shelvesthat can hold 6 boxes in each row.What else do you need to know to findout how many boxes of the cereal thestore can put out at once? F The height of the boxG How many rows of boxes fit on a

shelfH How much a box of cereal costsJ The brand of cereal

7. Write About It Explain how you could use a decimal square tomodel the product 0.3 � 0.2.

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NameLESSON 4.4

Divide with DecimalsWrite the correct answer.

1. Find the quotient.

7.4�1�5�3�.9�2�

2. Place the decimal point in thequotient.

235.468 � 8.6 � 2738

3. Jacob bought a new computer for$2,124.00. He is paying $88.50 a monthfor the computer. For how manymonths will he have to makepayments?


4. Selma needs a new notebook thatcosts $18.75 and a calculator that costs$23.64. How much money does sheneed to make the purchases?

5. Which expression is 211.68 � 12.6rewritten so that the divisor is a wholenumber? A 2116.8 � 126B 21168 � 126C 211.68 � 126D 21168 � 12.6

6. Which is the exponent form of theexpression?

24 � 24 � 24F 3 � 24 H 324

G 33 J 243

7. Loraine sleeps between 6 and 8 hourseach night. What is a reasonableestimate of the number of minutes shesleeps in a week? A Less than 1,500B Between 1,500 and 2,500C Between 2,500 and 3,500D Between 3,500 and 4,500

8. Hunter saves $3.50 each week to buy aCD boxed set that sells for $52.50. Hehas already saved $10.50. How manymore weeks does he need to savemoney? F 11 weeksG 12 weeksH 14 weeksJ 15 weeks

9. Write About It Describe a pattern you see 600 � 10 � 60 6 � 10 � 0.6in the set of problems at the right. 60 � 10 � 6 0.6 � 10 � 0.06

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NameLESSON 4.5

Use ContextIf there is a word, phrase, or paragraph you do not understand,context can help you. Context means the words, phrases,pictures, or graphic aids that go along with what you are reading.Context can help you decide how to interpret the remainder.

Read the following problem.

Thirty-eight sixth graders are going to see a band from PuertoRico that specializes in Caribbean music. Each driver can take4 students. How many drivers are needed?

1. Use context to help you decide how to treat the remainder, if thereis one. If there is a remainder, should you add 1 to the quotient,drop the remainder, or use it as the answer? Why?


Solve the problem. Use context to help you decide how to interpret theremainder.

3. The band needs 40 minutes of musicto make 1 CD. The songs they knowlast for 2 hours and 42 minutes. Howmany CDs could they cut now?

7. How many containers for 1 dozen eggsare needed for 2,000 eggs?

8. If 25 books fit on a shelf, how manyshelves are needed for 465 books?

4. Alexis Rivera wants to take somefriends to the concert. She has $135and each ticket costs $30. How manytickets can she buy?

5. The concert was attended by 1,000people. If there were 36 seats in a row,how many rows could have been filled?

6. The band has 5,000 copies of their newCD. If 73 music stores each get thesame number of copies of the CD, howmany CDs will be left over?

VOCABULARYcontext

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NameLESSON 4.6

Algebra: Decimal Expressions and EquationsWrite the correct answer.

1. Each child’s meal at a fast-foodrestaurant costs $2.79. What is thegreatest number of these meals thatcan be bought with $20.00?

2. Felipe is a teenager who is 10 yearsolder than his sister Irene. In 6 years,Felipe will be twice as old as his sister.How old is Felipe now?

3. The winning car in a race had anaverage speed of 203.7 miles per hour.This was b miles per hour faster thanthe second-place car. Write anexpression for the average speed of thesecond-place car.


4. The round-trip distance betweenKaitlin’s house and her school is 3.2 miles. Kaitlin rides her bike to school3 days per week. Write an expressionthat can be used to find the number ofmiles Kaitlin rides in w weeks.

5. At a self-service copy center, the costof making copies is $0.08 per copy forthe first 100 copies, $0.06 per copy forcopies 101–200, and $0.05 per copy forany above 200. Stan needs to make 7copies of a 30-page report. How muchshould he expect to pay? A $16.80 C $12.60B $14.50 D $10.50

6. Marla poured out g glasses of juice fora party she is hosting. If each glasscontained 0.2 liter of juice, whichexpression describes the total amountof juice she poured?

F 0.2g H 0g.2

G 0g.2 J 0.2 � g

7. After driving 159.7 miles, Rasheed hadr miles left to travel. If the totaldistance he needed to travel was 201.3miles, which equation can you use tofind the value of r? A r � 159.7 � 201.3B r � 201.3 � 159.7C 159.7r � 201.3D 201.3 � r � 159.7

8. At a school cafeteria, 6 carrot sticks areserved with each lunch order. Carrotsticks are purchased in bags of 120. If310 lunches were served today, howmany bags of carrots were opened? F 13 bagsG 14 bagsH 15 bagsJ 16 bags

9. Write About It Describe how you decided which operation wasneeded to find the total distance Kaitlin rides in w weeks in Problem 4.

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SamplesWrite the correct answer.

1. Find the product.

65.35 � 80.6

2. Evaluate the expression.

(72 � (5 � 3) � 22) � 40

3. Fred wanted to find out the favoritecolor of all the students in his middleschool. He surveyed all the students inhis class. Is this a random sample?Explain.

4. Cecily is ordering sodas for the classparty. She asks a student in the lunchline for her favorite soda and then asksevery tenth student. What kind ofsample is she using?


5. Thad conducted a survey on hair colorat his school. His results were 23students had blonde hair, 38 studentshad black hair, 7 students had red hair,and 19 students had brown hair. If hesampled 1 out of every 10 students athis school, how many people attendthe school?

A 900 peopleB 870 peopleC 820 peopleD 750 people

6. Jill surveyed students about their choicefor a new school color. The results werethat 45 people liked red, 33 liked green,16 liked orange, and 8 liked blue. If shechose a student at random from theschool’s enrollment list and then askedevery tenth student on the list, whichdescribes the school’s enrollment andher sample? F 1,020 students; random sampleG 1,002 students; systematic sampleH 1,020 students; systematic sampleJ 1,002 students; convenience sample

7. The owner of a grocery store ordered56 cases of cups. Each case holds 16packages. How many packages of cupsdid the store owner order? A 896 packages C 1,026 packagesB 1,006 packages D 1,128 packages

8. Paul has 1,716 eggs to put into cartons.Each carton holds one dozen eggs.How many cartons does Paul need tostore all the eggs? F 163 cartons H 143 cartonsG 153 cartons J 133 cartons

9. Write About It Why does a large sample generally give betterresults than a small sample?

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Bias in SurveysWrite the correct answer.

1. Bruce surveyed everyone in his mathclass to find out the favorite subject ofthe students in his school. Is hissample biased? Explain.

2. Lisa randomly surveyed 1 out of every10 people in her school to find outtheir favorite item in the cafeteria. Isher sample biased? Explain.

3. Tell how many people you wouldsurvey out of a group of 970, if yousurvey 1 out of every 10 people.


4. Tell how many people you wouldsurvey out of a group of 320, if yousurvey 1 out of every 10 people.

5. A supermarket wants to know thefavorite brand of juice of its customers.Which group of customers should thestore randomly survey to get resultsthat are not biased? A 1 out of every 50 child customersB 1 out of every 100 adult customersC 10 out of every 100 customers as

they leave the storeD 2 out of every 5 female customers

6. Rachel sold tickets for the local charity.On Monday she sold 245 tickets, onTuesday she sold 188 tickets, and onThursday she sold 96 tickets. Which isthe best estimate of how many ticketsRachel sold? F 300 ticketsG 400 ticketsH 450 ticketsJ 500 tickets

7. Larry needs to buy 60 cookies for hisparty. A dozen cookies cost $3.50,including tax. Which expression canbe used to find the total cost of thecookies that Larry wants to buy? A 60 � 12 � 3.50B 60 � 12 � 3.50C 60 � 12 � 3.50D 60 � 12 � 3.50

8. The head cook at a school wants toknow the favorite meal of the 870students who attend the school. Whichsample of students in the lunchroomwould not be biased? F 1 out of every 100 male studentsG 1 out of every 10 female studentsH Every eighth student passing

through the lunch lineJ Every student seated at one table

9. Write About It Why is it important to base your survey on arandom sample that is not biased?

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Use Graphic AidsOften you must look for relationships between data. You may have tocompare two or more numbers and add amounts. This is easier to doif you use a graphic aid such as a tally table.


Mr. Quang asked his students to name their favorite animal. Theresults are shown below. Which animal do most students likebest? Which animal was third in rank?

monkey squirrel dog squirrel catcat cat monkey dog monkeyrabbit dog cat cat monkeydog cat mouse snake dog

1. Make a tally table to organize the data. Read the data. Make onetally mark for each animal below its name.


Make a table to organize the data. Solve.

3. The Belle School Student Council soldbags of nuts to raise money. These aretheir results.peanuts walnuts peanutsbrazil nuts almonds almondsbrazil nuts peanuts almondswalnuts pecans pecanspecans almonds walnutswalnuts walnuts peanuts

How many bags of pecans or almondswere sold in all? Which type of nut soldbest?

4. The principal of a middle school neededto know how students travel to school.She randomly surveyed 20 students.

bike bike car bus

bus walk bike bike

walk bus bus bike

bike bike bus walk

walk bike bike bike

What fraction of students bike toschool? What fraction of studentstravel by car or bus?

Monkey Cat Rabbit Squirrel Dog Mouse Snake

VOCABULARYgraphic aid

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Frequency Tables and Line PlotsWrite the correct answer.

1. The scores on the last quiz are givenbelow. What is the range of the data?

2. The line plot shows the average lengthof a student’s stride in centimeters.How many students participated in thesurvey?

��

� � ��

30 31 32 33 34 35 36 37 38 39 40

3. The recorded temperatures of selectedcities were: 67°, 54°, 98°, 77°, 92°, 85°,83°, 90°, 63°, 74°, and 96°. What is therange of the temperatures? A 29°B 31°C 35°D 44°


4. Sara likes to swim between 20 and 30laps in her pool each day for exercise.What is a reasonable estimate of thenumber of laps she would swim in 35days? F Less than 300G Between 300 and 500H Between 500 and 700J More than 700

5. George helped his father plant 4,836trees last month. This month theyplanted 6,981 trees. Which is the bestestimate of how many more treesGeorge and his father planted thismonth than last month? A 2,000 treesB 2,500 treesC 3,000 treesD 3,500 trees

6. The results of the last test were: 67, 84,98, 70, 72, 66, 78, 74, 90, 92, 77, 93, 95,79, 91, 87, 88, 86, 68, 71, 62, and 78. Ifthe data were grouped by 60s, 70s, 80s,and 90s, what would the frequency befor the 90s? F 3G 4H 6J 8

7. Write About It If the results of a survey are displayed on a lineplot, how can you tell which answer was the most popular?

Scores15 11 8 19 2016 14 18 20 1916 14 11 19 20

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Measures of Central TendencyWrite the correct answer.

1. Find the mean of the numbers.

23, 86, 97, 45, 12

2. Evaluate the expression below.

a � b � 12.7 for a � 4.9 and b � 28.6

3. Find the median of the numbers.

13, 8, 9, 16, 18


4. If you survey 1 out of every 10 people,how many would you survey out of agroup of 23,800 people?

5. Yolanda has received scores of 98, 76,87, 98, and 80 so far this year on hermath tests. What is the mean of hertest scores? A 98B 87.8C 87.5D 87

6. Fred conducted a survey regarding haircolor. Which measure of centraltendency should he use to report thehair color that occurs most often? F rangeG meanH medianJ mode

7. A pilot logged 87,984 miles of flighttime in one month. If he flew the sameroute every day for 20 days, what is agood estimate for the length of hisroute? A 3,500 miB 4,000 miC 4,500 miD 5,000 mi

8. Mr. Jacob works between 9 and 12hours each day, 5 days a week. What isa reasonable estimate of the number ofhours he works in 50 weeks? F Less than 400 hrG Between 400 and 1,000 hrH Between 1,000 and 2,000 hrJ More than 2,000 hr

9. Write About It Explain why the mean of a set of data is sometimesa number that is not in the set of data.

NameLESSON 5.5

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Outliers and Additional Data Write the correct answer.

1. Brittany had test scores of 80, 85, 85,92, and 90. If her score on the next testis 65, which measures of centraltendency change?

2. While shopping, Debra estimated thesum of $48.99 and $78.85 as $130. Howdid she know that the result was anoverestimate?

3. Robert’s scores on six math tests are90, 80, 80, 85, 88, and 45. How muchhigher is the mean of his scoreswithout the outlier than when theoutlier is included?


4. In Grades 6 through 8 at Adams MiddleSchool, 45% of the members of thecomputer club are eighth graders and19% are seventh graders. What percentare sixth graders?

5. John wants to pay for a book that costs$28. He has 3 ten-dollar bills, 4 five-dollar bills, and 5 one-dollar bills. Inhow many different ways can John payexactly $28 for the book using hismoney? A 1 way C 3 waysB 2 ways D 4 ways

6. A custodian is changing all thelightbulbs in an auditorium. The bulbscome in packages of 4. There are 17light fixtures in the auditorium andeach has 5 bulbs in it. How manypackages of bulbs must the custodianopen? F 20 packages H 22 packagesG 21 packages J 23 packages

7. Danielle’s first 3 test scores were 86, 87,and 91. If a perfect score is 100, what isthe highest mean score she can haveafter 4 tests? A 89B 90C 91D 92

8. The five linemen on the football teamweigh 240 pounds, 228 pounds, 230pounds, 256 pounds, and 266 pounds.The quarterback weighs 172 pounds.How much greater is the mean weightof the five linemen than the meanweight of the six players? F 244 pounds H 20 poundsG 232 pounds J 12 pounds

9. Write About It In Exercise 3, what is the effect on the median andthe mode of Robert’s scores if the outlier is removed from hisscores?

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Data and ConclusionsWrite the correct answer.

1. Karin concludes from the table thatthe percent of glass recycled in Japan ismore than twice that recycled in theUnited States. Is she correct?

Use the table below for 3–4.

Choose the letter for the best answer.Use the survey results given in the chart below for 5–7.

2. Stefon concludes that the percent ofglass recycled in the Netherlands is 4times that in Britain. Is he correct?

3. If 15 sailors stand watch one at a timein order, what is the greatest numberof hours a sailor must stand watch inany 48-hour period?

4. If each watch is taken by a differentsailor, how many sailors will stand awatch during one week at sea?

6. Angela correctly concludes that thepercent of students who had cereal isabout . F 25%G 50%H 75%J 90%

?

5. Mark correctly concludes that the leastcommon breakfast was . A Toast C WafflesB Cereal D Nothing

?

7. How many more students hadsomething for breakfast than hadnothing for breakfast? A 14 more studentsB 54 more studentsC 68 more studentsD 82 more students

8. Write About It For Exercise 6, how did you estimate the percent ofstudents who had cereal?

Watches at Sea

Starting Time Noon 4 P.M. 8 P.M. Midnight 4 A.M. 8 A.M. 10 A.M.

Length of Watch 4 hr 4 hr 4 hr 4 hr 4 hr 2 hr 2 hr

PERCENT OF GLASS RECYCLEDBritain 17%Japan 55%

Netherlands 57%United States 20%

WHAT DID YOU HAVE FOR BREAKFAST?Toast 17 studentsCereal 39 studentsWaffles 12 studentsNothing 14 students

Use the table at the right for 1–2.

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Make and Analyze GraphsWrite the correct answer.

1. Jane wants to make a graph tocompare the types of music studentslisten to. She also wants to showwhether there is a difference betweenthe music girls like and the music boyslike. What type of graph should Janeuse?

2. The double-line graph shows theprofits of two companies in millions ofdollars. Which company made moremoney in 1996?

3. A city in the West recorded a hightemperature of 87°F and a lowtemperature of 32°F. What was therange of the temperatures?

Write the letter of the best answer.

4. When Dave was 9 years old, hisparents started recording his heightevery year. He started with a height of45 inches and is now 62 inches tall.What is the range of his height? A 21 in. C 19 in.B 20 in. D 17 in.

5. The Fredrickson family drove acrossthe country on vacation. They drovethrough 36 states in 9 days. What is theaverage number of states they drovethrough each day? F 6 H 4G 5 J 3

6. Albert gets paid about $225 a week.What is a reasonable estimate of how much he makes in a year? A Less than $12,000B Between $12,000 and $14,000C Between $14,000 and $18,000D Between $18,000 and $20,000

7. Which type of graph would be mostappropriate for displaying the numberof students in each of six homeroomsfor a sixth-grade class? F bar graph H line graphG circle graph J double-line

graph

8. Write About It When making a double-bar graph or a double-linegraph, why is it necessary to include a key?

PROFITSCompany ACompany B

Year

Am

ount

of

Mon

ey(m

illio

ns o

f do

llars

)

93 94 95 96 97

50403020100

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Find Unknown ValuesWrite the correct answer.

1. While driving from Cincinnati toToledo, Ohio, a distance of 200 mi,Jamie averages 40 mi per hr. If she leftat 10:30 A.M., at what time should sheexpect to arrive in Toledo?

2. In the 1990 Census, the population ofLos Angeles was 3,485,557. About howmany more people would it take forthe population to reach 4,000,000?


3. Kiona kept a record of how much shesaved by using an on-line groceryshopping service. Over the first 6weeks she has used this service, shesaved $102. If her savings continue atthe same rate, about how much canshe expect to save during the seventhweek she uses the shopping service?

4. Carmen pays $5.95 per month for along-distance calling plan that chargesher $0.07 per min for her long-distancecalls. She averages about 2 hr of longdistance calls per month. About howmuch does she save each month over aplan that charges $0.15 per min for hercalls, with no monthly fee?

5. Ty mows lawns after school for $45 perweek. He wants to use the money to payfor a trip that will cost $350. If he spends$20 each week and saves the rest, whatis the least number of weeks he mustwork to pay for the trip? A 12 weeks C 14 weeksB 13 weeks D 15 weeks

7. An airplane is climbing at a steady rateof 600 ft per min. From the time itreaches an altitude of 3,600 ft, howmany more minutes will it take to reachan altitude of 9,000 ft? A 6 min C 8 minB 7 min D 9 min

8. Brady counted 240 words on the firstpage of a reading assignment. If thereading assignment is 6 pages long,about how many words should heexpect to read? F 1,200 words H 1,440 wordsG 1,340 words J 1,500 words

6. For an art project, you need to cutsquares that measure 4 in. on eachside from a rectangular sheet of paperthat measures 8 in. by 12 in. What isthe greatest number of squares thatyou can cut? F 4 squares H 8 squaresG 6 squares J 10 squares

9. Write About It In Exercise 1, what formula could you use to findthe time Jamie would arrive in Toledo?

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Stem-and-Leaf Plots and HistogramsWrite the correct answer.

1. Harry wants to make a graph to showthe number of cars that go down hisstreet during 1-hour intervals duringthe day. Would a bar graph or ahistogram be more appropriate?

2. A contest to see who could jump thefarthest was conducted. The shortestjump was 87 centimeters and thelongest jump was 162 centimeters.What is the range for the data?

3. If you survey 1 out of every 10 people,how many would you survey out of agroup of 930 girls?


4. Gregg wants to compare thepopulation in five states. Would a bargraph or a histogram be moreappropriate?

5. A set of data ranges from 12 to 86.What intervals would you use todisplay this data in a histogram with 4 intervals? A 10–39, 40–49, 50–69, 70–89B 10–19, 20–39, 40–59, 60–89C 10–29, 30–49, 50–69, 70–89D 10–29, 30–39, 40–49, 50–89

6. This year Mary has scored 87, 89, 93,94, 78, 76, 99, and 100 on her mathtests. Which could be the stems of astem-and-leaf plot of the data? F 7, 8, 9, 10G 1, 7, 8, 9H 70, 80, 90, 100J 7, 8, 9

7. Dolly and her three friends pool theirbaby-sitting money. Last month theyearned a total of $90. If they share themoney equally, how much would eachgirl receive? A $21.50 C $23.50B $22.50 D $30.00

8. Rick has a book with 48 pages ofstickers. Each page has between 12and 23 stickers. What is a reasonableestimate of the total number ofstickers in Rick’s book? F Fewer than 550G Between 550 and 1,100H Between 1,100 and 1,600J More than 1,600

9. Write About It Why are the bars in a histogram connected ratherthan separated?

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LESSON 6.5

Box-and-Whisker GraphsWrite the correct answer.

1. What is the lower quartile of the data?

24, 26, 28, 29, 30, 32, 34, 36, 37

2. What is the upper quartile of the data?

56, 58, 58, 59, 60, 62, 64, 64, 90

3. George is 145 centimeters tall and hisbrother is 167 centimeters tall. What isthe mean of their heights?


4. If you survey 1 out of every 10 people,how many would you survey out of agroup of 145,910 people?

5. Ashley dusts the house for her motherevery 5 days. How many times in ayear does Ashley dust the house for hermother? A 52 C 73B 63 D 75

6. Peter wants to use a box-and-whiskergraph to display his test scores. If hisscores are 100, 79, 64, 89, 80, 86, and 89,what is the median? F 89 H 81G 86 J 25

7. Kate took 131 pictures of herclassmates during the year. She gaveeach of the 31 students in the class 2pictures. Which number sentencecould be used to find p, the number ofpictures Kate has left after giving someto her classmates? A p � 131 � (31 � 2)B p � 131 � (31 � 2)C p � 131 � (31 � 2)D p � 131 � (31 � 2)

8. On the last test, nine students scored64, 68, 68, 70, 72, 78, 82, 84, and 100points. What is the upper quartile ofthe data? F 78, 82, 84, and 100G 68H 72J 83

9. Write About It Into how many equal parts does the lower quartiledivide the lower half of the data? Explain.

NameLESSON 6.5

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Analyze GraphsWrite the correct answer.Use the graph below for 1–3. 1. After looking at the graph, Casey

decided that the area of Argentina wasabout three times the area of Mexico.Explain why Casey’s conclusion iswrong.

2. Explain how the graph could be fixedso that Casey would not have made themistake he did.


3. Use the graph to estimate the totalcombined area of Mexico andArgentina.

Use the graph below for 4–6. 4. During which of these times didDominique’s dog gain the least amountof weight? F from January to FebruaryG from February to MarchH from March to AprilJ from April to May

5. If the scale started at 0 and ended at60, with intervals of 2, how would theappearance of the graph change? A The line would be steeper.B The line would be flatter.C The line would look the same as it

does now.D The line would be a straight line.

6. If the scale began at 0, which intervalwould make Dominique’s dog’s weightgain seem the greatest? F an interval of 2 lbG an interval of 5 lbH an interval of 10 lbJ an interval of 15 lb

7. Write About It Why does increasing the size of the interval used inthe vertical scale of a line graph make the line seem flatter?

LAND AREAS

Mexico ArgentinaCountry

Are

a (in

mill

ions

of s

quar

e m

iles)

1.11.00.90.80.70.6

DOMINIQUE’S DOG

MonthJan Feb Mar Apr May

5856545250

0

Wei

ght

(in p

ound

s)

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DivisibilityWrite the correct answer.

1. A bolt manufacturing company has12,885 bolts to be put into bags. Thepacking machine can be set to sealeither 3, 5, or 6 bolts into each bag.Can the machine be set for any of thethree numbers without any bolts beingleft over? If so, which setting or settingscan be used?

2. Scott earned $35, $40, $40, $25, and$45 for 5 weeks of part-time work.During a school break, he worked full-time for one week and earned $187.How much greater were his meanweekly earnings with the full-timeweek included than without it?

3. What is the least number that isdivisible by 2, 3, 4, 5, 6, 8, 9 and 10?What is the least number if 7 isincluded?


4. A supermarket manager wants to makea pyramid of 110 cereal boxes fordisplay. If cereal boxes are packed incartons of 12, what is the least numberof cartons she needs to open?

5. A warehouse received 1,448 copies of abook. The manager wants to placethem on shelves. Which number ofshelves can he use if he wants thesame number of books on each shelf? A 3 shelves C 5 shelvesB 4 shelves D 6 shelves

6. Amy had a total of $81.60 to spend on4 gifts. She bought 3 copies of thesame book and then had $27 left tospend on a sweater. How much did shepay for each copy of the book? F $9.00 H $27.00G $18.20 J $54.60

7. Max sells popcorn and potato chips atthe ballpark. During one game, he solda total of 136 bags. He sold 12 fewerbags of chips than popcorn. Howmany bags of chips did he sell?A 124 bags C 74 bagsB 84 bags D 62 bags

8. A commercial jet made 3 trips duringone 24-hour period, each time carryingthe same number of passengers. Howmany passengers might the plane havecarried that day?F 516 passengers H 620 passengersG 586 passengers J 634 passengers

9. Write About It Explain how you solved Problem 8.

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Prime FactorizationWrite the correct answer.

1. Write the prime factorization of 42. 2. List the factors of 30.

3. The prime factors of a number aregreater than 6 and less than 12. Thesmallest prime factor is used twice; theother(s), only once. What are thefactors? What is the number?


4. Roger agreed to watch his youngersiblings on August 7th and everyseventh day after that. How many dayswill Roger watch his younger siblingsin August?

5. What is the prime factorization of 18 inexponent form? A 22 � 32

B 2 � 9C 3 � 6D 2 � 32

6. Which number is composite?

F 13G 21H 23J 29

7. Lucille is having a party. She invited 8friends and wants to have between 4and 8 balloons for herself and eachfriend. What is a reasonable number ofballoons to buy for the party? A 27 balloonsB 32 balloonsC 45 balloonsD 81 balloons

8. In her last 4 basketball games, Tarascored 26, 18, 34, and 27 points. Whichis the best estimate of Tara’s totalpoints scored for the 4 games?

F Less than 100G Between 100 and 120H Between 120 and 140J Between 140 and 160

9. Write About It Explain how you can tell which prime factorizationis for the greater number.

23 � 32 22 � 33

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LESSON 7.3

Least Common Multiple and Greatest Common FactorWrite the correct answer.

1. What is the GCF of 8 and 20? 2. Name the first four multiples of 30.

3. Balloons come in packages of 10 andparty favors come in packages of 8. Billwants to have the same number ofballoons and favors. What is the leastnumber of packages of balloons andparty favors he needs to buy so that hehas none left over?


4. Write the prime factorization inexponent form.

2 � 2 � 3 � 3 � 5 � 5 � 5

5. Which is the GCF of 72 and 200? A 2B 8C 12D 16

6. Which is the LCM of 4, 5, and 6? F 1G 20H 60J 120

7. Charley bought 7 packs of gum for$0.65 each, including tax. He gave theclerk $20. Which number sentencecould be used to find c, the change theclerk gave him back from hispurchase?

A c � $20 � (7 � $0.65)B c � $20 � (7 � $0.65)C c � $20 � (7 � $0.65)D c � $20 � (7 � $0.65)

8. Wesley needs 6 cans of paint, a brush,and a roller to paint his room. He has$127 saved to buy the supplies. Whatelse do you need to know to determinewhether Wesley has enough money topaint his room? F The cost of the paint, brush, and

rollerG The size of the paint cansH The height of his roomJ The length of his room

9. Write About It Explain how you can tell the number of primefactors a number has when its prime factorization is written inexponent form.

NameLESSON 7.3

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Reading Strategy PS35

Synthesize InformationTo synthesize means to form a whole by combining parts. You cancombine new information to make something from the separateparts. One way to do this is to make an organized list. Read thefollowing problem.

Al, Jo-Jo, and Tom are standing on the first step of astaircase. There are 16 steps in all. Al goes up thestaircase one step at a time. Jo-Jo skips one step eachtime. Tom skips two steps each time. On which stepswill they all place a foot?

1. Make a list to show on which step each person steps.

Al: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Jo-Jo:

Tom:

2. Synthesize the information by finding the number that appears inall three lists. Solve the problem.

Synthesize the information by making an organized list. Solve

3. Al, Jo-Jo, and Tom are climbing thestaircase, as described above. All threeboys start on their left foot. Which isthe next step on which they will allplace their left foot?

4. Al walks 1 mi in 14 min. Jo-Jo bikes 1mi in 6 min. Tom runs 1 mi in 7 min. Ifthey all start from the same place on a1-mi track, how many miles will eachboy have traveled when they are all onthat spot again?

5. Al, Jo-Jo, and Tom are climbing thestaircase. They all start on their leftfoot. Will all three boys ever step onthe same stair with their right foot?Explain.

6. Jo-Jo jogs every fourth day of eachmonth. Al jogs every sixth day of eachmonth. On which days of each monthcan they jog together?

VOCABULARYsynthesize

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Equivalent Fractions and Simplest FormWrite the correct answer.

1. Write �12

20� in simplest form. 2. What is the LCM of 4 and 6?

3. Pauline has 8 adventure books, 4 booksof poems, and 6 animals books. Whatfraction of the books are books ofpoems? Write the fraction in simplestform.


4. Vickie made 20 cookies to shareequally with friends. She will give thesame number of cookies to each friendand keep that same number forherself. With how many friends canshe share the cookies? List all thepossible numbers of friends.

5. What number is missing from thefactor tree?

36

2 � 18

2 � �

3 � 3A 2 C 9B 3 D 16

6. What are the factors common to thenumerator and denominator of �

25

44�?

F 1, 2, 3, 6G 1, 2, 3, 6, 8H 1, 2, 3, 4, 6J 1, 2, 3, 6, 18

7. Which is the simplest form of thefraction �

37

22� ?

A �25

� C �188�

B �49

� D �12

�

8. Abigail saved $3.58, $12.64, $9.45, and$23.60 in the last four weeks. What is agood estimate of how much Abigailsaved in the last four weeks? F Less than $20G Between $20 and $40H Between $40 and $60J Between $60 and $80

9. Write About It Explain why dividing the numerator and thedenominator of a fraction by the GCF is the most efficient way ofsimplifying the fraction.

NameLESSON 8.1

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Mixed Numbers and FractionsWrite the correct answer.

1. Write 4�35

� as a fraction. 2. Write �24

40� in simplest form.

3. Alex found a piece of lumber in thewood pile that is �

47

� feet long. He needs3 feet to do a project. Does he haveenough lumber for the project?Explain.


4. Jane has envelopes in packets of 4 andnote cards in packets of 6. What is theleast number of packets of each sheneeds in order to have an equalnumber of envelopes and note cards?

5. Which fraction is equivalent to 5�78

�?

A �681� C �

480�

B �487� D �

385�

6. Which mixed number is equivalentto �

897�?

F 8�79

� H 9�59

�

G 9�49

� J 9�23

�

7. Betty’s father earned $38,967.43 lastyear. Each month $245.32 was taken outof his pay for deductions. Which numbersentence could be used to find m, theamount of money he took home eachmonth? A m � ($38,967.43 � 12) � $245.32B m � ($38,967.43 � 12) � $245.32C m � ($38,967.43 � $245.32) � 12D m � ($38,967.43 � $245.32) � 12

8. Devin has between $12 and $20deducted from his check every monthfor charity. What is a reasonableestimate for the amount of money hewill have deducted for donations tocharity in a year? F $50G $200H $300J $400

9. Write About It Can any whole number be written as a fraction?Explain.

NameLESSON 8.2

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Compare and Order FractionsWrite the correct answer.

1. Beth has a box of 20 red pencils and abox of 16 blue pencils. If she makesequal-size groups of all red or all bluepencils, what is the greatest numberthat can be in each group so that nopencils will be left over?

2. Kim called her brother from her hotelafter stopping for the night while on atrip. She told him she had completed �

58

�

of her trip. Had she completed at leasthalf the trip? Explain.

3. A doughnut shop uses the followingformula when selling its doughnuts:

P � $0.75 � d,where d is the number of doughnutspurchased and P is the price thecustomer pays. What is the greatestnumber of doughnuts a customer canbuy with $5?


4. José read a cake recipe that called for �34

�

cup flour, �12

� cup sugar, and �23

� cup milk.He lined up the ingredients in order bythe amount, from least to greatest.Which ingredient did José put at theend of the line?

5. Evelyn said that she had finished lessthan half of her homework problems.What fraction of the problems mightEvelyn have completed?

A �35

� C �58

�

B �38

� D �45

�

6. Four friends are all reading the samebook. Gordon has read �

12

� the book,Nick has read �

23

�, Yvonne has read �26

�, andCurtis has read �

25

�. Which of them hasread the greatest part of the book? F Gordon H NickG Yvonne J Curtis

7. This year’s sixth grade in Glenn MiddleSchool has 6 classes. Which is thenumber of sixth-grade students if thereare the same number of students ineach class? A 184 students C 170 studentsB 172 students D 168 students

8. Di has 1 red marker, 1 blue marker,and 1 green marker. She plans to makea design having 3 vertical stripes, oneof each color. How many differentdesigns can Di make? F 3 designs H 9 designsG 6 designs J 12 designs

NameLESSON 8.3

9. Write About It What are some different ways to compare a fraction to �12

�?

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Fractions, Decimals, and PercentsWrite the correct answer.

1. Amir had �34

� of a dollar and Dale had$0.83. Who had more money?

2. Kate read the number 0.345 as “345hundredths.” Was she correct? Explain.

3. The winning times for the men’s100-meter run in three recent Olympicsare given below. Put the winning timesin order from fastest to slowest.

1988 1992 19969.92 sec 9.96 sec 9.84 sec


4. The winning times for the women’s400-meter relay in the 1988, 1992, and1996 Olympics are given below. Inwhich year was the fastest time run?1988 1992 1996

41.98 sec 42.11 sec 41.95 sec

5. Polly listens to 5 hours of classicalmusic each week. Which is the bestestimate of how many minutes ofclassical music she listens to in 19weeks? A 4,000 minB 6,000 minC 8,000 minD 10,000 min

6. Nancy wants to buy 24 sodas for herparty. A 6-pack of soda costs $2,including tax. Which expression can beused to find the total cost of the sodasthat Nancy wants to buy? F 24 � $2G 6 � $2H (24 � 6) � $2J (24 � 6) � $2

7. The distance from Shania’s house toschool is �

35

� of the distance from Faith’shouse to school. What percent of thedistance that Faith travels eachmorning does Shania travel? A 3.5% C 50%B 35% D 60%

8. Park ran 0.8 mile. Nicholas said that heran the same fraction of a mile. Howfar did Nicholas run?

F �45

� mi H �15

� mi

G �35

� mi J �18

� mi

NameLESSON 8.5

9. Write About It Explain how to compare the fraction �23

� and thedecimal 0.7 to see which is greater.

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LESSON 9.1

Estimate Sums and DifferencesWrite the correct answer.

1. Jon won �13� of his tennis matches. Tori

won 0.45 of her matches and Tim won�25� of his. If they all played the samenumber of matches, who won the most?

3. Mary has �34� gal of milk. She needs to use

�13� gal in one recipe and �

14� gal in another

recipe. Does she have enough milk?


5. Sid has two pieces of fabric. One pieceis �1

52� yd and the other piece is �

16� yd.

Estimate the total amount of fabric he has.

A1–4 yd C

3–4 yd

B1–2 yd D 1 yd

7. On Monday 45,789 people attended a game in the stadium. On Tuesday36,984 people attended a game in thestadium. Which is the best estimate ofhow many more people attended thegame on Monday than on Tuesday?A 7,000B 8,000C 9,000D 10,000

2. Working on the computer, Julie used15% of the available time. At that point60% of the time was left. How much ofthe computer time was available beforeJulie worked?

4. Thad practiced playing the flute for 1�

34� hr before dinner and 2�

18� hr after

dinner. About how long did Thadpractice playing his flute?

6. Kyle has 1�58� ft of twine. He gave �

12� ft to

his friend. About how much twine doeshe have left?

F 2 ft H 1 ft

G 11–2 ft J

1–2 ft

8. Nancy measured her stride to be 45.7 cm. She then went for a walk andcounted 352 steps. Which expressioncan be used to find the distance shewalked in centimeters?

F 352 � 45.7G 352 � 45.7H 352 � 45.7J 352 � 45.7

NameLESSON 9.1

9. Write About It Explain how you know whether to round afraction to 0, �

12�, or 1.

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Add and Subtract FractionsWrite the correct answer.

1. List all the factors of 24.

3. Olga has �34� yd of blue ribbon. She also

has �38� yd of red ribbon. How much

ribbon does she have altogether?


5. What is the prime factorization of 48?

A 2 � 2 � 3B 2 � 2 � 2 � 2 � 2C 2 � 2 � 2 � 2 � 3D 2 � 2 � 2 � 3 � 3

7. The third-grade class painted �14� of the

school fence, the fourth-grade classpainted �

15� of it, and the fifth-grade

class painted �25� of it. How much of the

fence has been painted?

A4–5

B13—15

C17—20

D9—

10

2. What is the prime factorization 3 � 3 � 5 � 7 � 11 � 11 written inexponent form?

4. Bruce walks �78� mi to school and

his friend walks �13� mi to school. How

much farther does Bruce have to walkthan his friend?

6. Todd had �78� gal of paint. He used �

12� gal

on one project and �14� gal on another

project. How much paint does he have left?

F1–8 gal H

5–8 gal

G3–8 gal J

5–3 gal

8. In the last four days, the localswimming pool has been used by 348people, 276 people, 573 people, and621 people. Which is the best estimateof the total number of people who haveused the pool in the last four days?

F 1,850G 2,000

H 2,200

J 2,350

9. Write About It Explain how you found the least commondenominator for Exercise 6.

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PS 42 Problem Solving

Add and Subtract Mixed NumbersWrite the correct answer.

1. Write �12


3. Devon worked on her homework for 2�

34� hr on Friday and 1�

12� hr on Saturday.

How much longer did she work onFriday than on Saturday?


5. What is the GCF of 30 and 40?

A 2B 10C 30D 40

7. Hank walks 4�14� blocks to school and

his friend Jonas walks 6�38� blocks to

school. How much farther does Jonashave to walk?

A 17–8 blocks

B 21–8 blocks

C 21–4 blocks

D 23–8 blocks

2. List all of the factors of 42.

4. Victoria taped a piece of ribbon thatwas 3�

13� yd long to a piece that was 1�

14� yd

long. How long are the two pieces ofribbon together?

6. What is �475� written as a mixed number?

F 73–5

G 63–7

H 65–7

J 55–7

8. At a flea market, Theresa bought 5�

23� yd of lace trim and 8�

34� yd of ribbon

trim. How much trim did she buyaltogether?

F 135–8 yd

G 135—

12 yd

H 137—

12 yd

J 145—

12 yd

9. Write About It When adding mixed numbers, what do you dowhen the fraction part of the sum has a numerator that is greaterthan the denominator?

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Problem Solving PS 43

Subtract Mixed NumbersWrite the correct answer.

1. Write 7�29� as a fraction.

3. The nature club hiked 5�18� km on

Saturday and 4�34� km on Sunday. How

much farther did they hike on Saturdaythan on Sunday?


5. What is the LCM of 4, 7, and 8?A 14B 28C 56D 224

7. The electrician had 45�12� ft of wire.

He used 3�78� ft of it to wire a CD player.

How much wire did he have left?

A 415–8 ft

B 417–8 ft

C 423–8 ft

D 425–8 ft

2. Write �51

21� as a mixed number or whole

number.

4. Rachel bought 8�12� yd of fabric. She used

4�23� yd to make a blouse and skirt. How

much fabric did she have left?

6. What is the GCF of 20 and 28?F 2G 4H 5J 7

8. In 1998, a northern city had 24�23� ft of

snow. In 1999 that same city had only8�

34� ft of snow. What was the difference

in the snowfall amounts?

F 167–8 ft

G 161–8 ft

H 1511—12 ft

J 157—

12 ft

9. Write About It Explain how to write a mixed number asa fraction.

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SummarizeTo summarize is to state something in a brief way. Knowing howto summarize information is a useful skill. Sometimes drawing adiagram to display information is a good way to summarizeinformation.


Rosie walks dogs to earn money. She leaves home with her owndog, Loki, and picks up a poodle, Dante, �

12� mi east of her home.

Next she gets Noni, another poodle, who lives �34� mi east of Dante.

Another �14� mi east, she picks up a spaniel, Higgins. Rosie then

drops off the dogs at their houses in this order: first Loki, thenDante, then Noni, then Higgins. Then Rosie walks home. How farhave Rosie and each dog walked?

1. Draw a diagram to summarize the information.


Rosie walked mi. Loki walked mi. Dante walked mi.

Noni walked mi. Higgins walked mi.

Draw a diagram to summarize the information. Solve the problem.

3. Bill, Samantha, and Tim are doing a science project together.Samantha lives �1

70� mi west of the school. Tim lives �

25� mi west of

Samantha. Bill lives �13� mi east of the school. After school, they walk

to Bill’s house to pick up some equipment. Then they go to Tim’shouse to work. When they are finished, Bill and Samantha walkhome. How far did each student walk after school?

Bill walked mi. Samantha walked mi. Tim walked mi.

NameLESSON 9.7

VOCABULARYsummarize

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NameLESSON 10.1

Estimate Products and QuotientsWrite the correct answer.


9. Write About It When is it appropriate to use an estimate?

1. The water behind a dam begins rising ata rate of 1�

45� in. per hr during a spring

thaw. The water will spill over the damif it rises 72 in. Estimate the number ofhours before the dam will overflow.

3. Mikel used 3�16� qt of potting soil per plant

to pot 15 small shrubs. About howmuch potting soil did Mikel use for allof the shrubs?

2. Dillon wants to survey 1 out of every 10adults in his neighborhood between theages of 25 and 40. He has generated alist of 220 people in this age group. Howmany people should he survey?

4. Ann is 136.8 centimeters tall andTheresa is 128.9 centimeters tall. Howmuch taller is Ann than Theresa?

5. Al is filling �34� lb packages of chocolate

chip cookies. About how manypackages can be filled from a 44 lbcontainer of chocolate chip cookies?A about 33 packages

B about 44 packages

C about 60 packagesD about 66 packages

7. Karl found that a garden measured4�

78� yd by 12�

56� yd. Which is the best

estimate of the area of the garden?A (4 � 12) yd2

B (4 � 13) yd2

C (5 � 12) yd2

D (5 � 13) yd2

6. Nikki’s 8 dogs each get 4�16� c of dry dog

food every day. Estimate the totalamount of dry dog food that sheprovides for the dogs each day. F about 4 c

G about 12 c

H about 33 cJ about 100 c

8. About how many �23� lb boxes of raisins

can be filled from a 15�12� lb bag of raisins?

F about 10 boxes

G about 15 boxes

H about 20 boxesJ about 25 boxes

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NameLESSON 10.2

Multiply FractionsWrite the correct answer.


9. Write About It Look at the model in Problem 3. Explain how you cantell which two fractions are factors and which fraction is the product.

1. Write �11


3. Write the multiplication shown by themodel. Then write the product.

2. List the first four multiples of 9.

4. Write the multiplication shown by themodel. Then write the product.

5. Which is the missing number?

�78

� � �■5

� � �170�

A 1 C 3B 2 D 4

7. Luke exercises �34� hr each morning. He

spends �13� of this time riding an exercise

bike. What part of an hour does Lukespend riding the bike?

A �14

� hr C �12

� hr

B �13

� hr D �34

� hr

6. Which is a list of all the factors of 50?F 5, 10

G 2, 5, 10, 25

H 1, 2, 5, 10, 25, 50

J 1, 2, 5, 10, 15, 20, 25, 50

8. Sally is reading a book for school. Shehas read 27 pages every day for the last15 days. How many pages has Sally readso far?F 42 pages

G 300 pages

H 405 pages

J 450 pages

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NameLESSON 10.3

Multiply Mixed NumbersWrite the correct answer.


9. Write About It When rewriting a mixed number as a fraction, why doyou multiply the whole number by the denominator of the fraction?

5. In the long jump, Bryn’s longest jump is14�

13� ft. April’s best jump is 1�

18� times as far

as Bryn’s. What is April’s longest jump?

A 13�12

14� ft C 16�

18

� ft

B 15�12

14� ft D 16�

12

� ft

7. Derick spent 1�12� hours cleaning up after

an event. Charles spent 2�14� times as

many hours as Derick did cleaning up.Which number sentence can be used tofind c, the amount of time Charlesspent cleaning up?

A c � 2�14

� � 1�12

� C c � 2�14

� � 1�12

�

B c � 2�14

� � 1�12

� D c � 2�14

� � 1�12

�

6. Andrew has a collection of 36 baseballcards. Jared has 1�

56� times as many

baseball cards as Andrew. How manybaseball cards does Jared have in hiscollection?F 38 cards H 66 cardsG 60 cards J 396 cards

8. Sam worked four different jobs lastweek. On the first job he earned $28.75,on the second job he earned $18.03, onthe third job he earned $50, and on thefourth job he earned $68.93. Which isthe best estimate of how much Samearned last week?F $200 H $120

G $170 J $100

1. Rewrite the problem by changing eachmixed number to a fraction. Thenmultiply; write the answer in simplestform.

4�23

� � 3�25

�

3. Peter needs �18� of a cup of butter to

make cookies and �18� of a cup of butter

to make bread. How much butter in alldoes Peter need to make cookies andbread?

2. Rewrite the problem by changing eachmixed number to a fraction. Thenmultiply; write the answer in simplestform.

7�14

� � 5�29

�

4. Darla needs to exercise �34� hour each day.

So far today she has exercised for�12� hour. How much longer does Darlaneed to exercise today?

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NameLESSON 10.5

Divide Fractions and Mixed NumbersWrite the correct answer.


9. Write About It Explain what a reciprocal is and how to find thereciprocal of a fraction and of a whole number.

1. Write the reciprocal of �59�.

3. Bill used 7�18� cups of flour to bake a batch

of bread. He started with 12�12� cups of

flour. Does Bill have enough flour tobake another batch of bread? Explain.

2. Write the reciprocal of 15.

4. Nancy has 19�34� feet of wallpaper

border. She bought an additional23�

58� feet. How much wallpaper border

does Nancy have in all?

5. Which is a list of all the factors of 26?

A 1, 2, 3, 9, 13, 26

B 1, 13, 26

C 1, 2, 13, 26

D 26, 52, 78, 104

7. Julie is hanging wallpaper in her house.The job requires 5�

12� rolls of wallpaper. If

she can hang 1�34� rolls of wallpaper each

hour, how long will it take her tocomplete the job?

A 2�14

� hr C 3�34

� hr

B 3�17

� hr D 7�14

� hr

6. Which is a list of the first fourmultiples of 5?F 1, 5, 10, 15

G 5, 10, 15, 20

H 5, 15, 25, 35

J 10, 20, 30, 40

8. Evan has a board that is 8 feet long. Hewants to cut it into pieces that are �

34� foot

each. Which number sentence can beused to determine p, the number ofpieces he will get from the board?

F p � 8 � �34

� H p � 8 � �34

�

G p � 8 � �34

� J p � 8 � �34

�

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NameLESSON 10.6

Multiple-Meaning WordsSome problems contain words that have more than one meaning. The wordsmay have the same spelling and different pronunciations or the same soundbut different meanings. You can use information given in the problem todetermine which meaning of the word is being used. Read the followingproblem.

The Continental Divide, or Great Divide, is the watershed ofNorth America. This means that it is the high point of land thatseparates the waters that flow east from those that flow west. Thechart below shows precipitation information for the ContinentalDivide. How much greater is the annual precipitation at thehighest elevation than at the lowest elevation?

1. Which word has both a mathematical meaning and an everyday meaning?

2. What operation is needed to solve the problem?


Read each problem carefully. Then solve.

Mr. Winston is building an addition onto his house. The area of theaddition is 150 square feet. The contractor is charging him $200 persquare foot. How much will the addition cost?




Mr. Winston’s house is in a suburban area. The original house had anarea of 1,750 square feet. When construction is complete, what will bethe area of the new house?




VOCABULARY

multiple-meaning

Elevation 4,000–7,000 ft 7,000–11,000 ft 11,000–14,000 ft

AnnualPrecipitation 11 in. 20 in. 40 in.

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NameLESSON 10.7

Algebra: Fraction Expressions and EquationsWrite the correct answer.


9. Write About It How is evaluating expressions involving fractionsdifferent from evaluating expressions that do not involve fractions?

1. Use GCFs to simplify the factors. Writethe new problem.

�25

� � �59

�

3. A 45-inch-tall rain barrel is filling upwith water at a rate of �

34� in. per hr. The

time it takes to fill can be found bysolving the equation 45 � �

34� h for h. How

long will it take the rain barrel to fill?

2. Use GCFs to simplify the factors. Writethe new problem.

�47

� � �38

�

4. Some videotapes are made so that thefirst 1�

13� ft of the tape cannot be recorded

on. Find how much of a 180-footvideotape can be recorded on bysolving the equation 180 � t � 1�

13� for t.

5. x � �35� is the solution to which of the

following equations?

A 3 � �35

� x

B 3 � 5 � x

C �25

� � 1 � x

D �53

� � 3x

7. Carlos rode his skateboard for 48 mineach day for the last 25 days. Howmany hours has Carlos ridden on hisskateboard over the last 25 days?A 20 hr

B 23 hr

C 25 hr

D 1200 hr

6. What is the value of the expression �37� � �

37� y, for y � �

37�?

F �37

�

G 0

H �499�

J �14

29�

8. Brad bought a new basketball for$35.87, including tax. He gave thecashier a $100 bill. How much changedid the cashier give back to Brad?F $75.87

G $64.87

H $64.13

J $35.87

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NameLESSON 11.1

Understand Integers

Write the correct answer.


9. Write About It On a number line, what value would best representsea level? Explain.

1. Write an integer that represents thesituation.

52 feet above sea level

3. There are three bags of apples. Theyweigh 3.1 pounds, 3.2 pounds, and 3.05pounds. Write the weights in order fromgreatest to least. Use >.


losing 25 yards in football

4. A hiker is 30 feet above sea level, on acliff. His friend is 15 feet below sea level,in a valley below the hiker. What is thedifference in elevation of the two hikers?

5. Maggie went deep-sea diving. Sheexplored a sunken ship at 78 feet belowsea level and a reef at 45 feet below sealevel. Which is the position of thesunken ship written as an integer?A �78

B �45

C �45D �78

7. Luis scored 98, 88, 76, 78, 98, and 65 onhis last 6 test. What is the range of Luis’stest scores?A 98

B 83

C 33D 22

6. Jon was in a hot-air balloon at 23,500feet above sea level. Phil was in a hot-air balloon at 15,200 feet above sealevel. Which is the elevation of Jon’s hot-air balloon written as an integer?F �23,500

G �15,200

H �15,200J �23,500

8. Kim works between 32 and 38 hours aweek. Which is a reasonable estimate ofhow many hours Kim works in a year?F Less than 2,000 hr

G Between 2,000 and 3,000 hr

H Between 3,000 and 4,000 hrJ Between 4,000 and 5,000 hr

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NameLESSON 11.2

Rational NumbersWrite the correct answer.


9. Write About It Explain how 0 can be written in the form �ab� .

1. Write 8�23� as a rational number in theform �ab�.


climbing up a cliff 856 ft

2. Find a rational number between �18� and �13�.


a drop in temperature of 48 degrees

5. The temperature outside was 36°F. Thetemperature inside was 72°F. Which isthe inside temperature written as aninteger?A �72

B �36

C �36D �72

7. The local newspaper wants to use agraph to report the number of touriststhat have visited the town each monthfor the last year. Which type of graphshould the newspaper use?A bar graph

B line graph

C histogramD line plot

6. Which rational number is equivalent to 2�59� ?

F �292�

G �293�

H �294�

J �295�

8. Nancy checked the gauge on herpropane tank and found that the tankwas between �14� and �12� full. Which fractioncould represent how full the tank waswhen Nancy checked?F �1

76�

G �1116�

H �196�

J �1136�

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NameLESSON 11.3

Compare and Order Rational NumbersWrite the correct answer.


9. Write About It Explain how you would order a group of rationalnumbers in which some are positive and some are negative.

5. The temperature outside was 67°F onMonday and 75°F on Tuesday. Which isthe temperature on Monday written asan integer?A �75 C �67B �67 D �75

7. Larry is making punch for a largegathering of people. The recipe calls for3 scoops of punch powder for every 10cups. He needs to make 85 cups. Whichis a reasonable estimate for how manyscoops of powder Larry needs to use?

A 18 scoops C 26 scoopsB 22 scoops D 30 scoops

6. Jason’s times for the 100-meter dash are11.72 sec, 11�

34� sec, 11�

45� sec, and 11.85 sec.

What is his lowest time for this race?F 11�45� sec H 11�34� sec

G 11.72 sec J 11.85 sec

8. Which group of rational numbers is inorder from least to greatest?

F ��23�, ��45�, ��67�, ��89�

G �3.4, �3�13�, �3.3, �3.1

H �8.7, 8.07, 8.007, 8.7

J �2�12�, �2�13�, 0, �2�14�

1. Compare the rational numbers andorder them from least to greatest.

4.2, 4.083, �54�, �29�

3. Find a rational number between �38� and �34�.


5�14�, 5�38�, 5.1, 5.4

4. Write 23�34� as a rational number in theform �ab�.

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NameLESSON 11.4

3. Ari, Latanya, Mary, and Jed each make adifferent dinner course, soup, salad,main course, or dessert, but notnecessarily in that order. Mary is theonly one whose recipe doesn’t requirevegetables. Latanya is the only one whodoesn’t need to use a stove. Jed’s courseis the only one that requires a spoon.What did they each prepare?

4. Fred, Georgia, Hal, and Inez allparticipated in the Geo-Bee. Theirscores were 92%, 75%, 100%, and 83%,but not necessarily in that order.Georgia’s score was �43� of Hal’s score.Inez’s score was 9 points less thanFred’s score. What score did eachreceive?

Analyze InformationThe information in a problem can offer clues about how to solve it. Analyze,or look carefully at, the problem. Underline or record details that help youunderstand the problem.


Abigail, Bart, Carlotta, and Donald each play a different sport,soccer, basketball, ice hockey, or lacrosse, but not necessarily inthat order. Abigail plays a sport that uses a round ball. Carlottaneeds a stick to play her sport. Donald can’t play his sport outsidein the summer. Bart’s sport isn’t played on grass. Which sport doeseach play?

1. Analyze the problem. Underline or record details that will help you solve theproblem. Which sport does each clue suggest?


Analyze the problem. Underline or record details that help you reach anunderstanding. Then solve.

VOCABULARY

analyze

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Algebra: Add IntegersWrite the correct answer.

1. Find the missing number in the pattern.

3 � 2 � 5

3 � 1 � 4

3 � 0 � 3

3 � �1 � 2

3 � �2 � 1

3 � �3 � ■


�3 � 1 � �2

�3 � 0 � �3

�3 � �1 � �4

�3 � �2 � �5

�3 � �3 � �6

�3 � �4 � ■

3. Carmen wants to share her money withher cousin Jasmine. Together they have$48. If Carmen gives Jasmine $3, theywill each have the same amount ofmoney. How much money does each girl have now?

4. Five students were waiting in line toreturn books at the library. There were 3students ahead of John. There were 3students behind Leila. Carla was first inline. Paul was last. What number in linewas Sara?


5. On three consecutive plays, a footballteam lost 2 yards, gained 5 yards, andgained 7 yards. Which expression couldbe used to find the total yards gained bythe team on these three plays?

A �2 � �5 � �7 C �2 � �5 � �7

B �2 � �5 � �7 D �2 � �5 � �7

6. By 10:00 A.M., the temperature hadrisen 7°C from a morning lowtemperature of �15°C. What was thetemperature at 10:00 A.M.?

F �8°C H 7°C

G �7°C J 8°C

7. Kirk is 131.9 centimeters tall and Thad is162.3 centimeters tall. Which is the bestestimate of how much taller Thad isthan Kirk?

A 10 cm C 30 cm

B 20 cm D 40 cm

8. Patty had 25.8 meters of wire to installlights in her backyard. She used only19.4 meters. How much wire was left?

F 7.4 m H 5.4 m

G 6.4 m J 3.4 m

9. Write About It Explain why 8 � �3 � �3 � 8.

NameLESSON 12.2

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Algebra: Subtract IntegersWrite the correct answer.


4 � 2 � 2

4 � 1 � 3

4 � 0 � 4

4 � �1 � 5

4 � �2 � 6

4 � �3 � ■


�2 � 1 � �3

�2 � 0 � �2

�2 � �1 � �1

�2 � �2 � 0

�2 � �3 � 1

�2 � �4 � ■

3. Five years ago, Sean was three times asold as his brother. Today Sean is twice asold as his brother. How many yearsolder than his brother is Sean? How oldis Sean now?

4. For one week of work, Roberto earned$615. He worked 25 hours at his regularpay of $15 per hour. He also workedovertime hours, for which he was paid$20 per hour. How many overtime hoursdid Roberto work?


5. Which addition problem is equivalent tothe subtraction problem�8 � �17?

A �8 � �17

B �8 � �17

C �8 � �17

D �8 � �17

6. Four hours ago, the temperature outsidewas +6°F. Since then the temperaturehas dropped 13°F. What is thetemperature outside now?

F �19°F H �7°F

G �7°F J �19°F

7. John collected n gadgets. Frank gavehim 18 more gadgets. John now has 51gadgets. Which equation could be usedto find the number of gadgets John hadbefore Frank gave him more?

A n � 18 � 51 C n � 51 � 18

B n � 51 � 18 D n � 18 � 51

8. Maria keeps old records stored inspecial boxes. Each box can hold 45 old records. If she has 16 boxes full ofold records, how many old records does she have?

F 690 records H 710 records

G 700 records J 720 records

9. Write About It Explain why 3 � 2 � 2 � 3.

NameLESSON 12.4

NameLESSON 13.2

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Algebra: Multiply IntegersWrite the correct answer.

1. Find the missing number in thepattern.

4 � 2 � 84 � 1 � 44 � 0 � 0

4 � �1 � �44 � �2 � �84 � �3 � �


�3 � 2 � �6�3 � 1 � �3�3 � 0 � 0

�3 � �1 � 3�3 � �2 � 6�3 � �3 � �


�35

�, �245�, 0.01, 0.55

4. Compare the rational numbers andorder them from greatest to least.

�74

�, �63

�, 1.8, 1.74


5. The temperature dropped by 4° eachhour from midnight until 5 A.M. Howmuch did the temperature change inthat time? A �24°B �20°C 20°D 24°

6. Stock in XYZ.com dropped 8 pointseach day from Monday to Friday.How much did the stock price changethat week? F 48 pointsG 20 pointsH �40 pointsJ �56 points

7. Which rational number is between1.45 and 1.5? A 1.4B 1.44C 1.48D 1.52

8. Which rational number is not between

�23

� and �78

�?

F �12

94� H �

34

�

G �56

� J �12

�


NameLESSON 13.3

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Algebra: Divide IntegersWrite the correct answer.


12 � 3 � 412 � 2 � 612 � 1 � 12

12 � �1 � �1212 � �2 � �612 � �3 � �


6 � �2 � �34 � �2 � �22 � �2 � �10 � �2 � 0

�2 � �2 � 1�4 � �2 � �


5.62, 5.7, 5 , 5�12

�4�5

4. Write 48�58

� as a rational number in theform �

ab

�.


5. The temperature changed 28° over aperiod of 7 hours. If the temperaturedropped at a constant rate, what wasthe change per hour? A �7°B �4°C �1°D 7°

6. A theme park recorded 1,800 fewervisitors this year than last year. Whatwas the shortage of visitors in anaverage month? F �150 visitorsG �140 visitorsH �130 visitorsJ �120 visitors

7. Grace scored 8, 7, 8, 8, 10, 6, 7, 8, 7, 6,and 9 on her last 11 quizzes. Gracescored 8 most of the time. What termdescribes the most frequent score? A mean C modeB median D range

8. Mr. Frank earns $4,987.34 each monthand Mrs. Frank earns $5,198.22 eachmonth. Estimate how much the twoearn together each month. F $8,000 H $10,000G $9,000 J $11,000


NameLESSON 13.4

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Combine Operations with IntegersWrite the correct answer.

1. The Li family camped in a valley at analtitude of �25 ft, or 25 ft below sealevel. During the morning they hikedto the top of a hill where the altitudewas �575 ft, or 575 ft above sea level.What is the difference in altitude of thetwo places?

2. Renee’s checking account allows her towrite checks for more than is in heraccount. She began with a balance of$326 and, after writing some checks,ended with a balance of �$108. Whatwas the total amount of the checks shewrote?

3. At 8 A.M. the outside temperature was�10° C. By noon the temperature hadrisen 15° C. Between noon and 5 P.M.the temperature dropped 12° C. Whatwas the temperature at 5 P.M.?


4. In a box of 48 candies, �14� are green, �14�

are red, and �12� are orange. If you giveaway all the candies except the greenones, how many candies will you havegiven away?

5. Chris bought a pen for $0.79. He gavethe cashier a $1 bill. The cashieraccidentally gave him $0.35 in change.How much extra did the cashieraccidentally give Chris? A $0.44 C $0.14B $0.21 D $0.06

6. Joann dove from a 6-ft-high divingboard into a 9-ft-deep pool and thentouched the bottom of the pool. Howfar did she travel from the top of theboard to the bottom of the pool? F 3 ft H 15 ftG 6 ft J 54 ft

7. A movie you want to see begins at3:00 P.M. and ends at 5:15 P.M. If you leaveyour house 30 min before the moviebegins and arrive home 15 min after itends, how long are you away? A 2 hr 45 minB 3 hrC 3 hr 15 minD 3 hr 30 min

8. You buy several boxes of markers foran art project and spread them out onyour desk. Adding 3 other markers thatyou already had, you now have 43markers. How many markers couldpossibly come in a box? F 6 markersG 7 markersH 8 markersJ 9 markers

9. Write About It How did you decide how many markers could havebeen in each box?

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Write ExpressionsWrite the correct answer.

1. James is baking bread for his classpicnic so he needs to triple his breadrecipe. The recipe calls for 2��

34� cups of

flour. How much flour should he use?

2. The length of the athletic field is threetimes its width. Write an algebraicexpression that represents the lengthof the field. Let l represent the length,and w, the width of the field.

3. Fred scored 8 points more than Daleduring the game. Write an algebraicexpression that represents the numberof points Fred scored. Let b representthe number of points Dale scored.

4. Some of the students will makesandwiches for the picnic. For eachsandwich, they need �

18� lb of turkey.

How much turkey is required to make46 sandwiches?


5. John’s dog, Rocky, weighs 15 kg. How many grams is that? A 150,000 g B 15,000 gC 1,500 gD 150 g

6. For the class trip the bus drivercharges $45.00 plus $3.10 for eachstudent. Which expression representsthe cost for n students? F 45 � 3.1nG 45 � 3.1nH 45 � 3.1nJ 45 � 3.1n

7. Patricia wants to share her package of30 pretzels equally among her 5 friendsand herself. How many pretzels willeach person receive? A 4B 5C 6D 7

8. Joan bought 5 yards of fabric for $2.85 a yard, including tax. Which expressioncould be used to find the change Joanreceived if she gave the cashier $50? F 50 � (5 � 2.85) G 50 – (5 � 2.85)H 50 – (5 � 2.85)J 50 � 5 � 2.85

9. Write About It Give examples of phrases that can usually be translated intosubtraction expressions.

NameLESSON 14.1

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Evaluate ExpressionsWrite the correct answer.

1. Write an expression for one hundredless than the product of 5 and anumber, c. Evaluate for c � 15.

2. Four times a number, z, is added to 12.This sum is then divided by 2. Write anexpression, then evaluate for z � �8.

3. Compare the rational numbers andorder them from greatest to least.

6 �1

10�, 6 ��

14

�, 6.05, 6.3


4. What is �96� written as a decimal?

5. To evaluate the numerical expression,in which order would you perform theoperations?

23 � 16 � 8 � 2

A add, subtract, multiplyB subtract, multiply, addC multiply, add, subtractD subtract, add, multiply

6. To evaluate the numerical expression,in which order would you perform theoperations?

15 � 3 � 2 � 7

F divide, subtract, multiplyG divide, multiply, subtractH multiply, subtract, divideJ subtract, divide, multiply

7. Greg made deposits to his checkingaccount of $105.32, $295.00, and $62.50.He wrote checks for $129.00, $57.43,$6.98, and $357.19. He started with abalance of $133.89. What is his presentbalance?A �$221.67 C $46.11B �$46.11 D $221.67

8. Blaine earned $115.89 on Monday,$87.33 on Tuesday, $121.08 onWednesday, $68.03 on Thursday, and$110.20 on Friday. What is a reasonableestimate for how much Blaine earnedduring the five days?F $300 H $500G $400 J $600

9. Write About It Explain the difference between an algebraicexpression and a numerical expression.

NameLESSON 14.2

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Expressions with Squares and Square RootsWrite the correct answer.

1. A square room needs exactly 169square tiles to cover the floor. Each tileis 1 foot on a side. If a wallpaperborder is hung near the ceiling, howlong will the border be?

2. Another square room, 12 ft by 12 ft,was tiled with the same square tiles.The tiles in a 4 ft by 2 ft area in thecenter of the room were painted. Howmany tiles are unpainted?

3. Connie loves dressing up in strangeoutfits. She has 4 pairs of jeans: a redpair, a striped pair, a green pair, and ayellow pair. She also has 3 tops, noneof which match any of the jeans. Howmany strange outfits can Connie makefrom these clothes?


4. In basketball, there are 2-point and3-point baskets and 1-point foul shots.During one game, Felipe scored 26points. He scored at least five 2-pointbaskets and at least three 3-pointbaskets. What is the greatest number offoul shots Felipe could have made?

5. Kate is three times as old as her cousin,Pam. The girls found an interestingrelationship between their ages. WhenPam is twice her current age, how oldwill Kate be?

A Twice as old as PamB 2�

12

� times as old as PamC 3 times as old as PamD 4 times as old as Pam

6. Scott is reading a novel that has 70pages. If he multiplies the number ofpages he has already read by 5 and thensubtracts 5 he will have the number ofpages in the book. How many pages hasScott already read?F 8G 12H 15J 18

7. A contractor has 7 boxes of 1-ftsquare tiles. Each box contains 20tiles. What is the length of the side ofthe largest square he can cover withthese tiles? A 10 ft C 12 ftB 11 ft D 13 ft

8. A contractor has 8 boxes of 1-ft squareglass blocks. Each box contains 10blocks. To build a square wall, what isthe greatest number of blocks that canbe used?F 100 H 80G 81 J 64

9. Write About It Explain how you eliminated some answer choicesin Exercise 8.

NameLESSON 14.4

NameLESSON 15.1

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Connect Words and EquationsWrite the correct answer.

1. A redwood tree that is 320 ft high is 6times the height of a pine tree. Writean equation.

2. The school-supplies store sold 35review books for a total of $278.25.What was the price of each book?

3. In the school baseball game, thenumber of runs scored by the winningteam was 6 more than the 3 runsscored by the losing team. Write anequation.

4. It takes Shakeia 12 min to walk toschool. She also stops for 3 min at astore for a snack. If she must be atschool no later than 8:20 A.M., what isthe latest she should leave home?


5. To celebrate her birthday, Julie took 5of her friends to the science museum.The total cost for the tickets was$40.50. Choose the correct equation. A t � 6 � 40.50B 6 � t � 40.50C t � 6 � 40.50D 6t � 40.50

6. When the school held a cookie sale, thesixth grade made $65 more than thefifth grade. The sixth grade made a totalof $230. Choose the correct equation. F x � 65 � 230G 65x � 230H x � 65 � 230J 230 ÷ 65 � x

7. Your new compact car averages 27miles per gallon of gas and you aregoing on a 247-mi trip. About howmany gallons of gas do you expect touse? A 14 gal C 10 galB 12 gal D 6 gal

8. A community is building 65 newhomes. The builder has 780 windowsto use in the new homes. What is theaverage number of windows perhouse? F 12 windows H 15 windows

G 14 windows J 16 windows

9. Write About It Explain how you chose the correct equation in Exercise 6.

NameLESSON 15.3

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Solve Addition EquationsWrite the correct answer.

1. The CN Tower in Toronto is 1,815 fttall. It is 1,353 ft taller than the ChicagoTribune building. Write and solve anaddition equation to find the height ofthe Chicago Tribune building.

2. Yesterday, the temperature rose from�3°F at 6 A.M. to 15°F at 3 P.M. Writeand solve an equation to find howmany degrees the temperatureincreased.

3. After paying for 3 adults’ movie ticketsat $7.50 each, 2 children’s tickets at$4.75 each, and snacks, that cost atotal of $9.50, Mr. Gould had $18.75left. How much did he have before hearrived at the theater?

4. During a basketball game, a playerattempted only three-point shots. Hemade one out of every two shots hetried and scored a total of 12 points.How many three-point shots did theplayer attempt during the game?


5. The moving van traveled 455 mi in 8 hrand 45 min. What was the averagespeed?

A 58 mph C 52 mphB 55 mph D 50 mph

6. A grandfather clock chimes every15 min on the quarter hour. How manytimes will it chime between 11:10 P.M.and 5:35 A.M.? F 26 H 24G 25 J 23

7. The athletic field is 134 ft long. Theplayground is 56 ft shorter. How long isthe playground? Choose the correctequation and solution. A x � 56 � 134; x � 190B x � 56 � 134; x � 190C x � 2 � 56; x � 112D x � 56 � 134; x � 78

8. Joann planted 38 more pansies thantulips. She planted 72 pansies. Howmany tulips did she plant? Choose thecorrect equation and solution. F 2t � 72; t � 36G t � 38 � 72; t � 110H t � 38 � 72; t � 34J 110 � t � 72; t � 38

9. Write About It How did you use the Subtraction Property ofEquality to solve Exercise 1?

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Solve Subtraction EquationsWrite the correct answer.

1. The weather service recorded rainfallof 1.4 in., 2.1 in., 0.85 in., 0.45 in., and1.75 in. during a 5-day period. Howmuch rain fell during that period?

2. Tom had 6 bags of mulch to use in hisgarden. Each bag contained 8�

13� lb of

mulch. What was the total weight ofthe mulch?

3. Lacy scored 6 points lower on her testthan her friend Opal. Lacy scored a 77on her test. Write and solve anequation to find Opal’s score.


4. Jon cut down 12 old trees on hisproperty. He now has 17 trees left.Write and solve an equation to findhow many trees Jon had on hisproperty before he started cutting.

5. Sixteen kittens were adopted from theanimal shelter today. There are 25kittens left. How many kittens did theshelter have to be adopted?A x � 16 � 25; x � 41B x � 16 � 25; x � 9C 25 � x � 16; x � 9D x � 9 � 16; x � 25

6. Tom is 5 years older than his brother,Jerry. Jerry is 7 years old. How old isTom?

F y � 5 � 7; y � 2G y � 7 � 12; y � 19H y � 7 � 12; y � 5J y � 5 � 7; y � 12

7. Warren ran a race in 65.71 sec. He camein second, behind his friend Kyle. Whatelse do you need to know to find outhow much faster Kyle ran the race?A Who finished thirdB When the race startedC Kyle’s race timeD The length of the race

8. Sharon is saving to buy a new car. Thecar costs $18,595. She wants to have atleast $5,000 saved before she buys thecar. If she saves $350 a week, how longwill it take her to save the money?F 14 wk H 16 wkG 15 wk J 17 wk

9. Write About It Explain why you use addition to solve asubtraction equation.

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Write the correct answer.

1. After exercising for 1 week, Ned wasable to do 60 push-ups. This was 5times as many as he could do before.How many push-ups could Ned dobefore? Write and solve an equation.

3. An Internet company’s stock startedthe week at $39.50 per share. The stockwent up 4�

14�, up 2�

34�, down 5, up 3�

12�, and

down 2�14� for the week. What was the

ending price of the stock at the end ofthe week?


5. The soccer club is divided into 4 teams.Each team has 20 players. Whichequation can be used to find howmany players are in the soccer club?

As–4 � 20

B 4s � 20C s � 4 � 20D s � 4 � 20

7. Kara’s history grades for the term are89, 83, 79, 90, 81, and 88. Find themean of her grades.A 87 C 85B 86 D 84

2. All of the money raised by students atthe town carnival was divided among 7 charities. Each charity received $406.How much was raised at the carnival?Write and solve an equation.

4. A state university has 18,500 freshmen,14,780 sophomores, 16,290 juniors, and15,820 seniors. About how manystudents attend the university?

6. Each set of chair pads requires 3 yd offabric. Which equation can be used tofind how many sets can be made from27 yd of fabric?F g � 3 � 27G 27 � g � 3

Hg–3 � 27

J 3g � 27

8. Craig can fit 28 books in each box. Hepacked 21 boxes. Estimate how manybooks Craig has packed.F 200 H 600G 400 J 800

9. Write About It What is the reciprocal of 8? Explain.

Solve Multiplication and Division Equations

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Use FormulasWrite the correct answer.

1. One day in Florida, the temperature fellto 10°C. What was the temperature indegrees Fahrenheit (°F)?

3. Maria’s muffin recipe requires 2�31

� cupsof whole-wheat flour. She wants totriple the recipe. How much flour doesshe need?


5. A jet pilot flew a distance of 3,311 miin 5 hr and 30 min. Find the plane’saverage rate of speed.A 662 mi per hr C 602 mi per hrB 625 mi per hr D 595 mi per hr

7. Luis earned $23.58 working part-timeand an additional $12.25 from hisregular allowance. How much moneydid Luis earn in all?A $11.33 C $35.83B $35.73 D $36.73

2. Sally timed a snail crawling at the rateof 3 feet per minute. How far would thesnail travel in 8 min?

4. The Krazy Bread Co. sells Maria’smuffins at $12.98 per dozen. What will it cost the Garden Club to buy 48 muffins?

6. Kerri had to heat the candy mixture toa temperature of 190°F. What is thetemperature in degrees Celsius (°C)?F 93.5°C H 83.1°CG 87.8°C J 80.7°C

8. The museum has admitted 58 peopleper hour for the last 6 hours. Duringthat period, 129 people have left. Howmany people are still in the museum?F 71 H 187G 123 J 219

9. Write About it Think about the formula d � rt. Explain howdistance is affected when time is increased or decreased andwhen the rate is increased or decreased.

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Draw Conclusions

When you look at the evidence and apply what you know to find theanswer, you are drawing conclusions. Read the following problem.

Bobbie rode her bike to the GreenMountain Hiking Center. She parked inthe parking lot and hiked for a coupleof hours. Bobbie did not walk any loopmore than once. She walked 2.9 mi.What loops did she take?

1. In the first column, complete the statements with informationcontained in the problem. In the second column, write someconclusions you can draw.

Examine the Evidence Draw Conclusions

Bobbie walked . Bobbie must have walked from the parking lot to the center spot and

She didn’t walk . back, for a total of .

The total number of miles walked onthe loops would be .


Solve.

3. The next day, Bobbie walked a total of2.9 mi again. She walked some loopstwice. Which loops did she walk?

4. The Hiking Center added a new pathcalled the Gazebo Loop. It is 0.55 milong. Bobbie walked a total of 2.9 mi,which included the Gazebo Loop. Shewalked one loop twice. Which loopsdid she walk?

NameLESSON 16.5

Parking Lot to Center SpotGarden LoopRiver LoopHilly LoopForest Loop

0.5 mi0.45 mi0.6 mi0.5 mi0.8 mi

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NameLESSON 17.1

Points, Lines, and PlanesWrite the correct answer.

1. Mr. Morgan wants to hang 13 triangleson the bulletin board. If he puts a pin in each corner of each triangle, howmany pins does he need?

3. What geometric figure is suggested bythe surface of a lake?


5. A company picnic was being held inthe park. Every table was set to hold 12 people and all 132 tables werecompletely filled. How many people attended the company picnic?A 1,584 C 132B 144 D 12

7. Fred’s class of 32 students is planning a trip to the zoo in school vans. If eachvan can hold 10 students, how manyvans will be needed?A 1 C 132B 2 D 4

2. Jean’s bowling scores for the month are 95, 130, 124, 103, 88, 137, 110, 121,and 127. Find the mean, median, andrange.

4. What geometric figure is suggested bythe tip of a pencil?

6. Which is a name for the figure?

F line segment JKG ray JKH line JKJ plane JKL

8. Which is a name for the figure?

F line BAG ray ABH line ABJ plane AB

9. Write About It What geometric figure would you get if you joined the endpoints of two rays and pointed the rays in oppositedirections?

J

KL

BA

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NameLESSON 17.3

Angle RelationshipsWrite the correct answer.

1. The N, S, E, and W on a compass are at90° angles from one another. What arethe measures of �1, �2, and �3?

3. During their last camping trip, thescouts hiked 1.25 mi east, 2.1 mi south,1.43 mi west, and 3.54 mi north. Howfar did they hike?


5. What are the measures of the twocomplementary angles if one anglemeasure is 30° less than the other?A 150°, 30° C 75°, 45°B 60°, 30° D 15°, 30°

7. How many bows can be made from 10 yd of ribbon if it takes �

34� yd of ribbon

to make one bow?A 15 bows C 13 bowsB 14 bows D 12 bows

2. Gavin designed a garden as shown.What are the measures of �1, �2, �3,and �4?

4. Gavin’s sister bought 2 flats of pansiesat $1.19 and 5 flats of zinnias at $1.98each. How much change did she receivefrom $20.00?

6. What are the measures of the twosupplementary angles if one anglemeasure is three times the other?F 22.5°, 67.5° H 20°, 60°G 45°, 135° J 60°, 180°

8. Angela had $100. She spent $39.15 on asweater and earned $22.75. How muchdoes Angela have now?F $116.40 H $61.90G $83.60 J $16.40

9. Write About It Explain how you found the answer to Exercise 6.

N

S

W E3 12

15°3

1

248° 111°4

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NameLESSON 17.4

Classify LinesWrite the correct answer.

1. Jon is twice as old as his sister, Jane,less 4 years. Jon is 18 years old. Howold is Jane?

3. Name the point where the two linesintersect.


5. Which names the point where line AEand line BD intersect?

A point A C point CB point B D point D

7. Line AB is parallel to which line?

A line EG C line BAB line EF D line CD

2. Vicki is �13� as old as her cousin, Ricky,

plus 5 years. Vicki is 14 years old. Howold is Ricky?

4. Name the two lines that are parallel toeach other.

6. George has saved 15 bags of recycledcans and 70 lb of newpapers. In eachbag he has 128 cans. How many canshas George saved?F 1,950 H 1,800G 1,920 J 128

8. Jane wants to cut a piece of ribbon into13 equal pieces. If the ribbon is 156 in.long, how long will each piece be?F 13 in. H 11 in.G 12 in. J 10 in.

9. Write About It Give an example of something that reminds you ofparallel lines.

CB

EA

D

D CE

BA

EGC

FH D

B

A

A

E

B

C

F

D

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TrianglesWrite the correct answer.

1. Sandra drew an acute triangle. Shelabeled the three angles as follows: 71°,53°, and 46°. How do you know Sandramade an error?

3. At the Downtown Cafe, donuts cost $0.75and muffins cost $1.05. If you bought adozen of each, how much would you pay?

2. When Eric tried to draw a triangle withan obtuse angle and a right angle, herealized that he had made an error. Howdid he know that?

4. Jermaine bought a box of donuts and atehalf of them himself. He gave one to eachof his two sisters and had one left. Howmany donuts did he buy?


5. A triangle was formed by the school’s20-ft flagpole, the wire from the top ofthe pole to a point 12 ft from the pole,and the ground. Which of the followingbest describes the triangle?

A acute scalene

B right scalene

C obtuse isosceles

D equilateral

7. When Mike kicked a ball against thehandball court wall, the angle betweenthe path of the ball and the wall was 75°.What was the angle between the path ofthe ball and the ground?

A 15° C 75°

B 25° D 105°

6. James arrives at school at 7:50 A.M. At 8:00A.M., the clock chimes once. At 9:00 A.M.,it chimes twice. At 10:00 A.M., it chimes three times. If the patterncontinues, how many chimes will Jameshear by 3:20 P.M.?

F 8 H 28

G 16 J 36

8. A building has 5 floors and each floor has6 apartments. Each apartment has 2bedrooms and each bedroom has 1closet. Each closet has 4 shelves. Howmany shelves are there in all?

F 60 H 240

G 120 J 480

9. Write About It How did you find the angle between the path of the ball and the ground in Problem 7?

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Make InferencesYou can make inferences, or logical connections, to help you solve a problem.Examine all the given facts and combine them to reach understandings thatare not stated directly in the problem. Read the following problem.

Ernesto’s classroom has triangular tables. If the tables are placed side-to-side, Ernesto wants to know how many students can be seated. Twostudents can sit on each side of a table. Find a pattern that will allowErnesto to predict how many students can sit at a given number of tables.

1. Examine the information given in the problem. Then make inferences.

2. Fill in the table to show the pattern.

3. Describe the pattern. Solve the problem.

Information

• Triangular tables are placed side-to-side.

• Two students can sit on each side of atable

Inference

Number of Tables (t)

1

2

3

4

Number of Sides (s)

3

4

Number of Students (n)

6

4. Ling’s classroom has square tables where2 students can sit at each side. Find thepattern that will allow her to predict howmany students can sit at a given numberof tables placed side-to-side.

5. Della’s classroom has hexagonal tableswhere 2 students can sit at each side.Find the pattern that will allow her topredict how many students can sit ata given number of tables placed side-to-side.

Make inferences based on the evidence. Then solve.

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9. Write About It How did you find the incorrect answer in 7?

NameLESSON 18.3

QuadrilateralsWrite the correct answer.

1. A football field is a rectangle 300 ft longand 160 ft wide. The end zones addanother 30 ft of length at each end. Howmuch greater is the perimeter of the fieldwith the end zones than without them?

3. Karen found that the length of herclassroom is just 1 ft greater than thewidth. The perimeter of the room is138 ft. What are the length and width?

2. A baseball diamond is a square whoseside measures 90 ft. For a home run, aplayer must run around the square. If aplayer hits 35 home runs, what is theleast number of feet he or she must run?

4. James has $30.00 to pay for a $28.00book. If the sales tax is $1.96, how muchchange will James get?


5. The school flagpole cast a shadow 15 ftlong. Mr. Hansen cast a shadow 4 ft long.Mr. Hansen is 6 ft tall. How tall is theflagpole?

A 90 ft C 22.5 ft

B 60 ft D 18 ft

7. Erik gave the following descriptions ofparallelograms. Which description isincorrect?

A A quadrilateral with two pairs ofparallel opposite sides

B A quadrilateral with opposite sidescongruent

C A four-sided polygon with oppositesides parallel

D A polygon with opposite sidesparallel

6. Mrs. Gibson bought �13� yd red ribbon, �4

3� yd

blue ribbon, 1�12� yd yellow ribbon, and

4 yd white ribbon. How much ribbon didshe buy altogether?

F 7�152� yd H 5�1

72� yd

G 6�172� yd J 5�1

12� yd

8. Jules gave the following descriptions ofrectangles. Which description isincorrect?

F A quadrilateral containing four rightangles

G A parallelogram containing fourcongruent angles

H A parallelogram containing fourcongruent sides

J A four-sided polygon with four rightangles

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Draw Two-Dimensional FiguresWrite the correct answer.

1. A basketball court is a rectangle. A linesegment drawn between oppositecorners divides the court into twocongruent figures. Describe these figures.

2. Harry cut out a rhombus with no rightangles. He drew the longer diagonal, thenfolded the rhombus along the diagonal tomake two congruent figures. Describethese figures.

3. A target in a game of darts has threesections: 1 point, 3 points, and 6 points.If you throw 3 darts at the target and theyall stick, how many different scores arepossible?


4. At the finals of the school contest, thesixth-grade basketball team scored 6three-point baskets, 13 two-pointbaskets, and 5 one-point foul shots. Howmany points did they score?

5. Adrianna has drawn three sides of aquadrilateral. They are 3 in., 7 in., and 4 in. long. What is the only quadrilateralshe can complete by drawing the lastside?

A rectangleB trapezoidC rhombusD parallelogram

6. Josh drew an equilateral triangle, whichhe labeled ABC. Then he drew a linesegment from vertex A to the middle ofside BC. What kind of triangles did heform?

F right isoscelesG acute isoscelesH right scaleneJ acute scalene

7. For every $5.00 Matthew earns, hespends $2.00 and saves the rest. Howmuch should he be able to save if heearns a total of $150?

A $30 C $90B $60 D $120

8. When Sophia was born, her father was 30 years old. How old will Sophia’s fatherbe when he is three times as old as hisdaughter?

F 40 years old H 50 years oldG 45 years old J 60 years old

9. Write About It In Exercise 6, would the result be the same if the linesegment were drawn from vertex B to the middle of side AC? Explainyour reasoning.

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CirclesWrite the correct answer.

1. A merry-go-round in the shape of a circlerotates around a central post. Thedistance from the center of the post tothe edge of the merry-go-round is 27 ft.What is the diameter of themerry-go-round?

2. A circular target has three sections, allwith the same center. The diameter ofthe largest section is 18 in. The radius ofthe smallest section is 4 in. Halfwaybetween these circles is the middlecircle. What is its diameter?

3. The Muffin Man has muffins on sale for$0.75 each or $1.75 for 3 muffins. What isthe greatest number of muffins that youcan buy for $5.00?


4. After saving for three months, Kali had$20 more than 3 times her initial depositin her savings account. If she had $200,what was her initial deposit?

5. The radius of a large truck tire is 19 in.The back of the truck is supported by arow of 3 tires from front to back. There is4 in. of space between tires. What is thedistance from the front of the row of tiresto the rear?

A 10 ft 2 in. C 10 ft 10 in.B 10 ft 6 in. D 11 ft

6. A circle graph shows how 120 studentsvoted in an election for class president.The sector that represents the winner’svotes is twice the size of the sector thatshows the runner-up’s votes. How manyvotes did the winner receive?

F 40 votes H 80 votesG 60 votes J 100 votes

7. An amusement park charges $15.50 foradmission. One day it collected $10,695.Which is the best estimate of the numberof customers?

A 600 customersB 700 customersC 800 customersD 900 customers

8. During the day, 102 T-shirts were sold.Each shirt cost $12.95. How much didthe park earn from the sale of the shirts?

F $129.50G $132.90H $1,295.00J $1,320.90

9. Write About It How does knowing the relationship between the radius and diameter of a circle help you answer questions?

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LESSON 19.1Name

LESSON 19.1

Types of Solid FiguresWrite the correct answer.

1. Paula carved a block of wood in theshape of a hexagonal prism. How manyfaces does the block have?

3. Irene has 17 quarters, 13 nickels, and34 pennies. How much does she have?


5. Blain used 3�34� yd of a 6�

12� yd long piece of

fabric. Then she bought an additional5�

13� yd. Which number sentence can be

used to find t, the total amount offabric Blain has now?

A t � 61–2 � 3

3–4 � 5

1–3

B t � 61–2 � 3

3–4 � 5

1–3

C t � 61–2 � 3

3–4 � 5

1–3

D t � 61–2 � 3

3–4 � 5

1–3

7. Janet bought a crystal paperweightshaped like a triangular prism. Howmany edges and vertices does it have?

A 9 edges, 6 verticesB 8 edges, 4 verticesC 12 edges, 8 verticesD 6 edges, 6 vertices

2. Ned made a clay pyramid with sixfaces. How many sides does the base ofhis pyramid have?

4. Alex has math scores of 97, 85, 88, 78,83, and 91. What is the mean of hisscores?

6. Roger earned $27,785 last year. Hechanged jobs and earned $36,924 thisyear. How much more did he earn this year than last year?

F $8,861

G $9,139

H $10,861

J $10,139

8. George carved an ornament in theshape of an octagonal pyramid. Howmany faces and edges does it have?

F 8 faces, 24 edgesG 10 faces, 10 edgesH 8 faces, 12 edgesJ 9 faces, 16 edges

9. Write About It Explain why a cylinder is not a prism.

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LESSON 19.2Name

LESSON 19.2

Different Views of Solid FiguresWrite the correct answer.

1. Name the solid figure that has the given views.

3. The entire middle school is going on afield trip. The school has 893 students.If each bus can hold 45 students, howmany buses do they need?


5. Every side view of a pentagonalpyramid shows what shape?A pentagonB circleC rectangleD triangle

7. Jack ran two laps in 45.8 sec each and then the last two laps in 58.7 seceach. Then he rested for 60 sec. Whichexpression can be used to find Jack’stotal running time?

A (2 � 45.8) � (2 � 58.7)B (2 � 45.8) � (2 � 58.7)C (2 � 45.8) � (2 � 58.7)D (2 � 45.8) � (2 � 58.7)

2. Name the solid figure that has the given views.

4. Tina bought a printer for $435. Shemade a down payment of $120 andpaid the rest in equal payments of $45per month. How long did it take her topay for the printer?

6. Every side view of a hexagonal prismshows what shape?F hexagonG circleH rectangleJ triangle

8. Jill worked for 3 hours each Saturdayfor 2 years helping her favorite charity.What else do you need to know to findout how many total hours Jill hasdonated to her favorite charity?F How many baskets she handed outG How many Saturdays there were in

each yearH What type of food she gave outJ The name of the charity

9. Write About It Describe the top, front, and side views of atriangular prism.

top

front side

top

front side

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NameLESSON 19.4

ParaphraseWhen you paraphrase, or restate, something in your own words,you show your understanding. Paraphrasing a problem helps youclarify and identify what you are asked to find and the facts thatare given in the problem.


The movie theater is having a benefit to raise money to build apark. Movie tickets cost $5 for adults, $1 for senior citizens, and$0.10 for children. In the first hour, they sell 100 tickets worth$100. Some of each kind of ticket were sold. How many of eachkind of ticket were purchased?

1. Paraphrase the problem by restating it in your own words.

2. How would you use the strategy solve a simpler problem to solvethis problem? Use your restatement of the problem.


4. The appliance department whereShawn works is having a sale. Blendersare $16, popcorn makers are $10, andmixers are $11. Shawn takes in $400and sells at least one of each kind ofappliance. How many of each might he have sold?

5. Harold owned �13� of a group of horses.

Moira owned �19� and Sandy owned �

12� of

the group. But they couldn’t split upthe horses until Joe joined the groupwith his own horse. Harold, Moira, andSandy each took the correct number of horses, and Joe kept his. How manyhorses did each one own?

Paraphrase the problem. Try solving a simpler problem first. Then solve.

VOCABULARYparaphrase

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LESSON 20.1Name

LESSON 20.1

Ratios and RatesWrite the correct answer.

1. There are 15 girls and 17 boys in oneclass. What is the ratio of boys to thetotal number of students? Write theratio three different ways.

3. Last month 156,980 people visited atheme park. This month 188,103 peoplevisited the park. Estimate how manymore people visited the park thismonth than last month.


5. Nina can walk 10 blocks in 5 minutes.At this rate, how many blocks couldNina walk in 1 minute?A 3 C 1B 2 D

1–2

7. Sharon used 3�13� yd of fabric for a

seat cover on her chair. She used anadditional 1�

12� yd to cover the arms.

How much fabric did Sharon use forthe chair?

A 45–6 yd C 4

2–5 yd

B 41–2 yd D 4

1–3 yd

2. A box holds 4 green apples, 3 redapples, and 8 yellow apples. Write theratio of red apples to green applesthree different ways.

4. Peter can hop a distance of 29 cm. Toraise money for the school carnival, hehopped that distance 147 times. Howfar did he hop?

6. Jason paid $8.50 for 5 lb of apricots.Lorren wants to buy 1 lb at the samerate. How much will Lorren have topay for 1 lb of apricots?F $1.90 H $1.80G $1.85 J $1.70

8. The forest service bought 24,975 bluespruce trees to plant on 15 hills. If theywant an equal number planted on eachhill, how many trees will they plant oneach?F 1,685 H 1,665G 1,675 J 1,655

9. Write About It In a unit rate, which number always equals 1?Explain.

LESSON 20.3©

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NameLESSON 20.3

Follow DirectionsRead and follow directions carefully to solve a problem. Look forwords that state the operation or process to follow. Sometimes, aproblem requires you to work within certain limits. Make sure youfollow the rules that are given.


Melina is from Greece. When she came to the United States, sheexchanged 1,500 Greek drachma and received $4.08 in U.S.dollars. Choose another amount of drachma that is not amultiple or factor of 1,500. How much would Melina receive ifshe exchanged that number of drachma for U.S. dollars?

1. Write the directions you must follow to solve the problem.

2. What information is given?

3. Choose a number and solve the problem. What equation can youwrite in the form of a proportion to solve the problem?

Follow directions to choose a number. Write a proportion. Then solve.

4. Brian exchanged 6 British pounds for$9.31 in U.S. dollars. Choose an amountin pounds that is neither a multiple nora factor of 6. Write a proportion andfind the amount’s equivalent in U.S.dollars.

5. Renata exchanged 100 German marksfor $47 in U.S. currency. Select anamount in marks that is not a factor ora multiple of 100. Write a proportionand find out how much the amount isworth in the United States?

VOCABULARYfollow directions

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LESSON 20.4Name

LESSON 20.4

Algebra: Ratios and Similar FiguresWrite the correct answer.

1. The two figures below are similar.Which angle corresponds to �A?

3. Irene has 23 quarters, 15 dimes, and 6 nickels. How much money does she have?


5. Triangle ABC has sides of 6 in., 8 in.,and 9 in. Which is a similar triangle?A 12 in., 16 in., 20 in.B 10 in., 16 in., 18 in.C 12 in., 16 in., 18 in.D 12 in., 14 in., 18 in.

7. Oscar scored an 88 and a 92 on his lasttwo tests. What is the mean of Oscar’stest scores?A 88 C 90B 89 D 91

2. How many pairs of similar circles canyou find in the figure below?

4. A roll of quarters contains 40 quarters.How many rolls of quarters would Jakeget for two $20 bills?

6. Triangle XYZ has sides of 5 mm, 10 mm, and 12 mm. It is similar totriangle MNP. The two longest sides oftriangle MNP are 30 mm and 36 mm.What is the length of the shortest side?F 25 mm H 18 mm G 20 mm J 15 mm

8. Tom’s shuffleboard scores for the firsttwo rounds are �10 and 4. What is histotal score?F 14 H �6G 6 J �14

9. Write About It �ABC is similar to �DEF, �A corresponds to �D,and �B corresponds to �E. Which side corresponds to side BC?Explain.

A

M 3 cm N

L

8 cm

4 cm4 cm

8 cm

C 6 cm B

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Algebra: Proportions and Similar FiguresWrite the correct answer.

1. Dale is 6 ft tall and his shadow is 4 ftlong. At the same time, a building castsa shadow that is 20 ft long. What is theheight of the building?

3. Vivian bought 6 apples at $0.15 eachand 7 bananas at $0.08 each. Howmuch change did she get from $5.00?


5. Tom is reading a book for English class.He reads 8 pages in 15 minutes. At thisrate how many pages can he read in 1 hour?A 8 C 24B 16 D 32

7. Blake is in charge of stocking shelves.He opened cases of soup and stockedthe shelves with 840 cans. Each caseholds 24 cans of soup. Which equationcan be used to find the number ofcases, c, Blake opened?A 24 � c � 840 C 24c � 840

B 24 � c � 840 D24—c � 840

2. A tree casts a shadow that is 12 m long.Nearby a stick that is 2 m tall casts ashadow that is 3 m long. What is theheight of the tree?

4. When a tree was cut down, its trunkwas found to contain 8 rings. Each ringis said to represent 13 yr of a tree’s life.How old was this tree?

6. Lisa has 48 dolls. The ratio of dolls fromthe U.S. to dolls from other countries is 3:5. How many dolls does she havefrom other countries?F 8 H 30G 28 J 40

8. Maria recorded the weights of thewatermelons she harvested from hergarden. They were 23.4, 19.8, 20.9, 28.7,32.1, 18.8, 19.8, 22.3, and 33.8 kg. Whatwas the median weight of Maria’swatermelons?F 19.8 kg H 24.4 kgG 22.3 kg J 32.1 kg

9. Write About It When you are using the lengths of two shadows to find an indirect measurement, why is it important that thelengths of the two shadows be taken at the same time of day?

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LESSON 20.6Name

LESSON 20.6

Algebra: Scale DrawingsWrite the correct answer.

1. A playroom is 12 ft wide. How wide is it on a floor plan drawn to the scale 1 in. � 10 ft?

3. Linda measured the height of 6 peoplein her class. They were 187, 167, 192,187, 190, and 181 cm. What is the modeof the heights?


5. The scale on a model airplane drawingis 1 in. � 18 ft. If the wing on thedrawing is 4 in., how long is the actualairplane wing?A 36 ft C 60 ftB 48 ft D 72 ft

7. The stadium can hold 18,752 people. Ifthe stadium has 32 equal rows of seatsthat go completely around the stadium,how many seats are there in each row?A 556 C 576B 566 D 586

2. The school auditorium is 25 mm longon a floor plan drawn to the scale 5 mm � 4 m. Find the actual length of the auditorium.

4. Al is �15� as old as his cousin, Val. Sal, at

27, is two years older than Val. How old is Al?

6. The scale on a drawing of a house is 1 in. � 4 ft. The patio of the house willbe circular with a diameter of 20 ft.What is the diameter of the patio onthe drawing?F 10 in. H 5 in.G 8 in. J 4 in.

8. Michael gave away 58 model airplaneshe had built. He now has 133 left.Which equation could be used to finda, the total number of model airplanesMichael had before he gave any away?F a � 58 � 133 H 58a � 133

G a � 58 � 133 Ja—58 � 133

9. Write About It Two drawings of the same floor plan are drawn. Thescale on one drawing is 1 in. � 5 ft. The scale on the other drawingis 1 in. � 10 ft. Explain how the sizes of the drawings will differ.

LESSON 20.7©

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NameLESSON 20.7

Algebra: MapsWrite the correct answer.

1. Use the scale 1 in. � 50 mi to find theactual distance for a map distance of 7 in.

3. McKenna has to read a 647-page bookin 3 days. She read 176 pages the firstday and 291 pages the second day. Howmany pages does she have left to read?


5. A rectangle is 32 feet long and 16 feetwide. A similar rectangle is 4 ft long.How wide is the similar rectangle?A 1 ft C 3 ftB 2 ft D 4 ft

7. The state capitol is 300 km from thebeach. How far is this on a map drawnto a scale of 1 cm � 20 km?A 10 cm C 15 cmB 12 cm D 20 cm

2. Use the scale 1 in. � 80 mi to find theactual distance for a map distance of 9 in.

4. Kirk is playing a game with a 12-sidedgeometric figure. If the figure has thenumbers 1 through 12 on it, how manyfavorable chances does he have to rolla multiple of 4?

6. The map of the city is drawn to a scaleof 1 in. to 3 mi. The high school is 4�

12� in.

from the swim club. Find the actualdistance.F 4

1–2 mi H 12 mi

G 9 mi J 131–2 mi

8. Jack and his three friends spent a totalof $24 for lunch. What was the meanprice for the lunches?F $8 H $4G $6 J $2

9. Write About It How can you measure a curvy road on a map?

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LESSON 21.1Name

LESSON 21.1

PercentWrite the correct answer.

1. The Panthers won 45 games last year.They played 49 home games and 41 away games. What percent of theirgames did they win?

3. Harriet is making a batch of cookies andis going to use 3 c of chocolate chipsfor every 24 cookies she makes. If sheplans on making 48 cookies, how manycups of chocolate chips does she need?


5. There are 25 students in a classroom.Fourteen of them are boys. Whatpercent of the class are boys?A 25% C 56%B 44% D 60%

7. Vicki colored 3–4 of a picture. She left the

rest for her sister to color. What percentof the picture did Vicki leave for hersister to color?

A 75% C 25%B 50% D 5%

2. Six out of 20 hiking club members own their own tent. What percent ofhiking club members do not own theirown tent?

4. Carol saw 34 cars and 19 trucks drivedown her street in a 2-hour period.What is the ratio of cars to trucks?Write the ratio in three different ways.

6. Warren ran the 100-m race in 48 sec. Atthis rate, how long would it take him torun 10 m?F 48 sec H 0.48 secG 4.8 sec J 0.048 sec

8. Joan bought a bag of green beans thatweighed 8.2 kg and Carrie bought a bagof green beans that weighed 12.1 kg.How much more did Carrie’s bag ofbeans weigh?F 3.9 kg H 4.1 kgG 4.0 kg J 4.2 kg

9. Write About It Why is it easy to change a fraction to a percentwhen the denominator of the fraction is 100?

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NameLESSON 21.2

Percents, Decimals, and FractionsWrite the correct answer.

1. Cheryl has invited 68 people to a party.She has 4 tables that each seat 5 people.A party-supply company rents tablesthat seat 6. How many tables does sheneed to rent?

3. In the school parking lot, the ratio ofsedans to minivans is 3 to 5. Whatpercent of the cars are minivans?


5. Eighteen out of the 25 members of the girls’ soccer team wear their hair in a ponytail. What percent of the girls on the soccer team wear theirhair in a ponytail?A 80% C 28%B 72% D 18%

7. Devon bought 12 child tickets and 23 adult tickets to a show. Each childticket cost $3.25 and each adult ticketcost $6.75. What equation can be usedto find a, the total cost of the tickets?A a � 12 � 3.25 � 23 � 6.75B a � (23 � 3.25) � (12 � 6.75)C a � (12 � 3.25) � (23 � 6.75)D a � (12 � 3.25) � (23 � 6.75)

2. Out of 1,450 books distributed at thebeginning of the school year, only 12%of them have not been returned. Whatfraction of the books have beenreturned?

4. Rosie’s Posies sells roses for $54.00 adozen. At that rate, what is the cost oftwo roses?

6. Sami, Tami, and Kami painted the fencearound their garden. Sami painted 35%of it, Tami painted �

25� of it. What fraction

of the fence did Kami paint?

F2–5 H

1–4

G1–3 J

1–5

8. Karen earned 221 bonus points at her local supermarket by buying thespecials. Denise earned five times asmany points and Beth earned 125 morepoints. How many bonus points didDenise earn?F 985 H 1,005G 995 J 1,105

9. Write About It When changing a percent to a decimal, why do youmove the decimal point two places to the left?

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LESSON 21.3Name

LESSON 21.3

Estimate and Find Percent of a NumberWrite the correct answer.

1. Greg found that 87.5% of the azaleabushes he planted in the springproduced flowers. He planted 24 azaleabushes. How many bushes producedflowers?

3. Lawn chairs cost $34 and recliningchairs cost twice as much. What is thecost of 2 lawn chairs and 2 recliningchairs?


5. The bill for dinner for 8 people comesto $126.67. Mr. Zamboni wants to leave15% as a tip. How much should heleave?A $17.59 C $18.75B $18.20 D $19.00

7. Grace is moving all of her 249 books tothe large bookcase downstairs. She cancarry 12 books at a time in her arms.What is a reasonable estimate of howmany trips Grace will need to make?A 10 C 30B 20 D 40

2. The bill for dinner for your family offive comes to $78.25. You want to leavea 15% tip. If you give the waiter $87.00is that enough? Explain.

4. Jon flew across the country in 5 hr 15 min. The distance is about 3,200 mi.About how fast was the plane flying?

6. The sixth-grade class is 120% as largeas the seventh-grade class. There are485 students in seventh grade. Howmany students are in sixth grade?F 582 H 465G 505 J 388

8. Peter ran the first 100 m of the race in45.8 sec. The race is 400 m long. If hemaintains this rate, which expressioncan be used to find the total number of seconds it will take Peter to run the race?F 45.8 � 45.8 H 45.8 � 4G 400 � 100 J 400 � 100

9. Write About It What is always true about the answer to a problemwhen you are finding less than 100% of a number?

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NameLESSON 21.5

Discount and Sales TaxWrite the correct answer.

1. A pair of shoes regularly sells for $36.80.They are on sale for 40% off. What is thesale price?

3. Paul bought a 3-pound bag of applesfor $2.58. Albert bought a 5-pound bagof the same kind of apples for $4.20.Which was the better buy? Explain.


5. Lacy bought a shirt that regularly sells for $40. The clerk gave her a $10discount. What percent of the regularprice was the discount?A 50% C 15%B 25% D 10%

7. Ralph and his family drove 2,876 mi in 8 days. If they drove about the sameamount each day, which is the bestestimate of how many miles they droveeach day?A 350 miB 450 miC 550 miD 650 mi

2. A jacket regularly sells for $140. It is onsale for 20% off. What is the sale price?

4. Bruce has a bag of candy. In it he has18 caramels and 15 chocolate-coveredcherries. What is the ratio of caramelsto chocolate-covered cherries? Writethe ratio in three ways.

6. Hank bought a power saw on sale. Theregular price was $120. He paid only$96. What percent of the regular pricedid Hank pay?F 80% H 40%G 60% J 20%

8. Patrick gave away 9 of his marbles. He now has only 42 marbles. Whichequation can be used to find the totalnumber of marbles, m, Patrick hadbefore he gave 9 away?

Fm—9 � 42

G m � 9 � 42H 9m � 42J m � 9 � 42

9. Write About It Why is it important to be able to estimate what thediscount is on sale items?

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LESSON 21.6Name

LESSON 21.6

Simple InterestWrite the correct answer.

1. If you invest $1,400 at a simple interestrate of 6.5% for 7 years, how muchinterest will you earn?

3. The ratio of apples to oranges is 6 to 5.If there are 25 oranges, how manyapples are there?


5. Fred put $400 in the bank at 10%simple interest. How much will he havein the bank in 5 years?A $450 C $600B $550 D $700

7. Ned made four consecutive jumps. Hisfirst jump was 1.45 m, his second jumpwas 1.15 m, his third jump was 1.68 m,and his fourth jump was 1.52 m. Whatis the total distance he jumped?A 4.28 mB 4.35 mC 5.7 mD 5.8 m

2. If you take a loan of $2,800 at a simpleinterest rate of 8.3% for 2 years, what isthe total you will have to repay?

4. If 22 fine-tip art pencils cost $3.96, howmany pencils can you buy for $2.70?

6. Karen put $600 in the bank at 5% simpleinterest. How many years will it take forher to double her original $600?F 5 years H 20 yearsG 10 years J 30 years

8. Melissa and Amy earned $54.40 babysitting together. Amy earned $6.26 more than Melissa. How muchdid Melissa earn? How much did Amy earn?F $24.07; $30.33G $20.94; $27.40H $30.33; $24.07J $27.20; $20.94

9. Write About It Explain how the amount of interest you earn whenmoney is invested in a bank is related to the amount of time themoney is invested.

NameLESSON 22.1

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Theoretical ProbabilityWrite the correct answer.

1. In a bag there are 12 red marbles, 3green marbles, and 4 yellow marbles.What is the probability of randomlyselecting a red marble from the bag?

2. Each letter of the alphabet is put intoa bag. What is the probability ofrandomly selecting an A, E, I, O, or Ufrom the bag?

3. A recipe for chili feeds 35 people andcalls for 3�

12� lb of onions. Juan wants to

make chili for 5 people. How manypounds of onions does he need?


4. During a basketball game, Stellaattempted 30 foul shots. She made80% of them. How many foul shots didshe miss?

5. Dale was paid $487.63 for the monthand Bob was paid $691.02 for themonth. How much more did Bob make than Dale?

A $203.39 C $204.38B $203.59 D $204.59

6. Lyle kept track of the temperature for a month. The lowest temperature herecorded was 45°F and the highesttemperature was 82°F. What is therange of the temperatures?F 34°F H 36°FG 35°F J 37°F

7. A spinner is divided into five sectionsand labeled 1, 2, 3, 4, and 5. If eachnumber is equally likely to occur, whatis the probability of the spinnerlanding on an even number?

A �15

� C �25

�

B �12

� D �26

�

8. Darla can select one friend to go onvacation with her. She will put thenames of her 15 best friends into a bag and randomly select one name.What is the probability she will selecther friend Cheryl?

F �115� H �

116�

G �11

45� J �

11

56�

9. Write About It Explain what a probability of 0 means.

NameLESSON 22.2

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Choose Relevant InformationSometimes a word problem contains information that may not help yousolve the problem. You must decide which information is relevant, orneeded to solve the problem. Unnecessary information is irrelevant. Onthe other hand, there may be facts that you need that are not included inthe problem. Read the following problem.

Evan is employed at the Squeaky-Clean Soap Company,and he likes his job. He starts at 8 A.M. and ends his shiftat 4:30 P.M. He must work a total of 5 hr each day, but hisjob is divided up. Every hour on the hour, he works for 15min. He takes a 20 min break at 10:20 A.M. On the halfhour of odd-numbered hours, he works for 25 min. He eatslunch at 12:15 P.M. After 4:30, he cleans up for 45 min andgoes home. Does he work 5 hr on this schedule? Explain.

1. Read each fact from the problem. Is the fact relevant or irrelevantto solve the problem? Write R for relevant and I for irrelevant.A Evan likes his job. B He works from 8 A.M. until 4:30 P.M.C He must work 5 hr. D He works 15 min every hour on the hour. E He takes a 20 min break. F He works 25 min on the half hour of odd-numbered hours. G He has lunch at 12:15. H He spends 45 min cleaning up after 4:30.


VOCABULARY

relevantirrelevant

Solve. Choose relevant information to help you.

3. Edna drinks a lot of water each day.She knows a glass is 8 oz. She has 10 ozwhen she wakes up and 14 oz in themiddle of the morning. She has 8 oz ofwater with each meal. She drinks 16 ozof water between 3 P.M. and 4 P.M.Before bed, she has a 12 oz mug ofapple cider. How many glasses of waterdoes she have each day?

4. Paul left home at 2 P.M. He walked 3blocks east and 1 block north to thedrugstore. Then he walked 1 block eastand 1 block north to the post office.After that, he walked 2 blocks west and1 block north to the library. Hecontinued 2 blocks west and 1 blocksouth to his friend Roberto’s house,where he ate a snack. Then he walked1 block west and 2 blocks south to hispiano teacher’s house. How far wasPaul from home?


NameLESSON 22.4

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Experimental ProbabilityWrite the correct answer.

1. Oscar’s scores for the dart game are45, 23, 32, 32, 12, 25, 65, and 78. Findthe mean of his scores.

2. In soccer, Bernice scored 8 goals out of25 tries. How many goals can sheexpect to score if she tries 100 times?

3. In a bag there are 9 green squares, 8 red squares, and 13 yellow squares. Is each color equally likely to beselected at random? Explain.

4. Jake flipped a coin 50 times. Theresults from the flipping were 31 headsand 19 tails. Based on his results, whatis his experimental probability ofgetting tails?

5. Charles had �34� ft of plywood and cut off

�18� ft for a doorstop. How much plywooddoes he have left?

A �78

� ft C �58

� ft

B �34

� ft D �12

� ft

6. Dale randomly threw darts at a targetand recorded the following results: 21hits on black and 79 hits on white.What is the ratio of the hits on black tothe hits in all?

F �17090

� H �27

19�

G �12010

� J �72

91�

7. Roger randomly selected marbles from a bag one at a time andrecorded the color. He put each marble back before selecting thenext one. The results were 12 red, 25 blue, 16 green, and 2 yellow.What conclusion can he make from these results? A There are very few yellow marbles in the bag.B There are the same amount of red and green marbles.C There are 55 marbles in the bag.D There are no other colors of marbles in the bag.

8. Write About It Is it possible to flip a coin and get 25 heads in a row? Explain.

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LESSON 23.1Name

LESSON 23.1

Classify and CategorizeOne way to organize information in a problem is to classify andcategorize it. To classify information is to group information that isalike in some way. To categorize information is to label the groupsthat you have made by classifying.


Elena’s family is giving her a special birthday treat. She can chooseone special outing to have with one special friend. The friendsElena might choose are Brad, Helen, Angie, Erica, or Roy. Theoutings she is considering are horseback riding, dinner and amovie, a rock concert, a ride in a private plane, or a day at anamusement park. How many different birthday treats involvingone friend and one outing are possible?

1. Complete the table to classify and categorize the informationfrom the problem.

Friend Outing

Brad horse, dinner/movie, concert, plane, amusement park

Helen horse, dinner/movie, concert, plane, amusement park

Angie horse, dinner/movie, concert, plane, amusement park

Erica horse, dinner/movie, concert, plane, amusement park

Roy horse, dinner/movie, concert, plane, amusement park


Classify and categorize the information. Then solve.

3. Virgil is baking a pie. He can make acoconut pie, banana cream pie, orvanilla pie. He can make a grahamcracker crust, regular crust, or chocolatecookie crust. How can you classify andcategorize the information? How manydifferent pies can he make?

4. Anita is choosing her song for the springconcert. She can sing a pop song,lullaby, folk song, or funny song. Shecan be accompanied by a piano, harp,or guitar. How can you classify andcategorize the information? How manypossible presentations can Anita make?

VOCABULARYclassify

categorize

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Compound EventsWrite the correct answer.

1. As a lunch special, the Kozy Kitchenoffers a choice of 6 sandwiches, 3 salads, 3 kinds of soup, and iced teaor lemonade. How many differentlunches could you make?

3. Sneakers that usually sell for $75 are onsale. The discount on Trek sneakers is �

14�.

The discount on Pro sneakers is �15�.

Which brand has the greater discount?Explain.


5. Nat wants to watch a TV special oncomputers. The program will be airedon Monday, Wednesday, and Friday at 11:00 A.M., 4:00 P.M., 8:00 P.M., andmidnight. How many choices does Nat have?A 7 choices C 12 choicesB 9 choices D 15 choices

7. Adam has a bag that contains 8 red, 16 blue, 12 green, and 14 yellow marbles.Without looking, Adam takes a marblefrom the bag. What is the probabilitythat Adam gets a yellow marble?

A2—

50 C7—

25

B1—

14 D8—

25

2. Flo wants to wrap 16 gifts for herfriends. She has 3 kinds of paper, bowsin 4 different colors, and 2 kinds ofribbon. Can she wrap each package in a different combination? Explain.

4. Kyle and 9 of his friends formed anature club last year in January. Theyeach paid an initiation fee of $5 and$2 per month dues. How much did theclub collect last year?

6. Carla is choosing cabinets for her newkitchen. The cabinets come in 2 sizes; a choice of oak, cherry, or pine wood;and a choice of 6 finishes. How manychoices does Carla have?

F 36 choices H 48 choicesG 42 choices J 60 choices

8. The Greenthumb Nursery usually sellsa flat of petunias for $12.50. This week,each flat is �

15� off with a coupon from the

newspaper. What is the price of 2 flatsof petunias if a coupon is used to buyone of them?F $19.50 H $22.50G $20.00 J $25.00

9. Write About It Would you rather draw a tree diagram or use theFundamental Counting Principle to find the number of possibleoutcomes for a compound event? Explain.

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LESSON 23.3Name

LESSON 23.3

Independent and Dependent EventsWrite the correct answer.

1. Your sock drawer contains 6 blacksocks, 4 blue socks, and 10 brown socks.What is the probability that you will geta pair of blue socks if you pick 2 sockswithout looking in the drawer?

3. Rick has three times as many baseballcards as Vic. Vic has one half as manyas Nick, who has 12 cards. How manybaseball cards do they have in all?


5. Sam and Renee have signed up witheight other students to be RecyclingMonitors. One student and an alternatewill be selected by drawing names froma hat. What is the probability that Samwill be selected as the monitor andRenee will be selected as the alternate?

A1—

10 C1—

90

B1—

45 D1—–

100

7. Petunias are sold in flats of 10 plants.Daisies are sold in flats of 6 plants. Youwant to buy an equal number of eachplant. What is the least number ofplants you can buy?

A 60 of each C 30 of eachB 40 of each D 20 of each

2. A bag contains 6 lettered tiles labeledA, A, B, C, D, D. Without looking, youselect a tile and keep it. Then you selectanother tile. What is the probability ofselecting an A and then a D?

4. Martha wants to make a decorativeframe for a rectangular painting that

measures 42–3 ft by 3

5–8 ft. How much wood

will she need to construct the frame?

6. There are 2 blue marbles, 5 redmarbles, and 3 green marbles in a bag.You close your eyes, select a marble,and replace it. Then you close youreyes and select another marble. What isthe probability of picking a red marbleboth times?

F3–4 H

1–3

G1–2 J

1–4

8. Hank jogs �12� mi per day 4 days each

week. Each week he increases thedistance he jogs by �

14� mi per day. In how

many weeks will Hank be jogging 2 miper day?

F 4 weeks H 8 weeksG 6 weeks J 10 weeks

9. Write About It You roll a number cube twice. Are these dependentor independent events? Explain.

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NameLESSON 23.4

Make PredictionsWrite the correct answer.

1. In a survey of 150 randomly selectedsixth graders, 25 of them said that theyread magazines on a regular basis.Predict about how many sixth gradersout of 2,400 will indicate that they readmagazines on a regular basis.

3. The probability of picking a yellow tilefrom a bag of 5 tiles is 2–5. You add a red tileto the bag. Now what is the probability ofpicking a yellow tile? Explain.


5. In a random sample of 300 VCRs, thequality control department found that18 were defective. If the companymanufactured 9,000 VCRs, about howmany of them would you expect to bedefective?A about 54 C about 270B about 180 D about 540

7. Kale counted 50 rose bushes in thepark’s rose gardens. Of those bushes, 14 of them were a variety known as tea roses. What percent of the rosebushes were tea roses?A 14% C 50%B 28% D 56%

2. In a survey of 175 randomly selectedcomputer users, 25 of them said thatthey used their computer for research.Predict about how many computerusers out of 4,200 will indicate thatthey used their computers for research.

4. A computer store charges monthly interest at the following rate: 1�

12�% for

the first $200, and 1% for any amountover $200. What is the interest chargeand total charge for a customer with abill of $512?

6. When a random sample of 100 carrotseeds was planted, 15 of the seeds didnot germinate. If 2,500 carrot seedswere planted, about how many wouldyou expect not to germinate?

F about 150 H about 375G about 250 J about 475

8. Fruit drinks are sold in 4 flavors:strawberry, banana, mango, andorange. They are sold in 3 sizes: small,medium, and large. How many differentchoices are available?F 12 H 4G 7 J 3

9. Write About It How can you use a ratio to make predictions basedon a sample?

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NameLESSON 24.1

Algebra: Customary MeasurementsWrite the correct answer.

1. Find the missing measurement.

32 ft � � in.

3. Felix walked 2,530 feet on Tuesday and558 yards on Wednesday. How manyfeet did Felix walk altogether?


5. Bill’s car weighs 3,450 pounds. Hisfriend Jack has a truck that weighs 2 tons. How many more pounds doesJack’s truck weigh than Bill’s car?A 550 lb C 570 lbB 560 lb D 580 lb

7. Gail made a spinner with 24 congruentsections. She labeled each section inorder as follows: A, B, C, D, A, B, C, A, B,A, B, A, B, A, B, C, A, B, C, D, A, B, C, D.What is the probability of spinning thepointer and landing on D?

A1—

12 C1–6

B1–8 D

1–4


16 qt � � gal

4. Which unit of measurement is larger,pints or cups? Explain.

6. Ellen is making punch for a party. Therecipe makes 2 quarts. If she makes 4 times the recipe, how many gallons of punch will she have?F 5 gal H 3 galG 4 gal J 2 gal

8. The Garcia family has five children.Their ages are 9, 11, 13, 18, and 19. Whatis the mean (average) of their ages?F 10 years H 13 yearsG 12 years J 14 years

9. Write About It Explain how you can change 1 mile to inches.

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NameLESSON 24.2

Algebra: Metric MeasurementsWrite the correct answer.

1. Which unit is larger, kilometers ormeters? Explain.

3. Claire’s baby brother is 19 months oldtoday, and Ellen’s baby sister is 3 yearsold today. How much older is Ellen’sbaby sister than Claire’s baby brother?


5. Thomas had 2 liters of water with himto drink. Larry had 2,500 milliliters ofwater to drink. How much more didLarry have to drink than Thomas?A 2,500 mL C 1,500 mLB 2,000 mL D 500 mL

7. Bob played ski ball at the arcade andwon 630 coupons. He played 18 gamesand got the same number of couponseach time he played. Which equationcan be used to find the number ofcoupons, c, he won each time heplayed?A 18c � 630 C c � 18 � 630

B 18 � c � 630 D18—c � 630


30 km � � m

4. Nancy measured her step to be 2 feet.She went for a walk and counted 5,280steps. How many miles did she walk?

6. Paul bought a piece of rope 6 meterslong. He used 480 centimeters tyingdown a tarp in his backyard. Howmuch rope does he have left?F 0.12 m H 5,520 cmG 1.2 m J 12 m

8. Mary made 3 long distance phone calls last month. The first call was toAustralia and cost $34.71, the secondcall was to Spain and cost $29.09, and the third call was to Japan and cost $58.12. Estimate the total cost of the calls.F $120 H $160G $140 J $180

9. Write About It Explain how you can change smaller metric units to largerones or larger metric units to smaller ones by moving the decimal point.

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NameLESSON 24.3

Relate Customary and MetricWrite the correct answer.

1. In international track and fieldcompetitions, race distances aremeasured in meters. One race is 400 mlong. To the nearest 10 yd, how long isthe 400-meter race?

3. Carrie is choosing between these sizesof the same cereal: 16 oz for $1.79, 20 oz for $2.59, and 25 oz for $3.29. Shewants to pick the one that is the bestbuy. Which box of cereal should Carriechoose?


5. Haley lives in Canada. On a map she sees that the distance from herhometown to Chicago, Illinois, is1,875 km. She wants to know thisdistance in miles. Which expression canshe use to find the number of miles?A 1,875 � 1.61B (1,875 � 1.61) � 1,875C (1,875 � 1.61) � 1,875D 1,875 � 1.61

7. Which expression can you use to findthe weight in kilograms that isequivalent to 16 lb?A 16 � 0.45 C 16 � 0.45B 16 � 0.45 D 16 � 0.45

2. On a cold winter morning, thetemperatures in five cities were 7°F, 9°F, 12°F, 4°F, and 13°F. What were themean and median temperatures forthese five cities?

4. Ana’s fish tank holds 80 L of water. The owner of the pet store where shebought a new fish told her that the fishneeds to be in a tank that holds at least30 gal. Does her tank hold enoughwater for the new fish? Explain.

6. Mr. and Mrs. Rojas are taking their 3 children ice skating. The cost foradults is $5.75. The cost for children is $3.25. They will also spend $12.00 ontraveling expenses. Which expressioncan Mrs. Rojas use to find the total costfor the entire family?F 12 � 2 � 5.75 � 3 � 3.25G 12 � 5(5.75 � 3.25)H 12 � 2 � 5.75 � 3 � 3.25J 12 � 5(5.75 � 3.25)

8. Marie is 24 years younger than hermother. Which equation can you use to find Marie’s age, x, if her mother is36 years old?F x � 24 � 36 H x � 24 � 36G x � 24 � 36 J x � 24 � 36

9. Write About It Explain how you would change 75 meters to feet.

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NameLESSON 24.4

Appropriate Tools and UnitsWrite the correct answer.

1. Cora filled a measuring cup with water.She looked at the scale on the side ofthe cup and recorded the amount inthe cup as 1�

78� c. Later, she changed the

amount she had written to 15 oz.Which measurement is more precise?

3. Nate is comparing the prices of trips toEurope. If he leaves between October 1and March 31, the trip costs $1,115. Thesame trip, taken between April 1 andMay 13 costs $1,339. If he travels duringthe summer, he will pay $380 morethan for winter travel. How much willNate pay if he leaves July 5?

5. A folded sheet of paper is 8�12� in. long. It

is placed in an envelope that is 9 in.long so that its ends are the samedistance from the envelope ends. Howmuch space is between each end of the letter and the envelope?

A 1 in. C1–2 in.

B3–4 in. D

1–4 in.

7. A school hallway is being measured fornew floor tiles. Which of these measuresgives the more precise length of thehallway?

A 180 ftB 60 yd

2. Josie is measuring the length of a roomfor carpeting. When she stretches thetape across the room, she has a choiceof two ways to read the length, 9�

12� ft or

114 in. Which is a more precise way ofmeasuring the room’s length?

4. Nate plans to fly from New York City toLondon. London is 5 hr ahead of NewYork City. His flight will leave New YorkCity at 7:45 P.M. on Tuesday. The flightto London takes 6�

12� hr. If the plane is on

time, at what time and on what day willNate arrive in London?

6. When Adita took her water bottle outof her backpack, she noticed that therewere four measurement scales on thebottle. Which of these measurements is the more precise measurement of the amount of water in Adita’s bottle?F 0.5 LG 500 mL

8. Henry exercises 25 min per day 3 dayseach week. If he increases the numberof minutes per day by 5 each week, howlong will it take him to reach 2 hr ofexercise each week?F 1 week H 3 weeksG 2 weeks J 4 weeks

9. Write About It The measurements 15 oz and 1�78� c are equivalent. Why is one

considered to be more precise?


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NameLESSON 24.5

Make PredictionsAn estimate is an approximate answer to a problem. If a problem asks you to find about how many or is phrased as a yes-or-no question, you can useestimation to make a prediction. When a problem asks for an exactanswer, you can estimate to check the reasonableness of your answer.Read the following problem.

Mattie has $34.23 in his savings account. He has $13.65 in hispiggy bank. He received $75 in birthday money. Does he haveenough to buy a CD player that costs $129.95?

1. Do you need to estimate or give an exact answer? Explain.

2. What prediction can you make?

3. How can you use estimation?


Use estimation to make predictions.

5. Phyllis has the following items in hergrocery cart: a chicken for $7.93, a loafof bread for $2.19, a gallon of milk for$2.98, a dozen eggs for $1.59, a bag ofpotatoes for $0.99, a pound of cheesefor $4.49, and 6 apples for $0.50 each.Her budget for food is $20.00. Predictwhether or not she will stay within herbudget.

6. Amy and Eddie are collecting food forthe town soup kitchen. Their goal is to collect 200 lb of food in 1 day. Theyhave collected sixty-one 16-oz cans ofvegetables, forty-three 32-oz cans offruit, nineteen 24-oz boxes of cereal,and ninety-eight 8-oz cans of soup.Predict whether or not they will meettheir goal.

VOCABULARYestimate

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NameLESSON 25.2

PerimeterWrite the correct answer.

1. Find the perimeter.

3. In order to put up a fence, Jane neededto measure the sides of her rectangulargarden. It was 102 in. long and 66 in.wide. Express the measurements ofJane’s garden in feet.


5. Todd started working on his scienceproject 12 days and 22 hours ago. Howmany hours has it been since hestarted working on his project?A 144 C 288B 166 D 310

7. The lengths of the sides of aquadrilateral are 23.5 cm, 36.4 cm,19.1 cm, and x cm. The perimeter is107.3 cm. What is x?A 19.1 cm C 28.3 cmB 26.8 cm D 42.6 cm

2. Find the perimeter.

4. Jane bought 4 flowering bushes to putat the corners of her square patio. Eachbush cost $29.95. How much changedid she get from $150.00?

6. Bernice bought a fish tank and was toldit held 12,800 mL of water. How manyliters does the tank hold?

F 12,800 L H 128 LG 1,280 L J 12.8 L

8. The school playground was built in the shape of a square. Its perimeter is1,408 yd. Find the length of each sideof the playground.F 704 yd H 176 ydG 352 yd J 140 yd

9. Write About It Explain how to find the perimeter of any polygon.

34 ft

56 ft

38 ft

85 ft

62 ft

12 yd

13 yd7 yd

8 yd

11 yd

8 yd

9 yd

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NameLESSON 25.3

Use Graphic AidsAs you read a problem that can be solved using a geometrical approach,make a diagram to record the information. Then you can use the graphicaid that you have created to help you solve the problem. Be careful to useaccurate labels, symbols, and abbreviations in creating and using yourgraphic aid. Read the following problem.

Yukio is designing a house for his hamster. He has 5 cube-shapedrooms. They can be attached to each other by any of the four walls so that any two cubes form a rectangular prism. How manydifferent-shaped houses can Yukio make for his hamster? (Do notcount mirror-image shapes as two different shapes.)

1. In your diagram, what shape would best represent each cube?

2. How can you use diagrams to solve the problem?

3. Yukio drew these arrangements. Draw other possiblearrangements.


Solve the problem. Make and use a graphic aid to help you.

5. Raoul is using blocks shaped like equilateral triangles to makelarger and larger equilateral triangles. Complete the pattern. Whatkind of pattern do you see in the numbers of triangles?

1 4

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NameLESSON 25.5

CircumferenceWrite the correct answer.

1. Earth’s two closest neighbors are Mars and Venus. The diameter of Mars is 4,214 mi. The diameter ofVenus is 7,522 mi. How much greater is the circumference of Venus than the circumference of Mars? Round tothe nearest mile.

3. Carmen had some wood, some chainlink fencing, and some iron fencing.She built a fence using wood for �

12� of

the fence, chain link for �14� of the fence,

and iron for the rest. She used 70 ft ofiron. How long was her fence?


5. During a special sale, a departmentstore sold shirts for $10 and pairs ofjeans for $12. Martin bought twice asmany shirts as pairs of jeans and spentless than $100. What was the greatestnumber of pairs of jeans he could havebought?A 10 C 4B 6 D 3

7. The rim of a passenger car tire can havea diameter of 13 in., 14 in., or 15 in. Tothe nearest whole number, how muchgreater is the circumference of a rimthat is 15 in. in diameter than one thatis 13 in. in diameter?A 4 in. B 5 in. C 6 in. D 7 in.

2. The radius of Earth is 3,960 mi (thedistance from the center of the planetto the surface). How much greater is the circumference of Earth than of Venus? How much greater is thecircumference of Earth than of Mars?Round to the nearest mile.

4. Students each paid $7 to go on a classtrip to the theater. For every 6 students,1 parent was admitted at no charge.The total cost of the trip was $210. Howmany students and parents in all wenton the trip?

6. A baseball diamond is a square. Thedistance from home plate to first baseis 90 ft. During the 1998 baseballseason, one player hit 70 home runs.What is the least number of feet hecould have run after hitting thosehome runs?F 6,000 ft H 32,400 ftG 25,200 ft J 64,800 ft

8. A light truck tire may have a diameterof 31 in. If the tire is on a rim that is 15 in. in diameter, to the nearest wholenumber, how much greater is thecircumference of the tire than thecircumference of the rim?F 50 in. G 54 in. H 60 in. J 100 in.

9. Write About It Explain why you had to use different formulas to answerExercises 1 and 2.

NameLESSON 00.0

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Estimate and Find AreaWrite the correct answer.

1. Estimate the area of the figure. Eachsmall square on the grid represents 1 m2.

2. Find the area of the triangle.

3. A rectangle has a length of 23 ft and awidth of 6 ft. What is the perimeter ofthe rectangle?

4. How many seconds are equal to 3 weeks and 5 days?


5. Ron’s new house has a den that is 14 ftby 16 ft. How many square feet ofcarpet should he buy to cover thefloor? A 60 ft2 C 224 ft2

B 196 ft2 D 256 ft2

6. The high school athletic field is 45 ydlong and 30 yd wide. How many squareyards of fertilizer should they order tofertilize the entire field twice this year? F 2,700 yd2 H 1,350 yd2

G 1,900 yd2 J 900 yd2

7. Mr. Jones is planning a field trip for theentire middle school. The school has893 students. If each bus can hold 45students, how many buses do theyneed?A 19 buses C 21 busesB 20 buses D 22 buses

8. Cassie mailed 67 graduationinvitations to her friends and family. Ifeach stamp costs $0.33, how much didit cost her to mail all of the invitations?

F $22.11 H $13.40G $21.22 J $2.24

9. Write About It Why is area always written with square units?

NameLESSON 26.1

22m6m

NameLESSON 00.0

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Algebra: Areas of Parallelograms and TrapezoidsWrite the correct answer.

1. Find the area of the parallelogram. 2. Find the area of the trapezoid.

3. The length of a rectangle is 15 yd andthe width is 4 yd. Find the area.


4. How many centimeters are equal to 2 km?

5. A trapezoid has bases of 12 cm and 15 cm and a height of 20 cm. What isthe area of the trapezoid? A 540 cm2 C 360 cm2

B 500 cm2 D 270 cm2

6. A parallelogram has a base of 7.5 mand a height of 2.5 m. What is the areaof the parallelogram?F 18.75 m2 H 12.75 m2

G 15 m2 J 10 m2

7. Paul decided to survey 1 out of every10 people in his school. There are 976people in Paul’s school. What is areasonable estimate for how manypeople Paul should survey?

A 10 C 98B 76 D 196

8. At a recent gathering in the stadium,there were about 52,980 people inattendance. If between 4 and 6 peoplecame in each car parked in thestadium parking lot, estimate howmany cars were at the stadium parking lot. F 1,000 cars H 10,000 carsG 5,000 cars J 20,000 cars

9. Write About It A rectangle and a parallelogram with the same base and height have the same area. Draw a diagram and explain why this is true.

NameLESSON 26.2

7 ft 9 cm

4 cm

12 cm22.3 ft

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NameLESSON 00.0

Algebra: Areas of CirclesWrite the correct answer.

1. Find the area of the circle. Use 3.14 forπ. Round to the nearest whole number.

2. Find the area of the circle. Use 3.14 forπ. Round to the nearest whole number.

3. The height of a triangle is 20 cm andthe base is 15 cm. Find the area.


4. The length of a rectangle is 12 in. andthe width is 4 in. Find the area.

5. The diameter of a circle is 42 ft. What isthe area to the nearest whole number?

A 5,539 ft2

B 1,385 ft2

C 441 ft2

D 132 ft2

6. A semicircle has a radius of 10 m.What is the area of the semicircle tothe nearest whole number?F 1,256 m2

G 628 m2

H 314 m2

J 157 m2

7. Dennis walks up and down the stairsat school between 6 and 9 times aday. Which is a reasonable estimateof how many times he walks up anddown the stairs in 180 school days? A Less than 1,000B Between 1,000 and 1,800C Between 1,800 and 2,200D More than 2,200

8. John earned $48,600 last year. Which isthe best estimate for how much moneyhe earned each week?

F $800G $1,000H $1,200J $1,400

9. Write About It Explain how the diameter of a circle is related tothe radius.

NameLESSON 26.4

6 ft 15 yd

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Algebra: Surface Areas of Prisms and PyramidsWrite the correct answer.

1. Find the surface area. 2. Find the surface area.

3. The radius of a circle is 16 cm. Find thearea. Use 3.14 for π. Round to thenearest whole number.


4. The base of a parallelogram is 22 ft andthe height is 38 ft. Find the area.

5. The height of a triangle is 40 m and thebase is 52 m. What is the area?A 1,040 m2

B 1,050 m2

C 2,080 m2

D 2,090 m2

6. Henry walked 3 mi. How many feet didHenry walk?F 15,940 ftG 15,880 ftH 15,860 ftJ 15,840 ft

7. A cube measures 5 cm on each edge.What is its surface area?

A 200 cm2

B 150 cm2

C 120 cm2

D 100 cm2

8. A rectangular pyramid has a base 18 in.by 10 in., and the triangular faces eachhave a height of 25 in. What is thesurface area?F 4,500 in.2

G 1,400 in.2

H 880 in.2

J 700 in.2

9. Write About It How are the areas of opposite faces on a rectangular prismrelated? How does knowing this relationship help you find the surface area?

NameLESSON 00.0

NameLESSON 26.5

3m

7m5m

12ft

2ft5ft

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NameLESSON 27.1

Estimate and Find VolumeWrite the correct answer.

1. Find the volume of a moving carton usedas a wardrobe for clothes that is 5 ft wide,4 ft deep, and 8 ft tall.

3. The radius of a circle is 4.5 yd. Find thearea. Use π= 3.14. Round to the nearestwhole number.

2. Find the volume of an ice cream cartonshaped like a triangular prism. Thecarton is 9 cm tall and the bottom is atriangle with a base of 5 cm and a heightof 6 cm.

4. The height of a triangle is 6 in. and thebase is 4 in. Find the area.


5. Marty has decided to store all his gardenequipment in a big box that measures 3m on each side. Find the volume.

A 27 m3

B 18 m3

C 12 m3

D 9 m3

7. Sharon bought 25 pieces of candy thatlooked identical. Without looking, sheselected one from the bag. If 18 are darkchocolate and 7 are light chocolate, whatis the probability that Sharon picked alight chocolate one?

A �178� C

B D

6. Rita bought a flower vase that is 10 in.tall. The base is a square that measures3.5 in. on each side. Find the volume.

F 350.5 in.3

G 122.5 in.3

H 70 in.3

J 35 in.3

8. Monica earns $3 a day doing choresaround the house. At this rate, what is areasonable estimate for how much shemakes in a year?

F Less than $200

G Between $400 and $600

H Between $600 and $800

J More than $1,0007�25

18�25

7�18

9. Write About It Explain how the volume of a rectangular prismrelates to the volume of a triangular prism if the prisms have thesame length, width, and height.

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NameLESSON 27.2

Activate Prior Knowledge

Readers use what they already know about different topics to helpthem solve problems. Prior knowledge can give you insight into how toapproach a solution. Read the following problem.

Barney has 120 ft of wire. He wants to use it as the edges of a rectangularprism with the largest possible volume. What length, width, and heightshould he choose?

1. Explain how your prior knowledge about each topic listed can helpyou solve this problem.

a. Making models with centimeter cubes

b. Symmetry

2. Make a model. Then complete the table.

3. Solve the problem by comparing the volumes in the table.

Length Width Height Total length of Total Volumewire needed

120 ft

120 ft

120 ft

120 ft

120 ft

4. Eliza has 100 centimeter-cubes. Find thesize of a rectangular prism that she canmake that uses the greatest number ofcubes?

5. Rob makes two rectangular prisms. Oneis 8 cm long, 2 cm deep, and 2 cm high.The other is 4 cm long, 4 cm deep, and 2cm high. Which one has the greatervolume?

Make a model. Solve using your prior knowledge.

VOCABULARYprior knowledge

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NameLESSON 27.3

Algebra: Volumes of PyramidsWrite the correct answer.

1. Mark has a pyramid-shape box with arectangular base. The length is 4 cm, thewidth is 5 cm, and the height is 12 cm.Ming has a cube-shape box thatmeasures 5 cm along each side. Whichbox has the greater volume? Explain.

3. A container with a volume of 230.4 in.3

holds 1 gal of water. How many gallons ofwater will a fish tank hold that is 24 in.long, 12 in. wide, and 12 in. high?

2. Sara has a pyramid-shape box with asquare base. The base is 6 in. on eachside and its height is 6 in. Kyra has arectangular prism-shape box. The lengthis 5 in., the width is 4 in., and the heightis 3 in. Which box has the greatervolume? Explain.

4. You want to plant a bush every 2 ft alongthe curved side of a semi-circular patiothat has a radius of 12 ft. How manybushes do you need?


5. Carlos planted a flowergarden in this shape.Estimate the area of theflower garden.

A About 12 ft2 C About 200 ft2

B About 50 ft2 D About 800 ft2

7. Kristi spent $588 on bark mulch for herplant beds. The landscape supplycompany has a sale price of 4 yd3 for$112. How many cubic yards of mulchdid Kristi buy?

A 5�14

� yd3 C 28 yd3

B 21 yd3 D 84 yd3

6. The art gallery is showing a sculpture inthe shape of a square pyramid. It is 4�

12� yd

high. Each side of the base measures1�

23� yd. Find the volume.

F 33�34

� yd3 H 7�56

� yd3

G 12�12

� yd3 J 4�16

� yd3

8. The volume of a cube that measures 4 cmon each side is 64 cm3. How does thatcompare to the volume of a pyramid withthe same base and height?

F Less than H Greater than

G Equal to J Not related

9. Write About It Explain your solution to Exercise 8.

r � 8 ft

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NameLESSON 27.5

Volumes of CylindersWrite the correct answer.

1. Find the volume of thissoup can. Use π� 3.14.Round to the nearestwhole number.

3. The school playground is a rectanglewith an area of 72 m2. If the length is12 m, what is the perimeter?

2. Find the volume of thisoil drum. Use π� 3.14.Round to the nearestwhole number.

4. The area of a triangular-shape island is100 mi2. If the base of the triangle is20 mi, what is the height?


5. Our new hot water tank is 5�12� ft tall and

has a diameter of 30 in. About how muchwater will it hold?

A 27 ft3

B 43 ft3

C 108 ft3

D 518 ft3

7. Paula rolled a number cube 78 times.Her results are shown in the table. Basedon Paula’s results, what is the probabilityof rolling a 5?

Number Rolled 1 2 3 4 5 6 Frequency 12 8 14 15 11 18

A �16

� C �17

18�

B �16

17� D �

71

81�

6. A cylindrical water bottle has a diameterof 5 in. and is 11 in. tall. About how muchwater can it hold?

F 86 in.3

G 173 in.3

H 216 in.3

J 864 in.3

8. According to the newspaper, the highschool graduating class for this year is12% greater than last year’s class. Lastyear 734 students graduated. How large isthis year’s graduating class?

F 646

G 722

H 746

J 822

9. Write About It Cylinder A and Cylinder B have the same size bases.The height of Cylinder A is twice the height of Cylinder B. How arethe volumes of the two cylinders related?

6 cm

10 cm

12 yd8 yd

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NameLESSON 28.1

Cause and Effect

Information in a math problem is related to other information in thesame problem. For example, a rule can cause a pattern to occur. Thepattern is the effect of the rule.


Josh has an unusual way of saving money. On each day of themonth, the number of coins he saves matches the date. The firstmonth he saves pennies. The second month he saves nickels. Thethird month he saves dimes. Then he starts over. If he begins hisplan on March 1, how much money will he have at the end of May?

1. Use the information in the problem above to complete the chart.

2. What pattern can you use for adding the numbers?


Solve.

4. Joylyn is memorizing math facts. Shememorizes 1 fact on the first day, 2 onthe second day, 3 on the third day, and soon. On which day will she know 28 facts?

5. Larry is learning to type. He alternateslearning 2 new letters a day and 3 newletters a day. If he starts on Tuesday, onwhat day of the week will he know all26 letters?

Cause Effect

Number of pennies per day to 1¢ + 2¢ + 3¢ + . . . 31¢ match the date—31 days

VOCABULARYcause, effect

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NameLESSON 28.2

Patterns in SequencesWrite the correct answer.

1. The third term in a sequence is 35. Therule is add �8 to each term. What are thefirst and sixth terms in the sequence?

3. The fifth term in a sequence is �324. Therule is multiply each term by �3. What arethe second and seventh terms in thesequence?

4. George can type 125 words in 5 min. Howmany words can he type in 1 min?

2. If the trend continues, what will the salesbe in the year 1998?


5. Lisa had 7 friends each bring 25 CDs toher party. She had 48 CDs. Whichexpression could be used to determinehow many CDs were at the party?

A 25 � 7 � 48

B 25 � 7 � 48

C 25 � 7 � 48

D 25 � 7 � 48

7. Mark started saving with $20. He plans toincrease his savings by $10 each week.How much will he save in the eighthweek?

A $70 C $90

B $80 D $100

6. Paul makes $50 a day by workingpart-time. He works five days a week. Atthis rate, which is the best estimate ofhow much he will make in a year?

F $5,000

G $8,000

H $10,000

J $13,000

8. Rainfall is expected to decrease by �12� in.

each year for the next 3 yr. Four inches ofrain fell this year. How much rain isexpected the year after next?

F 3 in. H 4�12

� in.

G 3�12

� in. J 5 in.

Sale

s (t

hous

ands

)

10080604020

0

120

140

160Growing Stronger Every Day

Years1997 1998 1999 2000 2001

9. Write About It A sequence of numbers begins with 6. Each term ismultiplied by �

12� to get the next term. Explain how you can tell if the

sequence is increasing or decreasing.

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NameLESSON 28.3

Number Patterns and FunctionsWrite the correct answer.

1. Hiroshi earns $6.50 an hour. He wants tobuy a CD player that costs $117. Write anequation and find how many hoursHiroshi will have to work to buy the CDplayer.

3. The lunch menu in the cafeteria includes4 kinds of sandwiches, 3 salads,3 beverages, and 2 desserts. How manylunch combinations do you have tochoose from?

2. Jennifer is taking a cab to a museum thatis 5 mi away. The cost of the cab is $0.85per mile plus $1.50. Write an equationand find how much the cab ride will costJennifer.

4. José is building a model ship from a kit.The scale of the model is 2 cm to 5 m. Ifthe length of the model ship is 30 cm,what is the actual length of the ship?


5. The members of Mark’s football teamaverage 2�

34� lb for each inch of height.

Which equation shows the relationshipof weight to height for the members ofMark’s football team?

A w � 2�34

� � h C w � 2�34

� � h

B w � 2h � �34

� D w � 2h � �43

�

7. Brent has a bag that contains 10 red,12 blue, 8 green, and 6 yellow marbles.Without looking, Adam takes a marblefrom the bag. What is the probability ofAdam getting a yellow marble?

A �23

� C �61

�

B �14

� D �316�

6. Rebecca is cutting rectangles to make acollage. The length of each rectangle is2 less than 3 times the width. Whichequation can you use to find the length ofa rectangle that is 4 in. wide?

F l � 3w � 2 H l � 3w � 2

G l � 3 w � 2 J l � 3w � 2

8. Irene’s plane leaves at 5:45 P.M. She wantsto allow 35 min to get to the airport fromher house. If she allows another half hourfor check-in and getting to the gate, whattime should she leave her house?

F 5:10 P.M. H 4:30 P.M.

G 4:40 P.M. J 3:40 P.M.

9. Write About It If x represents the color of a package and yrepresents the cost of mailing the package, is y a function of x?Explain.

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NameLESSON 28.4

Geometric PatternsWrite the correct answer.

1. Susan is building apattern with blocks.Describe the nextfigure in her pattern.

3. Morgan has 28 videos. The ratio ofcartoon videos to music videos is 3 to 4.How many cartoon videos does Morganhave?

2. Yuko is designinga wall hangingusing a patternof squares. Describe the next figure in her pattern.

4. Sam tossed a coin 63 times and got29 heads and 34 tails. Based upon Sam’sresults, what is the probability of gettingheads?


5. Donald bought 63 pens. He paid $2 eachfor the pens, not including tax. What wasthe total price Donald paid for the pens,not including tax?

A $124 C $128

B $126 D $130

7. The Tic Toc Nursery School has a bigclock face on the wall. The numbers arepainted in this order: red, yellow, green,starting at 12. What colors are thenumbers 7 and 11?

A green, yellow

B yellow, red

C red, green

D yellow, green

6. Roger traveled 4,644 mi in 18 days. Hetraveled the same distance each day.How far did Roger travel each day?

F 260 mi H 258 mi

G 259 mi J 257 mi

8. Ms. Dunn used a circle, a triangle, asquare, then a pentagon to make nametags. The shapes were repeated in thesame order. If this pattern continues,what shape was used for the 18thname tag?

F circle H square

G triangle J pentagon

9. Write About It How could you use multiples to help you do Exercise 8?

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1. Tell whether the second figure is areflection, translation, or rotation ofthe first figure.

3. Harry built a desktop that fits perfectlyinto a corner, and it has three sides.What geometric shape is the desktop?

5. What transformation could make a6 become a 9?

A translationB 90° rotationC reflectionD 180° rotation

7. What transformation could make anarrow pointing south become anarrow pointing west?

A translationB 90° rotationC reflectionD 180° rotation

2. Tell whether the second figure is areflection, translation, or rotation ofthe first figure.

4. An angle with a measure of 107.5°would be classified as what type ofangle? Find its supplement.

6. Kirk used 12.8 m of copper pipe onthe first job and 27.08 m on thesecond job. How many meters ofcopper pipe did he use in all?

F 12.8 m H 29.88 mG 15 m J 39.88 m

8. At the start of her trip, Lucy wrotedown the odometer reading as12,993.8 mi. At the end of her tripshe recorded the odometer reading as13,311.8 mi. How far did Lucy travelon her trip?

F 428 mi H 328 miG 418 mi J 318 mi

Name LESSON 29.1

9. Write About It Explain why an arrow pointing east will still be pointing east ifyou translate it.

Transformations of Plane FiguresWrite the correct answer.



1. Can Grace make a tessellation out ofthis figure?

3. Chuck has to pack 12,881 baseballsinto cartons. If each carton holds 32baseballs, how many cartons doesChuck need?

5. Luci is choosing a figure to make atessellation. Which figure should shechoose?

A the letter “P”B quarter circleC half-moonD triangle

7. Bob had a piece of rope �23� ft long that

he laid end to end with another piecethat was �

34� ft long. How long were the

two pieces together?

A �57� ft

B 1 ftC 1�

14� ft

D 1�152� ft

2. Can Sam make a tessellation out ofthis figure?

4. Miranda made a tablecloth shapedlike an octagon. Each side was 28 in.Find the perimeter of the tablecloth.

6. Harry is choosing a figure to make atessellation. Which figure should henot choose?

F circleG hexagonH squareJ trapezoid

8. Vinnie is looking at used trucks. Hehas found the following prices:$15,595, $19,500, $16,300, and$21,650. What are the mean and themedian?

F $19,250.50; $17,400G $18,565.25; $18,100H $18,261.25; $17,900J $17,634.50; $18,300

Name LESSON 29.2

9. Write About It If you rotate a shape about the origin and a corner of the shape ison the origin, that point never changes position. Explain why.

TessellationsWrite the correct answer.


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Details What I See

1. Use the details to make a mental picture. Then use words to describe what you see.

3. Erin is wondering if it is possible tomake a tessellating shape with acurved edge. She draws the shapebelow. Does her shape tessellate?Show how.


4. The middle school has decided toallow students to decorate one insidewall. Tia and Al are designing atessellating border for the wall. Canthey use a triangle and a square tomake their border? If so, show how.

Name LESSON 29.3

Form Mental ImagesSometimes it is helpful to form mental images, or draw a mental picture,of the information in a problem. Using the details or facts to make apicture in your mind can help you organize and understand information.


Arthur is helping his family design a patio. He is using octagonal tiles and square tiles. Can he tessellate the plane with those two shapes? Show how he can do it.

Make a mental image for each problem. Then solve.

VOCABULARYform mental images

Octagonal tiles (8 sides)

Square tiles (4 sides)

Tessellate the plane

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1.

Use transformations to decide whichplug (A, B, or both) will fit the receptor.

3. Five friends are standing in line fortickets. Paula is standing betweenChuck and Chris. Zack is first in line.Chris is directly in front of Maria. Listthe order in which they are standing.

5.

This cube has one black face. Rollthe cube along the line using 90°rotations. How many rotations willoccur before the black face willappear on top again?A 3 C 5B 4 D 6

7. If you double the length and widthof a prism, how does this affect thevolume?A doubles C quadruplesB triples D stays the same

2.

Look at the first figure. Which imageis a 180° rotation of the originalfigure?

4. Maria is stacking books in the librarystoreroom. The shelves are 0.8 mapart, and the bottom shelf is 1.5 mfrom the floor. There are 5 shelves.How far from the floor is the topshelf?

6. The total monthly revenue for thegym is $8,000. Half of this is used topay salaries and 25%, to pay rent andutilities. Finally, 12% is used to payinsurance. The remaining amount isset aside for the purchase of newequipment. How much remains to bespent on new equipment?F $7,913 H $1,760G $6,960 J $1,040

8. Gia is buying a brush and a hairribbon. Each item costs $3.50. Salestax is 5%. What is Gia’s total cost?F $0.35 H $7.35G $7.05 J $10.50

Name LESSON 29.4

9. Write About It Explain how you found the answer to Exercise 7.

Transformations of Solid FiguresWrite the correct answer.

A BPlug A Plug B Receptor

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1. Naomi drew this line ofsymmetry. Was she correct?Explain.

3. Gail made placemats as a gift. Eachplacemat had 4 equal sides but noright angles. What shape was theplacemat?

5. How many lines of symmetry doesthe figure have?A 8B 2C 1D 0

7. A “2-by-4” piece of lumber is really1�

12� in. by 3�

12� in. Find the area of a

cross section of a “2-by-4.”

A 2�13� in.2 C 5�

14� in.2

B 5 in.2 D 6�12� in.2

2. Willie drew this lineof symmetry. Was hecorrect? Explain.

4. Find three consecutive odd integersthat have a sum of �249.

6. How many lines of symmetry does aregular pentagon have? F 0G 1H 3J 5

8. Paul’s budget for food is $10 more than�13 of his total budget. He spent $100 onfood. What his total total budget.

F $250 H $300G $270 J $310

Name LESSON 29.5

9. Write About It Can a figure have line symmetry and notrotational symmetry? If so, give an example.

SymmetryWrite the correct answer.


Name LESSON 30.0


Name

1. Jodi is �13� as old as her brother, Tom.

Jodi is 6 years old. Write an equationto find Tom’s age and solve.

3. If 3 apples cost $0.59, how much will16 apples cost?

5. All the trees in the yard are at least6 ft tall. Which inequality representsthis statement?

A n � 6B n � 6C n � 6D n � 6

7. All the sixth graders are younger than14. Which inequality represents thisstatement?

A x � 14B x � 14C x � 14D x � 14

2. We should all eat at least 4 servingsof vegetables every day. Representthat requirement with an inequality.

4. The speed limit is 55 mi per hr. Writean inequality to represent the speedlimit.

6. Which classroom showed the leastincrease in the number of books readfrom last year to this year?

F Room 1 H Room 3G Room 2 J Room 4

8. Kyle started at an elevation of a ftabove sea level. He climbed 1,200 ftin 4 hr and was at an elevation of8,765 ft. Which equation could beused to determine the elevation atwhich he started climbing?F a � 8,765 � 1,200G a 8,765 � 1,200H a � 1,200 � 8,765J a 1,200 � 8,765

LESSON 30.1

9. Write About It Explain how you can tell from a graph of integers on a numberline that the integers go on forever?

Inequalities on a Number LineWrite the correct answer.

Cla

ssro

oms

Room 1

Room 2

Room 3

Room 4

Last Year

Books Read in April

Number of Books0 25 50 75 100 125 150

This Year


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Name

1. In which quadrant does the point(4,�5) lie?

3. Sherry had 57 quarter sandwiches leftover from the party. How manysandwiches is that?

5. Use the coordinate plane above andconnect points (3,2), (3,0), and (�2,0)to form a triangle. What is the area ofthis triangle?A 10 units2 C 6 units2

B 8 units2 D 5 units2

7. Dave bought 9 pizzas to feed32 people at a party. What is areasonable estimate for how muchpizza each person will get if everyoneshares equally?A �

17� pizza C �

15� pizza

B �16� pizza D �

14� pizza

2. Which point has coordinates (�3,2)?

4. Phil has 30 quarters, 28 dimes, and21 nickels. How much does he have?

6. Use the coordinate plane above andconnect points (3,2), (�3,2), (3,–2), and(�3,�2) to form a rectangle. What isthe area of this rectangle?F 36 units2 H 16 units2

G 24 units2 J 9 units2

8. The Weslake family drove 1,856 miand used 80 gal of gas. Which is thebest estimate of how many miles theydrove on 1 gal of gas?

F 10 mi H 30 miG 20 mi J 40 mi

LESSON 30.2

9. Write About It Describe the coordinates of an ordered pair for a point inQuadrant II.

Graph on the Coordinate PlaneWrite the correct answer.


x

y

0-2

-2

2

2-4-6

-4

-6

4

6

4 6

B

D

AC

HG

FE

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Name LESSON 30.0Name

1. Use the first three values of x and y tocomplete the table.

3. Jon has a square pizza. He cuts it intopieces along all the lines of symmetryof the square. How many pieces doeshe have?

5. During Math Challenge, Margechallenged Hal to name a rationalnumber between �

56� and �

78�. Which

number should Hal not choose?

A 0.86 C 0.84B 0.85 D 0.83

7. Each time Tony gets a paycheck, hekeeps $5 and puts the rest in hissavings account. Which ordered pairrepresents this relationship if x equalsthe amount of his paycheck?

A (25,30) C (50,10)B (50,45) D (1,10)

2. Use the coordinate plane to graph theordered pairs from the table.

4. Solve. 6x � 72

6. Mrs. Harris found that 7 math booksfilled one shelf in the bookcase.Which ordered pair represents thisrelationship if x equals the number ofbooks? F (1,7) H (21,3)G (1,14) J (7,7)

LESSON 30.3

9. Write About It Explain how to graph the ordered pair (4,�2).

Graph FunctionsWrite the correct answer.

x

y

0-2-2

2

2-4-6-8

-4

-6

-8

4

6

8

4 6 8

Input (x) 1 2 3 4 5

Output (y) 5 10 15

Input (x) 3 4 5 6 7

Output (y) 0 1 2 3 4


8. To win the game, Sam needs to spina 4 or 7. The spinner is dividedequally into 10 sections andnumbered from 1 through 10. What isthe probability that Sam will win onhis next turn?F �

15� H �1

10�

G �1110� J �

12�

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Name

1. Complete the table.

3. Use the generalization to solve the problem.

5. Duane biked across the county toraise money for charity. In themorning, he rode for 2.5 hr andtraveled 20 mi. In the afternoon, herode for 1.5 hr and traveled 12 mi.That evening he biked for 3�

14� hr and

traveled 26 mi. How far did he travelin 3�

34� hr?

2. Find the relationship between x and y. Divide the amount ofthe sales tax by the cost of the car in each case to find thegeneralization.

4. For each cup of dry white beans thatyou want to cook, you need 3 c ofwater. How many cups of white beanswould you be cooking if you wereusing 20 c of water?

LESSON 30.4

Make GeneralizationsGeneralizations are broad conclusions drawn from experiences or from pieces of information. Generalizations are statements about a group of similar situations. Equations that show the relationship between two variables are one kind of generalization.


Agatha’s family bought a car for $7,600. They paid $456 insales tax. Tim’s grandfather bought a car for $11,900. He paid$714 in sales tax. Cindy’s aunt Amelia bought a car for $5,400.She paid $324 in sales tax. How much sales tax would therebe on a car that cost $9,300?

Solve by making a generalization.

cost of car, x $7,600

sales tax, y $456

cups of beans (x) 1 2 3 4

cups of water (y) 3 6 9 12

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Name LESSON 30.6

1. Rectangle A(�3,4) B(�1,4) C(�1,1)D(�3,1) was transformed intorectangle A′(0,5) B′(2,5) C′(2,2)D′(0,2). Describe the transformationthat took place.

3. Al is older than Mac. Nan is olderthan Al but younger than Don. Don isyounger than Bob. List the people inorder from oldest to youngest.

5. Lori bought $23.80 worth of groceries.The tax was $1.90. What was Lori’stotal bill, including tax?A $26.80 C $25.90B $26.87 D $25.70

7. Triangle ABC has coordinates A(1,4),B(3,4), and C(1,6). If it is translatedleft 4 units, which are the coordinatesof the new triangle?A A′(�3,4), B′(�1, 4), C′(�3,6)B A′(�2,4), B′(0,4), C′(�2,6)C A′(�4,4), B′(�2,4), C′(�4,6)D A′(1,0), B′(3,0), C′(1,2)

2. Rectangle W(0,2) X(3,2) Y(3,0) Z(0,0)was transformed into rectangle W′(0,�2) X′(�3,�2) Y′(�3,0) Z′(0,0).Describe the transformation that tookplace.

4. The train leaves at 7:30 A.M. It takesDana 20 min to walk to the trainstation and 15 min to eat breakfastthere. When should she leave home?

6. Dale had �78� ft of rope. Gregg borrowed

�12� ft of rope from Dale. How muchrope does Dale have left? F �

34� ft H �

38� ft

G �12� ft J �

14� ft

9. Write About It Describe how the coordinates of a figure change when youreflect it across the x-axis.

Graph TransformationsWrite the correct answer.


8. Triangle XYZ has coordinates X(2,2),Y(2,7), and Z(5,8). If it is reflectedacross the x-axis, which are thecoordinates of the new triangle?F X′(�2,2), Y′(�2,7), Z′(�5,8)G X′(�2,�2), Y′(�2,�7), Z′(�5,�8)H X′(2,�2), Y′(2,�7), Z′(5,�8)J X′(0,�2), Y′(�7,2), Z′(�8,5)

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