prb harc class iv

Problem Solvingand

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

Grade 4

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

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ISBN 0-15-320450-8

2 3 4 5 6 7 8 9 10 054 2004 2003 2002 2001

Unit 1: UNDERSTAND NUMBERS ANDOPERATIONS

Chapter 1: Place Value and Number Sense1.1 Benchmark Numbers . . . . . . . . . . . . . 11.2 Understand Place Value . . . . . . . . . . 21.3 Place Value Through Hundred

Thousands . . . . . . . . . . . . . . . . . . . . . . 31.4 Place Value Through Millions . . . . . 41.5 Reading Strategy: Summarize . . . . . 5

Chapter 2: Compare and Order Numbers2.1 Compare Numbers . . . . . . . . . . . . . . 62.2 Order Numbers . . . . . . . . . . . . . . . . . 72.3 Reading Strategy: Use

Graphic Aids . . . . . . . . . . . . . . . . . . . 82.4 Round Numbers . . . . . . . . . . . . . . . . 9

Chapter 3: Add and Subtract GreaterNumbers3.1 Estimate Sums and Differences . . 103.2 Use Mental Math Strategies . . . . . . 113.3 Add and Subtract 4-Digit

Numbers . . . . . . . . . . . . . . . . . . . . . . 123.4 Subtract Across Zeros . . . . . . . . . . . 133.5 Add and Subtract Greater

Numbers . . . . . . . . . . . . . . . . . . . . . . 143.6 Reading Strategy: Make

Predictions . . . . . . . . . . . . . . . . . . . . 15

Chapter 4: Algebra: Use Addition andSubtraction4.1 Expressions . . . . . . . . . . . . . . . . . . . . 164.2 Use Parentheses . . . . . . . . . . . . . . . . 174.3 Match Words and Expressions . . . 184.4 Use Variables . . . . . . . . . . . . . . . . . . 194.5 Find a Rule . . . . . . . . . . . . . . . . . . . . 204.6 Add Equals to Equals . . . . . . . . . . . . 214.7 Reading Strategy: Form Mental

Images . . . . . . . . . . . . . . . . . . . . . . . . 22

Unit 2: DATA, GRAPHING, AND TIME

Chapter 5: Collect and Organize Data5.1 Collect and Organize Data . . . . . . 235.2 Find Median and Mode . . . . . . . . . 245.3 Line Plot . . . . . . . . . . . . . . . . . . . . . . 255.4 Stem-and-Leaf Plot . . . . . . . . . . . . . 265.5 Compare Graphs . . . . . . . . . . . . . . . 275.6 Reading Strategy: Summarize . . . . 28

Chapter 6: Analyze and Graph Data6.1 Double-Bar Graphs . . . . . . . . . . . . . 296.2 Read Line Graphs . . . . . . . . . . . . . . 306.3 Make Line Graphs . . . . . . . . . . . . . . 316.4 Choose an Appropriate Graph . . . 326.5 Reading Strategy: Draw

Conclusions . . . . . . . . . . . . . . . . . . . 33

Chapter 7: Understand Time7.1 Before and After the Hour . . . . . . 347.2 A.M. and P.M. . . . . . . . . . . . . . . . . . . 357.3 Elapsed Time . . . . . . . . . . . . . . . . . . 367.4 Reading Strategy: Sequence

Information . . . . . . . . . . . . . . . . . . . . 377.5 Elapsed Time on a Calendar . . . . . 38

Unit 3: MULTIPLICATION ANDDIVISION FACTS

Chapter 8: Practice Multiplication andDivision Facts8.1 Relate Multiplication and

Division . . . . . . . . . . . . . . . . . . . . . . . 398.2 Multiply and Divide Facts

Through 5 . . . . . . . . . . . . . . . . . . . . . 408.3 Multiply and Divide Facts

Through 10 . . . . . . . . . . . . . . . . . . . . 418.4 Multiplication Table

Through 12 . . . . . . . . . . . . . . . . . . . . 428.5 Multiply 3 Factors . . . . . . . . . . . . . . 438.6 Reading Strategy: Choose

Relevant Information . . . . . . . . . . . 44

CONTENTS

Chapter 9: Algebra: Use Multiplicationand Division Facts9.1 Expressions with Parentheses . . . . 459.2 Match Words and Expressions . . . 469.3 Multiply Equals by Equals . . . . . . . 479.4 Expressions with Variables . . . . . . 489.5 Equations with Variables . . . . . . . . 499.6 Find a Rule . . . . . . . . . . . . . . . . . . . . 509.7 Reading Strategy: Interpret

Symbols . . . . . . . . . . . . . . . . . . . . . . . 51

Unit 4: MULTIPLY BY 1- AND 2-DIGITNUMBERS

Chapter 10: Multiply by 1-Digit Numbers10.1 Mental Math: Multiplication

Patterns . . . . . . . . . . . . . . . . . . . . . . . 5210.2 Estimate Products . . . . . . . . . . . . . . 5310.3 Model Multiplication . . . . . . . . . . . 5410.4 Multiply 3-Digit Numbers . . . . . . . 5510.5 Multiply 4-Digit Numbers . . . . . . . 5610.6 Reading Strategy: Classify and

Categorize . . . . . . . . . . . . . . . . . . . . . 57

Chapter 11: Understand Multiplication11.1 Mental Math: Patterns with

Multiples . . . . . . . . . . . . . . . . . . . . . . 5811.2 Multiply by Multiples of 10 . . . . . 5911.3 Estimate Products . . . . . . . . . . . . . . 6011.4 Model Multiplication . . . . . . . . . . . 6111.5 Reading Strategy: Cause and

Effect . . . . . . . . . . . . . . . . . . . . . . . . . 62

Chapter 12: Multiply by 2-Digit Numbers12.1 Multiply by 2-Digit Numbers . . . . 6312.2 More About Multiplying by

2-Digit Numbers . . . . . . . . . . . . . . . 6412.3 Multiply Greater Numbers . . . . . . 6512.4 Practice Multiplication . . . . . . . . . 6612.5 Reading Strategy: Use Context . . . 67

Unit 5: DIVIDE BY 1-AND 2-DIGITDIVISORS

Chapter 13: Understand Division13.1 Divide with Remainders . . . . . . . . 6813.2 Model Division . . . . . . . . . . . . . . . . 69

13.3 Division Procedures . . . . . . . . . . . . 7013.4 Reading Strategy: Analyze

Information . . . . . . . . . . . . . . . . . . . . 7113.5 Mental Math: Division Patterns . . 7213.6 Estimate Quotients . . . . . . . . . . . . . 73

Chapter 14: Divide by 1-Digit Divisors14.1 Place the First Digit . . . . . . . . . . . . . 7414.2 Divide 3-Digit Numbers . . . . . . . . . 7514.3 Zeros in Division . . . . . . . . . . . . . . . 7614.4 Divide Greater Numbers . . . . . . . . 7714.5 Reading Strategy: Use Graphic

Aids . . . . . . . . . . . . . . . . . . . . . . . . . . 7814.6 Find the Mean . . . . . . . . . . . . . . . . . 79

Chapter 15: Divide by 2-Digit Divisors15.1 Division Patterns to Estimate . . . . 8015.2 Model Division . . . . . . . . . . . . . . . . . 8115.3 Division Procedures . . . . . . . . . . . . 8215.4 Correcting Quotients . . . . . . . . . . . 8315.5 Reading Strategy: Draw

Conclusions . . . . . . . . . . . . . . . . . . . 84

Chapter 16: Patterns with Factorsand Multiples16.1 Factors and Multiples . . . . . . . . . . 8516.2 Factor Numbers . . . . . . . . . . . . . . . 8616.3 Prime and Composite Numbers . . 8716.4 Find Prime Factors . . . . . . . . . . . . . 8816.5 Reading Strategy: Form Mental

Images . . . . . . . . . . . . . . . . . . . . . . . . 89

Unit 6: FRACTIONS AND DECIMALS

Chapter 17: Understand Fractions17.1 Read and Write Fractions . . . . . . . 9017.2 Equivalent Fractions . . . . . . . . . . . . 9117.3 Equivalent Fractions . . . . . . . . . . . . 9217.4 Compare and Order Fractions . . . 9317.5 Reading Strategy: Compare . . . . . 9417.6 Mixed Numbers . . . . . . . . . . . . . . . . 95

Chapter 18: Add and Subtract Fractionsand Mixed Numbers18.1 Add Like Fractions . . . . . . . . . . . . . 9618.2 Subtract Like Fractions . . . . . . . . . 9718.3 Add and Subtract Mixed

Numbers . . . . . . . . . . . . . . . . . . . . . . 98

18.4 Reading Strategy: UnderstandCause and Effect . . . . . . . . . . . . . . . 99

18.5 Add Unlike Fractions . . . . . . . . . . 10018.6 Subtract Unlike Fractions . . . . . . . 101

Chapter 19: Understand Decimals19.1 Relate Fractions and Decimals . . 10219.2 Decimals Greater Than 1 . . . . . . . 10319.3 Equivalent Decimals . . . . . . . . . . . 10419.4 Compare and Order Decimals . . 10519.5 Reading Strategy: Text Format . . 10619.6 Relate Mixed Numbers

and Decimals . . . . . . . . . . . . . . . . . 107

Chapter 20: Add and Subtract Decimals20.1 Round Decimals . . . . . . . . . . . . . . 10820.2 Estimate Sums and Differences . 10920.3 Add Decimals . . . . . . . . . . . . . . . . . 11020.4 Subtract Decimals . . . . . . . . . . . . . . 11120.5 Add and Subtract Decimals . . . . . 11220.6 Reading Strategy: Synthesize

Information . . . . . . . . . . . . . . . . . . . 113

Unit 7: MEASUREMENT, ALGEBRA,AND GRAPHING

Chapter 21: Customary Measurement21.1 Choose the Appropriate Unit . . . 11421.2 Measure Fractional Parts . . . . . . . . 11521.3 Algebra: Change Linear Units . . . . 11621.4 Capacity . . . . . . . . . . . . . . . . . . . . . . 11721.5 Weight . . . . . . . . . . . . . . . . . . . . . . . 11821.6 Reading Strategy: Sequence . . . . . 119

Chapter 22: Metric Measurement22.1 Linear Measure . . . . . . . . . . . . . . . 12022.2 Algebra: Change Linear Units . . . . 12122.3 Capacity . . . . . . . . . . . . . . . . . . . . . 12222.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . 12322.5 Reading Strategy: Make

Inferences . . . . . . . . . . . . . . . . . . . . 124

Chapter 23: Algebra: Explore NegativeNumbers23.1 Temperature: Fahrenheit . . . . . . . 12523.2 Temperature: Celsius . . . . . . . . . . . 12623.3 Negative Numbers . . . . . . . . . . . . . 127

23.4 Reading Strategy: Multiple-Meaning Words . . . . . . . 128

Chapter 24: Explore the Coordinate Grid24.1 Use a Coordinate Grid . . . . . . . . . 12924.2 Length on the Coordinate Grid . 13024.3 Use an Equation . . . . . . . . . . . . . . . 13124.4 Graph an Equation . . . . . . . . . . . . . 13224.5 Reading Strategy: Draw

Conclusions . . . . . . . . . . . . . . . . . . . 133

Unit 8: GEOMETRY

Chapter 25: Plane Figures25.1 Lines, Rays, and Angles . . . . . . . . . 13425.2 Line Relationships . . . . . . . . . . . . . 13525.3 Congruent Figures and Motion . . 13625.4 Symmetric Figures . . . . . . . . . . . . . 13725.5 Reading Strategy: Paraphrase

Information . . . . . . . . . . . . . . . . . . . 138

Chapter 26: Perimeter and Area ofPlane Figures26.1 Perimeter of Polygons . . . . . . . . . . 13926.2 Estimate and Find Perimeter . . . . 14026.3 Estimate and Find Area . . . . . . . . . 14126.4 Relate Area and Perimeter . . . . . . 14226.5 Relate Formulas and Rules . . . . . . 14326.6 Reading Strategy: Compare . . . . . 144

Chapter 27: Solid Figures and Volume27.1 Faces, Edges, and Vertices . . . . . . 14527.2 Patterns for Solid Figures . . . . . . . 14627.3 Estimate and Find Volume

of Prisms . . . . . . . . . . . . . . . . . . . . . 14727.4 Reading Strategy: Choose

Relevant Information . . . . . . . . . . 148

Chapter 28: Measure and Classify PlaneFigures28.1 Turns and Degrees . . . . . . . . . . . . . 14928.2 Measure Angles . . . . . . . . . . . . . . . 15028.3 Circles . . . . . . . . . . . . . . . . . . . . . . . . 15128.4 Circumference . . . . . . . . . . . . . . . . 15228.5 Classify Triangles . . . . . . . . . . . . . . 15328.6 Classify Quadrilaterals . . . . . . . . . 15428.7 Reading Strategy: Use Graphic

Aids . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Unit 9: PROBABILITY

Chapter 29: Outcomes29.1 Record Outcomes . . . . . . . . . . . . . 15629.2 Tree Diagrams . . . . . . . . . . . . . . . . . 15729.3 Reading Strategy: Classify and

Categorize . . . . . . . . . . . . . . . . . . . . 15829.4 Predict Outcomes of

Experiments . . . . . . . . . . . . . . . . . . 159

Chapter 30: Probability30.1 Probability as a Fraction . . . . . . . 16030.2 More About Probability . . . . . . . . 16130.3 Test for Fairness . . . . . . . . . . . . . . . 16230.4 Reading Strategy: Draw

Conclusions . . . . . . . . . . . . . . . . . . 163

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Problem Solving PS1

Benchmark NumbersWrite the correct answer.

Choose the letter of the correct answer.

1. Write an estimate of the number ofcoins in pile B.

3. Ned buys a used car for $2,860.He must write the amount inwords on his check. Write theword form for this number.

2. Write an estimate of the number ofpeanuts in the jar.

4. There were 360 people at the fair onSunday and 165 people at the fairon Monday. How many people wentto the fair Sunday and Monday?

10 peanuts

10 pennies

A B

5. Each snowball in a snowman isexactly one half as wide as thesnowball below it. The snowmanis made from 4 snowballs. The topsnowball is 6 inches wide. Howwide is the bottom snowball?

A 12 in. C 48 in.B 24 in. D 96 in.

6. Harry kicked a soccer ball 3 yardsfarther than Jim. Jim kicked hisball 1 yard less than 20 yards.How far did Harry kick his ball?

F 21 yd H 23 ydG 22 yd J 24 yd

7. Write About It Explain the strategy you used to solve

Problem 5.

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PS2 Problem Solving

Understand Place ValueWrite the correct answer.


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

1. Write seventy thousand, twohundred four in standard form.

3. Nina spent $8.50 for movie tickets,$3.25 for popcorn, and $1.25 for adrink. How much did Nina spendin all?

2. Write the number 55,095 inexpanded form.

4. Write the number that is 1,000more than sixty-five thousand,four hundred ninety-one.

5. What is the word form for thenumber 8,407?

A eight thousand, seventyB eight thousand, forty-sevenC eight hundred forty-sevenD eight thousand, four hundred

seven

7. Light from the sun takes about 8minutes to get to Earth. Pam seesthe sun peek out from behind acloud at 10:52 A.M. At what timedid the sunlight leave the sun?

A About 2:52 A.M.B About 10:44 A.M.C About 10:46 A.M.D About 10:54 A.M.

6. What is the standard form for 20,000 � 2,000 � 200 � 2?

F 22,220G 22,202H 22,022J 22,002

8. Samantha deposits two checks ather bank. One check reads “fivethousand, seven dollars.” Theother check reads “four hundredthirty-one dollars.” Which numbershows the total amount Samanthadeposits?

F $5,431G $5,437H $5,438J $5,439

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Problem Solving PS3

Place Value Through Hundred ThousandsWrite the correct answer.


1. If 485,938 is increased by 10,000,what is the new number instandard form?

3. What number am I? I have 2digits which have a sum of 7.Both of my digits are less than 5.My tens digit is greater than myones digit.

2. If 762,485 is decreased by100,000, what is the new numberin standard form?

4. John went to 72 baseball gamesduring the summer and Marywent to 27 baseball games. Howmany more games did John see?

5. Which number is four hundredforty thousand, seven hundredtwo?

A 44,000,702B 440,702C 44,702D 44,072

7. In a 3-digit number, the leastplace-value digit is 7. Thegreatest place-value digit is 9.Which number can it be?

A 979B 972 C 907D 729

6. What is the value of 8 in 780,762?

F 800G 8,000H 80,000J 800,000

8. Billy lives 2,345 miles from hisgrandma who lives 1,640 milesfrom his uncle. How far will Billytravel if he visits both?

F 3,595 milesG 3,854 milesH 3,985 milesJ 3,995 miles

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PS4 Problem Solving

NameLESSON 1.4

�Place Value Through MillionsWrite the correct answer.

Choose the correct answer.

9. Write About It Explain your answer to Problem 8.

1. There were 4,542,328 visitors atthe park. What is this number inexpanded form?

3. Joe bought three tickets. Eachticket was $12.00. How much didhe spend on tickets?

2. A famous painting costs$6,780,402. What is this numberin word form?

4. There were 450 books at theschool book sale. There were 156books sold. How many books areleft?

5. What is the standard form for thenumber four million, two hundredforty-eight thousand, eighthundred six?

A 400,248,806 C 4,248,860B 40,248,860 D 4,248,806

7. It takes Robert ten minutes to getfrom school to home. If Robert leftschool and arrived home at 3:00,at what time did he leave school?

A 2:50 C 3:10B 2:55 D 3:15

6. What is the value of the 6 in6,453,789?

F 6 hundredG 6 thousandH 6 hundred thousandJ 6 million

8. Jack purchased a hat that cost$2.50. He gave the clerk thechange in his pocket: 7 quarters,6 dimes, and 4 nickels. Howmuch change will he get?

F 1 quarter H 5 centsG 1 dime J 3 cents

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Reading Strategy PS5

SummarizeUsing a graph to display information is a good way tosummarize data. Read the following problem.

Sue presented this data to her classmates.

The class wanted to know which type of pet is ownedby the most people.

1. Complete the graph to summarize the data in the table.

2. Solve the problem.

3. Describe the strategy you used.

4. Make a bar graph to summarize.

NUMBER OF PETS OWNED

Dog CatPet Type

Bird0

5

10

15

Hamster

Num

ber

(in m

illio

ns)

VOCABULARYsummarize

WEEKLY WORK SCHEDULE AT SCHOOL LIBRARY

Student Alice Ralph Trixie Ed

Hours Worked 4 6 8 5

NUMBER OF PETS OWNEDDogs Cats Birds Hamsters

5,000,000 8,000,000 12,000,000 10,000,000

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PS6 Problem Solving

Compare Numbers Write the correct answer.


7. Write About It Explain why you made the choice you did inProblem 5.

1. Write the greatest place-valueposition in which the digits of thetwo numbers are different in 385,844 and 385,855.

3. There were 56,731 people whovisited the King Tut exhibit inMay and 56,371 people whovisited the exhibit in June. Whichmonth had more visitors?

2. Compare the numbers 111,287and 111,197. Write thecomparison, using �, �, or �.

4. Mike got three checks forpainting houses. He wrote thisexpression to add the three values:$4,000 � $800 � $90. Write thetotal in word form.

5. The heaviest grizzly bear weighs1,720 pounds. The heaviest mooseweighs 1,312 pounds. Theheaviest Arabian camel weighs1,323 pounds. Which statement istrue?

A The grizzly bear weighs lessthan the moose.

B The moose weighs more thanthe Arabian camel.

C The Arabian camel weighsmore than the moose.

D The Arabian camel weighsmore than the grizzly bear.

6. Four friends go bowling. Theirscores are 126, 128, 136, and 149.Jacob’s score is less than Martin’sand greater than Becky’s. Elisewins the game. Who scored136 points?

F MartinG EliseH JacobJ Becky

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Problem Solving PS7

Order Numbers Write the correct answer.


1. Write the numbers in order fromgreatest to least.

3,340; 3,675; 3,430

3. Brittany threw the javelin 119 ftin Tuesday’s meet. In Friday’smeet, she threw the javelin 115 ft.During which meet did she throwit farther?

2. Write the numbers in order fromleast to greatest.

843,956; 848,965; 846,696

4. Caleb has three word-processingfiles on a diskette. The first file is8,800 bytes. The second file is6,500 bytes. The third file is 7,250bytes. Write the numbers in orderfrom greatest to least.

5. Which line shows the numbersordered from least to greatest?

A 63,248; 63,284; 63,824B 24,824; 24,284; 24,248C 17,824; 17,248; 17,284D 9,284; 9,248; 9,824

7. Kate is 3 years older than Heidi.Their ages added together are21 years. How old is each girl?

A Kate: 18 yr; Heidi: 15 yrB Kate: 13 yr; Heidi: 10 yrC Kate: 12 yr; Heidi: 9 yrD Kate: 11 yr; Heidi: 10 yr

6. Which line shows the numbersordered from greatest to least?

F 45,092; 45,902; 45,029; 45,920G 37,902; 37,920; 37,092; 37,029H 26,029; 26,092; 26,902; 26,920J 12,920; 12,902; 12,092; 12,029

8. Write About It Explain themethod you used to order thenumbers in Problem 6.

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PS8 Reading Strategy

Use Graphic Aids

Graphic aids such as tables, maps or diagrams help yousolve problems. One way to organize information is tomake a table.

Read the following problem.

Juan lives in Mexico in the city of Leon, which has apopulation of 589,950. Rosa lives in Culiacan, which has apopulation of 282,000. Juan’s brother, Pedro, lives inGuadalajara which has a population of 1,650,205. Nowthey all live in Monterrey, which has a population of1,069,238. Juan’s uncle, who lives in Puebla, wants to seewhere his city of 646,599 stands in order of population.Can you help him?

1. Complete the table to help you solve the problem.



4. Which cities have a smaller population than Puebla?

5. Which city has a population of about two million?

City Population

VOCABULARYgraphic aids

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Problem Solving PS9

Round NumbersWrite the correct answer.


9. Write About It Explain how you chose your answer toProblem 8.

1. The United States has149,129 miles of railroad track.Round this number to the nearestten thousand.

3. Describe the set of numbers whichwill round to 716,000 when youround to the nearest thousand.

2. The ballpark recorded theattendance at the opening gameas 48,376. Round this number tothe nearest ten thousand.

4. Light travels about 186,000 milesin one second. Which digit is inthe ten-thousands place?

5. What is the value of theunderlined digit? 352,448

A 4B 40C 400D 4,000

7. Willy collected 3,542 pop topsfrom aluminum cans. Round thisnumber to the nearest thousand.

A 3,000B 3,500C 4,000D 4,500

6. What is the standard form for400,000 + 3,000 + 600 + 3?

F 40,363G 43,603H 400,363J 403,603

8. The surface of the Earth covers196,949,970 square miles. Roundthis number to the nearest million.

F 196,000,000G 196,900,000H 197,000,000J 197,500,000

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PS10 Problem Solving

Estimate Sums and DifferencesWrite the correct answer.


9. Write About It Describe the method you used to solve Problem 6.

1. Round $243.79 to its greatestplace value.

3. A dolphin at the DolphinResearch Center ate about 720pounds of silverside, 990 poundsof capelin, and 950 pounds ofherring in three months. Abouthow many hundreds of pounds offish did the dophin eat in all?

2. Estimate the difference byrounding to the greatest placevalue.

4. About 875 people passed througha toll booth on Wednesday, about792 people on Thursday, and 901people on Friday. About howmany hundreds of people passedthrough this toll booth?

5. At two years old, a child is aboutone-half as tall as he or she willbe as an adult. Bobbie is twoyears old and is 34 inches tall.About how tall will she probablybe as an adult?

A About 34 in. C About 78 in.B About 68 in. D About 80 in.

7. Which number is the mostreasonable estimate of the sum?

136 � 785 � 205A 1,400 C 1,000B 1,100 D 900

6. Ted is playing a game on acheckerboard. He moves hispiece forward 4 squares, left 3squares, backward 2 squares, andright 3 squares. How manysquares does he have to move tobe back where he started?

F 0 H 2G 1 J 3

8. Which number rounds to 70,000when it is rounded to the greatestplace value?F 59,960 H 76,999G 68,235 J 78,354

4,739 � 3,267

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Problem Solving PS11

NameLESSON 3.2

Use Mental Math StrategiesWrite the correct answer.


1. Find the difference between 52and 46.

3. Danielle weighs 43 pounds andLydia weighs 52 pounds. Howmuch will the scale show if theyboth stand on it together?

2. How much greater is 95 than 86?

4. Ashley has saved 58 stickers andher grandmother gives her 24more. How many does she havenow?

5. Which mental math problem hasa sum of 8,400?

A 3,200 + 5,200B 2,100 + 5,300C 2,400 + 5,100D 4,100 + 4,100

7. Which shows the amounts inorder from greatest to least?

A $38.70; $46.72; $64.50B $54.70; $54.35; $54.28C $68.50; $68.79; $64.30D $74.34; $17.80; $21.56

6. Marchand has saved $6.00.Which items can he buy?Ball $2.49 Kite $3.99Frisbee $2.00 Book $3.95F a kite and a bookG a book and a frisbeeH a ball and a kiteJ a book and a ball

8. Which number rounds to 140,000?

F 114,637G 134,862H 137,428J 146,951


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Add and Subtract 4-Digit NumbersWrite the correct answer.


1. Jon has 4,326 baseball cards andAntoine has 5,639 baseball cards.If they combine their collections,would they have more or lessthan Steven’s collection of9,845 cards?

3. Mr. Smith saved $3,228 andpurchased a motorcycle for$2,988. How much did he haveleft for his helmet?

2. The Miller family drove 2,578miles during their long vacation.The Brown family went acrossthe country and traveled 5,429miles. How much farther did theBrowns travel?

4. Zelda buys four items that cost$3.89, $4.59, $6.89, and $3.99.Will her $20.00 bill be enough topay for all four items?

5. Mr. Lester has $8,349 to invest inartwork. He buys a painting for$5,245 and a statue for $1,750.How much more can he invest? A $1,354 B $1,445C $2,300D $3,005

7. The health club bought newequipment. They boughttreadmills for $2,975 and exercisebikes for $2,835. How much didthey spend?A $5,410 C $5,800B $5,645 D $5,810

6. Which is the answer if you roundthe numbers to nearest thousandand then subtract them? F 5,000G 4,000H 3,000J 2,000

8. What number comes after ninemillion, ninety-nine thousand,ninety-nine? F ten million G nine million, ninety-nine

thousand, one hundredH nine million, ninety-nine

thousandJ nine million, one hundred

6,709�4,206


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Subtract Across ZerosWrite the correct answer.



1. Mr. Banker has $8,000 to invest.He puts $2,679 in the bank andbuys a bond for $1,500. How muchdoes he have to invest stocks?

3. The Weddell seal can dive 1,969feet. The sperm whale can dive3,773 feet. Which dives deeper,and by how many more feet?

2. Bill’s car has a 36,000 milewarranty. He has already traveled17,689 miles. How much furthercan he drive while the car is underwarranty?

4. Charlie buys two books that cost$6.99 and $4.99. How muchchange will Charlie get from a$20.00 bill?

5. 577,052 � 524,917 � �

A 51,135 C 53,135B 52,135 D 53,945

7. In the number 6,431,598, what isthe value of the digit 3?

A 300 C 30,000B 3,000 D 300,000

6. Which subtraction problem has adifference of 3,111?

F 8,900 � 5,799 H 5,000 � 2,890

G 8,900 � 5,789 J 3,111 � 3,111

8. In 1996, Central City got a total of28 inches of snow. In 1997, it got atotal of 30 inches of snow. The1998 total was between the 1996total and the 1997 total. Abouthow much snow did Central Cityget during the three years?

F About 29 in. H About 60 in.G About 58 in. J About 87 in.

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Add and Subtract Greater NumbersWrite the correct answer.


7. Write About It What strategy did you use to solve Problem 6?

1. The museum has an art budget of$1,500,000 this year. It bought twostatues for $500,000 and threepaintings for $600,000. How muchmore can the museum spend thisyear?

3. Alaska, the largest state, has615,230 square miles. Is the totalarea of South Dakota with 77,121square miles and Texas with267,277 square miles bigger orsmaller than Alaska?

2. Bryce Canyon National Park has35,835 acres and Mesa VerdeNational Park has 52,121 acres.How much land do the parks havealtogether?

4. In Vermont, Montpelier has apopulation of 7,856; Burlingtonhas a population of 39,004; andRutland has a population of17,605. How much greater is thepopulation of Burlington thanRutland and Montpelier?

5. John thinks his car engine will last125,000 miles. His odometer reads63,286. How many more milesdoes he predict that he will beable to drive his car?

A 71,714 miles C 61,714 miles

B 61,724 miles D 61,704 miles

6. Mr. T. gets in line at the bank.There are three people ahead ofhim. Mr. W. has Ms. U. in front ofhim and Mr. V. behind him. Whichis the correct order of the bankline?

F Mr. T., Mr. W., Ms. U., Mr. V.

G Mr. W., Ms. U., Mr. V., Mr. T.

H Ms. U., Mr. V., Mr. W., Mr. T.

J Ms. U., Mr. W., Mr. V., Mr. T.

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Make Predictions

By examining information in a problem, you can often use itto make a prediction. A prediction is your best guess basedon the information given. Read the following problem.

A newspaper office will move to alarger building in 2001 if thenewspaper’s circulation increasesby 4,000 or more. If the change incirculation is less than 4,000, theoffice will remain where it is.What do you predict will happen?Explain.

1. Examine the information in the table. Write what happened tothe number of copies in circulation between the given years.



Make a prediction based on the information given. Solve.

4. Zephyr Book Company plans tochange their book covers if booksales in 2001 are less than in 2000.Do you predict they will changetheir book covers in 2001? Explain.

from 1996 to 1997?

from 1997 to 1998?

from 1998 to 1999?

from 1999 to 2000?

Year Number of Copies Increase fromin Circulation Previous Year

1996 14,798 —1997 15,430 6321998 16,630 1,2001999 18,935 2,3052000 22,275 3,340

Year Sales

1996 682,371

1997 640,023

1998 521,052

1999 402,056

2000 298,120

VOCABULARY

prediction

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ExpressionsWrite the correct answer.


9. Write About It Explain how to find the expression in Problem 6.

1. Jasmine wanted to buy a book for$17.50 and a CD for $4. She has$25.00. How much change willshe receive?

3. Find the value of (72 � 30) �14.

2. A company shipped 140 books onMonday and 260 books onTuesday to a bookstore. Thebookstore returned 125 books.How many books did thebookstore keep?

4. Tell what you would do first.

7 � (5 � 3)

5. There were 53 tennis balls in thebasket. The coach added 9 moreand gave 21 out to the players.Which expression shows howmany balls were still in the basket?

A 53 � (9 � 21)B (53 � 9) � 21C (53 � 9) � 21D (21 � 9) � 53

7. Find the value of 92 � (16 � 6).

A 60 C 82B 70 D 92

6. Billy used his $10 bill at theschool fair buying ride ticketsfor $3 and food for $4. Whichexpression shows how muchmoney Billy had left?

F 10 � (3 � 4)G 10 � (3 � 4)H (10 � 3) � 4J (3 � 4) � 10

8. What is the value of 19 nickels?

F 80¢ H 90¢G 85¢ J 95¢

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Use ParenthesesWrite the correct answer.


1. Which expression equals 16?

(25 � 10) � 1 or 25 � (10 � 1)

3. Mrs. Green printed flyers for herclass of 28 and Mr. White’s classof 26. Thirteen of them were notused. Write an expression usingparentheses to show how manywere used.

2. Place parentheses to make theexpression equal to 14.

10 � 3 � 7

4. Carrie biked 186 miles across thestate. Then she biked 152 miles tothe beach. How far did she bikealtogether?

5. The band wanted to sell 200 candybars. The fourth grade sold 85 barsand the fifth grade sold 95 bars.How many were not sold?

A (85 � 95) �200B (200 � 95) � 85C 200 � (95 � 85)D 200 � (85 � 95)

7. What is the value of300 � (41 � 13)?

A 256 C 328B 272 D 354

6. Of the 100 pictures at the artexhibit, 25 pictures were done inwatercolor and 28 pictures inpastels. How many were othertypes of pictures?

F 43 picturesG 47 picturesH 53 picturesJ 57 pictures

8. Which number is not a multiple of 3?

F 42 H 83G 57 J 96

9. Write About It How did you solve Problem 6?

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Match Words and ExpressionsWrite the correct answer.


1. Six baseball players sat on thebench. One got up to bat andthree more sat down. Write theexpression that matches thewords.

3. Ms. Smith’s class collected 4,326juice cans and 6,859 soda cans.How many more soda cans thanjuice cans did they collect?

2. Mario received 4 large birthdaygifts and 3 small gifts. He openedtwo gifts. Write an expressionthat matches the words. Howmany does he have left to open?

4. Byron had 18 newspapers. Hedelivered 5 on Fair Way andseven on Post Road. How manynewspapers does he have now?

5. Mary made 6 chocolate chipcookies and 7 sugar cookies.Mike ate 3. Which expressionmatches the words?

A (6 � 7) � 3B (6 � 3) � 7C 6 � (7 � 3)D (6 � 7) � 3

7. Round 48,597 to the greatestplace value.

A 48,000B 48,600C 49,000D 50,000

6. The tomato plant had 6 blossomson Sunday and on Monday arabbit ate 2 blossoms. OnTuesday 3 more blossoms grew.Which expression matches thewords?

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

8. The population of Greenville was48,299. Now it is 54,812. Howmuch has it grown?

F 6,513 peopleG 6,843 peopleH 6,947 peopleJ 7,943 people

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Use VariablesWrite the correct answer.



1. Sam returned 5 books to thelibrary and found more to return.Write an expression to show howmany library books he hadborrowed. Choose a variable forthe unknown.

3. Juan had 22 clay animals and gotmore for his birthday. He now has25. Write an equation and choosea variable for the unknown.

2. Forty-two passengers boardedthe airplane. Some got off theplane at the first stop. Write anexpression to show how manypassengers remain on the planeafter the first stop.

4. What is the next number in thepattern?

7, 10, 13, 16, __, 22

5. The 25 students in Mrs. Dona’sclass took a trip. The 14 girlsboarded the bus first. How manyboys were left to board the bus?

A 9 C 14B 11 D 25

7. William had some marbles. Hegave 3 marbles away and hasseven left. Which equationdescribes the situation?

A m � 3 � 7B 7 � 3 � mC 7 � m � 3D m � 3 � 7

6. What is the most reasonableestimate of the sum?

478 � 778 � 994 �

F 2,000 H 2,300G 2,100 J 2,500

8. I am thinking of a number with 7tens more than 4,339. Whichequation best describes thisnumber?

F n � 7 � 4,339G n � 70 � 4,339H 4,339 � 7 � nJ 4,339 � 70 � n

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Find a RuleWrite the correct answer.


1. Find a rule. Write the rule as anequation. x y

5 10

10 15

15 20

3. Sarah has a stamp collection with254 stamps. She gave some to herbrother. Write an expression todescribe the number of stamps shehas left.

2. Find a rule. Write the rule as anequation. x y

14 10

19 15

24 20

4. Sam has 10 friends coming to hishouse. He takes 5 glasses fromone cabinet and 2 from another.Write an expression to show howmany more he will need.

5. If the rule is w + 15 = z and w = 24,what is the value of z?

A 9

B 29

C 31

D 39

7. Which is true?

A 1,942 < 1429

B 4,912 > 4,921

C 9,142 > 9,124

D 9,421 < 9,412

6. Which is a rule for 2, 4, 6, 8, 10,12, x?

F Add 2.

G Add 4.

H Subtract 3.

J Subtract 4.

8. What number is next? 19, 28, 37, 46

F 45 H 55G 54 J 57

9. Write About It What strategy did you use to solve Problem 6?

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Add Equals to EqualsWrite the correct answer.


1. Tell whether the values are equal.Find the value on each side.

3 nickels � 1 dime � 1 quarter

3. Mary has 1 dime and 3 quarters.Joe has 4 dimes and 6 nickels. Dothey have the same amount ofmoney? Explain.

2. Ed has 3 quarters and 1 dime. Hegave $0.50 to his friend. Howmuch does he have left?

4. Glenn has 6 more books than Bob.Bob has 4 fewer than Sue. If Suehas 10 books, how many booksdoes Glenn have?

5. Which equation would be true if� � 4?

A 5 � � � 4 � 6

B 6 � � � 12 � 4

C � � 4 � 2 � 6

D 5 � 4 � � � 3

7. Which does not equal 80¢?

A 3 quarters, 1 nickel

B 2 quarters, 3 dimes

C 5 dimes, 20 pennies

D 14 nickels, 10 pennies

6. In an election, Jones had 12,345votes, Edwards had 12,453 votesand Smith had 12,436 votes. Whohad the greatest number of votes?

F Edwards

G Jones

H Smith

J Williams

8. Our product is 96. Our sum is 20.Who are we?

F 6 and 14

G 6 and 16

H 8 and 12

J 9 and 11

9. Write About It How did you solve Problem 5?

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Form Mental ImagesDrawing a picture can help you visualize, or form mentalimages of what a problem is describing. As you read theproblem, draw a picture of what is being described. Readthe following problem.

At the flower shop, the plants are in 3 rows of 2 boxesin each row. There are 4 plants in each box. Howmany plants are there in all?

1. Draw a picture to show what is being described in each partof the problem.



Draw a picture to visualize and solve each problem.

Problem Visualize/Use a Picture

At the flower shop, the plants are in 3 rows of 2 boxes in each row.

There are 4 plants in each box.

4. The rose bouquets at the flowershop are in 3 rows of 3. Janice put3 more bouquets in each row. Inall, how many bouquets of rosesare there?

5. Bob made two identical flowerarrangements. Each one had fourcarnations and four roses. Howmany flowers did Bob use?

VOCABULARY

visualize

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Collect and Organize DataWrite the correct answer.


7. Write About It Explain the difference between the frequency column andthe cumulative frequency column in a frequency table.

1. Use the frequency table. Howmany stars did Chas identify onThursday night?

2. Use the frequency table fromProblem 1. By the end ofThursday night, how many starshad Chas identified in all?

3. On which night did Chas identifythe greatest number of stars?

STARS I IDENTIFIED EACH NIGHTFrequency Cumulative

Night (Number of Stars) Frequency

Wed 22 22

Thurs 28 50

Fri 46 96

4. Use the frequency table below.On which day did the fewestnumber of students sign up?

A Monday C TuesdayB Wednesday D Thursday

5. Use the frequency table fromProblem 4. How many studentssigned up during the first threedays?

F 12 G 15 H 36 J 42

6. Joan’s car goes 420 miles on atank of gas. She needs to make a1,480-mile trip. What is the leastnumber of tanks of gas she willneed?

A 1 B 2 C 3 D 4

BASKETBALL PRACTICE SIGN-UPFrequency Cumulative

Day (Number of Students) Frequency

Mon 12 12

Tues 15 27

Wed 9 36

Thurs 41 77

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Find Median and Mode

For 3–6 use the HOT DOGS SOLD table.

9. Write About It Explain median and mode.

NameLESSON 5.2

1. Use the table. What is themedian? What is the mode?

2. Use the table from problem 1.What was the total amount ofmoney collected last week?

3. What is the mode?

5. What is the median?

A 27 C 29B 28 D 30

7. Round 183,473 to the nearestthousand.

A 180,000 C 184,000B 183,000 D 190,000

4. How many hot dogs were soldaltogether?

6. If 28 hot dogs were sold in week6, what is the mode?

F 31 H 28G 30 J 27

8. Use the table from problem 1.If there were 4 people onMonday’s paper route, and eachperson paid the same amount,how much did each pay?

F $1.00 H $3.00G $2.00 J $4.00

HOT DOGS SOLDWeek 1 2 3 4 5Number Sold

PAPER ROUTE MONEY COLLECTEDDAY AMOUNT

Monday $4.00Tuesday $2.50Wednesday $6.00Thursday $7.50Friday $4.00

30 27 24 28 34

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Line PlotWrite the correct answer.


1. Each X on the line plot stands forone student. How many studentswatched 4 movies?

3. Order 88,416; 88,614; 88,418 and88,641 from greatest to least.

2. Chris swam 30 laps at swim teampractice. Then he swam somemore. Write an expression toshow how many total laps Chrisswam.

4. What is the range of the data inthe line plot in Problem 1?

0 1 2 3

Number of Movies4 5 6 7

✗✗✗✗

✗✗

✗✗

✗✗✗✗

✗

✗

✗✗✗✗

✗✗✗

✗

5. In the line plot from Problem 1,which number of movies did thegreatest number of students see?

A 0 B 1 C 2 D 3

7. Kerri spent a total of $25.00 at thepet store. She spent $8.00 onchew toys for her dogs, and therest on two bags of dog food. Theprice was the same for both bags.How much did she spend for onebag of dog food?

A $7.00 C $10.00B $8.50 D $17.00

6. In the line plot from Problem 1,how many students watched 2movies?

F 0 G 1 H 2 J 3

8. Write About It Describe the stepsyou took to solve Problem 7.

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Stem-and-Leaf PlotWrite the correct answer.


1. The stem-and-leaf plot shows thescience test scores of Ms.Sitomer’s students. What is themedian of the scores?

SCIENCE TEST:MS. SITOMER’S CLASS

Stem Leaves

7 0 2 2 4 8 98 0 0 3 3 4 5 9 9 99 0 1 1 2 3 5 8 9

3. Use the stem-and-leaf plot. Whatwere the highest and lowestscores on the test?

2. Central City voters were askedwhat they thought was the city’smost important issue. Which issuegot the most votes?

WHAT IS CENTRAL CITY’S MOSTIMPORTANT ISSUE?

Issue Votes

Crime 32

Land Use 14

Poverty 35

Taxes 29

4. Use the survey. Each personsurveyed chose one issue. Howmany people were surveyed?

5. Use the stem-and-leaf plot. Whatis the total number of students inMs. Sitomer’s class who took thescience test?A 23 B 24 C 26 D 30

7. Ollie makes a pay-phone call thatcosts $0.75 for the first 3 minutesand $0.15 for each additionalminute. Ollie’s call costs him$2.10. How long did he talk?

A 12 min C 9 minB 10 min D 8 min

6. Use the stem-and-leaf plot. Whatis the mode of the scores?

F 9 G 80 H 85 J 89

8. Write About It Explain how youfound your answer to Problem 7.

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Compare GraphsWrite the correct answer.


7. Which is the best estimate of the total number of votescast for all four fruits in the graph in Problem l?

A 210 B 320 C 380 D 420

8. Write About It Describe the rule for the pattern in Problem 5.

NameLESSON 5.5

1. How could you make the graphbelow easier to read?

3. How would the graph in Problem1 change if the interval were 10?

2. Suppose the bars in the graph inProblem 1 were drawn vertically.What would the tallest barrepresent?

4. Cinzia spent 3 days of hervacation at the beach and 4 daysat her grandparents’ house. Shespent the rest of her 10-dayvacation at home. Write anequation to model this.

5. Gary builds an upside-downpyramid with blocks. He puts 1block in the first layer, 4 blocks inthe second, and 9 blocks in thethird. How many blocks would goin the sixth layer?

A 24 B 30 C 36 D 45

6. In the graph in Problem 1, whichfruit received about 40 votes?

F bananas H applesG grapes J oranges

Frui

t

GRAPES

BANANAS

APPLES

ORANGES

RIVERVIEW SCHOOL’S FAVORITE FRUITS

0 20 40Number of Votes

60 80

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Summarize

To summarize is to state something in a brief way.Knowing how to summarize information is a useful skill.Sometimes using a graph or a plot to display informationis a good way to summarize. Read the following problem.

Sue presented this data to her classmates.

The class wanted to compare the different types of pets at the pet store. For which type of pet was the number in stock the greatest? Explain.

1. Complete the graph to summarize the data in the table.



4. Make a bar graph or line plot to summarize.

VOCABULARYsummarize

NUMBER OF PETS IN STOCK

Type of Pet Dog Cat Bird Hamster

Number of Animals 5 8 12 10

Num

ber

of A

nim

als

Type of Pet

0

5

Dog Cat Bird Hamster

10

15

NUMBER OF PETS IN STOCK

WEEKLY WORK SCHEDULE AT SCHOOL LIBRARYStudent Alice Ralph Trixie Ed

Hours Worked 4 6 8 5

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Double-Bar GraphsWrite the correct answer.


9. Write About It Explain how you chose a scale and interval in Problem 1.

5. Use your bar graph. Which eyecolor did more 5th graders havethan 4th graders?

A Brown C Green/HazelB Blue D Red

7. Use your bar graph. Which eyecolor did the fewest 5th gradershave?

A Brown C Green/HazelB Blue D Red

6. Estimate. 48,670�12,600

F 50,000 H 40,000G 30,000 J 60,000

8. Evaluate: (20 � 3) � (4 � 1)

F 12 H 12G 20 J 14

1. Use the data to write the bestscale and interval for a double-bar graph.

3. Round 987,654 to the nearest tenthousand.

2. Make a double-bar graph for thedata.

4. Write an equation. There were9 cats in the shelter. Some wereadopted. Now there are 4 cats.

Eye Color Fourth Fifth Graders Graders

Brown 12 9Blue 6 13

Green or 10 7Hazel Brown Blue Green/

Hazel

1512963

Eye Color

Num

ber

of S

tude

nts

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Read Line GraphsWrite the correct answer.

Choose the letter of the correct answer.For 5–6, use the graph.

1. Use the graph. What isHorseville’s average Octobertemperature?

3. Use the graph. During whichmonth is the average Horsevilletemperature about 55°F?

2. Use the survey table. Duringwhich two weeks were there thesame number of absences?

4. Use the survey table. What wasthe total number of absencesduring February?

Tem

pera

ture

(in °F

)

April

January July

80

60

40

20

0

Octobe

r

Average Temperatures in Horseville

Month

5. Which month had an averagetemperature of 40°F?

A September C JulyB April D January

For 7–8, use the table.

7. How many more absences werethere in Week 3 than in Week 1?

A 21 B 12 C 8 D 6

6. Which month had the highestaverage temperature?

F January H AprilG July J September

8. During which week were therethe most absences?

F Week 1 H Week 3G Week 2 J Week 4

FEBRUARY ABSENCES AT DIERKER SCHOOL

Week Absences

1 13

2 15

3 21

4 15

9. Write About It Explain how you got your answer to Problem 6.

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Make Line Graphs


1. The table shows the number ofpeople visiting the HeritageMuseum in each month. Make aline graph to show this data.

Write the correct answer.3. What was the total attendance at

the museum in the summermonths of June, July, and August?

2. Write a rule and an equation forthe input/output table.

4. Order from greatest to least:45,892; 4,392; 483,394; 393,303

5. In what month did the fewestpeople visit the museum?

A May C JulyB September D August

7. Which trend does your graphshow?

A Museum attendance wasgreatest in the summer months.

B The number of visitorsdecreased from May to June.

C The number of visitorsincreased from August toSeptember.

D Most visitors came in January.

6. What is the value of the digit 7 in370,304,204?

F 70 million H 70 thousandG 7 million J 70

8. What is the word form of 300,012?

F three hundred twelve thousandG three hundred thousand and

twelveH three hundred thousand, twelveJ three hundred, twelve

Month Visitors

May 900

June 1,500

July 1,300

August 1,100

September 1,000

Input Output

y z

4 16

2 8

5 20

3 12


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Choose an Appropriate GraphWrite the correct answer.


9. Write About It Explain your choice in Problem 8.

1. Write whether you would use aline graph, bar graph, or stem-and-leaf plot to show how theprice of a gallon of milk changeseach month over a year.

3. The stem-and-leaf plot shows thelongest bike trip each student ofthe fourth-grade class has taken.What is the median distance?

4. Use the stem-and-leaf plot. Writethe mode of the distances.

2. Write whether you would use aline graph, bar graph, or stem-and-leaf plot to show the types ofpets your classmates have.

LONGEST BIKE TRIPS OF THEFOURTH-GRADE CLASS (in miles)

Stem Leaves

0 0 0 3 5 81 0 0 0 0 0 2 2 5 5 52 0 0 5 5 5 53 04 5

5. Which type of display would bethe best to show the changes indaily class attendance for themonth?

A bar graphB line graphC stem-and-leaf plot D NOT HERE

7. Use the stem-and-leaf plot. Howmany fourth graders rode 25miles?

A 3 B 4 C 7 D 9

6. Tommy recorded his high jumps:48 in., 55 in., 40 in., 58 in., and 55in. He wants to show this on abar graph. What would be thebest interval for his graph?

F 1 in. H 50 in.G 5 in. J 100 in.

8. Which type of graph would bestorganize the list of ages of peopleat a family reunion?

F bar graph H stem-and-leaf plotG line graph J line plot

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Draw Conclusions

A table can display a large amount of data. Looking at a graphof the data makes it easier to draw conclusions about the data.

When you examine the graph and use what you already knowto solve a problem, you are drawing conclusions. Read thefollowing problem.

Jamie looked at the graph to comparethe numbers of each type of animalavailable at two pet stores. She knowsthat stores that specialize in birds aremore likely to carry her favorite brandof bird food.

In which store should Jamie look forthe bird food?

Since Jamie has concluded that Pet Palace specializes inbirds, she should look for the food there.

VOCABULARYdrawing

conclusions

What Jamie Sees on the Graph

Pet Palace has about thesame numbers of dogs and catsas Pets-R-Fun.

Pet Palace has many more birds thanPets-R-Fun.

What She Concludes

The stores are about the same size.

Stores with many more birds thanother stores of the same sizespecialize in birds.

Use the graph. Draw conclusions to solve.

1. Which month was best for theLockwood family to take their cartrip across the country? Explain.

2. In which month was a new lawprobably passed raising the taxon gasoline? Explain.

Dogs Cats Birds

20

10

PET PALACE vs PETS-R-FUN

15

0

5

Pets

Num

ber

of P

ets

Pet Palace

Pets-R-Fun

AVERAGE GASOLINE PRICES

$1.60$1.50$1.40$1.20$1.00

May JunApr Jul Aug OctSepMonth

•• •

••

••

Pric

e p

er G

allo

n

$0.00

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Before and After the HourWrite the correct answer.


9. Write About It Explain why you chose the answer you didfor Problem 5.

1. Write seconds, minutes, hours, ordays to describe the unit youwould use to measure the amountof time it takes to read this mathproblem.

3. In the 1970s, Chesterfield had13,998 mm of snowfall. In the1980s it had 5,390 mm and in the1990s it had 11,302 mm. Write theyears in order from the greatestsnowfall to the least.

2. Write the time shown on theclock. Include seconds.

4. The town budget of Chesterfieldis thirteen million, three hundredninety-five thousand, eighthundred eleven dollars. Write thisamount in standard form.

8910

11 12

7 6 543

21

5. It is 26 minutes until noon lunch.What time is shown on the digitalclock?

A 1:30 C 11:34B 5:44 D 12:26

7. What is the value of 5 dimes,5 quarters and 5 nickels?

A 15¢ C $1.75B 55¢ D $2.00

6. A digital clock shows 3:42. Whichletter shows the same time?

F 42 minutes before 3G 42 minutes past 3H 18 minutes before 2J 34 minutes before 2

8. How much greater is 46,010 than45,999?

F 1,001 H 21G 121 J 11

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A.M. and P.M.Write the correct answer.


9. Write About It Describe the method you used to find youranswer to Problem 8.

1. Vijay and Claudia were born onthe same day in the same year.Vijay was born at 2:57 A.M., andClaudia was born at 1:23 P.M.Who was born first?

3. Ned sleeps about 8 hours eachnight. About how many hoursdoes he sleep in 1 week?

2. One evening, 4,009 people attendan important town meeting. Thetown’s auditorium can seat only1,248 people. How many peoplewon’t be able to get a seat?

4. Write the time you leave school.Include A.M. or P.M.

5. The space shuttle lifted off at15 minutes before 9 o’clock in themorning. Which shows a correctway to write that time?

A 9:15 A.M. C 8:45 A.M.B 8:45 P.M. D 9:15 P.M.

7. Tom, Jim, Les, and Marie have ameeting 45 minutes before1 o’clock this afternoon. Each onewrites down the time for themeeting in a different way. Whichway of writing the time is notcorrect?

A 12:15 P.M.B fifteen minutes after twelve

o’clock this afternoon.C 15 minutes after noonD 1:45 P.M.

6. Which letter shows the time 12minutes past 3 as it would appearon a digital clock?

F 12:03 H 3:12G 3:21 J 1:23

8. Ben plays a computer gamecalled Galaxy. The first time heplayed he scored 5,762 points.The second time he scored 10,801points. The third time he scored17,119 points. What was Ben’stotal score?

F 33,682G 37,268H 39,619J 40,206

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Elapsed TimeWrite the correct answer.


1. The city budget of Carrollton is$293,447,893. Write the wordform for this amount.

3. Corrinna needs to arrive at herfriend’s house no later than7:30 P.M. She knows that theerrands she has to run first will takethree and one quarter hours. Whattime must Corrinna leave home torun errands and then go directly toher friend’s house?

2. Renee takes a train that leavesDanson at 2:27 P.M. and arrives inGoodville at 4:55 P.M. How muchtime does Renee spend on thetrain?

4. Henry had some rocks in hiscollection. He got 7 more at arock show, and now his collectionhas 43 rocks. Write an equationusing the variable r to stand forthe number of rocks Henry hadbefore the rock show.

5. The clock in Nancy’s car shows10:07 when she leaves home inthe morning. That afternoonwhen she arrives home, it shows2:39. How much time haselapsed?

A 2 hr 46 min C 4 hr 46 minB 4 hr 32 min D 3 hr 32 min

7. Which expression has a valueof 18?

A 28 � (26 – 7) � 29B 28 � 26 – (29 � 7)C 28 � 26 – 7 � 29D (28 � 26) – (7 � 29)

6. Karl counts 128 CDs on a shelf inthe school media center. If thereis another shelf holding 194 CDs,what is a reasonable estimate ofthe total number of CDs?

F 600 H 300G 550 J 150

8. Roger worked on his homeworkfor 1 hour and 49 minutes. If hestarted at 3:33 P.M., at what timedid he finish?

F 4:16 P.M. H 5:16 P.M.G 4:22 P.M. J 5:22 P.M.

9. Write About It Explain why you chose the answer you didfor Problem 5.

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Sequence InformationPutting events in order, or sequencing the information, canhelp you solve a problem. You can use sequence clues todetermine the order of events in a problem. Look for wordssuch as first, second, last, next, then, now, before, after, andalready. Read the following problem.

Deana wants to go swimming for 2 hours Saturday afternoon,but before that she has to get her hair cut. She needs to behome for dinner by 6:00 P.M. If Deana’s haircut is scheduled for1:30 and takes 45 minutes, will she have time to visit Kathy for2 hours and then take 20 minutes to drive home?

1. List each activity and its length in order.

Event 1: Event 2: Swimming: 2 hours

Event 3: Event 3:

2. List the starting and ending times of each event.

Event Start Time End Time

Hair Cut 1:30 A.M. 2:15 P.M.

Swimming

Visit Kathy

Drive Home

The schedule shows that Kathy will not be able to do all the things shewants to do and still be home for dinner at 6:30 P.M.

Use sequencing to help solve these problems.

VOCABULARY

sequenceinformation

3. Mr. Zapata is working from12:00 P.M. until 6:00 P.M. He hasa two-hour meeting at 3:30 P.M.He needs to make two 30-minutephone calls and write twomemos that will take one houreach. Can he do everything?Explain.

4. Zoe is taking a cross-countrytrip. She is going to leave onMay 1st. She has to be in SantaFe on May 8th. It will take her3 days to drive to Dallas, whereshe wants to visit a friend for fivedays, then make the 2-day trip toSanta Fe. Can she do it? Explain.

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Elapsed Time on a CalendarWrite the correct answer.


S M T

8152229

7142128

6132027

9162330 31

3101724

421111825

5121926

WMarch

T F S S M T

5121926

4111825

3101724

6132027 28 29 30

71421

181522

291623

WApril

T F S S M T

10172431

9162330

8152229

111825

5121926

64321132027

7142128

WMay

T F S

1. Use the calendars above. Writethe day of the week that is 5 daysafter March 4.

3. Nyla starts her workout at10:45 A.M. She works out for 1hour and 18 minutes. What timeis it when she ends her workout?

2. Use the calendars above. Writethe date that is exactly 6 weeksbefore May 18.

4. Chuck scored 88, 97, 87, 88, 99,90, and 97 on his first 7 mathtests. What is the median of thesescores?

5. Which digit is in the ten millionsplace of 583,129,450?

A 8 C 4B 5 D 2

7. Ella looks at her digital clock. Shesees that the number of minutes is2 times the number of hours. Thesum of the digits is 15. What timeis it?

A 4:08 C 7:08B 6:12 D 8:16

6. Use the calendars at the top of thepage. Which date is 24 days afterMarch 20?

F April 10 H April 12G April 11 J April 13

8. Use the calendars at the top ofthe page. How many days afterthe first day of April is the lastMonday in May?

F 62 days H 60 daysG 61 days J 59 days


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Relate Multiplication and DivisionWrite the correct answer.



1. Write a related multiplicationfact.

18 � 3 � 6

3. Charles wants to plant 35 flowersin 5 flower beds. He decides toplant the same number in eachflower bed. How many does heplant in each?

2. Write the fact family for thenumbers 4, 7, and 28.

4. Didi made an $11.87 purchase.She gave the cashier a $20.00 bill.The cashier gave her $6.13 inchange. Did the cashier give herthe correct change? Explain.

5. Which multiplication fact couldyou use to help you find thequotient of 36 � 9?

A 6 � 6 � 36 C 4 � 9 � 36B 2 � 2 � 4 D 3 � 3 � 9

7. Dan sells a total of 32 candy barsto 8 neighbors. Each neighborbuys the same number of candybars. How many candy bars doeseach buy?

A 2 C 4B 3 D 5

6. A car drives around a 4-mileracetrack 4 times. Which can youuse to find the total number ofmiles the car drives?

F 4 � 4 H 16 � 4G 4 � 4 J 8 � 4

8. Blaise is playing a bongo drum.He taps the drum with his righthand 3 times, his left hand 1 time,then his right hand 2 times. Herepeats this pattern 6 timesduring a song. How many timesdoes he tap the drum?

F 16 H 42G 36 J 56

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Multiply and Divide Facts Through 5Write the correct answer.


9. Write About It Explain how using a number line can help you find theproduct in Problem 3.

1. MaryJo went to a 2:10 P.M. movie.It got out at 4:32 P.M. How longwas the movie?

3. Label the number line to find 5 � 3.

2. What are the median and mode ofthe following data?

10,11,11,12,12,13,13,13,18

4. Write a related multiplicationfact.

12 � 3 � 4

5. Carly is in a weight-liftingprogram and wants to graph theimprovement in the amount shecan lift over a period of months.What is the most appropriategraph to use?

A Stem and leaf C Bar graphB Line graph D Pictograph

7. If 3 � 4 � 12, then 12 � 3 � �

A 2 C 4B 3 D 5

6. Charlene counts her pennies byplacing them in piles of ten. Shemakes 4 piles. Which shows howmuch money Charlene has?

F 4 � 10 H 4 � 10G 10 � 4 J 10 � 4

8. Solve.� � 7 = 5

F 35 H 21G 28 J 10

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Multiply and Divide Facts Through 10Write the correct answer.


9. Write About It What other strategy could you have used to solve Problem 3?

1. Jimmy spent 4 hours and 20minutes driving from Clevelandto Pittsburgh. He left Clevelandat 2:50 P.M. At what time did hearrive in Pittsburgh?

3. Find the product. Show thestrategy you used.8 � 7

2. Find the value of n. Write arelated equation.

42 � n � 7

4. A concert attracts 30,000 fans.The hall has only 22,500 seats.How many fans will not get in tothe concert?

5. In the number 653,218, what digitis in the hundreds place?

A 1B 2C 3D 6

7. Which of the following shows theOrder Property?

A 3 � 9 � 9 � 3B 3 � 9 � 3 � 3 � 3C 3 � 9 � (3 � 4) � (3 � 5)D 27 � 9 � 3, so 3 � 9 � 27

6. Find the median.127, 143, 251, 197, 143, 154, 182

F 143G 154H 171J 182

8. Which of the following equationsis not in the fact family for 4, 2,and 8?

F 4 � 2 � 8G 2 � 4 � 8H 8 � 2 � 4J 4 � 2 � 2

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NameLESSON 8.4

�Multiplication Table Through 12Write the correct answer.



1. Find the value of the variable.Write a related equation.

12 � n = 60

3. Write the fact family for 7, 8,and 56.

2. Write 862,092 in word form.

4. Find the value.

96 � 8

5. Joe makes $12 for each lawn thathe mows. He mowed 8 lawns.How much does he makealtogether?

A $20 C $96B $72 D $100

7. Nigel and Linda spent $6 each onmovie tickets. They also shared alarge popcorn for $5. How muchdid they spend altogether?

A $11 C $17B $16 D $22

6. How much time has elapsed from8:27 A.M. to 12:20 P.M.?

F 4 hours 47 minutesG 3 hours 47 minutesH 4 hours 53 minutesJ 3 hours 53 minutes

8. What is 132 � 11?

F 11G 12H 10J 121

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Multiply 3 FactorsWrite the correct answer.



1. Show two ways to group thefactors using parentheses.

6 � 5 � 7

3. Mark buys 3 packs of baseballcards. Each pack holds 5 cards.How many cards does he buy?

2. Write the product.

9 � (4 � 3)

4. Vicki needs 500 points to win agame. In the first round she gets187 points. In the second roundshe gets 212 points. In the thirdround she gets 236 points.Estimate to find if she has enough points to win.

5. Which does not have a productof 64?

A (4 � 2) � 8 C (12 � 5) � 4B (10 � 9) � 6 D (6 � 2) � (1 � 7)

7. Will drives for three days. Everyday he drives twice as manymiles as the day before. Afterthree days he has driven a total of630 miles. How many miles didhe drive on the first day?

A 30 mi C 158 miB 90 mi D 315 mi

6. Which is the product of8 � (3 � 2)?

F 88 H 48G 56 J 19

8. There are 8 fruit bars in a box.There are 6 boxes in each case.A store orders 5 cases. Whichexpression could you use to findthe total number of fruit bars thestore orders?

F 8 � 3 � 5 H (5 � 6) � 5G 8 � (6 � 5) J (8 � 6) � 5

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Choose Relevant InformationSometimes a word problem contains information thatmay not help you solve the problem. You must decidewhich information is relevant, or needed to solve theproblem. Read the following problem.

Donna’s brother Chip plays on the football team. Shehas been the team’s statistician for two years. It is herjob to record and classify all the points the teamscores. This season, the team has scored 11touchdowns, worth 6 points each; 10 field goals, worth3 points each; 8 extra-points, worth one point each;and 2 safeties, worth 2 points each. A football gameconsists of 4 quarters of 15 minutes each. What is thetotal number of points scored this season?

1. Read each fact from the problem. Write whether the fact isrelevant or not relevant to solve the problem.

a. Donna has been the team’s statistician for two years.

b. The team has scored 11 touchdowns.

c. The team has scored 2 safeties.

d. A quarter is 15 minutes long.

e. The team has scored 8 extra-points.

f. The team has scored 10 field goals.



Draw a line through the information that is not relevant. Solve.

4. Lauren’s best friend lives out ofstate. They talked on the phonefor one 5-minute call, three 10-minute calls, and two 20-minutecalls. There are two phones inLauren’s house. How long did thefriends talk altogether?

5. Benny earns $3.00 per hour baby-sitting and $10 for shovelling adriveway. It snowed 6 inches onMonday and Benny baby-sat for 4hours. How much money did hemake baby-sitting?

VOCABULARY

relevantnot relevant

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Expressions with ParenthesesWrite the correct answer.


9. Write About It Describe how you found the answer to Problem 8.

1. Find the value of the expression.

4 � (7 � 8)

3. Erin needs to earn $24.00. Shegets paid $3.00 per hour baby-sitting. Erin baby-sits for 5 hourson Saturday and 4 hours onSunday. Does she earn at least$24.00?

2. Find the value of the expression.

(25 � 5) � (6 � 2)

4. Jeff has been working in thegarden for 3 hours and 17 minutes.How many minutes has Jeff beenworking?

5. What is the value of theexpression?

(20 � 4) � 1

A 6 C 4B 5 D 3

7. Thomas needs to write thestandard form for two million,three hundred five thousand, sixhundred seventy. What is thecorrect number for Thomas?

A 2,356,700 C 2,305,670B 2,350,607 D 2,305,607

6. What is the value of theexpression?

87 � (7 � 9)

F 720 H 31G 250 J 24

8. Play practice was supposed tobegin at 1:30 P.M., but it started18 minutes late. It ended at3:35 P.M. How long did playpractice last?

F 2 hr 47 min H 2 hr 25 minG 2 hr 37 min J 1 hr 47 min

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Match Words and ExpressionsWrite the correct answer.


9. Write About It Describe the steps you took to find the answer to Problem 8.

1. Jada had 64 colored pencils. Shegave away 3 sets of 4 coloredpencils each. Write an expressionfor the number of colored pencilsshe still had.

3. Vance wants to plant 6 rows ofroses with 8 plants in each row.How many plants does he needto buy?

2. Joachim fell asleep at 9:15 P.M. on Friday night and woke up at7:24 A.M. on Saturday morning.How long did Joachim sleep?

4. Tom made 3 model airplanes eachday during his 5 day vacation. Hiscat knocked 5 models off the shelfand broke them. Write anexpression that matches thesewords, and then find its value.

5. Matthew began mowing lawns at9:17 A.M. He mowed for 4 hours55 minutes. What time did hefinish?

A 1:12 P.M. C 11:12 A.M.B 2:12 P.M. D 13:72 P.M.

7. What is the standard form of3,000,000 � 20,000 � 5,000 � 400 �40 � 8?

A 32,544,800 C 3,250,448B 30,025,484 D 3,025,448

6. Choose the expression thatmatches the words.Brad had 50 keys. He put 4 keyseach onto 7 rings.

F 4 � (50 � 7) H 50 � (4 � 7)G 50 � (7 � 4) J (50 � 4) � 7

8. Judith is knitting a scarf that isgoing to have 100 rows of stitcheswhen complete. She has knitted6 rows each night for 8 nights.How many rows are left to knit?

F 42 H 58G 52 J 62

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Multiply Equals by EqualsWrite the correct answer.


9. Write About It Explain how you arrived at your answer for Problem 6.

1. Lucia needs to order programs fora football game. There have been5,883 tickets sold, but theprograms can only be ordered insets of 100. How many programsshould Lucia order?

3. Multiply both sides of theequation by 4.

6 � 3 � 3What is the new value of each side?

2. Ann took 3 rolls of pictures with12 pictures on each roll of film.When she developed them, 8pictures were bad. Write anexpression for the number ofgood pictures Ann took, then findits value.

4. Multiply both sides of theequation by 8.

9 � 1 � 5 � 2 What is the new value of each side?

5. Joel multiplied both sides of thisequation by a number and got anew value of 30. What numberdid Joel multiply by?

18 � 3 � 23 � 17

A 7 C 5B 6 D 4

7. When this equation is multipliedby 9, what is the new value ofeach side?

15 � 7 � 64 � 8

A 45 C 63B 54 D 72

6. Elena wraps yarn around a squarespindle. The spindle measures 4inches on each side. How manyinches of yarn are wrapped on thespindle when Elena has completed4 turns around it?

F 32 inches H 52 inchesG 44 inches J 64 inches

8. Bollard has a population of734,989 and Pollard has apopulation of 592,176. What is areasonable estimate of the sum ofthe populations of the two towns?

F 1,500,000 H 1,300,000G 1,400,000 J 1,200,000

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Expressions with VariablesWrite the correct answer.



1. Dom divided 36 cards evenlyamong some friends. Write anexpression for the number of cardseach person got. Use the variablep for the number of friends.

3. Anna studied her spelling wordsfrom 11:36 A.M. until 11: 55 A.M.and again from 2:46 P.M. until 3:03 P.M. How long did she study?

2. Mr. Henderson’s class had thefollowing scores on their math test:88, 90, 85, 83, 76, 99, 100, 87, 90

Find the median and mode of thescores.

4. Find the value of 80 � m if m � 8.

5. Bridget the Baker can decorate 4birthday cakes in a day. If sheworks 3 days per week and 2weeks per month, how many cakeswill she decorate in a month?

A 24 C 14B 20 D 9

7. Bob counts the tiles on a floor. Hesees that there are 23 tiles in eachof c rows. Which of these is anexpression for the total numberof tiles?

A 23 � c C 23 � cB c � 23 D c � 23

6. Burk’s population is 752,584 whileCob’s is 683,998, Finch’s is 781,551,and Park’s is 679,490. Order thetowns from the greatest to least population.

F Finch, Park, Cob, Burk.G Cob, Park, Finch, BurkH Finch, Burk, Cob, ParkJ Cob, Finch, Park, Burk

8. Which expression matches thewords?

30 greeting cards, sorted intosome equal stacks.

F 30 � s H 30 � sG 30 � s J 30 � s

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Equations with VariablesWrite the correct answer.


9. Write About It Describe the steps you took to solve Problem 7.

1. Marc put 60 balls into boxes with10 balls in each box. Write anequation with a variable. Tellwhat the variable represents.

3. Ben counted 46 beans and tookaway 16. Now he must fill 5 bagsequally with the rest. Write andevaluate an expression thatmatches these words.

2. Anneke wants to plant 35 pansiesin 5 equal rows. Write an equationusing a variable and tell what thevariable represents.

4. There are 3,704,291 people inFayette County and 2,825,428 inneighboring Clarke County.What is the difference in thepopulations of the two counties?

5. Chuck wrote 100 � n � 5 todescribe banners passed out at arally. Which situation bestmatches the equation?

A 5 banners per person is 100total banners.

B 100 banners passed out to somepeople is 5 banners each.

C 5 banners to each of 100 peopleis the total number of banners.

D 100 people are passing out 5banners each.

7. David started reading at 11:23 A.M.He spent 3 hours 46 minutesreading. When did he finish?

A 2:69 P.M. C 3:09 P.M.B 3:09 A.M. D 2:09 P.M.

6. Karen shelved videotapes at thenew video rental store. She foundthat 8 videos fit on each displayshelf. At the end of the hour,Karen had filled a number ofshelves and had shelved a total of96 videos. Which equationmatches this situation?

F 8 � s � 96 H 8 � s � 96G 8 � s � 96 J 8 � s � 96

8. Which is the standard form foreight million, eight hundred eightthousand, forty-one?

F 8,888,041 H 8,808,041G 8,808,410 J 8,088,041

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Find a RuleWrite the correct answer.


9. Write About It Explain how you arrived at your answer for Problem 8.

1. Find a rule. Write the rule as anequation.

Input Output s b

48 842 736 630 5

3. Put the numbers in order fromleast to greatest.

64,923; 64,832; 63,933; 65,834

2. Find a rule. Write the rule as anequation.

Input Outputg r4 325 406 487 56

4. A’s profits were $33,494,002.B’s were $50,405,986. Whichearned more? How much more?

5.

Which equation shows the rule?

A z � 4 � y C z � 3 � yB z � y � 3 D z � 5 � y

7. Barbara has 103 crayons. She putssome of them into 5 boxes with 20in each box. Which expressionshows this?

A 103 � (5 � 20) C (5 � 20) � 103B (103 � 5) � 20 D 103 � 5 � 20

6. Which equation is in the same factfamily as 3 � 8 = 24?

F 24 � 4 � 6 H 24 � 8 � 3G 2 � 12 � 24 J 24 � 6 � 4

8. The inputs, I, are 88, 77, 66, 55,and 44. The outputs, O, are 8, 7, 6,5, and 4. Which shows the rule inequation form?

F I � 11 � O H I � 11 � OG 11 � I � O J I � 11 � O

Input z 4 5 6 7Output y 12 15 18 21

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VOCABULARYinterpreting

symbols

4. Stan spent $238.50 on computerprograms. Stella spent $152.75 oncomputer programs. How muchmore did Stan spend than Stella?

5. Jody spends 125 minutes eachmorning and 75 minutes eachnight, 3 days a month, on theInternet. How much time eachmonth does Jody spend on theInternet?

Interpret SymbolsIt is important to be able to interpret symbols whenreading or writing a number sentence. Interpretingsymbols means understanding what each symbol in thenumber sentence means. Mathematical symbols includenumbers and $, ( ), �, �, �, �, �, and variables suchas n. Read the following problem.

Alex bought 4 computer games. Each game cost $8.00.Then Alex bought a shirt for $18.00. Alex had $5.00 left.How much money did Alex have to start with?

Think about the problem. Tell what the bold facedsymbols stand for.

1. (4 � 8) � 18 � 5 � n

(4 � 8) � 18 � 5 � n

(4 � 8) � 18 � 5 � nn



Write a number sentence for each problem. Tell what the symbolsmean. Solve.

NameLESSON 10.1


Mental Math: Multiplication Patterns

Write the correct answer.



1. What is the first step in findingthe value of 12 � (8 � 3)?

3. Nina’s number machine changesone number into another. Itchanges the number 3 into thenumber 27, 10 into 90, and 12 into108. What rule does the machineuse?

2. There are 40 coins in each roll ofquarters. How many coins are in8 rolls?

4. What basic fact is used to findthe product 6 � 700? What isthe product?

5. Use a basic fact and a pattern todetermine which of these is theproduct 3 � 900.

A 27 C 2,700B 270 D 27,000

7. Which type of graph makes iteasiest to find the median of a setof data?

A Bar graphB Line graphC Stem-and-leaf plotD Double-bar graph

6. How many seconds are there in4 minutes?

F 60 H 240

G 120 J 400

8. Liang mails some cassette tapes tohis cousin. He packs his tapes in3 boxes of 8 tapes each. He alsoputs 6 tapes in a bag. Whichexpression matches this?

F (3 � 8) � 6 H 6 � (3 � 8)G 5 � (6 � 3) J (5 � 6) � 3

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LESSON 10.2

Estimate ProductsWrite the correct answer.


9. Write About It List the steps you took to solve Problem 7.

1. A project that took 5 hours and 17minutes was finished at 3:30 P.M.When was the project started?

3. What is the value of the digit 6 inthe number 164,012?

2. Eric estimates the product 7 � 428to be 2,800. What basic fact did heuse to arrive at this estimate?

4. Each of the 12 months has about30 days. About how many days arein the year?

5. One mile of highway has 264center lines. Which of thefollowing basic math facts wouldbe used to estimate the number ofhighway center lines in 9 miles ofhighway?

A 3 � 7 � 21 C 9 � 6 � 54B 4 � 2 � 8 D 3 � 9 � 27

7. Which of the following is a goodestimate for the product 279 � 8?

A 20 C 2,400B 24 D 24,000

6. What type of graph is shown?

F Line plotG Stem-and-leaf H Bar graphJ Double-bar graph

8. School starts at 7:30 A.M. Studentshave three 1-hour classes and one30-minute study period beforelunch. When is lunch?

F 12:00 P.M. H 11:30 A.M.G 12:00 A.M. J 11:00 A.M.

8

6

4

2

0 Joe Karl Rick Maury

Cousins

Name

Num

ber

of C

ousi

ns

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Model MultiplicationWrite the correct answer.


9. Write About It Describe your reasoning for your answer to Problem 4.

1. What are the factors of 36?

3. Wanda is using base-ten blocks tomodel the multiplication sentence3 � 104. What should she do withthe twelve blocks that representones?

2. Marlena had 8 books. She put 2 inher desk and 4 on a shelf. Write anexpression to model this situation.

4. Below is a model for amultiplication sentence. Write themultiplication sentence.

5. Below is a model for amultiplication expression. Whatexpression does the modelrepresent?

A 3 � 243 C 1 � 213B 2 � 313 D 3 � 213

7. Use base-ten blocks to find theproduct 310 � 9.

A 271 C 2,700B 279 D 2,790

6. Paul has to buy 7 balloons for thedance. Each one costs $3.75.About how much money will heneed?

F $4.00 H $21.00G $7.00 J $28.00

8. Which of the following is amultiple of 12?

F 3 H 9G 4 J 24

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Multiply 3-Digit NumbersWrite the correct answer.


9. Write About It Explain the steps you took to solve Problem 2.

1. Dolores earns $10.75 for everyyard she mows and trims.Estimate the amount of moneyshe will make if she finishes 7yards.

3. Estimate 7 � 391, and then findthe actual product.

2. Mrs. Walker’s class has 9 boysand 12 girls. Each boy has 5pencils, and each girl has 4pencils. How many pencils doesthe class have altogether?

4. The salespeople at Car Worldhave a monthly sales goal of$3,000,000. So far their sales are$1,204,403. How far are they fromtheir goal?

5. Which basic fact is used toestimate the product 9 � 871?

A 9 � 7B 9 � 8C 9 � 9D 9 � 10

7. Find the product 9 � 871.

A 3,879 C 7,839B 7,239 D 8,100

6. What is the expanded form of937?

F 937G 9 � 3 � 24H 90 � 30 � 7J 900 � 30 � 7

8. Which of the following numbersis the greatest?

F 432,911 H 40,329G 409,321 J 40,239

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Multiply 4-Digit NumbersWrite the correct answer.

Choose the letter of the correct answer. For 5–6, use the table.

8. The cities Brandonville, Dover, and Franklin have a summer soccer league.Each city has four teams, and each team needs five practice balls. Howmany soccer balls do they need?

A 12 C 20B 15 D 60

9. Write About It Explain the steps you took to find the answer to Problem 8.

1. What operation should be donefirst in finding the value of

3 � (5 � 4)?

3. Mr. Rose wants to buy 8 bushesto line his driveway. Each bushcosts $19.95. Estimate how muchall 8 bushes will cost.

2. A car manufacturer made 1,617cars in the month of January.Each car needs 4 tires. How manytires does the car manufacturerneed in all for those cars?

4. Find the exact cost of Mr. Rose’sbushes.

5. How much would Mr. Rose haveto pay for 3 hardy mums and 2golden pothos?

A $9.90 C $32.82B $22.92 D $83.22

6. About how much change shouldMr. Rose expect if he pays for3 pine trees with a $100 bill?

F $90.00 H $50.00

G $75.00 J $10.00

7. Which of the following is thirty-two thousand, four hundred fortyin standard form?

A 23,440 C 32,440 B 32,404 D 32,444

Greenhouse pricesType of plant PriceGolden pothos $4.95Pine tree $28.19Hardy mums $7.64

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4. Mike went to the grocery store tobuy fruit. He bought mangos for$2.76 and a sack of oranges for$4.89. How much money did hespend in all?

5. Amber’s mother gives her $4.75each week for an allowance.Amber plans to save all of herallowance for 6 weeks. Howmuch money will she have saved?

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Classify and Categorize

When you read a problem, it is often helpful to see if youcan classify the information in the problem into categories.The things in a category have something in common, suchas operations: addition, subtraction, multiplication, ordivision. As you read, look for words and phrases that areclues to which operation you can use.

Underline the words that help you categorize the information.

Daisy is the class treasurer. She needs to give $50 to each of fourclass committees. There is $300.00 in the class treasury. How muchmoney will be in the treasury after Daisy gives out the money?

1. Write some other words that give clues about eachcategory of problems.

Addition Problems

Subtraction Problems

Multiplication Problems

Division Problems

2. Solve the problem. In which category or categories—addition, subtraction, multiplication, or division—does this problem fit?

3. Describe the problem solving strategy used.

Name the category. Solve.

CATEGORIESADDITION SUBTRACTION MULTIPLICATION DIVISION

in all more than in all groups in 1 group

NameLESSON 10.6

VOCABULARYclassify

category

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Mental Math: Patterns with MultiplesWrite the correct answer.


9. Write About It Describe the pattern that you could useto solve Problem 6.

1. Use a basic fact and a pattern tofind the products.

4 � 70 =40 � 70 =

40 � 700 =

3. Hal brings 8 rolls of dimes to thebank. Each roll holds $5.00 indimes. How many $20 bills shouldthe bank give Hal for his rolls ofdimes?

2. Solve.800

� 60

4. Carla’s favorite piece of music is17 minutes long. She likes to playit over and over again. About howlong does it take her to listen to it9 times?

???

5. Which number will complete thepattern?

6 � 90 � 54060 � 90 � 5,40060 � � 54,000

A 9 B 90 C 900 D 9,000

7. Which type of graph best comparesdata for two similar groups?

A Double-bar graphB Line GraphC Stem-and-Leaf PlotD Line Plot

6. Which product completes thenumber sentence?

50 � 7,000 �

F 3,500 H 42,000G 35,000 J 350,000

8. Six partners agree to start abusiness together. Each partnerwill contribute $4,000 toward thebusiness. The business will alsotake out a $15,000 loan. How muchmoney will the business have?

F $19,000 H $39,000G $24,000 J $45,000

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Multiply by Multiples of 10Write the correct answer.


9. Write About It Describe the strategy you used to solve Problem 8.

1. Write the missing number tocomplete the pattern.

3 � 50 � 1503 � 500 � 1,500

3 � 5,000 �

3. Find the product.

43 � 60

2. Write the missing number tocomplete the pattern.

5 � 90 � 4505 � 900 � 4,5005 � � 45,000

4. Find the product.

32 � 40

??

5. What number completes themultiplication sentence?

21 � � 1,260

A 9,000 B 900 C 600 D 60

7. Ralph goes to the movies with afriend. He buys 2 tickets for $7.50each. He also buys a $3.50 bucketof popcorn and a $2.25 cup ofsoda. He has $3.50 left when hegets home. How much did he havewhen he went to the movies?

A $25.75 C $19.50 B $24.25 D $16.75

6. What number completes themultiplication sentence?

32 � � 2,880

F 60 G 70 H 80 J 90

8. Lila puts the coins from her coinjar into rolls. She has 9 rolls ofquarters. Each roll holds 40quarters. She has 7 rolls of nickels.Each roll holds 40 nickels. What isthe total value of her rolls of coins?

F $36 H $104G $44 J $640

??

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Estimate ProductsWrite the correct answer.


1. Round each factor to its greatestplace value, and then estimate theproduct.

56� 34

3. The Rocky Glen Amusement Parkis open for 70 days during thesummer. About 800 children visitthe park every day. About howmany children visit the parkduring the summer?

2. Round each factor to its greatestplace value, and then estimate theproduct.

481� 18

4. The Rocky Glen Amusement Parkhas a roller coaster which has 32seats. Write an expression for thenumber of riders in some numberof trips, t.

5. Which is the most reasonableestimate of the product?

166� 84

A 16,000 C 7,200B 9,000 D 1,600

7. Mike places some tiles in an arraythat is 5 tiles long by 7 tiles wide.He has 7 more tiles in a pile. Howmany tiles does Mike havealtogether?

A 19B 28

C 42

D 54

6. Which is the most reasonableestimate of the product?

28 � 910

F 27,000 H 2,700G 18,000 J 1,800

8. There are 276 students at NorrisElementary. The cafeteria managerestimates that each student usesabout 28 napkins each month atlunch. Which box of napkinsshould she order for next month’ssupply?

F the 500-napkin boxG the 1,000-napkin boxH the 10,000-napkin boxJ the 20,000-napkin box

9. Write About It Explain how you chose your answer to Problem 7.

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Model MultiplicationWrite the correct answer.


9. Write About It Describe the strategy you used to solveProblem 4.

1. Find the product modeled by

3. The Lancaster School District has14 fourth-grade classes. Each ofthe classes has 20 students. Writethe total number of fourth-gradestudents in the Lancaster SchoolDistrict.

2. Make a model to solve17 � 37 �

4. There are 18 volunteers collectingvoter signatures on a petition.Each volunteer collected 630signatures. About how manysignatures were collected?

?

5. 19 � 24 �

A 456 B 400 C 396 D 240

7. Write an equation: There are atotal of 40 light bulbs in somenumber of light fixtures, b, with 4bulbs in each fixture.

A 4 � 40 � b C 10 � b � 4B 40 � b � 4 D b � 40 � 4

6. 14 � 18 �

F 200 G 232 H 252 J 681

8. Dr. Stephanie sees 36 patientseach day. She works 20 days permonth. How many patients doesshe see in one month?

F 800 H 700G 720 J 620

??

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Cause and Effect

Sometimes the information in a problem is related. Thecause is the reason something happened. The effect isthe result.


Rita needs to make programs to hand out at the school play.She needs one program per seat. There are 34 rows of seatsand 20 seats in each row. How many programs does Ritaneed to make?

1. List the causes in the CAUSE column.List the effects in the EFFECT column.



List a cause and effect in each problem. Solve.4. Juan built a fence to keep his dog

in the yard. Each fence sectioncost $25. He used 20 sections. Howmuch money did the fence cost?

5. To prepare for a predicted snowstorm, Jean needs to have on hand10 bottles of water for each of her123 hotel guests. How manybottles of water does Jean need?

VOCABULARYcauseeffect

CAUSE EFFECT

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Multiply by 2-Digit NumbersWrite the correct answer.


9. Write About It Describe how you found the number ofinches in 15 yards in Problem 8.

1.

74� 23

3. Each bag holds 18 oranges. Astore gets a shipment of 42 bags oforanges. How many oranges are inthe shipment?

2.

36 � 48

4. If a school bus can carry 25students, how many students can40 buses carry?

5. 87 � 44

A 348,348 C 3,848B 4,268 D 3,828

7. A pica is a unit of measure usedby book designers. A page in abook of poems has 1 line of textper pica. There are 26 lines of texton the page. The top and bottommargins of the page are each 6picas. How many picas high is thepage?

A 54 C 38B 46 D 26

6. What is the most reasonableestimate of 78 � 78?

F About 64,000 H About 6,400G About 49,000 J About 640

8. There are 36 inches in 1 yard.How many inches are there in15 yards?

F 1,296 inchesG 540 inchesH 510 inchesJ 410 inches

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More About Multiplying by 2-Digit NumbersWrite the correct answer.


9. Write About It Explain how you found the answer to Problem 8.

1.711

� 55

3. Suppose your heart beats about67 times per minute. Estimate thenumber of times it beats in 1 hour.

2.

39 � $237

4. Judy changes the oil in her carevery 5,000 miles. She haschanged the oil a total of 12 timessince she bought the car. Howmany miles has the car beendriven?

5. 77 � $830

A $58,158 C $65,510

B $63,910 D $67,810

7. Doug’s Pet Shop sells ultrasonicflea collars for $49.95. Over thepast year, it has sold 93 of thecollars. How much money hasthe shop received from the saleof the flea collars?

A $5,196.20 C $4,842.30

B $4,645.35 D $3,679.25

6. 64 � 371

F 24,544 H 23,644

G 23,744 J 23,544

8. The moon is full about every 29days. About how many full moonswill there be in a 90-day periodstarting after the next full moon?

F 9G 4H 3J 2

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Multiply Greater NumbersWrite the correct answer.



1.

2,162� 32

3. The New Bedford Soccer Leaguehas 6 teams. Each team has 13players. How many players arethere in the New Bedford SoccerLeague?

2.

8,543� 29

4. The Century Scholarship Fundgives out 18 scholarships eachyear. If each of the scholarships isworth $2,500, how much moneydoes the fund give out each year?

5. 11 � $2,113

A $23,243 C $21,130B $22,243 D $4,226

7. Eileen is a marathon runner. Eachweekday, she runs 13 miles. EachSaturday and Sunday, she runs 17miles. How much farther does sherun in all during the 5 weekdaysthan she runs on Saturday andSunday?

A 99 mi C 55 miB 65 mi D 31 mi

6. 4,132� 16

F 65,012 H 66,021G 65,021 J 66,112

8. Each time Chris shovels Mrs. Barr’sdriveway after it snows, shedeposits $9 into Chris’s collegetuition fund. During the winter, itsnowed 27 times. How muchmoney did Mrs. Barr deposit intoChris’s college tuition fund?

F $270 H $243G $253 J $234

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Practice MultiplicationWrite the correct answer.



1. Solve.

$2.77 � 35

3. Nathan decides to write a bookabout his experiences in fourthgrade. He plans to write at least250 words each day. After 5 daysof writing, what is the leastnumber of words he should have?

2. Solve.$76.44� 24

4. Maura reads that there are anaverage of 3 radios for everyperson in the country. She lives ina town of about 7,000 people.About how many radios can sheexpect there to be in her town?

5. 6,543� 42

A 298,805 C 219,485B 274,806 D 219,480

7. Ellen builds an electric motor from akit. She winds 500 turns of wire in acoil to make an electromagnet. Sheestimates there are about 2 inches ofwire in each turn. About how manyinches of wire did she use?

A 750 in. C 1,000 in.B 900 in. D 1,100 in.

6. Which number completes thepattern?

8 � 40 � 320

8 � � 3,200

8 � 4,000 � 32,000

F 4 G 40 H 400 J 4,000

8. Liang moves to a new home.He packs his tapes in 3 boxes of8 tapes each. He also puts 6 tapesin a bag. Which expression canyou use to find out how manytapes Liang owns?

F (3 � 8) � 6 H (5 � 6) � 3G (6 � 3) � 8 J 3 � (8 � 6)

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Use Context

Words or phrases in a problem can help you understand themeaning and the mathematical operations you must perform.Read the following problem.

Julia has $45.00 to spend at the party store. She selects 16favors, which cost $1.29 each. Then she finds 32 balloons,which cost $0.59 each. Then she selects 2 packs of paperplates, which cost $1.79 per pack, and 1 pack of napkinswhich costs $1.89. How much money will her purchasescost? Does she have enough money to buy everything?

1. Underline the context clues to help you decide whetheryou need to give an exact answer or an estimated answerto each question in the problem. Then explain what thecontext clues tell you.

2. Solve the problems.

Underline the context clues. Solve the problem.

VOCABULARYcontext

3. The club has $63.85 in itstreasury. There are 23 newmembers and they must pay$2.50 each to join the club. Howmuch money will the club havethen?

4. A one-way bus trip from Atlantato Tallahassee costs $45. Mr.Jones has $150. Does he haveenough money for 2 tickets fromAtlanta to Tallahassee and back?Explain.

Context Clues

How much money will herpurchases cost?

Does she have enough money tobuy everything?

Explanation

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NameLESSON 13.1

Divide with RemaindersWrite the correct answer.



1. Mrs. Wong is giving her teacupcollection to her 9 grandchildren.She has 67 teacups. What is thegreatest number of teacups shecan give to each grandchild?

3. Roy is painting his house. Herents a paint sprayer for $29.95 aday. It takes him 13 days to paintthe house. Write his total cost forrenting the sprayer.

2. How many teacups will be leftover?

4. Jeanna and Crystal take an 8-daybike trip. They bike 60 miles eachday. Do they bike more than 500miles?

5. 7��4�3�A 5 r7 C 6 r1B 6 D 6 r4

7. A typical baby wears about 5diapers a day for the first 2 yearsof life. About how many diapersdoes the baby need?

A 2,000 B 3,000 C 4,000 D 7,000

6. 5��3�8�F 6 r8 H 7 r5G 7 r3 J 8 r2

8. Earth’s diameter is about 7,900miles. The distance from Earth tothe moon is about 30 times thisdiameter. Estimate the distancefrom Earth to the moon.

F about 21,000 miG about 31,000 miH about 240,000 miJ about 310,000 mi

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NameLESSON 13.2

Model DivisionWrite the correct answer.


9. Write About It Explain your solution to Problem 7.

1. What division problem is modeledby the following?

3. Make or draw a model to solve.

34 � 7

2. Theresa’s state sales tax requiresher to pay 6 cents for each dollarshe spends. If she buys a dog collarfor $4.00 and a leash for $7.00, howmuch sales tax will she pay?

4. Make or draw a model to solve.

87 � 6

5. 67 � 5

A 13 r1 C 13 r3B 13 r2 D 13 r4

7. The Band Boosters are sellingT-shirts. Each T-shirt costs $5.00 tomake and is sold for $11.00. TheBand Boosters ordered 300 shirtsand have sold 250. How muchmoney have they made?

A $250 C $1,500B $1,250 D $2,750

6. What division problem is shown?

F 35 ÷ 2 = 17 r1 H 35 ÷ 1 = 17 r1G 34 ÷ 2 = 17 r1 J 35 ÷ 17 = 17 r1

8. Write an equation using a variable:68 cars in 4 rows is some numberof cars in each row.

F 68 � 4 � b H 68 � 4 � bG 68 � 4 � b J 68 � 4 � b

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NameLESSON 13.3

Division ProceduresWrite the correct answer.


9. Write About It Explain how you estimated the first digit of the quotientin Problem 6.

1. Solve. 7��9�4�

3. Mr. Butterfield bakes a batch of48 cookies for his 5 children. Ifeach child gets the same numberof cookies, how many will be leftover?

2. Solve. 3��9�8�

4. Outer space is not very far fromwhere you are right now. At aspeed of 60 miles per hour, youcould travel out of the Earth’satmosphere in about 10 hours.Estimate this distance.

5. 6��7�5�

A 12 r2 C 12 r5B 12 r3 D 12

7. Jerry had 64 baseball cards. Hegave half to Craig. Craig gavehalf of his cards to Steve. Howmany cards did Craig give Steve?

A 16 cardsB 18 cardsC 32 cardsD 48 cards

6. 4��8�9�

F 22 r1 H 23G 22 r3 J 42 r1

8. The principal wants to invite the3 fourth-grade classes to a party.Two classes have 27 studentseach, and the third class has18 students. How many tables areneeded to seat 8 students at eachtable?

F 6 tables H 8 tablesG 7 tables J 9 tables

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NameLESSON 13.4

Analyze InformationIt is helpful to analyze, or examine, the details in aproblem. You can then use the details to solve theproblem. Underline the details so you will rememberthem. Read the following problem.

Mary Lou’s parents saved money for a piano that cost$1,845. They made a down payment of $1,215. They paidoff the remaining amount in 9 months, paying the sameamount every month. What was their monthly payment?

1. Analyze each detail of the problem. Complete the sentencein the Explanation column of the table for each detail.



Underline the details. Write a number sentence to solve.4. It costs the press club $81.73 to

print each issue of theirnewspaper, School Scoop. If theyprint 6 issues of the paper duringthe year, how much money willthey spend?

5. Kyla saved $108.60 in the bankin one year. She earned $7.24 ininterest on the money in the bank. Kyla then took out $47.25to buy a camera. How much didshe have left in the bank?

Detail Explanation

The piano cost $1,845. The total cost was .

They paid $1,215 down payment. Subtract from .

They paid the rest in 9 equal Divide by .payments.

VOCABULARYanalyze

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NameLESSON 13.5

Mental Math: Division PatternsWrite the correct answer.



1. Write the number to finish thepattern.

240 � 6 � 402,400 � 6 � 400

24,000 � 6 �

3. Use a basic fact and a pattern tofind the quotient.

5,320 � 6

2. Four friends play a game with adeck of 52 cards. The playersdivide all of the cards equally.Write the number of cards eachplayer gets.

4. Renee has 76 quarters. Write thevalue of her quarters.

?

5. What is the most reasonableestimate of the quotient? 4,178 � 5

A 250 B 600 C 800 D 700

7. Chesterton was hit with a hugesnowstorm that left an average of2 inches of snow each hour. Thestorm left a total of 2 feet of snow.How long did the storm last?

A 12 hrB 18 hrC 24 hrD 36 hr

6. 63,000 � 7

F 800 G 900 H 7,000 J 9,000

8. A train leaves Station 1 at8:15 A.M. It travels east for 45minutes and stops at Station 2 for30 minutes before leaving again.At what times does the train leaveStation 2?

F 8:45 A.M.G 9:15 A.M.H 9:30 A.M.J 9:45 A.M.

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NameLESSON 13.6

Estimate QuotientsWrite the correct answer.


9. Write About It Explain how you chose compatible numbers to estimatethe quotient in Problem 2.

1. Write an estimate of the quotientby using compatible numbers.

522 � 6 �

3. Koala Airlines carries an averageof 272 passengers on its Dallas toPerth flight. It runs 620 of theseflights each year. About howmany passengers travel fromDallas to Perth each year?

2. Write a pair of compatiblenumbers. Use them to estimatethe quotient.

8��6�,3�2�1�

4. Chester runs his horses in aneight-sided pen. Each of the pen’s sides measures 240 ft. What is thedistance around the pen?

?

5. Which expression would be bestto estimate the quotient?

312 � 6 �

A 300 � 6 C 310 � 6B 290 � 6 D 320 � 6

7. A group of 12 friends buys 125concert tickets. Which of thefollowing is not a way the ticketscan be split?

A Each friend gets 11 tickets.B Each friend gets 10; 5 are

returned.C Seven friends get 10; 5 friends

get 11.D Five friends get 18; 7 friends

get 5

6. Which is the most reasonableestimate of the quotient?

5,549 � 8 �

F 700 G 80 H 75 J 70

8. Bart wrote his name 53 times in266 seconds. About how long doesit take him to write his name eachtime?

F about 10 secG about 8 secH about 5 secJ about 3 sec

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NameLESSON 14.1

�Place the First Digit Write the correct answer.



1. Tell where to place the first digitof the quotient.

4��9�6�5�

3. Find the mode: 3, 7, 4, 9, 4, 2, 3, 4,6, 9.

2. Divide. 6��8�2�2�

4. When the BookPort has its bookson sale for $9.99 each, Pennybuys 8 books. How much do the8 books cost her?

5. 5��6�7�6�

A 225 r1 C 125 r1B 135 r1 D 115 r1

7. Sam plans to see a 97-minutemovie at the twin theater. Themovie starts at 7:45 P.M. After thathe wants to see the other moviethe theater is showing. Which isthe earliest time the other moviecould start for Sam to be able tosee both movies?

A 9:05 P.M. C 9:45 P.M.B 9:15 P.M. D 10:35 P.M.

6. 7��4�4�9�

F 64 r5 H 64 r1G 64 r3 J 64

8. To find her math grade, Edna addsup all 7 of her test scores and thendivides that sum by 7. What isEdna’s grade?

F 86 H 88G 87 J 92

Test 1 2 3 4 5 6 7

Score 92 82 76 88 95 71 98

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NameLESSON 14.2

�Divide 3-Digit NumbersWrite the correct answer.


9. Write About It Explain the pattern you found in Problem 7.

1. Divide.4��8�7�1�

3. Heidi spends $2.10 each on a stripof 4 Priority Mail stamps. Howmuch did she spend altogether?

2. Divide. 3��5�5�5�

4. Sheldon’s dog had to spend 12days in a veterinary hospital. Thecost was $98 each day. How muchwas the total hospital bill?

5. 6��4�5�8�A 76 r2 C 78 r4

B 78 r2 D 79 r4

7. While flipping through thecalendar in his date book, Mattsees this pattern: 31, 28, 31, 30, 31,30, 31, . . . . Which is the nextnumber in the pattern?

A 31B 30C 29D 28

6. 5��9�1�1�F 168 r1 H 182 r1

G 178 r1 J 190 r1

8. Raul drives his car to work andback 5 days each week. Hisbusiness is 7 miles from his home.On Saturdays, he drives to themall, which is 12 miles from hishome. How many miles does Rauldrive each year?

F 6,512 mi H 3,888 mi

G 4,888 mi J 3,360 mi

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Zeros in DivisionWrite the correct answer.



1. Solve.8��8�7�5�

3. The fleshy hawthorn is a smalltree. One of the tallest ones is only8 feet tall. The tallest redwood isabout 360 feet tall. About howmany of the fleshy hawthornswould it take to equal the heightof the 360-foot redwood?

2. Solve. 6��$�9�.6�0�

4. Coach Jared orders new uniformsfor all 22 of the team members. Ifeach uniform costs $38.85, howmuch will the uniforms costaltogether?

5. 7��7�6�4�

A 108 C 109 r4B 109 r1 D 111 r3

7. Byron divides $474.40 by 4. Hewrites his answer as 118.6. Howshould he have written it?

A $118.6B 118.60C $118.60D $118.00

6. 4��$�8�.2�8�

F $2.07 G 2.07 H 2.03 J $2.03

8. At Green’s Grocery, detergent isselling at 3 bottles for $9.00. AtO’Malley’s, the same detergent is5 bottles for $10.00. Which storehas the better buy and how muchwould you save on each bottle?

F Green’s; save $3.00 per bottleG Green’s; save $2.00 per bottleH O’Malley’s; save $2.00 per bottleJ O’Malley’s; save $1.00 per bottle

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Divide Greater NumbersWrite the correct answer.



1. Solve.8��$�4�1�.2�8�

3. If an egg weighs about 45 grams,about how much will 1 dozen eggsweigh?

2. Solve. 9��3��,77�1

4. The Trueblue Theater holds 345people. If it sold out every showduring a 22-show run, how manypeople had tickets to the show?

5. 4��$�2�2�.3�6�

A $5.64 C $5.54B $5.59 D $4.55

7. Harriet wants to find the cost perpound of a 5-pound bag ofpotatoes that is labeled $7.85. Shedivides $7.85 by 5 and writes heranswer as $157 per pound. Howshould she have written heranswer?

A $157.00 per lbB 157 per lbC $15.70 per lbD $1.57 per lb

6. 997� 37

F 32,449 H 36,889G 36,209 J 38,989

8. Sweet corn is priced at 3 earsfor $0.99. Shawna wants to buy14 ears for a party. How muchwill the corn cost?

F $17.50G $5.62H $4.95J $4.62

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Use Graphic Aids Graphic aids such as maps and diagrams give importantinformation for solving problems. Read the followingproblem.

Josh is conducting a survey along Grove Street,beginning at 18 GroveStreet, and surveying thebuildings in numericalorder. He has 90 minutesbefore meeting his friend.It takes him 8 minutes tosurvey each building. Howmany buildings can Joshsurvey before his meeting?Where should he tell his friend to meet him?

1. Use the map to help you solve the problem.



Use the map to help you solve the problem.

4. Josh conducts a survey along Oak Street. It takes him 6 minutes for eachbuilding beginning at 1 Oak Street. He has 135 minutes before meeting hisfather. How many buildings can Josh survey? Explain how you know and tellwhere his father should meet him.

Divide to find the number of buildings Josh can survey beforemeeting his friend.

He can survey buildings and meet his friend on time.

At what address will Josh be when he completes that number ofsurveys?

GROVESTREET

OAK STREET

OAK STREET

1

18

3

20 22

19 21 23

24

25

26

27

28

29

32

33

31

Libra

ry

30

57 9 11 35

1820

2224 26

37 39 4143

4534

46

28

1719

21

25 27 29 3123

38 40 444236

15Garage

2

84

610 12 14 16

School

Coffee shopMinimart

Diner

Bookstore

Petstore


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NameLESSON 14.6

�Find the MeanWrite the correct answer.



1. Jana went to a 3:30 P.M. movie.The movie lasted one and one-halfhours. If the drive home took 45minutes, at what time did Jana gethome?

3. The four 4th grade classes atRitchie Elementary have 20, 18,20, and 22 students. What is themean class size?

2. Jeffrey bought 3 pounds of applesat $1.29 per pound and paid with a$10.00 bill. How much changeshould he receive?

4. Sara’s basketball team has scored55, 60, 70, 47, and 53 points in theirfirst five games of the season. Findthe mean number of points scored.

5. What type of graph should thescience teacher use to record thegrowth of a bean plant throughoutFebruary?

A stem-and-leaf plotB bar graphC line graphD double-bar graph

7. What is the range of Steve’sspelling test scores?

A 13B 82C 88D 92

6. Steve’s report card score inspelling will be the average of histest scores. His scores are 95, 82,82, 92, and 89. What will beSteve’s average?

F 13 H 88

G 82 J 92

8. Jenna worked four shifts as awaitress. Her tips were $22.10,$19.80, $12.90, and $25.60. Whatis the average tip amount?

F $80.00 H $20.10

G $21.00 J $20.00

NameLESSON 15.1

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Division Patterns to EstimateWrite the correct answer.


9. Write About It Describe the pattern you used to help youfind the missing number in Problem 5.

1. Round the divisor and thedividend. Estimate the quotient.

446 � 93

3. Write the basic fact you can use tohelp you estimate the quotient.

351 � 6

2. Round the divisor and thedividend. Estimate the quotient.

652 � 77

4. Divide.267 � 3

5. Which number will finish thepattern?

90 � 30 � 3900 � 30 � 30

9,000 � 30 � 30090,000 � 30 �

A 30,000 C 300B 3,000 D 30

7. Ms. Felton makes $22 an hour as aconsultant. How much did sheearn during the week of January19, 1998?

Hours Worked Week of Jan. 19, 1998

Day Mon. Tue. Wed. Thu. Fri. Sat.

Time 6 hr 8 hr 10 hr 9 hr 5 hr 6 hr

A $360 C $898B $880 D $968

6. Which number will finish thepattern?

20 � 40 � 800200 � 40 � 8,000

2,000 � 40 � 80,00020,000 � 40 �

F 800 H 80,000G 8,000 J 800,000

8. A theater company rents a stagefor a total of 32 hours. They pay$296 for the space. Which is themost reasonable estimate of whatthey pay for the space each hour?

F $18 H $10G $12 J $6

??

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Model DivisionWrite the correct answer.


1. What division problem is shownby the model?

3. Bailey’s baby brother was born128 days ago. If there are 7 days ineach week, how many weeks agowas Bailey’s baby brother born?

2. Jennifer is arranging flowers intobouquets. She has 258 flowersand needs to make 8 bouquets.About how many flowers will bein each bouquet?

4. Make a model to solve.

115 � 36

5. Which division problem is shownby the model?

A 51 � 22 � 2 r7B 51 � 2 � 22 r7C 22 � 7 � 51 r2D 22 � 2 � 51 r7

7. Divide. 834 � 26

A 320 C 31 r2B 32 r2 D 30 r2

6. An Internet service provider runs37 servers. Each server gets about30,000 visits, or “hits,” each day.Which is the most reasonableclaim for the service providerto make?

F More than 500 hits a day!G More than 1 million hits a day!H More than 2 million hits a day!J More than 5 million hits a day!

8. Multiply. 21 � 6,518

F 136,878 H 126,878G 136,778 J 126,778

9. Write About It Explain how you chose your answer for Problem 6.

�

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Division ProceduresWrite the correct answer.


9. Write About It Describe how you answered Problem 4.

1. Kim earned $578 in 34 weeks. IfKim earned the same amount eachweek, how much money did Kimearn in one week?

3. Jerry runs probability experimentson his computer. Each experimenttakes 20 days to complete. What isthe greatest number ofexperiments he can run in 1 year(365 days)?

2. Jim earned $921 in one year, or 52weeks. Did he earn more or lessthan $17 in one week?

4. Lee completes a 985-mile car tripat an average speed of 52 milesper hour. About how many hoursdid she spend driving on the trip?

5. 28��6�5�6�

A 22 r16 C 23 r12B 22 r18 D 23 r2

7. Tina slept 8, 9, 7, 10, 8, 8, and 9hours the past 7 nights. What is themode of the number of hours sheslept?

A 7 hours C 9 hoursB 8 hours D 10 hours

6. 47��7�8�1�

F 12 r15 H 18 r2G 16 r29 J 19 r29

8. Felicia’s school has 427 students.There are 19 teachers. About howmany students are in each class?

F 30 H 20G 25 J 15

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NameLESSON 15.4

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Correcting QuotientsWrite the correct answer.



1. Write too high, too low, or justright to describe the estimatedquotient.

942��3�6�8�

3. The wrestling team spent $375buying sweatshirts for its 25wrestlers. How much did eachsweatshirt cost?

2. Write too high, too low, or justright to describe the estimatedquotient.

277��2�3�1�

4. The administrator who managesthe school computers orders 36copies of a software package. Thetotal charge will be $972. What isthe cost for a single copy?

5. 71��3�6�5�A 4 r10 C 6 r10B 5 r10 D 6 r61

7. Ben takes 7 rolls of the same coinsto the bank. Which choice cannotbe the total value of the 7 coinrolls?

Coin penny nickel dime quarter

Numberin roll 50 40 50 40

A $3.50 C $14.00B $7.00 D $70.00

6. 58��4�4�7�F 5 r33 H 7 r41G 6 r45 J 8 r3

8. Brita has 372 dimes and 185nickels. She puts the dimes in rollsof 50 per roll and the nickels inrolls of 40 per roll. How many rollsdoes she have?

F 7 rolls of dimes, 3 rolls of nickelsG 6 rolls of dimes, 4 rolls of nickelsH 7 rolls of dimes, 4 rolls of nickelsJ 6 rolls of dimes, 3 rolls of nickels

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NameLESSON 15.5

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Draw Conclusions Being able to draw conclusions is an important part of solvingproblems. To draw conclusions, you must examine theinformation in the problem and use what you already know tofind the answer. Read the following problem.

Carol practiced her flute for 360 minutes this week.Alberto practiced his flute for 7 hours. Who practicedlonger?

1. Under Examine the Information complete the informationthat is given in the problem. In the next column, write somehelpful information that you already know. Use thisinformation to help you draw a conclusion.



Examine the information, and use what you already know to drawconclusions. Solve.

4. On Friday, Pam’s niece was just 18 months old. Peter’s niece wasexactly 64 weeks old. What is theage of Peter’s niece in months?Whose niece is older?

5. Jack worked in the yard for 2 hours. His brother, Jake, workedin the yard for 180 minutes. Howmany hours did Jake work? Whoworked in the yard longer?

Examine the Information Use What You Already Know

• Carol practiced her flute for • There are minutes in 1 hour.

.

• Alberto practiced his flute for • To change minutes to hours,

. .

Draw Conclusions

360 min = hr

VOCABULARYdraw

conclusions

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NameLESSON 16.1

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Factors and MultiplesWrite the correct answer.


9. Write About It Explain how you used factors to solve Problem 7.

1. Solve.7,942� 87

3. Write the first 6 multiples of 8 thatyou can find on the multiplicationtable.

2. Solve.9,000

� 100

4. List as many factors of 100 as youcan.

5. The factors of 36 are:

A 0, 2, 4, 6, 9B 1, 6, 36, 72C 1, 3, 4, 8, 9D 1, 2, 3, 4, 6, 9, 12, 18, 36

7. Will has 24 guppies. He wants toshare them with some friends.Which is not a way he couldshare the fish?

A 12 guppies to 2 friends B 3 guppies to 6 friendsC 6 guppies to 4 friendsD 8 guppies to 3 friends

6. Which number completes theequation?

8 � � 72

F 7 H 9

G 8 J 16

8. Sarah is sending cookies to herfriends. She made 32 cookies, andshe would like to put 8 in eachpackage. What equation can youuse to show the number offriends, m, to whom Sarah cansend her cookies?

F 32 � 8 � m H 32 � 8 � mG 8 � m � 32 J 8 � m � 1

?

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NameLESSON 16.2

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Factor NumbersWrite the correct answer.


9. Write About It Explain how you used factoring to solve Problem 5.

1. Write an equation for the arrayshown.

3. List 5 multiples of 7.

2. Sam wants to make a rectangularpattern using 36 square tiles.How many different rectanglescan he make? Explain.

4. Solve. (520 � 10) � 100

5. Which of the following numbersof tiles could be used to make asquare array?36, 42, 49, 55, 72, 100

A 49, 36, and 100B 42 and 49C 55 and 100D 36 and 72

7. Melissa has made 3 rectangles.Each one is 10 blocks long and 5blocks wide. What is the rightexpression for the total number ofblocks in the rectangles?

A 15 � 3B 30 � (50 � 10)C 13 � 5D 3 � (10 � 5)

6. How could the model be brokendown?

F 3 � (3 � 8) H 3 � (4 � 3)

G 8 � (2 � 3) J 3 � (3 � 2)

8. Bill needs to buy strawberries.A quart of strawberries costs $3.00.There are about 18 strawberriesin a quart. Bill needs 100strawberries. How many quarts willhe need and what will they cost?

F 5 quarts, $15.00G 6 quarts, $18.00H 7 quarts, $21.00J 8 quarts, $24.00

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NameLESSON 16.3

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Prime and Composite NumbersWrite the correct answer.



1. Sally has 7 friends. Each onewants to take home 3 pieces ofcarrot cake. If there are 6 slices inone carrot cake, how many cakeswill Sally need?

3. Is the number 80 prime orcomposite? Explain.

2. Chuck bought colored notebooks.He spent $6.00 on red notebooks,$8.00 on green notebooks, and$12.00 on yellow notebooks. Ifeach notebook cost $2.00, howmany notebooks did he buyaltogether?

4. In how many ways can you stack27 books? Name them.

5. Amy is 5 years younger thanJosh. She is twice Sam’s age.Josh’s age is less than 16. Sam isolder than 4. How old is Sam?

A 4 C 7B 5 D 8

7. In which set are all the numberscomposite?

A 4, 44, 144 C 56, 43, 39B 31, 35, 39 D 11, 21, 31

6. In which set are all the numbersprime?

F 3, 12, 36 H 5, 31, 53G 18, 28, 48 J 7, 27, 57

8. Which is not a way you couldplace 60 cans in equal rows?

F 2 rows of 30 H 3 rows of 20G 6 rows of 10 J 4 rows of 13

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NameLESSON 16.4

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Find Prime FactorsWrite the correct answer.


9. Write About It Explain how you found the prime factors of48 in Problem 6.

1. Scientist George WashingtonCarver lived from 1864 until 1943.How many years did he live?

3. Write 90 as a product of primefactors.


4. Order from greatest to least:5,555; 5,505; 5,550; 55,055; 5,050

5. Michael drove his car to highschool and back 5 days one week.The school is 5 miles from hishome. If he used 2 gallons ofgasoline in one week, how manymiles did he drive per gallon?

A 10 C 20B 15 D 25

7. Which expression equals 36?

A 3 � 11 � 3 C 3 � 3 � 2 � 2B 2 � 6 � 6 D 2 � 2 � 3 � 4

6. Which is written as the product ofthe prime factors of 48?

F 4 � 12G 2 � 6H 2 � 3 � 6J 2 � 2 � 2 � 2 � 3

8. Rebecca begins a marathon at12:16 P.M. She crosses the finishline at 5:38 P.M. How long did ittake her to run the marathon?

F 5 hr H 5 hr 12 minG 4 hr 22 min J 5 hr 22 min

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NameLESSON 16.5

Form Mental Images

Sometimes it is helpful to visualize, or form a mentalimage of, the information in a problem. Using the detailsor facts to form mental images can help you organize andunderstand information. Read the following paragraph.

Jeannie is painting a border along the ceiling of herroom. She is painting elephants, giraffes, and snakesin a pattern. First she paints an elephant, then agiraffe, then two snakes. She repeats this patternaround the entire room. Which animal will be 7th inher painting?

1. Use the details to make a mental picture. Then use thewords to describe what you see.



Form mental images to solve.

Details Visualize/Form Mental Images

Jeannie is painting a border.

First she paints an elephant.

Then she paints a giraffe.

Then she paints two snakes.

She repeats the pattern.

4. The first row of Lara’s garden hascarrots. Then there are two rows ofradishes and one row of lettuce.This pattern continues. What is inthe 8th row of Lara’s garden?

5. On Monday Haley worked at theconcession stand for 25 minutes.Each day he worked 25 minutesmore than the day before. Howlong did he work on Friday?

VOCABULARYvisualize

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NameLESSON 17.1

�Read and Write FractionsWrite the correct answer.


1. Write a fraction for the shadedpart.

3. Tia’s family is having a reunion.117 people will be seated, 8 to atable. How many tables will beneeded?

2. Shade the model to show thefraction �45�.

4. Harry is setting traps for lobsters.Each trap can hold about 30lobsters. If he sets 82 traps, abouthow many lobsters could he catch?

5. Which type of graph is best forshowing the change in data overtime?

A bar graph C stem-and-leaf plot

B double-bar D line graphgraph

7. A building has 7 floors. A bookcompany takes up 3 floors. An adagency takes up 2 floors. A designfirm takes up the remaining floors.What fraction of the building isused by the design firm?

A �17� C �37�

B �27� D �47�

6. Which fraction shows the part ofthe model that is not shaded?

F �15� H �5

3�

G �25� J �3

2�

8. Rosa and Tim are trying to win adance marathon. They dancedfrom 6:50 A.M. until 11:45 P.M. Howlong did they dance?

F 5 hr H 17 hr 5 minG 17 hr J 16 hr 55 min

9. Write About It Explain how you chose the fraction to write for Problem 1.

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1. Find two fractions equivalent to �12�.


2. A hockey game is divided into 3periods. If Suzanne played for 2periods, write the fraction of thegame she played.

4. Find a fraction that is equivalent to�34� and has a denominator of 8.

NameLESSON 17.2

�Equivalent FractionsWrite the correct answer.


5. Which fraction is not equivalent to�132�?

A �12� C �28�

B �14� D �624��

7. Which fraction is equivalent to �190�?

A �34� C �180�

B �1280� D 1�

19�

6. Which of these numbers is prime?

F 30 H 99

G 47 J 100

8. Talia jogged 46 times last year.About how many times did she jogeach month?

F 5 times H 3 times

G 4 times J 2 times

9. Write About It Explain how you answered Problem 5.

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NameLESSON 17.3

�

1. Use multiplication or division towrite a fraction equivalent to �2

94�.

3. What is the next fraction in thepattern? �

14�, �

28�, �1

32�, �1

46�, . . .

2. Write a fraction in simplest form forthe picture.

4. Write �39� in simplest form.

Equivalent FractionsWrite the correct answer.


5. Which fraction is not equivalent to �

34�?

A �1284� C �3

267�

B �38� D �1162�

7. Which number is not a factor of 92?

A 2 C 23

B 4 D 30

6. Scott is setting up a display in agrocery store. He needs to stackequal rows of cans. Whicharrangement uses the most cans?

F 4 rows of 12 cans

G 3 rows of 10 cans

H 5 rows of 10 cans

J 2 rows of 15 cans

8. Which fraction is not in simplestform?

F �17� H �23�

G �36� J �25�

9. Write About It Explain how you answered Problem 3.

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NameLESSON 17.4

�Compare and Order FractionsWrite the correct answer.


9. Write About It What rule did you use to help you order thefractions in Problem 5?

1. Write a number sentence using� , �, or � that compares the twofractions shown in the models.

3. On the soccer team, �59� of theplayers are girls. On the fieldhockey team, �56� of the players aregirls. Which team has a greaterfraction of girls?

2. Write a fraction to show the part ofthe group that is shaded.

4. Leonard stood on the corner andcounted the cars that went by. Outof 22 cars, 17 were taxis. Whatfraction of the cars were taxis?

5. Which set of fractions is orderedfrom the least to the greatest?

A �23� , �27� , �25� C �15� , �19� , �17�

B �38� , �37� , �34� D �45� , �47� , �49�

7. In Rowayton one spring, it rainedon March 22 and every day afterthat until May 2. How many daysin a row did it rain in Rowaytonthat spring?

A 42 daysB 39 daysC 24 daysD 12 days

6. Which set of fractions is orderedfrom the greatest to the least?

F �38� , �58� , �78� H �15� , �35� , �45�

G �29� , �79� , �59� J �67� , �57� , �27�

8. In Mr. Wile’s class, �35� of thestudents try out for a play. In Ms.Kane’s class, �1

60� of the students try

out. In which class does a greaterfraction of the students try out?

F Mr. Wile’s

G Ms. Kane’sH Neither; the fractions are

equivalent.J Not Here

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NameLESSON 17.5

�CompareTo solve some problems, you can compare and contrastinformation in a problem. Find things about the problem that arealike, and things that are different. Read the following problem.

A recipe calls for �38� teaspoon of nutmeg, �

14� teaspoon of baking

soda, and �23� teaspoon of cinnamon. List the ingredients in

order from the greatest amount to the least amount.

1. Write at least one way in which the fractions are alike in theCompare column. Write one way in which the fractions aredifferent from each other in the Contrast column.



Compare and contrast the fractions in each problem. Solve.4. Lizzie has �

58� gallon of red paint, �

18�

gallon of blue paint, and �38� gallon of

white paint. List the paint colors inorder from the least to the greatestamount.

6. Al made punch for a party. Therecipe called for �12� gallon of orangejuice, �34� gallon of pineapple juice,and �45� gallon of grape juice. Listthe ingredients in order from thegreatest to the least amount.

5. Scott has �38� cup of nuts, �

34� cup of flour,

and �23� cup of sugar for baking

cookies. List the ingredients in orderfrom the greatest to the least amount.

7. Karen used a recipe calling for �34�

cup of cherries, �58� cup of water, and�12� cup of honey. List the ingredientsin order from the least to thegreatest amount.

Compare Contrast

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NameLESSON 17.6

�Mixed NumbersWrite the correct answer.


1. Write a mixed number for thenumber of figures that are shaded.

3. A cake calls for 6 cups of flour.Elena uses whole wheat flour for �

12�

of the recipe, white cake flour for�13� of the recipe, and regular whiteflour for the remaining �

16� of the

recipe. Which kind of flour doesElena use most in the cake?

2. Write a mixed number for thenumber of figures that are shaded.

4. A bridge is divided into 9 equalsections. At one end of the bridge,2 sections are over land. At theother end, 3 sections are over land.The rest are over water. Whatfraction of the bridge is overwater?

5. Which mixed number isequivalent to �92�?

A 18 C 9�41�

B 9�12� D 4�12�

7. Amy plays a 30-minute cassette.The counter on her tape playermoves from 0 to 360 while the tapeis playing. Amy wants to play thelast 10 minutes of the tape again.About how far back on the countershould she rewind the tape?

A to 300 C to 180

B to 240 D to 10

6. Which mixed number isequivalent to �73�?

F 7�13� H 3�17�

G 6�13� J 2�13�

8. Renee bought �12� pound of turkey,�34� pound of cheese, and �13� pound oftomatoes to make sandwiches. Listthe fractions in order from theleast to the greatest.

F �13�, �12�, �34� H �12�, �34�, �13�

G �34�, �13�, �12� J �13�, �34�, �12�


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NameLESSON 18.1

Add Like FractionsWrite the correct answer.


9. Write About It Write a rule for the pattern you saw in Problem 7.

1. Use the fraction bars to help youfind the sum.

�36� � �

26�

3. Steven measures the thicknessof a board. He records themeasurement as �

52� inches. Write

his measurement using a mixednumber.

2. Use the fraction bars to help youfind the sum.

�18� � �

38�

4. In the fourth-grade class, �58� of the

students buy milk at lunch. In thefifth-grade class, �

34� of the students

buy milk at lunch. In which classdoes a greater fraction of the classbuy milk?

16

16

16

1

1

616

5. Find the sum. �47� � �

27�

A �27� C �

34�

B �164� D �

67�

7. What are the missing numbers inthe pattern?

316, 332, 348, 364, �, �, 412

A 378, 396 C 380, 386

B 374, 390 D 380, 396

6. Which fraction is equivalent to �198�?

F �23� H �

12�

G �69� J �

2576�

8. When Annette makes pumpkinpie, she adds �

14� teaspoon nutmeg,

�14� teaspoon cloves, and �

14� teaspoon

allspice. What is the total amountof these three ingredients?

F �34� teaspoon H �

38� teaspoon

G �12� teaspoon J �

14� teaspoon

18

18

18

1

1

8

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NameLESSON 18.2

Subtract Like FractionsWrite the correct answer.


9. Write About It Explain why you chose the answer you did for Problem 7.

1. Use fraction bars to find thedifference.

�180� � �1

30�

3. Betty puts two strips of woodaround the edge of a table. Thecherry strip is �

34� inch wide, and the

maple strip is �38

� inch wide. Whichstrip is wider?


�89� � �

49�

4. Claudia’s pie recipe includes�18� teaspoon nutmeg, �

14� teaspoon

cloves, and �12� teaspoon ginger.

Order the three ingredients fromgreatest to least amount.

5. �89� � �

29� �

A 1�19� B �

23� C �

1108� D �

13�

7. One number is 5 more than 9. Theother number is 19 less than 22.Find the prime factors of theproduct of the two numbers.

A 6, 7

B 2, 3, 7

C 2, 21

D 3, 10

6. �170� � �1

30� �

F 2 G 1�130� H 1 J �

25�

8. Sheila is building bookshelves.She needs a board that is at least1�

12� in. thick. She has no boards that

thick, so she decides to gluetogether two boards. Which pair ofboards can she use?

F a �38�-in. board and a �

18�-in. board

G a �18�-in. board and a �

78�-in. board

H a �34�-in. board and a �

34�-in. board

J a �12�-in. board and a �

12�-in. board

??

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NameLESSON 18.3

Add and Subtract Mixed NumbersWrite the correct answer.


9. Write About It How did you find the answer to Problem 7?

1. 2�18� � 3�

38� �

3. Neal eats �78� of a pizza. Verne eats �

68�

of a pizza. How much more pizzadoes Neal eat than Verne?

2. 5�35� � 4�

25� �

4. Hilary finds 3 quarters in herjacket pocket. What fraction of adollar does she have?

??

5. 8�34� � 2�14�

A 6�12� C 9

B 6�34� D 11�12�

7. Wendy needs a 6 �14�-in. piece of

trim. She has a box of smallerlengths of trim. Which pair ofpieces can she put together to getthe length she needs?

A 3�34�-in. piece and a 2�

34�-in. piece

B 4�24�-in. piece and a 1�

34�-in. piece

C 2-in. piece and a 4�34�-in. piece

D 3�14�-in. piece and a 2�

34�-in. piece

6. �39� � �

29�

F �29� H �59�

G �158� J 1�

45�

8. The sum of the digits of a 3-digitodd number is 13. The digit in thetens place is 4 less than the digitin the hundreds place and 3 morethan the ones digit. What is thenumber?

F 625 H 841

G 733 J 952

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NameLESSON 18.4

Understand Cause and Effect A cause is the reason something happens. An effect iswhat happens as a result of the cause. A cause may havemore than one effect. An effect may have more than onecause. Read the following problem.

An ice storm caused power lines to fall down. As aresult, only �1

10� of the population in one town had power.

The power company promised special emergencyrepairs if more than �

12� of the population lost power.

What fraction of the population lost power? Will thepower company make emergency repairs?

1. List the causes in the Cause column. List the effects in theEffect column.



List a cause and an effect in each problem. Solve.

VOCABULARY

causeeffect

Cause Effect

ice storm

Think: Did over one half of the Think: What will happen?population lose power?

4. Mr. Bowers tells 8 students that ifmore than half lost power for atleast 3 days, he will postpone themath test. In the group, �

28� lost

power for 1 day. The rest lostpower for 3 days. Will Mr. Bowerspostpone the test?

5. Ryan decided to do his homeworkby candlelight. Of the total timethat he had, he spent �

15� doing math

and �25� doing science. The candles

burned out before he had time todo English. What fraction of thetime was left?

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NameLESSON 18.5

Add Unlike FractionsWrite the correct answer.



1. 8�38� � 2�18�

3. �16� � �23�

2. Write three fractions that areequivalent to �

23�.

4. Carolyn walked �25� mile on Monday,

and �160� mile on Wednesday. How

far did Carolyn walk in all?

5. Which pair shows like fractions?

A �13�, �15� C �25�, �35�

B �12�, �14� D �36�, �37�

7. Veronica’s dresser is 4 �122� feet long.

Her bed is 6 �152� feet long. How

much longer is her bed than herdresser?

A 10 �172� feet C 2�4

1� feet

B 8�12� feet D �

131� feet

6. Which is a prime factor of 40?

F 9 H 7

G 8 J 2

8. Serena must practice her clarineteach day. She practiced in themorning for �

14� hour and in the

afternoon for �13� hour. How long did

Serena practice in all?

F �172� hour H �1

52� hour

G �12� hour J �

13� hour

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NameLESSON 18.6

Subtract Unlike FractionsWrite the correct answer.


9. Write About It Explain how you chose your answer to Problem 8.


�170� � �

25�

3. A 2�13�-yard length is cut off of a

5�23�-yard strip of vinyl siding. What

is the length of the remaining stripof siding?

2. Add.

2�14� � 3�

34�

4. A recipe calls for �34� cup sugar.

Emily has �12� cup. How much sugar

does she still need?

5. �12� � �

13�

A �16� C �

56�

B �12� D 1

7. The gravity on the moon and someof the planets would make youweigh less than you weigh onEarth. Order the moon and thethree planets from the one youwould weigh the greatest on to theone you would weigh the least on.

Moon Pluto Mercury Mars

Fractionof Weighton Earth

A Moon, Pluto, Mercury, MarsB Pluto, Moon, Mercury, MarsC Mars, Mercury, Pluto, MoonD Mars, Mercury, Moon, Pluto

6. �1112� � �

23�

F 1 H �23�

G �34� J �

14�

8. Twelve grandchildren want to payequal amounts to buy a gift fortheir grandparents’ fiftiethwedding anniversary. For whichgift would they be able to payequal whole-dollar amounts?

F a $100 silver platterG a $90 punch bowlH an $84 sculptureJ a $77 painting

�11070� �10

40� �1

3070� �1

3080�

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NameLESSON 19.1

Relate Fractions and DecimalsWrite the correct answer.


9. Write About It Explain the strategy you used to solve Problem 7.

1. Write the decimal and the fractionfor the part that is shaded.

3. In Mrs. Valerio’s class, �23� of the

students bring lunch and �13� of the

students buy lunch at school.Which is greater—the fraction ofthe students that brings lunch orthe fraction of the students thatbuys lunch?

2. Write the decimal and the fractionfor the part that is shaded.

4. In a survey, �130� of the people

interviewed said they liked theirjobs a great deal. Another �1

20� said

they liked their jobs somewhat.What was the total fraction ofthose interviewed who liked theirjobs?

5. Add �13� � �34� �

A �49� B �47� C 1 �112� D 1 �37�

7. Mike draws a square with a lineconnecting opposite corners. Thenhe draws another line connectingthe other pair of opposite corners.How many triangles are there inMike’s square?

A 2 triangles C 6 triangles

B 4 triangles D 8 triangles

6. Which fraction is equivalent to thedecimal 0.24?

F �24� G �

214000� H �

2140� J �1

2040�

8. Jill and Kate have $0.60. Jill saysthey have 0.6 dollar. Kate saysthey have �

35� dollar. Who is right?

F Jill H KateG Both J Neither

?

�

Decimals Greater Than 1Write the correct answer.


9. Write About It Write a rule for the pattern you used to solve Problem 7.

1. Write a decimal for the model.

3. Carol’s recipe for modeling claycalls for 1�

34� cups flour and 1�

14� cups

salt. A greater amount of whichingredient is used in this recipe?

2. Write 6�140� as a decimal.

4. The distance from Al’s school tosoccer practice is 2�

14� miles. The

distance from soccer practicehome is 1�

34� miles. If Al walks from

school to soccer practice and thenhome, how far does he walk?

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NameLESSON 19.2

5. Which decimal is equivalent to3�1

30�?

A 0.33 C 3.3

B 3.03 D 3.33

7. Jan is building a model trestlebridge. He measures from one endof the bridge to drill holes for thesupports. Here are the lengths hemeasures: 1�

34� in., 4�

14� in., 6�

34� in., 9�

14� in.,

11�34� in. Continue the pattern to

decide where he should mark thehole for the sixth support.

A 14�34� in. C 13�

34� in.

B 14�14� in. D 12�

34� in.

6. Which mixed number isequivalent to 16.11?

F 16�110� H 16�1

1010�

G 16�1,10100� J 16�11

10�

8. Kit has a digital stopwatch thatcounts seconds. He turns it on at40 seconds after 12:58 P.M. Heturns it off at 10 seconds after1:09 P.M. How many secondshave passed?

F 630 sec H 750 sec

G 670 sec J 1,030 sec

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NameLESSON 19.3

Equivalent DecimalsWrite the correct answer.


9. Write About It Explain your choice for Problem 7.

1. Write a decimal which isequivalent to 0.6.

3. Marlee picked 0.3 pounds ofblackberries. Write an equivalentdecimal for this amount.

2. Write 3�12� as a decimal.

4. Solve. 9�78� � 1�18�

5. Which pair of decimals is notequivalent?

A 0.40 and 0.4

B 0.05 and 0.50

C 0.90 and 0.9

D 0.3 and 0.3

7. Paul went to the toy store 5 timeslast month. Each time he bought4 baseball cards for $2.00 each.Which operations could be used tofind the total amount of moneyPaul spent?

A addition or multiplication

B addition or subtraction

C division or addition

D multiplication or subtraction

6. Mariah’s fish tank holds 30.5gallons of water. Which is notequivalent to this amount?

F 30.05 gallons

G 30�150� gallons

H 30.50 gallons

J 30�12� gallons

8. Koko’s test scores last year were89, 80, 81, 90, 99, 92 and 81. Whatwas her median test score?

F 81

G 89

H 90

J 92

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NameLESSON 19.4

Compare and Order DecimalsWrite the correct answer.



1. Write � , � , or � to compare thetwo decimals.

0.33 0.3

3. Of the 10 members of Justin’ssoccer team, 6 played last year.Write a fraction and a decimal forthe part of Justin’s soccer teamthat played last year.

2. Order the decimals 0.71, 0.81,0.73, 0.8, and 0.7 from least togreatest. Use the number line.

4. Krista spends 3�14� hours building a

wall unit out of oak and another4�

34� hours applying finish to it. How

many hours does she spend on thewall unit altogether?

5. Which decimal is the greatestnumber?

A 0.02 C 0.2

B 0.20 D 0.22

7. Mr. Morrel bought a package of90 picture hangers. He is hanging13 pictures which require 4hangers each. How many hangerswill he have left over?

A 38 C 48

B 40 D 52

6. Which group of decimals is orderedfrom greatest to least?

F 0.38, 0.49, 0.4, 0.39G 0.35, 0.4, 0.41, 0.44H 0.22, 0.38, 0.3, 0.4J 0.41, 0.4, 0.38, 0.3

8. Jeremy’s friend Lena names fourrandom numbers. The numbers areall decimals between 0 and 1.Which of the four decimals is least?

F 0.4 H 0.1

G 0.28 J 0.09

0.7 0.8 0.9 1.0

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NameLESSON 19.5

Text Format Sometimes the way that text is arranged on a page can helpyou see the important information. The way the informationis arranged is called text format.

A speaker is coming to speak to Bobby’s scout troop. Thespeaker has prepared some notes for his speech. Bobbylooks at the notes and uses the text format, or the way thewords are organized, to get information about the speech.

What will the speech be about?

Bobby can see from the title of the notes that the speech willbe about the most important things about camping.

1. How many categories of important things will the speakerbe talking about? What are they?

The Most Important Things about Camping

Equipment• a good tent• good cooking supplies• a place to put garbage

Safety• know how to SAFELY put out a fire• be aware of wildlife that could harm people• be aware of plants that could harm people

Skills• know how to build and light a fire• know how to put up and take down a tent• know how to tie knots

VOCABULARYtext format

2. What does the speaker probablythink is the most important piece ofequipment? How do you know?

3. What will the speaker emphasizeabout putting out a fire? How doyou know?

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NameLESSON 19.6

Relate Mixed Numbers and DecimalsWrite the correct answer.


9. Write About It Explain why you chose the answer you did for Problem 7.

1. Write a mixed number anddecimal for the shaded part.

3. A library has 10 bookshelves.Each has 10 shelves in it, all thesame size. Out of all of the shelvesin the library, 21 hold fiction.Write a decimal to show the partof the shelves that hold fiction.

2. Write a mixed number anddecimal for the shaded part.

4. Leo’s famous chocolate chipcookie recipe calls for 2�

12� cups of

flour. Leo finds he has only 1�12�

cups of flour. How much moreflour will he need to get to makethe cookies?

5. Which decimal is equivalent to 3�34�?

A 3.25 B 3.5 C 3.75 D 9.75

7. Gina’s family moves into a newhome on a 7-acre lot. The lot is ina 100-acre development. Whichdecimal shows what part of the100-acre development Gina’s newlot is?

A 0.007 C 0.7

B 0.07 D 7.00

6. Which fraction is equivalent to10.60?

F �160� G 10�1

600� H 10 �35� J 10 �65�

8. James leaves his house at 8:45 A.M.to go walking. He walks steadilyat about 4 miles an hour and getsback home at 10:15 A.M. Abouthow far has he walked?

F about 4 mi H about 6 mi

G about 5 mi J about 10 mi

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NameLESSON 20.1

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Round DecimalsWrite the correct answer.



1. Marion’s mass is 34.4 kilograms.Round her mass to the nearestkilogram.

3. Round 87.45 to the nearest tenth.

2. Compare. Write �, � , or � inthe .

6.3245 6.2345

4. Charlene’s class has 26 students. Ifeach student makes 22 flashcards,how many cards are needed?


A 47.5 C 47.6B 47.54 D 48

7. Buck collected bus fares on theLincoln Line for 2 hours onMonday. He collected $95.50 inthe first hour and $91.50 in thesecond hour. Then, he switched tothe Andrews Line and collected$41.30 for each of the 2 hours.How much money did he collectin all?A $259.30 C $274.90B $269.60 D $275.16

6. 14.23 � 9

F 14.14 H 5.00G 5.23 J 4.77

8. Jamie collected $1,254.64 from theafternoon symphony performanceand $1,986.28 from the eveningsymphony performance. Roundthe total amount of moneycollected to the nearest dollar.

F $3,242.00 H $3,240.92G $3,241.00 J $3,240.90

NameLESSON 20.2

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Estimate Sums and DifferencesWrite the correct answer.



1. Estimate the sum by rounding tothe nearest whole number.

2.41.8

� 3.7

3. Order from greatest to least.

0.59 0.32 0.412

2. Estimate the difference byrounding to the nearest wholenumber.

6.79� 2.31

4. A chemist has a beaker with 14.8liters of alcohol in it. She pours 3.9liters of it into a container. Abouthow much alcohol is left in thebeaker?

5. Which is the most reasonableestimate of the sum?

1.72� 1.93

A 4 C 2B 3 D 1

7. A song is played at a fast tempo of150 beats per minute. If the songlasts for 3 minutes 50 seconds,about how many beats are there inthe song?A 300 beatsB 400 beatsC 500 beatsD 600 beats

6. Which is the most reasonableestimate of the difference?

7.58� 2.81

F 4 H 10G 5 J 11

8. A pixel is an individual dot. Somecomputer monitors are 1,024pixels wide by 768 pixels high.About how many pixels are thereon such a computer screen?F about 8,000,000G about 800,000H about 80,000J about 8,000

�

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NameLESSON 20.3

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Add DecimalsWrite the correct answer.



1. 0.8� 0.5

3. Natasha has a handful of pennies.She counts 28 pennies. Whatdecimal part of a dollar does shehave?

2. 31.83� 40.58

4. Mr. Moore fills the gasoline tankin his car. He then uses �

14� of the

gasoline driving to his brother’shouse. What fractional part of thetank of gasoline does he have left?

5. 22.75� 31.35

A 53.00 B 53.10 C 54.00 D 54.10

7. A composer writes a symphony in4 parts. Each part is twice as longas the previous part. The secondpart lasts for 6 minutes. How longis the entire symphony?


6. 0.9� 0.7

F 1.6 G 1.16 H 1.06 J 0.16

8. Mike spends $10.90 on dinner and$7.50 on a movie. He then spends�12� of what he has left on a cab ridehome. When he gets home he has$10.80 left. How much did Mikespend on the cab ride home?F $5.40 H $21.60G $10.80 J $40.00

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NameLESSON 20.4

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Subtract DecimalsWrite the correct answer.



1. 32.45� 9.61

3. Hank catches the flu, and histemperature rises to 3.2°F abovenormal. If normal is 98.6°F, what isHank’s temperature?

2. 9.23� 6.48

4. Jenny cuts 3 lengths of molding:3�

34� inches, 3�

38� inches, and 3�1

36� inches.

Which is the shortest length shecuts?

5. 2.4� 1.5

A 1.9 B 0.99 C 0.9 D 0.09

7. Long-playing vinyl records wereusually meant to be played ata speed of 33�

13� revolutions per

minute. At this rate of speed,how many turns would a recordmake in 3 minutes?

A Less than 100B Exactly 100C More than 100D Exactly 1,000

5. 52.57� 19.39

F 34.8 G 33.18 H 33.018 J 32.18

8. At the start of the track season,Alicia’s time in the 100-meter dashwas 12.25 seconds. By the endof the season, her time droppedto 11.78 seconds. Which mostaccurately describes how Alicia’stime improved?

F It decreased almost 0.5 sec.G It decreased more than 0.5 sec.H It decreased almost 0.75 sec.J It decreased more than 0.75 sec.

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NameLESSON 20.5

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Add and Subtract DecimalsWrite the correct answer.



1. 6.7� 3.19

3. Kate prices turquoise beads at fourstores. She finds these prices forsingle beads: $0.98, $0.88, $0.95,$0.93. Order the prices from leastto most expensive.

2. 46.18� 7.2

4. Victor works 5�14� hours on Friday

and 7�34� hours on Saturday. How

much longer does he work onSaturday than on Friday?

1. 48.4� 2.05

A 32.8 C 50.45B 46.35 D 279

7. Two standard settings for laserprinters are 300 dots per inch (dpi)and 600 dots per inch (dpi). In aspace that is one inch by one inch,the 300 dpi printer prints 300 �300 dots. The 600 dpi printerprints 600 � 600 dots. How manydots are printed in the space bythe 600 dpi printer?

A 2 times as many as the 300 dpi printer

B 3 times as many as the 300 dpi printer

C 4 times as many as the 300 dpi printer

D 5 times as many as the 300 dpi printer

6. $32 � $9.85

F $9.57 H $22.00G $10.00 J $22.15

8. Leanne buys a bookshelf that hasthe lowest shelf 3�

24� in. above the

floor. The next shelf up is 12�34� in.

above the floor. Which book willstand up straight on the lowestshelf?

F a 9�34�-in.-tall book

G a 9�58�-in.-tall book

H a 9�12�-in.-tall book

J a 9�14�-in.-tall book

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NameLESSON 20.6

�Synthesize InformationWhen a problem presents a lot of information, it ishelpful to synthesize, or combine, the related facts.You can group the related facts in a chart. Some chartsmight have more than two headings. Read thefollowing problem.

Mr. Webb drove from his home to the airport. Hedrove 78.6 miles before lunch. He drove 201.7 milesafter lunch. He drove 50.4 more miles. Then herealized he had missed the airport. He turned aroundand drove 11.6 miles back down the same road to theairport. How many miles was it from Mr. Webb’shouse to the airport?

1. Synthesize the information in theproblem. Group the facts that arerelated in a chart.Complete the chart.



Synthesize the information. Show it in a chart. Solve.

Numbers to Add Numbers to Subtract

78.6� 11.6

4. Kyra donated $2.85 to the KidsCare fund. Alex donated $7.55.May donated $5.00 less than Kyraand Alex combined. How muchmoney did May donate? Howmuch did the three studentsdonate in all?

5. Susanna had $58.42. She spent$6.59 for a belt and $25.83 for apair of jeans. Then she got herallowance, which was $4.50. Howmuch money does Susanna havenow?

VOCABULARYsynthesize

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NameLESSON 21.1

�Choose the Appropriate UnitWrite the correct answer.


9. Write About It Solve Problem 8 and explain your solution.

1. Choose the most reasonable unit ofmeasure. The distance from yourtown to the state line is 37______.

3. Write the most reasonable unit ofmeasure. The distance a footballplayer carried the ball down thefield was 21 ______.

2. Order �23�, �

12�, �

14�, and �

78� from greatest to

least.

4. Add.

3.8 � 4.92

5. Add.2�

38� � 5�8

1�

A 7�47� C 7�

14�

B 7�21

� D 6�85

�

7. Which is the longestmeasurement?

A 322 in.B 322 ydC 322 ftD 322 mi

6. Which unit would be the mostreasonable one to use to measurethe amount of rain that falls inone month?

F in. G ft H yd J mi

8. A square pasture is surroundedby 12,000 feet of fencing. Whichoperation can you use to find thelength of each side?

F additionG subtractionH multiplicationJ division

?

?

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NameLESSON 21.2

�Measure Fractional PartsWrite the correct answer.


9. Write About It What are the longest and the shortestlengths that could be labeled “7 inches to the nearestinch”?

1. Estimate the length of the screw tothe nearest inch.

3. William measures the height of his2-year-old brother to see howmuch he has grown. Which unit ofmeasure should he use?

2. Measure the length of the clip tothe nearest �

14� inch.

4. An award-winning running backhas carried the football for a totalof 1,760 yards this season. Howmany miles is this?

5. Subtract. 4�78� � 3�

18�

A 1 C 1�24�

B 1�14� D 1�

34�

7. If February 29 falls on a Friday inone year, which day of the weekwill April 1 fall on in that year?

A Monday C WednesdayB Tuesday D Thursday

6. Which is the measure of the clipin Problem 2 to the nearest �

12� in.?

F 1 in. H 2 in.

G 1�12� in. J 2�

12� in.

8. Henry measured a length of woodas 7 inches to the nearest inch.Which of the following lengths couldnot be the one Henry measured?

F 6�34� in. H 7�

58� in.

G 7�38� in. J 6�

78� in.

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NameLESSON 21.3

�Algebra: Change Linear UnitsWrite the correct answer.



1. Complete.

48 in. � ft

3. Jocelyn wants to measure the sizeof her computer screen. Whichunit of measure should she use?

2. Complete.

2 mi � ft

4. Brad wants to measure the lengthof his pickup truck. Which unit ofmeasure should he use?

5. Which word makes the sentencetrue?

To change from yd to mi, you .

A add C multiplyB subtract D divide

7. The distance from Earth to theMoon is about 250,000 miles. Thedistance from Earth to the Sun isabout 400 times the distance fromEarth to the Moon. Estimate thedistance from Earth to the Sun.

A About 250,000,000 miB About 150,000,000 miC About 100,000 miD About 100,000,000 mi

6. Which measurement is equivalentto 360 in.?

F 36 ft H 10 yd

G 30 yd J 100 yd

8. What is the remainder when 482 isdivided by 7?

F 3G 6H 9J 5

?

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NameLESSON 21.4

�CapacityWrite the correct answer.



1. Complete.

4 gal � qt

3. Carol has a 2�34�-hour radio show.

There are 1�14� hours just for music.

The rest are devoted to talk. Howmany hours of Carol’s show aredevoted to talk?

2. Complete.

8 cups � pt

4. On Tuesday, Jean runs 3 miles onthe school track. Philippe runs8,000 yards. How much fartherdoes Philippe run?

??

5. Which is the greatest measurementof capacity?

A 2 gal C 2 ptB 2 qt D 2 c

7. Ray and Bob are driving 1,200miles by car. They drive at anaverage speed of 60 miles perhour. How long will the drivetake?

A 18 hrB 19 hrC 20 hrD 25 hr

6. Which measurement is equal to4 quarts?

F 2 c H 1 galG 16 pt J 32 c

8. Connie’s new car gets 32 milesper gallon of gasoline. About howmany miles can Connie drive perquart of gasoline?

F 2 miG 4 miH 8 miJ 16 mi

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NameLESSON 21.5

�WeightWrite the correct answer.



1. Choose the most reasonable unitof measure. Write oz, lb, or T.

3. Dave needs 4 cups of whippingcream for a pie. The store sellswhipping cream in 1-pintcontainers. How many pintsshould Dave buy?

2. Choose the most reasonable unitof measure. Write oz, lb, or T.

4. Lucy needs to fill up a largewashtub so she can give her GreatDane a bath. She wants to knowthe capacity of the washtub. Whatunit of measure should she use?

5. How many pounds are in 3 tons?

A 2,000 lb C 600 lbB 6,000 lb D 6,000 oz

7. Chas has 6 coins in his pocket.Which amount could not be thetotal value of his 6 coins?

A $0.10B $0.15C $0.20D $1.50

6. How many pounds are in64 ounces?

F 2 lb G 4 lb H 6 lb J 8 lb

8. A riddle asks, “Which weighsmore: a ton of bricks, or a ton offeathers?” Suppose a brick weighs1 lb. Together, 20 feathers weighabout 1 oz. About how many morefeathers than bricks would youneed to have 1 T?

F about 160 times as manyG about 200 times as manyH about 320 times as manyJ about 1,600 times as many

BUTTER

SequenceA sequence is an arrangement of one thing after another.You can use sequence clues to determine the order ofevents in a problem. Look for words such as first, last,next, then, now, before, after, and already. Read thefollowing problem.

Henry made a coat rack from a board. He placed thefirst peg 4 in. from the left end. He placed the last peg4 in. from the right end. He also placed 1 peg every 4 in. between the end pegs. The board he used wasalready cut to 3 ft long. How many pegs did he use?

1. Underline the sequence clues below. Then list each event inthe order in which it happened.



Underline the sequence clues in each problem. Solve.4. Lenore hung paintings on one

wall in the art gallery. After shemeasured the wall and found it tobe 8 yd, she hung the first picture6 ft from the left end of the wall.Then she hung 1 painting every 6ft. The last thing she did was hanga painting 6 ft from the right end ofthe wall. How many paintings didLenore hang?

5. Howard made a long banner withflags from different countries. Aftercutting out a 4-ft-long piece ofcloth for the banner, he glued thefirst flag 6 in. from the left end.Next he glued 1 flag every 6 in. Heglued the last flag 6 in. from theright end. How many flags didHoward glue onto the banner?

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NameLESSON 21.6

�

VOCABULARYsequence

Sequence Clues Order of EventsHe placed the first peg 4 in. from the left end.

He placed the last peg 4 in. from the right end.

He placed 1 peg every 4 in.

The board he used was already cut to 3 ft.

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NameLESSON 22.1

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Linear MeasureWrite the correct answer.


9. Write About It Describe how you decided whether to multiply or divide Problems 3 and 4.

1. Choose the most reasonable unitto measure the length of a baseballfield. Write cm, dm, or m.

3. Ty says that his new baby sisterweighs 128 ounces. Write hissister’s weight in pounds.

2. Choose the most reasonable unitto measure the width of acomputer disk. Write cm, dm, or m.

4. Melanie is 48 inches tall. WriteMelanie’s height in feet.

5. Which measurement is equivalentto 1 meter?A 10 cm C 100 dmB 100 cm D 1,000 dm

7. The heights of the 5 startingplayers on the basketball teamare 73 inches, 76 inches,64 inches, 69 inches, and78 inches. What is their averageheight in feet?

A 5 ft C 6 ft

B 5�12� ft D 6�

12� ft

6. Which measurement is equivalentto 15,840 feet?F 2 mi H 1,760 ydG 3 mi J 3,520 yd

8. A book with 28 chapters has anaverage of 16 pages per chapter.The book also has 12 pages inthe front and an index of 8 pages.Which expression could you use tofind the total number of pages inthe book?F 28 � (16 � 12 � 8)G 28 � (16 � 8) �12H (28 � 16) � 12 � 8J (28 � 16) � 12 � 8

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Algebra: Change Linear UnitsWrite the correct answer.


1. Write the number you wouldmultiply by to change meters todecimeters.

dm � � m

3. Sonia is 132 centimeters tall. Howmany meters tall is she?

2. Write the number that makes themeasures equivalent.

18 dm � � cm

4. Diane knows her family’s pickuptruck can carry a load of as muchas 2 tons. How many pounds is this?

?

5. Which measure is equivalent to37 decimeters?A 3.7 cm C 370 mB 370 cm D 3,700 cm

7. Pedro has one dollar more thanKate. Patti has $5 less than Kate.They have $20 in all. How muchmoney does Kate have?A $3 C $8B $5 D $10

6. Which measure is equivalent to 420 meters?F 4,200 cm H 42 dmG 42,000 cm J 420 dm

8. Jon has scores of 88, 92, 81, 98, and 86 on his math tests. What is Jon’s median score?F 81 H 89G 88 J 92


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CapacityWrite the correct answer.



1. Choose the more reasonable unitfor measuring the capacity of acoffee mug. Write mL or L.

3. Joy estimates that her drippingbathtub faucet would take only 1week to fill the bathtub. She wantsto estimate how much water thatis. Choose the most reasonableunit for measuring capacity. Writecup, quart, or gallon.

2. Choose the more reasonable unitfor measuring the capacity of apunch bowl. Write mL or L.

4. Brian is school champion in the100-meter dash. He wants to knowhow many centimeters are in 100meters. Find the answer for Brian.

5. What is the most reasonablemeasurement for the capacity of agoldfish bowl?

A 2 L C 200 mLB 20 L D 20 mL

7. Brandon opens a bottle of applejuice and drinks 8 oz of it. Hepours the same amount into a potof applesauce he is making. Hissister then drinks 4 oz of the juiceand pours a 4-oz glass for theirmother. Brandon and his fathereach drink a 4-oz glass. How manyounces of juice did they drink?

A 32 oz C 96 ozB 40 oz D 128 oz

6. What is the most reasonablemeasurement for the capacity of acar’s gasoline tank?

F 4 L H 40 mLG 40 L J 400 mL

8. What is the next number in thepattern?

12, 24, 36, 48, 60, 72,

F 68 H 192G 74 J 84

?

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MassWrite the correct answer.



1. Sandy is a star basketball player.Which is the more reasonableunit to measure his mass: 110 g or110 kg?

3. Charles is the state javelinchampion. Which is the mostreasonable unit to measure thelength of his best throw: mm, cm,m, or km?

2. Ms. Masters likes to sew dresses.Which is the more reasonable unitto measure the mass of her sewingneedle: 500 mg or 500 g?

4. Nikita finds a broken spring inthe wrist watch she is repairing.Which is the most reasonableunit to measure the length of thespring: mm, m, or km?

5. Which is the most reasonable unitto measure the mass of a pickuptruck?

A mg B g C kg D km

7. A cheer starts, “Two bits, four bits,six bits, a dollar.” If a dollar isworth 8 bits, what coin is worthtwo bits?

A nickel C quarterB dime D half-dollar

6. Which is the most reasonable unitto measure the mass of a flute?

F mg G g H kg J cm

8. Wesley needs to move 820 kg ofgrain across the river in a canoethat can carry no more than 120 kg.Wesley has a mass of 70 kg. What isthe fewest number of trips he willhave to make?

F 17 trips H 32 tripsG 18 trips J 33 trips

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Make InferencesTo make inferences means to draw conclusions based onthe given information. In order to make an inference, youmust examine all of the given information. Read thefollowing problem.

In the morning, Mary and Billy each caught one fish.Mary’s fish measured 9 decimeters and Billy’s fishmeasured 1 meter. In the afternoon, Mary caughtanother fish. Mary caught the longest fish of the day.What inference can you make about the fish thatMary caught in the afternoon?

1. Examine the information given in the problem. Then makeinferences about that information.



Make inferences to solve.

4. Stan and Tomiko raced toy cars. In the first trial, Stan’s car went 18 decimetersand Tomiko’s car went 110 centimeters. In the second trial, Stan’s car went 110centimeters and Tomiko’s car went the longest distance out of the two trials. Whatinference can you make about the second trial?

VOCABULARYmake

inferences

Information Inference

Length of Mary’s first fish is .Length of Billy’s fish is .Length of Mary’s second fish is unknown.Mary caught the longest fish.

Mary’s first fish is cm long.Billy’s fish is cm long.

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NameLESSON 23.1

Temperature: FahrenheitWrite the correct answer.



1. Find the change in temperaturefrom �2°F to �32°F.

________________________________

3. Order from least to greatest.

0°F, �2°F, �10°F, 55°F, 10°F, 2°F.

________________________________

2. Compare. Write >, < , or = forthe �.

3.12 � 3.13

________________________________

4. Write 491,637 in expanded form.


A 22.0B 22.1C 22.2D 22.3

7. The temperature dropped 15degrees after noon to 31°F. Whatwas the temperature before itdropped?

A�31°F

B�15°F

C 16°FD 46°F

6. 2.35 � 6.2

F 2.97G 8.37H 8.55J 29.7

8. The temperature was 55°F at 6 P.M.,but it got colder as it got later. By11 P.M., it was 32°F. How much didthe temperature change?

F 32°G 23°H 12°J

�10°

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NameLESSON 23.2

Temperature: CelsiusWrite the correct answer.



1. The thermometer shows the watertemperature in ºC. The airtemperature is 30ºC. What is thechange in temperature?

________________________

3. Nora finds a package of paper thatis marked “width: 8.5.” Which isthe more likely unit of measure—inch or foot?

2. The thermometer shows the noontemperature in ºC. The midnighttemperature was 6ºC. How manydegrees did the temperature risebetween midnight and noon?

________________________

4. Jonathan weighs each letter to findthe postage needed for mailing.Which unit of measure would heprobably use—ounce or pound?

0

10

20

Celsius

50

60

70

Celsius

5. Find the change in temperaturefrom 10ºF to �20ºF.

A 10ºF C 30ºFB 20ºF D 40ºF

7. Which is the most reasonableestimate for the temperature insideyour freezer?

A 30°CB 10°CC �2°CD �50°C

6. Find the elapsed time between halfpast noon and quarter to one.

F 15 min H 45 minG 30 min J 1 hr 15 min

8. Chad, Linda, Janey, and Josh are inline. Linda is right behind Josh. Theboys are between the girls. In whatorder are they?

F Josh, Linda, Chad, JaneyG Chad, Josh, Linda, JaneyH Janey, Josh, Linda, ChadJ Janey, Chad, Josh, Linda

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NameLESSON 23.3

Negative NumbersWrite the correct answer.



1. Order from least to greatest.�10, �1, 0, �10.

________________________________

3. Gertie and Pete want to build awooden fence around the backyardfor the new puppy. The cost of thefencing is $10.50 per foot, and theyneed 9 yards. How much will thefencing cost them?

2. Compare. Write <, or > for the �.�6 � �5

________________________________

4. Jim ran the length of his driveway(10 yards), walked the length of theneighbor’s sidewalk (40 feet), ranthe length of the track (200 feet),and ran home (50 feet). How manytotal feet did he run?

5. The temperature at the top of themountain was 30 degrees colderthan at the base of the mountain,where the thermometer read 5°C.What was the temperature at thetop of the mountain?

A�35°C C

�25°CB

�25°C D�30°C

7. Estimate. 3,465 � 8,787

A 12,000 C 10,000B 11,000 D 9,000

6. The Celsius temperatures were�5°C, �5°C, �1°C, 0°C, �2°C, �3°C,and �2°C during the week. Whatwas the coldest temperature?

F�5°C H 0°C

G�2°C J

�5°C

8. Which is not true?

F 2 > �7 H 4 > �9G

�3 > 9 J�2 > �5

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NameLESSON 23.4

Multiple-Meaning WordsSome problems contain words that have more than one meaning.You can use information given in the problem to determine whichmeaning of the word is being used. Read the following problem.

Mr. Wilson is an architect. He has a degree inarchitecture. He is designing an office building whosetwo wings sit at forty-five degree angles. As soon as theground temperature is about 40 degrees Fahrenheit,construction crews can start working on the officebuilding. The ground temperature is currently28 degrees Fahrenheit. How much does the groundtemperature have to rise before construction can begin?

1. Read the problem carefully to determine which word is used withmore than one meaning. Write the word and the words around it.Write the meaning of the word each way it is being used.



Read the problem carefully to determine which word or wordsmight have multiple meanings. Underline the words. Solve.

4. The construction crew will poundnails to build the wooden frame forthe office building. They ordered200 pounds of nails. Each pound ofnails has about 150 nails. About howmany nails did they order in all?

5. The electric meter for the officebuilding will be placed on the sideof the building, 200 centimeters offthe ground. How many metershigh is this?

Multiple-Meaning Word

degree

Surrounding Words

He has a degree in architecture.

Definition

a diploma earned in aparticular subject

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NameLESSON 24.1

Use a Coordinate GridWrite the correct answer.


8. Write About It What can you conclude about a point that has 0 as one of its coordinates?

1. Write the ordered pair for eachpoint on the coordinate grid.

2. Which axis on a coordinate grid isa vertical line?

3. The product of two numbers is 96.Their difference is 10. What arethe numbers?1 2 3 4 5 6 7 8 9 100

1234567

A B

C

DE

F

x-axis

y-ax

is

4. In an ordered pair, what is thefirst number called?

A x-axisB y-axisC x-coordinateD y-coordinate

6. How much greater than 949,146is 1,010,103?

A 171,249B 70,967C 60,957D 59,057

5. To locate a point at (2,3) where doyou start?

F at 3G at 2H at 1J at 0

7. Roger has 3 quarters, 2 dimes,and 5 pennies. How much moneydoes he have in all?

F $0.95G $1.00H $1.10J $1.25

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NameLESSON 24.2

Length on the Coordinate GridWrite the correct answer.



1. What is the length of the linesegment with the endpoints(23,15) and (9,15)?

3. Mrs. Ricci pays $14.77 for 2 lb offish and 3 lb of chicken. If fishcosts $3.95 a pound, what is theprice of a pound of chicken?

2. Anne’s mug holds 0.4 L. Steve’sglass holds 0.25 L. How muchmore does Anne’s mug hold thanSteve’s glass?

4. Jen and Austin are standing onan imaginary coordinate grid. Jenis at the point (2,12) and Austin isat the point (2,1). How far arethey from each other?

5. Which set of numbers is orderedfrom least to greatest?

A 1.85, 18.5, 0.185, 185B 0.039, 0.42, 1.04, 1.4C 3.27, 3.413, 3.82, 3.809D 2.35, 3.151, 4.34, 4.295

7. Solve.

4�9�2�

A 24 C 22B 23 D 21

6. Which two points have a verticaldistance between them of 5 units?

F (2,7) and (2,8)G (7,1) and (7,9)H (4,2) and (4,7) J (12,3) and (12,6)

8. What is the length of this line segment?

F 4 units H 8 unitsG 5 units J 10 units

67

54321

0 2 31 4 5 76

910

8

8 109

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NameLESSON 24.3

Use an EquationWrite the correct answer.


9. Write About It Explain how you could use the equation y � 2x � 3 to solveProblem 2.

1. Each student in Mr. Merz’s classhas 2 pens and 3 pencils. Thereare 27 students in Mr. Merz’sclass. How many pens is this?

3. How much greater than 1,191,978is 2,164,025?

2. Tracy has 3 less than 2 times thenumber of shirts Masey has. IfMasey has 6 shirts, x, how manyshirts does Tracy have, y?

4. What is y in the equation y � 3x � 2 if x is equal to 9?

5. What is y in the equation y = 19x � 22 if x is equal to 12?

A 246B 248C 250D 252

7. Which of the ordered pairs makethe equation y � (x � 3) � 7 true?

A (2,11)B (5,15)C (1,28)D (2,35)

6. Add.

$2.49�$3.57

F $5.96G $6.05H $6.06J $6.07

8. Which number is not divisibleby 9?

F 8,613G 7,524H 6,543J 5,969

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NameLESSON 24.4

Graph an EquationWrite the correct answer.


9. Write About It Explain the steps you used to graph the equation inProblem 1.

1. Graph the equation y � 2x � 1.

3. The sum of the 3 digits of an evennumber is 9. What is the numberif its tens digit is 1 more than itsones digit?

2. Graph the equation y � 3x – 2.

4. How much greater is the productof 25 and 25 than the sum of 198and 367?

5. When x � 5, what does y equal iny � 3x � 5?

A 5 C 15B 10 D 20

7. Pam studied from 1:43 P.M. to3:14 P.M. How long did she study?


6. Jeff has 9 less than 5 times thenumber of dollars that Carl has.Carl has 10 dollars. How manydollars does Jeff have?

F $40 H $84G $41 J $85

8. When x � 8, what does y equal iny � 2x � 1?

F 20 H 16G 17 J 15

1 2 3 4 5 6 7 8 9 100

123456789

1011

x-axis

y-ax

is

1 2 3 4 5 6 7 8 9 100

123456789

1011

x-axis

y-ax

is

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NameLESSON 24.5

VOCABULARYdraw

conclusions

Draw ConclusionsTo solve a problem you may need to draw conclusionsbased on two or more ideas or pieces of information.Sometimes the information you need is in a table.


Sarah wants to identify the relationshipbetween the cost of a box of a certain brandof cookies and the number of cookies in thebox. What relationship can she identify?

1. Look at the table. Draw conclusions to solve the problem.


Underline information you can use to draw conclusions about 3and 4. Solve.

Cost per box $2 $3 $4 $5 $6

Number of 16 24 32 40 48cookies

3. Suppose the numbers of cookies inthe table above were changed to10, 15, 20, 25 and 30. What rela-tionship could you identify?

5. Describe therelationshipbetween x and y.

4. Suppose the costs per box ofcookies in the table above werechanged to $0.80, $1.20, $1.60,$2.00, and $2.40. What relationshipcould you identify?

6. Describe therelationshipbetween x and y.

x 2 4 6 8 10y 4 8 12 16 20

x 10 20 30 40 50y 5 10 15 20 25

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Lines, Rays, and AnglesWrite the correct answer.


1. Which of the following terms bestdescribes the corner of a pictureframe: ray, line, angle, or linesegment?

3. Write acute, obtuse, or right todescribe the angle in Problem 1.

2. Which term does the surface ofthis sheet of paper most resemble:point, line, line segment, orplane?

4. Which term does the answerblank below most resemble: point,line, line segment, or plane?

5. Which name describes the angle?

A acute C right

B obtuse D parallel

7. How many sides are there in acircle?

A ten C three

B five D none

6. Which statement is not true aboutlines?

F They go on in both directions.

G They are straight paths ofpoints.

H They have no endpoints.

J They can be curved.

8. Ned has five coins in his pocket.Which amount cannot be the totalvalue of the coins?

F $1.05 H $0.25

G $0.29 J $0.20


A B

C

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Line RelationshipsWrite the correct answer.


1. Write the term that bestdescribes the line relationship:parallel, perpendicular, orintersecting.

3. Write acute, obtuse, or right todescribe the angle formed bythe rays in Problem 2.

2. Write the term that bestdescribes the line relationship:parallel, perpendicular, orintersecting.

4. Write rays, lines, or linesegments, to describe the figuresin Problem 1.


5. Which name describes the angle?

A acute C rightB obtuse D parallel

7. Emilio draws two parallel lines.Which statement about the lines istrue?

A They form two angles.B They form four acute angles.C They intersect.D They do not intersect.

6. Which term describes the figure?

F plane H pointG line segment J line

8. Lisa gets a quarter, a dime, and2 pennies change from a $20 bill.How much did she pay?

F $20.67G $19.73H $19.63J $19.37

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Congruent Figures and MotionWrite the correct answer.

9. Write about It Explain why you chose the answer you didin Problem 7.

1. Write congruent or not congruentto describe the two figures.

3. Write slide, flip, or turn todescribe how the figure on the leftwas moved to become the figureon the right in Problem 1 above.

2. Write congruent or not congruentto describe the two figures.

4. Kim has $25.78. Juan has twice asmuch money as Kim who hastwice as much as Mark. Howmuch money do they have in all?

5. What kind of lines always formfour right angles?

A parallel C intersectingB congruent D perpendicular

7. The word kilobyte means “onethousand bytes” of information. Akilobyte is actually 1,024 bytes ofinformation. How many morethan 1,000 bytes are actually ina kilobyte of information?

A 2 bytes C 24 bytesB 16 bytes D 1,000 bytes

6. What kind of angle does thecorner of a rectangle form?

F right H acuteG obtuse J parallel

8. Which of the following does nothave to be true about twocongruent figures?

F They have the same size.G They have the same shape.H They have the same number

of sides.J They are in the same position.

Choose the letter of the correct answer

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Symmetric FiguresWrite the correct answer.


9. Write About It Describe the method you used to test for rotationalsymmetry in Problems 1 and 2.

1. Does the figure have rotationalsymmetry? Write yes or no.

3. Maura’s bedroom rug is a 10-footby 13-foot rectangle. Her brother’sbedroom rug is a 13-foot by 10-footrectangle. Are the rugs congruent?

2. Does the figure have rotationalsymmetry? Write yes or no.

4. I am a 3-digit odd number. Mytens digit is one less than myhundreds digit but two more thanmy ones digit. The sum of mydigits is 20. Who am I?

5. What kind of angle is the cornerof this page?

A acute C rightB obtuse D straight

7. What is the difference betweenthe product of 56 and 72 and theproduct of 24 and 79?

A 1,896B 2,136C 2,246D 3,146

6. Which of these letters does nothave a line of symmetry?

F A H PG D J W

8. AB↔

and CD↔

are parallel. Which ofthe following is also true aboutthem?

F They are intersecting.G They are perpendicular.H They do not meet.J They form an angle.

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Paraphrase InformationSometimes it is helpful to paraphrase, or state again in your own words, what a problem is asking you to do.


Suppose you want to make a larger copy of the picture ofthe turtle at the right. How could you make a copy of thefigure, square by square, and make a larger picture?

1. Complete the sentence to paraphrase what the problem isasking you to do.

The problem asks me to



Paraphrase what each problem is asking you to do.Solve.

4. Suppose you want to make a smaller picture ofthe kite at the right. Use 1-cm grid paper. Thencopy the figure, square by square, to make asmaller picture.

5. Suppose you want to make a larger picture ofthe design at the right. Use 1-inch grid paper.Then copy the figure, square by square, to makea larger picture.

NameLESSON 25.5

VOCABULARYparaphrase

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NameLESSON 26.1

�Perimeter of PolygonsWrite the correct answer.



1. Write polygon or not a polygon todescribe the figure.

3. What is theperimeter ofthis polygon?

2. Name the polygon and tell howmany sides and angles it has.

4. What is the difference between781,346 and 319,528?

5. Which is the correct name for thepolygon?

A quadrilateralB pentagonC hexagonD octagon

7. Floyd sets out on an 11-mile hikeat 9:15 A.M. He walks for 165minutes and stops for 45 minutesto have lunch. At what time doeshe finish his hike?

A Noon C 12:45 P.M.B 12:15 P.M. D 1:15 P.M.

6. Keith draws a polygon that has 8angles. Which is the correct namefor the polygon?

F quadrilateral H pentagonG hexagon J octagon

8. The Mervin family took a 6-dayvacation. Each day, they drovetwice as far as they had driven theday before. If they drove 12 mileson the first day, how far did theydrive during their entire vacation?

F 384 mi H 756 miG 592 mi J 1,244 mi

3 m

3 m

6 m

2 m

2 m

4 m

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NameLESSON 26.2

�Estimate and Find PerimeterWrite the correct answer.



1. Write the perimeter.

3. The perimeter of a rectangle is42 inches. The length is 12 inches.What is the width?

2. Write the perimeter.

4. Write the product of the number ofsides of a triangle, a quadrilateral,a pentagon, a hexagon, and anoctagon.

6 cm 6 cm

6 cm6 cm

6 cm

5. Which of these has a remainderof 2?

A 70 � 8 C 55 � 6B 65 � 9 D 48 � 7

7. Gina puts on a CD at 7:35 P.M. Sheplays one half of the CD, thenpauses the player at 8:10 P.M. Howmany minutes of music are thereon the CD?


6. Which name best describes thelines formed by the two rails on astraight stretch of railroad track?

F perpendicular H intersectingG parallel J obtuse

8. Steven’s living room is L-shaped. He measures four of the walls.They measure 12 ft, 14 ft, 14 ft,and 12 ft. The perimeter of theroom is 104 ft. If the last two wallshave the same length, what is thelength of each?

F 52 ft H 22 ftG 26 ft J 20 ft

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NameLESSON 26.3

�Estimate and Find AreaWrite the correct answer.


9. Write About It Explain how you found the area in Problem 7.

1. Write the area of the rectangle.

3. What is the perimeter of a gardenthat has sides that measure 36 ft,18 ft, 28 ft, 19 ft, and 17 ft?

2. Write the area of the rectangle.

4. Name the solid figure that has onesquare face and four triangularfaces.

6 ft

9 ft

5 cm

7 cm

5. Which plane figure has more thansix angles?

A quadrilateralB pentagonC hexagonD octagon

7. Rhonda drew this diagram of herkitchen. What is the area of thekitchen floor?

A 24 sq ftB 30 sq ftC 42 sq ftD 48 sq ft

6. The perimeter of a square is 24feet. What is its area?

F 12 sq ftG 24 sq ftH 36 sq ft J 48 sq ft

8. How many four-digit numbers canyou make using the digits 1, 2, 3,and 4 without repeating any of thedigits in the same number?

F 10 numbersG 12 numbersH 24 numbersJ 28 numbers

5 ft8 ft

3 ft

4 ft

6 ft

2 ft

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NameLESSON 26.4

�Relate Area and PerimeterWrite the correct answer.


9. Write About It What strategy did you use to solve Problem 8? Explain.

1. Write the perimeter and the areaof the figure.

3. Nadia’s parents are carpeting theirfamily room. The room is arectangle that measures 6 yardsby 5 yards. How many squareyards of carpeting do they need?

2. Which two figures have the samearea but different perimeters?

4. Pete walks to the intersection oftwo roads. He notices that thecorner he is standing on is a rightangle. What type of intersectinglines do the roads form?

a

b

c

d

5. Which of these letters is notformed entirely of line segments?

A A B X C Y D R

7. The area of a rectangle is 36 sq in.Which of these is not a possibleperimeter?

A 40 in. C 26 in.B 36 in. D 24 in.

6. Which figure is not a polygon?

F triangle H hexagonG square J circle

8. Les is cutting polygons out ofpaper. He cuts the four cornersoff of a square. What polygon didhe make?

F pentagon H hexagonG octagon J triangle

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NameLESSON 26.5

�

1. Area = 300 sq in.

Length = 20 in.

Width = � in.

3. The perimeter of Jennica’srectangular house is 78 yards andthe length of the house is 22 yards.What is the width of the house?

2. ��

4. The length of Kerim’s book cover is8 inches and the area of the bookcover is 40 inches. What is thewidth of the book?

�Relate Formulas and RulesWrite the correct answer.


5. James has a TV screen with oneside that is 24 centimeters wide.The perimeter of his TV is 104centimeters. What is the otherdimension of his TV?

A 36 cm C 28 cm

B 30 cm D 26 cm

7. Salem likes to run. He ran 2 km onMon., 2 km on Tue., 3 km on Wed.,5 km on Thur., and 4 km on Fri.What is the median distance thathe ran during this week?

A 2 km C 4 km

B 3 km D 5 km

6. Katie has a $5 bill. A pack ofbaseball cards costs $1.55. Howmuch change should Katie get ifshe buys 2 packs of baseball cards?

F $3.45 H $2.45

G $3.05 J $1.90

8. Molly keeps her hamsters in a boxthat has a bottom with an area of153 square inches. The width is 9inches. What is the rectangularlength of the bottom of the box?

F 17 in. H 12 in.

G 16 in. J 9 in.

9. Write About It How did you find the median in Problem 7?

4 124

CompareSometimes it is helpful to compare and contrastinformation when you are solving a problem. When youcompare and contrast, you identify ways that items arealike and ways they are different.


Janine has cut different size pieces offabric to make pillowcases. Thesecond piece of fabric in each pair islarger than the first. She wants toknow how the perimeters are related.How do the perimeters change?

1. Compare and contrast each pair offabrics. Complete the chart.

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NameLESSON 26.6


Use a chart to compare and contrast the perimeters in each problem. Solve.

Fabric Alike Different

A and B

C and D

E and F

3. Table A has a length of 6 feet anda width of 4 feet. Table B is 2 feetlonger and 2 feet wider. How doesthe increase in length and widthaffect the perimeter?

4. Picture A has a length of 8 feetand a width of 4 feet. Picture B ishalf as wide and half as long. Howdoes the decrease in length andwidth affect the perimeter?

3 ft 3 ft

4 ft 4 ft

4 ft

2 ft

2 ft

3 ft

3 ft

5 ft 5 ft

1 ftA B

DC

E F

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Name

�

LESSON 27.1

Faces, Edges, and VerticesWrite the correct answer.


1. Write the names of the planefigures that are faces of the solidfigure.

3. Name a solid figure that has 8vertices.

2. What solid figure can you see inthe drawing?

4. Write the names of the faces andthe number of each kind of faceon a triangular pyramid.

5. Which figure has the fewestfaces?

A cubeB triangular pyramidC rectangular prismD square pyramid

7. A football team wins a nationalchampionship and 43,180 peopleare expected to attend thecelebration. The arena holds only22,520 people. About how manypeople will have to be turnedaway?

A About 32,000 C About 18,000

B About 20,000 D About 11,000

6. Neal challenges Lynn to name asolid figure that has no edges.Lynn names one. Which figuredoes she name?

F cube H cylinderG cone J sphere

8. Karen decorated picture frames.She put 6 flowers on each of 5frames. She put 4 flowers on eachof 3 frames. How many flowersdid she use?

F 42 H 29

G 35 J 18


TOMATOSOUP

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�

1. What solid figure model does thenet below make?

3. How many squares will the net ofthis solid figure have?

2. Valerie needs to estimate the costof her bill. Her bill includes $3.56,$1.35, $3.67, and $7.15. Roundeach price to the nearest dollarthen add.

4. What fraction of the circle isshaded in the picture shown?

Patterns for Solid FiguresWrite the correct answer.


9. Write About It How did you find the area in Problem 8?

5. What solid figure model does thisnet make?

A cube B rectangular prismC coneD square pyramid

7. What is the perimeterof the figure below?

A 35 cmC 28 cmB 31 cmD 27 cm

6. What solid figure does this netmake?

F triangular prismG triangular pyramidH cubeJ cylinder

8. What is the area of the figurebelow?

F 48 sq in. H 16 sq in.G 32 sq in. J 9 sq in.

4 cm

4 cm

3 cm

2 cm

2 cm

7 cm

5 cm

4 cm

4 cm

12 in.

4 in.

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Estimate and Find Volume of PrismsWrite the correct answer.



1. What is the volume of the solidfigure shown below?

3. 683� 23

2. What is the volume of the cubeshown below?

4. The area of a rectangle is 432 square meters and the widthis 9 meters. What is the length ofthe rectangle?

5. The sum of the number of faces,edges, and vertices on a figure is14. What is the figure?

A rectangular prism B triangular prismC triangular pyramidD square pyramid

7. Find the length of the unknownside if the perimeter of thetriangle below is 56 meters.

A 14 m C 35 mB 16 m D 96 m

6. George has a box that is 3 feetwide, 4 feet long, and 1 foot high.What is the volume of his box?

F 12 cubic feetG 12 square feetH 8 cubic feetJ 4 square feet

8. Jamie’s basement is 13 yardslong, 12 yards wide, and 3 yardshigh. What is the volume of herbasement?

F 28 cubic yd G 39 cubic ydH 468 cubic ydJ 486 cubic yd

19 m

21 m

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Choose Relevant InformationSometimes a word problem contains information that may not help you solve the problem. You must decide which information is relevant, or needed to solve the problem. Read the following problem.

Antonia is going to travel 2,500 miles. She will be gone 10 days. She has asuitcase that is 36 inches long, 18 inches wide, and 20 inches deep. What isthe volume of her suitcase?

1. Read each fact from the problem.Write whether the fact is relevantor not relevant to solve theproblem.

a. Antonia is going to travel 2,500 miles.

b. Antonia will be gone 10 days.

c. She has a suitcase that is 36 inches long, 18 inches wide, and 20 inches deep.



4. Lauren dug a hole that was 4 feetdeep, 5 feet wide, and 6 feet long.She buried a box in that hole. Thebox was 2 feet by 2 feet by 3 feet.What was the volume of the boxLauren buried?

5. Rocky has a box that has a volumeof 36 cubic inches. The width ofthe box is 4 inches. The height of the box is 3 inches. He has 3 crickets and one 7-inch snake in his box. What is the length ofthe box?

Draw a line through the information that is not relevant. Solve.

VOCABULARYrelevant

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Turns and DegreesWrite the correct answer.



1. Tell whether the hour hand of aclock has been turned 90˚, 180˚,270˚, or 360˚ when it is 3:00.

3. Mike is in the kitchen icing acake. The cake is 12 inches long,8 inches wide, and 2 inches high.What is the volume of the cake?

2. Jimmy makes a �34� turn in his car.

How many degrees did he turn?

4. Beth is doing her homework. Herworksheet is 8 inches wide and11 inches long. What is the area ofher worksheet?

5. An airplane flew 8 hours to NewYork, 9 hours to Los Angeles, andthen 4 hours to Cincinnati. Howmany hours did the airplane fly?

A 288 hoursB 22 hoursC 21 hoursD 20 hours

7. Into how many 20° angles can acircle be divided without anyoverlapping?

A 16B 18C 21D 360

6. 5,422 � 67

F 324,657G 353,128H 363,274J 373,274

8. Into how many 45˚ angles can acircle be divided without anyoverlapping?

F 2G 4H 6 J 8

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Measure AnglesWrite the correct answer.


9. Write About It How do you use a protractor to find the measure of the angle

in Problem 2?

1. Measure the anglewith a protractor.

3. Name the solidfigure shown.

2. Measure the anglewith a protractor.

4. Sondra had $2.78 in the bank.Three weeks later she had 4 timesthis amount. How much moneydid she have then?

5. Carol needs 21 square feet ofwallpaper and Sarah needs53 square feet of wallpaper. Howmuch wallpaper do they needin all?

A 76 sq ft C 74 sq ftB 75 sq ft D 73 sq ft

7. Which bestdescribes thisangle?

A greater than 90°B less than 90°C 90°D 180°

6. Which best describesthis angle?F greater than 90°G less than 90°H 90°J 180°

8. How many degrees are in a�34� turn?

F 90°G 180°H 270°J 360°

A

B C

A

B C

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CirclesWrite the correct answer.


9. Write About It Explain how you found the diameter in Problem 3?

1. The diameter of one circle is 2 feetlonger than the diameter ofanother circle. Together thediameters equal 20 feet. How longis each diameter?

3. If the radius of a circle is 38centimeters, what is the length ofits diameter?

2. If Andy can run 6 miles in an hour,how many miles can he run in 10minutes?

4. Suu Kim has 30 math problems todo for homework. If it takes Suu 1hour to do 15 problems, how longwill it take her to do all of hermath homework?

5. Round 142,456 to the nearesthundred.

A 142,000B 142,400C 142,460D 142,500

7. Which best describes AB in thepicture below?

A radiusB rayC diameterD chord

6. What is the radius of a circle witha diameter of 92 inches?

F 45 inchesG 46 inchesH 184 inchesJ 186 inches

8. How many degrees are in a�14� turn?

F 90°G 180°H 270°J 360°

A B

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CircumferenceWrite the correct answer.


9. Write About It How did you find the circumference in Problem 2?

1. A triangle has a perimeter of 49yards. One side has a length of 21yards and another side has alength of 10 yards. What is thelength of the third side?

3. 3,257 � 45

2. Estimate the circumference of acircle with a radius of 9 cm.

4. Estimate thecircumference ofthe circle shownat the right.

5. Which of the solids below has atriangular face?

A cube B rectangular prismC cylinder D triangular pyramid

7. What is the perimeter of arectangle with a length of 26inches and a width of 14 inches?

A 82 in.B 80 in.C 78 in.D 76 in.

6. Estimate the diameter of a circlewhose circumference is about12 meters long.

F about 1 m H about 4 mG about 2 m J about 6 m

8. Estimate the circumference of acircle whose diameter is256 centimeters long.

F 798 cmG 792 cmH 791 cmJ 768 cm

12 mi

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Classify TrianglesWrite the correct answer.


9. Write About It How did you choose your answer to Problem 8?

1. How many congruent sides does ascalene triangle have?

3. Matt has a sign in the shape of atriangle. The sign has 2 sides thatare congruent. Classify the shapeof Matt’s sign as isosceles, scalene,or equilateral.

2. What is thevolume of the solidfigure shown atthe right?

4. Write twelve thousand, threehundred ninety-four in expandedform.

5. A pack of bubble gum costs $0.53.If Patrick buys 9 packs of bubblegum, how much money will heneed?

A $4.75 C $4.77B $4.76 D $4.78

7. How many congruent sides mustan isosceles triangle have?

A 0B 2C 3D 4

6. What is the perimeter of anoctagon with sides that measure3 feet, 6 feet, 1 foot, 2 feet, 10 feet,8 feet, 4 feet, and 12 feet?

F 45 ft H 47 ftG 46 ft J 48 ft

8. The perimeter of an equilateraltriangle is 36 meters. What are thelengths of the sides of thistriangle?

F 10 m, 10 m, 16 mG 12 m, 12 m, 12 mH 11 m, 11 m, 14 m J 8 m, 8 m, 20 m

21 m 12 m

18 m

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�Classify QuadrilateralsWrite the correct answer.


1. This quadrilateral has only 1 pairof parallel sides. It has no rightangles. What quadrilateral is it?

3. Harold notices that the sign,“RoadSlippery When Wet”, has 5 angles.What kind of polygon is the sign?

2. Name the quadrilateral shown below.

4. Pies are usually sliced from thecenter out to the edge. What partof a circle does such a cut make?

5. Which of the kinds of lines andangles are not in the figure below?

A parallel lines B right anglesC perpendicular lines D acute angles

7. Which solid figure could youmake by cutting out and foldingthe net in Problem 5?

A square pyramidB cubeC rectangular prismD triangular prism

6. Bart walks 12 dogs that belong tohis neighbors to make extramoney. He takes 2 walks each daywith each dog. How many walksdoes he take in a week?

F 124 walks

G 148 walks

H 168 walks

J 180 walks

8. Which of the following is a goodestimate for the product?

13 � 289

F 300G 2,000H 3,000J 30,000

9. Write About It Explain why this statement is true: All squares arerectangles but not all rectangles are squares.

Use Graphic Aids

Using graphic aids such as a graph, table, or diagram can help you see relationships in a problem.Read the following problem.

Six groups are going on a tour. The tableat the right gives the group names and thenumber of people in each group. The tourguide needs to divide each group into smaller groups of either 3 or 5. The tour guide made this Venn diagram:

1. Answer each question about the Venn diagram.

a. What does each label tell you?

b. Are there any groups that belong in both circles? Explain.

Groups that can be divided into groups of 5

Groups that can be divided into groups of 3

A CE

BD F

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NameLESSON 28.7


Use a Venn diagram to help you solve each problem.

Tour GroupsGroup Name A B C D E F

Number 24 25 33 20 27 35

2. Sort these numbers into thosethat are Divisible by 4 and NotDivisible by 4.

2, 3, 4, 6, 8, 10, 12

3. Sort these numbers into thosethat are Divisible by 2 andDivisible by 3.

2, 3, 4, 8, 9, 10, 14, 15, 20, 21,22, 26, 27, 28

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LESSON 29.1

Record OutcomesWrite the correct answer.


9. Write About It Explain how you got your answer forProblem 8.

1. How many possible outcomes arethere for tossing a coin andtossing a cube labeled 1 to 6?

3. Write �, �, or � in the .

10 � (4 � 2) 3 � (6 � 2)

2. Donna and Alex toss a 2-colorcounter colored yellow and red,and spin the pointer on a spinnerlabeled 1, 2, 3, and 4. List thepossible outcomes of thisexperiment.

4. Find the value of the variable in

11 � n � 121

5. How many possible outcomes arethere when you toss a coin andspin the pointer on a spinner with3 colors?

A 4 C 12B 6 D 18

7. On Monday, Russell and hisgrandfather gathered 16 eggs; onTuesday, 21 eggs; on Wednesday,27 eggs and on Thursday, 12 eggs.What is the average number ofeggs they gathered?

A 27 eggs C 17 eggsB 19 eggs D 12 eggs

6. 253,647 � 36,988 � ■

F 216,649 H 216,699G 216,659 J 226,679

8. Thomas tossed a coin and spunthe pointer on a spinner with 4colors (blue, green, red, andyellow). How many differentoutcomes are there?

F 6 H 9G 8 J 12

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LESSON 29.2

Tree DiagramsWrite the correct answer.


1. Maria is training for a triathlon.One day, she ran 10.3 miles,swam 4.2 miles and biked 19.6miles. How much distance didshe cover altogether?

3. Hector is packing for a trip. Hepacks 4 shirts and 5 pairs ofshorts. How many differentoutfits can he make?

2. Nina has a choice of 4 differentsandwich spreads (tuna salad,chicken salad, ham salad, andegg salad) along with 3 types ofbreads (white, whole wheat,and rye). How many differentsandwiches could she make?

4. A locker is 14 inches deep, 9 inches wide and 34 inches tall.What is the volume of the locker?

5. Find the number of clothingchoices:

Shoes: black, brown, graySocks: black, brown, beige

A 18 C 9B 12 D 6

7. How many different outfits canKatrina make from these choices?

Sweaters: blue, green, tan, whiteSlacks: navy, black, brown

A 6 C 12B 9 D 18

6. Write six million seven hundredfifty-three thousand, one hundredforty-four in standard form.

F 735,144G 6,753,144H 7,653,144J 7,735,134

8. Ryan’s garden measures 10 feetby 8 feet. He wants to put a smallfence around the garden to keepanimals out. How much fencingwill he need?

F 18 feet H 80 feetG 36 feet J 98 feet

9. Write About It Explain how you determined the numberof outfits in Problem 7.

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LESSON 29.3

Classify and CategorizeWhen a problem involves a great deal of information, it ishelpful to classify and categorize the information.

To classify information means to group togetherinformation that is related.

To categorize information means to put a label on thosegroups.

The Garcias are building a new house. They can choose among tan, blue,gray, and white for the color of the siding. The shutters can be eitherblack, green, or red. They can also choose siding or shutters in maroon.The trim can be either white or cream.

Use a table to help classify and categorize the information. Fill in the missinginformation.

1. Name 2 choices of siding, shutters, and trim.

2. Teri is decorating cakes. Shemakes green icing and white rosesand buys yellow and blue icingand pink and red roses. How manydifferent ways can Teri decoratea cake?

3. The parents are having an icecream sundae party. Mrs. Wongbrings vanilla and chocolate icecream and caramel topping. Mr.Petty brings strawberry ice creamand fudge topping. How manydifferent sundaes can be made?

Classify and categorize to solve.

SIDING TRIM

tan black white

green

maroon

maroon

← Categories

Classify, or grouptogether, information thatis related.

VOCABULARYclassify andcategorize

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Predict Outcomes of ExperimentsWrite the correct answer.


9. Write About It Describe how you solved Problem 7.

1. Write likely or unlikely to describelanding on blue when spinningthe pointer on a spinner that has4 equal sections colored blue,yellow, red, and green.

3. List all the possible outcomes oftossing a coin and a cube labeled1–6.

2. Write likely, unlikely, or equallylikely to describe tossing a 3 or a5 on a number cube labeled 1–6.

4. Which type of graph would bebest to show the number ofchildren in each of the houses inyour neighborhood?

5. If you spin the pointer 20 times,on which number is it most likelyto stop?

A 5B 10C 15D 20

7. Toni is 5 years older than Fran.Fran is twice as old as AnnMarie. Ann Marie is 5 years old.How old is Toni?

A 15 yr C 8 yrB 10 yr D 6 yr

6. Which type of graph would bebest to show how much you havegrown over the past five years?

F line graphG line plotH bar graphJ stem-and-leaf plot

8. If you toss a number cube labeled1–6, how likely is it that you willtoss a composite number?

F certain H unlikelyG likely J impossible

5 20

10

15

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LESSON 30.1

Probability as a FractionWrite the correct answer.


1. Write a fraction for the probabilityof the pointer on this spinnerstopping on an odd number.

3. How many different outfits canbe made with 4 shirts and 2 pairsof pants?

2. Write a fraction for theprobability of the pointer on thespinner in Problem 1 stopping onan even number.

4. Find the area and perimeter ofthe rectangle.

5. Which fraction shows theprobability of getting a 7 whenyou toss a cube labeled 1–6?

A �06� C �

16�

B �17� D �

76�

7. Violette has an appointment inthe city at 3:00 P.M. To get there,she takes a train and then asubway. The subway ride willtake 20 minutes. The train ridewill take 50 minutes. Which trainshould she take if she wants toget to her appointment early?

A the 1:25 P.M. C the 2:05 P.M.B the 1:55 P.M. D the 11:25 P.M.

6. Which fraction shows theprobability of getting an oddnumber when you toss a cubelabeled 1–6?

F �13� H ��

12�

G �26� J �

56�

8. Write About It Explain how youchose your answer for Problem 5.


12 in.

3 in.

5 34

1 2

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LESSON 30.2

More About ProbabilityWrite the correct answer.


1. n � 6 � 12

3. Alex has a spinner with 5 equalparts labeled 1, 2, 3, 4, and 5.After 10 spins, the pointer hadstopped on 3 four times. Based onthe experiment, write theprobability of spinning a 3.

2. Taylor is going to pull a letterfrom the alphabet out of a bag ofcards. What is the probability thatthe letter will be a vowel?

4. Lelah and 12 other children writetheir names on pieces of paperand put them in a hat. If Jon pullsa name out of the hat, what is theprobability that Lelah’s name willbe pulled?

5. Tina has a bag of marbles with 6 red, 3 green, and 4 yellowmarbles. She pulls a marble fromthe bag without looking at it.What is the mathematicalprobability of pulling a redmarble from the bag?

A �162� C ��1

43�

B �163� D �1

33�

7. Tyree tossed a coin 100 times andgot 70 heads. How does herprobability compare to themathematical probability?

A It is less. C They are equal.B It is more. D can’t tell

6. Vivian has a spinner with 8 equalsections. Three of the sections arered and 2 of the sections aregreen. Blue, yellow, and orangeeach have one section. What isthe probability of spinning green?

F �12� H �

14�

G �38� J �

18�

8. Which is a reasonable outcomefor the number of heads if a coinis tossed 300 times?

F 100 H 200G 157 J 270

9. Write About It Explain your answer to Problem 7.

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LESSON 30.3

1. Is the spinner fair? Explain why itis or is not.

3. Write a fraction for theprobability of spinning a 5 in Problem 1.

2. Is the spinner fair? Explain why itis or is not.

4. Write a fraction for theprobability of the pointerstopping on a square or a trianglein Problem 2.

Test for FairnessWrite the correct answer.


9. Write About It Describe the steps you took to solveProblem 6.

5. What is the median score in thestem-and-leaf plot?

Chia’s Science Quiz Scores

Stem Leaves7 5 5 7 8 98 1 3 3 5 8 99 0 2 2 4 5 9 9 9

A 99 C 83B 88 D 75

7. A large carnival spinner isnumbered 1–36. Which are youleast likely to spin?

A even number C multiple of 2B odd number D multiple of 9

6. Wu leaves on a train ride that isscheduled to take 26 hours. Thetrain stalls for 6 hours, and isdelayed at one stop another 4 hours. How long does Wuspend on the train?

F 32 hr H 46 hrG 36 hr J 50 hr

8. What is the mode on the stem-and-leaf plot in Problem 5?

F 99 H 87G 88 J 25

4 4

3 31 1

5 5

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Draw Conclusions

When you examine the evidence and use what youalready know to solve a problem, you are drawingconclusions. Read the following problem.

Jamie made a spinner divided into 6 parts. One half ofthe spinner is blue, yellow, and red. The blue andyellow parts are equal. The red part is �14� of the spinner.The other half of the spinner is blue, yellow, andgreen. The blue and yellow parts are equal. Togetherthey are �14� of the entire spinner. Is the spinner fair?Explain.

1. Under Examine the Evidence, write two more facts that are given. Thenwrite two more helpful facts that you already know.



Draw conclusions to solve.4. A rectangular gameboard is divided

into 5 parts. The red part is �14� of the

rectangle. The blue part is also �14� of

the rectangle. The remainder of theboard is divided into equal-sizedyellow, green, and white parts. Isthe gameboard fair? Explain.

5. Allen’s spinner is divided into 8 parts. One-fourth of the spinneris white and �

14� is black. There are

2 yellow parts and 2 red parts ofequal size. Is the spinner fair?Explain.

EXAMINE THE EVIDENCE USE WHAT YOU ALREADY KNOW

The red part of the first half is �14

�. Four fourths make one whole.

VOCABULARYdrawing

conclusions

Y BYB

R G

�

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