· unit 1: understand numbers and operations chapter 1: place value and number sense 1.1 just down...

ChallengeWorkbook

P U P I L E D I T I O NGrade 4

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Unit 1: UNDERSTAND NUMBERS AND OPERATIONS

Chapter 1: Place Value and Number Sense1.1 Just Down the Road a Bit . . . . . . . . . 11.2 Broken Records . . . . . . . . . . . . . . . . . . 21.3 Spin That Number . . . . . . . . . . . . . . . 31.4 Sun to Planet . . . . . . . . . . . . . . . . . . . . 41.5 The Complete Picture . . . . . . . . . . . . 5

Chapter 2: Compare and Order Numbers2.1 The Number Machine . . . . . . . . . . . . 62.2 In Between . . . . . . . . . . . . . . . . . . . . . 72.3 Miles to Go . . . . . . . . . . . . . . . . . . . . . 82.4 Basketball Bonanza . . . . . . . . . . . . . . 9

Chapter 3: Add and Subtract Greater Numbers3.1 Estimating Populations . . . . . . . . . . . 103.2 Number Pyramids . . . . . . . . . . . . . . . 113.3 Money Math . . . . . . . . . . . . . . . . . . . . 123.4 Daily Cross-Number Puzzle . . . . . . . 133.5 My Balance! . . . . . . . . . . . . . . . . . . . . 143.6 Popular Hot Spots . . . . . . . . . . . . . . . 15

Chapter 4: Algebra: Use Addition and Subtraction4.1 Par for the Course . . . . . . . . . . . . . . . 164.2 Parentheses Fun . . . . . . . . . . . . . . . . . 174.3 Whose Number is Closer to 10? . . . 184.4 Another Look at Variables . . . . . . . . 194.5 Find a Rule . . . . . . . . . . . . . . . . . . . . . 204.6 Balance It . . . . . . . . . . . . . . . . . . . . . . . 214.7 Deciphering the King’s Numbers . . . 22

Unit 2: DATA, GRAPHING, AND TIME

Chapter 5: Collect and Organize Data5.1 Find the Missing Data . . . . . . . . . . . . 235.2 Find the Median and the Mode . . . 245.3 Line Plot . . . . . . . . . . . . . . . . . . . . . . . . 255.4 How Many Marbles in a Jar? . . . . . . 265.5 Did You Know? . . . . . . . . . . . . . . . . . . 275.6 Use Graphic Aids . . . . . . . . . . . . . . . . 28

Chapter 6: Analyze and Graph Data6.1 Strike Up the Band . . . . . . . . . . . . . . 296.2 Temperature Patterns . . . . . . . . . . . . 306.3 Find the Missing Scales . . . . . . . . . . . 316.4 Data Display . . . . . . . . . . . . . . . . . . . . 326.5 What’s the Reason? . . . . . . . . . . . . . . 33

Chapter 7: Understand Time7.1 Stop That Watch! . . . . . . . . . . . . . . . . 347.2 What Time Is It? . . . . . . . . . . . . . . . . . 357.3 Replace the Batteries . . . . . . . . . . . . 367.4 Trina’s Tuesday . . . . . . . . . . . . . . . . . . 377.5 Hatching Eggs . . . . . . . . . . . . . . . . . . . 38

Unit 3: MULTIPLICATION ANDDIVISION FACTS

Chapter 8: Practice Multiplication andDivision Facts8.1 Fact Family Bingo . . . . . . . . . . . . . . . . 398.2 Math Machinery . . . . . . . . . . . . . . . . . 408.3 Fingers and Factors . . . . . . . . . . . . . . 418.4 Hand-y Multiplication . . . . . . . . . . . 428.5 Up, Down, or Diagonal . . . . . . . . . . . 438.6 Birthday Greetings . . . . . . . . . . . . . . . 44

CONTENTS

Chapter 9: Algebra: Use Multiplicationand Division Facts9.1 Parentheses Puzzles . . . . . . . . . . . . . . 459.2 What’s the Problem? . . . . . . . . . . . . . 469.3 Keep It Equal . . . . . . . . . . . . . . . . . . . . 479.4 Variable Grab Bag . . . . . . . . . . . . . . . . 489.5 Say It Again, Sam . . . . . . . . . . . . . . . . 499.6 Play by the Rules . . . . . . . . . . . . . . . . 509.7 Flying Around . . . . . . . . . . . . . . . . . . . 51

Unit 4: MULTIPLY BY 1- AND 2-DIGITNUMBERS

Chapter 10: Multiply by 1-Digit Numbers10.1 The Powers That Be . . . . . . . . . . . . . 5210.2 About the Same . . . . . . . . . . . . . . . . 5310.3 Doubling and Halving . . . . . . . . . . . 5410.4 Multiply 3-Digit Numbers . . . . . . . . 5510.5 Napier’s Rods . . . . . . . . . . . . . . . . . . 5610.6 Comparison Shopping . . . . . . . . . . . 57

Chapter 11: Understand Multiplication11.1 Moving Day . . . . . . . . . . . . . . . . . . . . 5811.2 Multiply Wheels . . . . . . . . . . . . . . . . 5911.3 Target Practice . . . . . . . . . . . . . . . . . 6011.4 Cross-Number Puzzle . . . . . . . . . . . 6111.5 Use the Word! . . . . . . . . . . . . . . . . . 62

Chapter 12: Multiply by 2-Digit Numbers12.1 Digit Detective . . . . . . . . . . . . . . . . . 6312.2 The Bigger, the Better . . . . . . . . . . . 6412.3 Lattice Multiplication . . . . . . . . . . . 6512.4 Doubling Tales . . . . . . . . . . . . . . . . . 6612.5 Letter Go! . . . . . . . . . . . . . . . . . . . . . 67

Unit 5: DIVIDE BY 1-AND 2-DIGITDIVISORS

Chapter 13: Understand Division13.1 Number Riddles . . . . . . . . . . . . . . . . 6813.2 Cookie Coordinating . . . . . . . . . . . . 69

13.3 Remainders Game . . . . . . . . . . . . . . 7013.4 Grouping Possibilities . . . . . . . . . . . 7113.5 Riddle-jam . . . . . . . . . . . . . . . . . . . . . 7213.6 What’s the Problem? . . . . . . . . . . . . 73

Chapter 14: Divide by 1-Digit Divisors14.1 Break the Code . . . . . . . . . . . . . . . . . 7414.2 Remainders Game . . . . . . . . . . . . . . 7514.3 Super Checker! . . . . . . . . . . . . . . . . . 7614.4 Create a Problem . . . . . . . . . . . . . . . 7714.5 Diagram Division . . . . . . . . . . . . . . . 7814.6 Find the Missing Scores . . . . . . . . . 79

Chapter 15: Divide by 2-Digit Divisors15.1 Cookie Giveaway . . . . . . . . . . . . . . . 8015.2 Puzzled . . . . . . . . . . . . . . . . . . . . . . . . 8115.3 Evenly Divided . . . . . . . . . . . . . . . . . 8215.4 Division Cipher . . . . . . . . . . . . . . . . . 8315.5 What’s for Lunch? . . . . . . . . . . . . . . . 84

Chapter 16: Patterns with Factors and Multiples16.1 Birthday Party Math . . . . . . . . . . . . 8516.2 Shipping Basketballs . . . . . . . . . . . . 8616.3 Number Pyramids . . . . . . . . . . . . . . . 8716.4 Something in Common . . . . . . . . . . 8816.5 Pascal’s Triangle . . . . . . . . . . . . . . . . 89

Unit 6: FRACTIONS AND DECIMALS

Chapter 17: Understand Fractions17.1 A Fraction of a Message . . . . . . . . . 9017.2 Equivalent Fraction Bingo! . . . . . . . 9117.3 Colorful Fractions . . . . . . . . . . . . . . 9217.4 Estimating Fractional Parts . . . . . . . 9317.5 Language Exploration . . . . . . . . . . . 9417.6 A Mixed-Number Challenge . . . . . 95

Chapter 18: Add and Subtract Fractionsand Mixed Numbers18.1 Amazing Maze . . . . . . . . . . . . . . . . . 9618.2 What’s Left? . . . . . . . . . . . . . . . . . . . . 9718.3 All Mixed Up! . . . . . . . . . . . . . . . . . . 98

18.4 What Breed Is Each Dog? . . . . . . . . 9918.5 Total Cost . . . . . . . . . . . . . . . . . . . . . 10018.6 Cut Up! . . . . . . . . . . . . . . . . . . . . . . . 101

Chapter 19: Understand Decimals19.1 Riddlegram! . . . . . . . . . . . . . . . . . . . 10219.2 Decimal Drift . . . . . . . . . . . . . . . . . . 10319.3 Designing with Decimals . . . . . . . . 10419.4 First-Second-Third . . . . . . . . . . . . . 10519.5 Money Combos . . . . . . . . . . . . . . . . 10619.6 Missing Number

Mystery . . . . . . . . . . . . . . . . . . . . . . . 107

Chapter 20: Add and Subtract Decimals20.1 Super (Market) Estimations . . . . . . 10820.2Shop Till You Drop! . . . . . . . . . . . . 10920.3 Play Ball . . . . . . . . . . . . . . . . . . . . . . . 11020.4Amazing Mazes . . . . . . . . . . . . . . . . 11120.5 Addition and Subtraction

Puzzles . . . . . . . . . . . . . . . . . . . . . . . . 11220.6Think About It . . . . . . . . . . . . . . . . . 113

Unit 7: MEASUREMENT, ALGEBRA,AND GRAPHING

Chapter 21: Customary Measurement21.1 Pathfinder . . . . . . . . . . . . . . . . . . . . . 11421.2 Biking Adventure . . . . . . . . . . . . . . . 11521.3 Cap This! . . . . . . . . . . . . . . . . . . . . . . 11621.4 Half Full or Half

Empty? . . . . . . . . . . . . . . . . . . . . . . . 11721.5 Which Weight? . . . . . . . . . . . . . . . . 11821.6 Atlas Stones . . . . . . . . . . . . . . . . . . . 119

Chapter 22: Metric Measurement22.1 Point A to Point B . . . . . . . . . . . . . . 12022.2 Wedding Fun . . . . . . . . . . . . . . . . . . 12122.3 Punch All Around . . . . . . . . . . . . . . 12222.4 Sweet Enough . . . . . . . . . . . . . . . . . 12322.5 Ring-A-Ling . . . . . . . . . . . . . . . . . . . 124

Chapter 23: Algebra: Explore Negative Numbers23.1 Fahrenheit Match-Up . . . . . . . . . . . 12523.2 Heating Up . . . . . . . . . . . . . . . . . . . . 12623.3 Number Riddles . . . . . . . . . . . . . . . 12723.4 Logical Conclusions . . . . . . . . . . . . 128

Chapter 24: Explore the Coordinate Grid24.1 Checkmate! . . . . . . . . . . . . . . . . . . . 12924.2 Length on the

Coordinate Grid . . . . . . . . . . . . . . . 13024.3 Use an Equation . . . . . . . . . . . . . . . 13124.4 Graph an Equation . . . . . . . . . . . . . 13224.5 Problem Solving Skill: Identify

Relationships . . . . . . . . . . . . . . . . . . 133

Unit 8: GEOMETRY

Chapter 25: Plane Figures25.1 Semaphore Code . . . . . . . . . . . . . . 13425.2 Mapmaker, Mapmaker,

Make Me a Map! . . . . . . . . . . . . . . . 13525.3 Shapes in Motion . . . . . . . . . . . . . . 13625.4 Let it Snow! . . . . . . . . . . . . . . . . . . . 13725.5 Problem Solving Strategy:

Make a Model . . . . . . . . . . . . . . . . . 138

Chapter 26: Perimeter and Area of Plane Figures26.1 Polygons in Art . . . . . . . . . . . . . . . . 13926.2 Block It Out! . . . . . . . . . . . . . . . . . . 14026.3 Unusual Measures . . . . . . . . . . . . . . 14126.4 Flying Carpet Ride . . . . . . . . . . . . . 14226.5 Relate Formulas and Rules . . . . . . 14326.6Problem Solving Strategy:

Find a Pattern . . . . . . . . . . . . . . . . . . 144

Chapter 27: Solid Figures and Volume27.1 Riddle, Riddle . . . . . . . . . . . . . . . . . 14527.2 Puzzle Watch . . . . . . . . . . . . . . . . . . 146

27.3 Estimate and Find Volume of Prisms . . . . . . . . . . . . . . . . . . . . . . 147

27.4 Problem Solving Skill: Too Much/Too Little Information . . . . . . . . . . 148

Chapter 28: Measure and Classify Plane Figures28.1 Pentamino Turns . . . . . . . . . . . . . . . 14928.2 Angle Analogies . . . . . . . . . . . . . . . . 15028.3 Circles . . . . . . . . . . . . . . . . . . . . . . . . 15128.4 Circumference . . . . . . . . . . . . . . . . . 15228.5 Classify Triangles . . . . . . . . . . . . . . . 15328.6A Scavenger Hunt . . . . . . . . . . . . . . 15428.7 Diagram Detective . . . . . . . . . . . . . 155

Unit 9: PROBABILITY

Chapter 29: Outcomes29.1 Three Coins in a Fountain . . . . . . . 15629.2 The Path of Probability . . . . . . . . . 15729.3 Mystery Cube . . . . . . . . . . . . . . . . . 15829.4 A Likely Story . . . . . . . . . . . . . . . . . 159

Chapter 30: Probability30.1 Certainly Not! . . . . . . . . . . . . . . . . . 16030.2 Heads or Tails? . . . . . . . . . . . . . . . . . 16130.3 Word Wonders . . . . . . . . . . . . . . . . 16230.4 Name Mix-up . . . . . . . . . . . . . . . . . . 163

Just Down the Road a Bit

The distance from Taylorville to Rye is 10 miles.

Use the map. Estimate the distances.

1. Taylorville to North Adams

2. Hancock to Black Creek

3. Bristol to Dover

4. Belmont to Black Creek

5. Taylorville to Hancock

6. The distance between Taylorville and North Adams is aboutthe same as the distance between which other two towns?

7. The distance between which two towns is about 2 timesas great as the distance between Rye and Taylorville?

8. It takes Don longer to bicycle from Bristol to NorthAdams than to bicycle from Bristol to Dover, althoughthe distance is shorter. Explain why this might be so.

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Challenge CW1

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LESSON 1.1

•

•

•••

•

•

•HancockBlack Creek

Belmont

Taylorville North Adams Bristol

Rye

Dover

Broken Records

Read each world record for the largest collection. Write the missing digit. Then place the letter over the digit at the bottom of the page to answer the question.

1. Ties: ten thousand, four hundred fifty-three 10,4 3 (W)

2. Refrigerator magnets: twelve thousand 1 ,000 (A)

3. Pens: fourteen thousand, four hundred ninety-two 1 , 492 (G)

4. Parking meters: two hundred sixty-nine 26 (S)

5. Get-well cards: thirty-three million 3 ,000,000 (M)

6. Four-leaf clovers: seven thousand, one hundred sixteen

,116 (R)

7. Earrings: eighteen thousand, seven hundred fifty 8,750 (U)

8. Credit cards: one thousand, three hundred eighty-four

1,3 4 (P)

9. Soda bottles: six thousand, five hundred ten , 510 (E)

10. Miniature bottles: twenty-nine thousand, five hundred eight

29,5 8 (B)

11. What does John collect?

0 1 0 0 6 4 1 3 5 7 2 8 8 6 7 9L

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CW2 Challenge

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LESSON 1.2

Spin That Number

Work Together

Use a pencil and a paper clip to make a spinner like the one shown.

Play this game with a partner.Each player spins the paper clip six times. The player’s score is the number that the paper clip points to. The other player keeps score, using tally marks.

After each round, find the total value for each player. The playerwith the higher value wins. Play three rounds.

1.

2.

3.

4. What is the highest possible total value for one round?

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Challenge CW3

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LESSON 1.3

Sample ScorecardName 100,000 10,000 1,000 100 10 1 Total Value

ScorecardName 100,000 10,000 1,000 100 10 1 Total Value

LESSON 1.4Name

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Sun to Planet

For Problems 1–7, use the table.

1. Which two planets are closest together?

2. Which planet is about twice as far from the sun as Mercury is?

3. What is the distance between Earth and Saturn?

4. Which planet is closest to Earth?

5. Which planet is closest to Jupiter?

6. Which two planets are 856,000,000 miles apart?

7. Which planet is about ten times as far from the sun as Earth is?

Planet Distance from the Sun in Miles

Mercury 36,000,000

Venus 67,000,000

Earth 93,000,000

Mars 141,000,000

Jupiter 486,000,000

Saturn 892,000,000

The Complete Picture

Complete the pictograph and the chart using the informationprovided.

The Five Most Populated States in the U.S.A. and their Estimated Populations

California: 30,000,000

Florida:

New York: 20,000,000

Pennsylvania: 10,000,000

Texas:

1. Explain how you completed your chart and pictograph.

2. Could the sixth most populated state have an estimatedpopulation of fourteen million? Explain.

California

Florida

New York

Pennsylvania

Texas

The Five Most Populated States in the U.S.A.

Key: Each = people.

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LESSON 1.5

The Number MachineHow can the number machinechange the number 2,744 to 2,044 in one step?

Subtract 700.

Tell how the number machine can change one number to theother in one step.

1. 3,825 → 3,805 2. 1,649 → 649 3. 4,646 → 4,006

4. 421,715 → 420,715 5. 893,686 → 893,286 6. 57,237 → 50,007

7. 54,764,823 → 8. 1,335 → 1,835 9. 738,231 → 739,23154,764,826

10. 77,123 → 77,723 11. 50,234 → 50,555 12. 914,695 → 914,700

Find the numbers that are described.

13. 6,314 a. 2,000 greater 14. 5,967 a. 5,000 greater

b. 2,000 less b. 5,000 less

15. 16,802 a. 10,000 greater 16. 81,043 a. 500 greater

b. 10,000 less b. 500 less

17. 99,999 a. 1,000 greater 18. 20,000 a. 1,000 greater

b. 1,000 less b. 1,000 less

NameLESSON 2.1

CW6 Challenge

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In Between

For 1–8, fill in the blanks by choosing one of the numbers from the box.

1. Heights of mountains in feet: 1,535 � � 1,025

2. Temperatures in degrees Celsius: 25 � � 36

3. Populations of cities: 615,450 � � 615,490

4. Lengths of tunnels in feet: 5,280 � � 5,046

5. Ages of trees in years: 241 � � 356

6. Lengths of rivers in miles: 3,710 � � 2,980

7. Numbers of stamps in collections: 490 � � 563

8. Numbers of mosquitoes in swamps: 2,500,000 � � 3,300,000

For 9–14, circle the number that is between the greatest number and the least number.

9. Depths of lakes in feet: 328 230 390

10. Heights of mountains in feet: 20,320 14,573 14,730

11. Heights of volcanic eruptions in feet: 9,991 9,175 9,003

12. Numbers of Kennel Club collies registered: 14,025 14,281 14,073

13. Highest recorded Alaska temperatures: 107 112 115

14. Daily log-ons to the internet 3,673,471 3,841,391 3,897,100

NameLESSON 2.2

Challenge CW7

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1,335 5,160 57 2,015,675

349 498 3,145,000 15,721

5,289 615,460 1,672 4,900

3,456 572 1,020 365

29 3,450,000 43 15,440

Miles to Go

Follow these steps to find the driving distance betweenNew York, NY, and Tallahassee, FL.

• Locate New York along the top of the chart.Locate Tallahassee along the side of the chart.

• Follow the column down, and the row across.

• The number at which they intersect is the driving distance, in miles, between them.

So, the driving distance between New York andTallahassee is 1,105 miles.

The Coronado family traveled from New York to Charleston, SC,in 3 days. Use the mileage chart to find the number of miles theytraveled each day.

1. 2. 3.

4. On which day did they travel the greatest distance? the least distance?

NameLESSON 2.3

CW8 Challenge

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Charleston, SC

Jacksonville, FL

New Orleans, LA

Raleigh, NC

Tallahassee, FL

Washington, D.C.

New York, NY

Charleston, SC

Jacksonville, FL

New

York, NY

Raleigh, NC

Tallahassee, FL

Washington, D

.C.

New

Orleans, LA

239 781 764 281 404 525

239 546 940 455 165 702

781 546 1,324 860 390 1,085

764 940 1,324 492 1,105 238

281 455 860 492 615 256

404 165 390 1,105 615 868

525 702 1,085 238 256 868

Mileage Chart

DAY 1New York, NY

toWashington, D.C.

DAY 2Washington, D.C.

toRaleigh, NC

DAY 3Raleigh, NC

toCharleston, SC

Basketball BonanzaThe basketball club held a contest to guess the number ofpoints famous players scored in their career. Winners gota basketball autographed with the player’s name.Guesses closest to the players’ scores won. These are thewinning guesses.

Billy guessed 27,300. Antoine guessed 38,400.

Shaun guessed 29,300. Samantha guessed 26,700.

Terry guessed 26,500. Pat guessed 27,400.

Willie guessed 31,400. Jon guessed 26,400.

Place the name of the winner on the basketball.

9. If you round the scores to the nearest thousand, whichfour players would have the same score?

10. Who scored the most points in his career?

NameLESSON 2.4

Challenge CW9

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1.

OscarRobertson

26,710

2.

DominiqueWilkins

26,534

3.

MosesMalone

27,409

4.

JohnHavlicek

26,395

5.

MichaelJordan

29,277

6.

ElvinHayes

27,313

7.

WiltChamberlin

31,419

8.

KareemAbdul Jabbar

38,387

Estimating Populations

The table shows how the populations of four New England states changed from 1790–1820. Use the table to answer the questions. Estimate each answer to the nearest ten thousand.

1. About how many people lived in either New Hampshire or Connecticut in 1790?

2. About how many people lived in either Connecticut or Massachusetts in 1820?

3. About how many more people lived in Massachusetts than New Hampshire in 1820?

4. About how many more people lived in New Hampshire in 1820 than in 1790?

5. About how many people lived in the four New England states in 1790?

6. About how many people lived in the four New England states in 1820?

7. About how many more people lived in the four New England states in 1820 than in 1790?

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LESSON 3.1

POPULATIONS: 1790 – 1820

State 1790 1800 1810 1820

Connecticut 237,655 251,002 261,942 275,248

Massachusetts 378,556 422,845 472,040 523,287

New Hampshire 141,899 183,858 214,460 244,161

Rhode Island 69,112 69,122 76,931 83,059

Number PyramidsNumber pyramids gain new squares by adding together thetwo numbers in the squares beneath. Use this simple pattern:

For example, given 6 � 4 � 10. So,

Depending on which numbers are given, you may also usesubtraction: C � B � A or C � A � B.

Solve the number pyramids using mental math.

1. 2.

3. 4.

5. 6.

7. Make two of your own pyramids.

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LESSON 3.2

CA B

A � B � C6 4

106 4

130 170

90 80

120

20 80

240

90

80

190

60 30

260

80 70

350

180

100

.

Money Math

Write each amount from the box below in a money bag to makethe number sentences true.

9. If you put the money from each money bag into onelarge money bag, will you be putting in an amount thatis greater than or less than $10,000?

$645 $2,107 $1,310 $2,306$1,632 $448 $1,099 $893

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LESSON 3.3

1. $1,685 � = $792

3. $690 � $409 =

5. $923 � $1,184 =

7. $1,945 � = $1,497

2. � $576 = $1,886

4. $2,257 � = $1,612

6. � $456 = $1,850

8. � $1,163 = $2,795

Daily Cross-Number Puzzle

Find the difference. Enter your answers in the cross-number puzzle.

Across

1. 4.

7. 8.

9. 10.

11. 14.

15. 18. 19. 20.

Down

1. 2. 3. 4.

5. 6. 11. 12.

13. 15. 16. 17. 3,114� 3,053��

9,001� 8,909��

104� 30��

8,907� 5,709��

10,106� 3,807��

4,003� 1,865��

1,000� 973��

1,280� 1,192��

25,000� 12,245��

700� 465��

5,200� 985��

3,008� 1,191��

324� 226��

9,007� 4,789��

501� 402��

10,201� 2,238��

1,710� 189��

5,001� 2,438��

10,000� 9,925��

800� 685��

1,400� 1,113��

2,000� 1,177��

284� 102��

300� 158��

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LESSON 3.4

1 2 3 4 5 6

7 8

9

10 11 12 13

14

15 16 17 18

19 20

My Balance!

Ted forgot to enter all of his checks and deposits into his check register. Fill in the missing information from these checks to helpTed find the balance in his account.

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CW14 Challenge

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LESSON 3.5

Check Date Description Amount of Amount of BalanceNumber Check Deposit

$897.54

645 1/17 Shirts Galore $38.75

646 1/18 Newton News $16.88

1/18 paycheck $325.76

647 1/18 Burger Buster

648 1/19 Snipper Salon $13.67

649 1/20 Ring-A-Ling $144.91

650 1/20 Walkin’ Wear

651 1/20 Harry’s Hats $478.23

652 1/21 Auto Al $30.99

1/21 bonus check $675.25

Popular Hot SpotsMany people like the warm weather in the state of Florida.Listed below are the populations for major cities in Florida.

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LESSON 3.6

Florida Cities City Population

Fort Lauderdale 149,377

Hialeah 188,004

Jacksonville 635,230

Miami 358,548

Orlando 164,693

St. Petersburg 238,629

Tallahassee 124,773

Tampa 280,015

Tell if an estimate or exact answer is needed. Solve.

1. What is the difference in population between Hialeah and Orlando?

2. Which three cities have a total population about the same asJacksonville?

3. The cities of Tampa and St. Petersburg share an airport. Do you thinkthat the Tampa-St. Petersburg airport would be larger than theJacksonville airport? Explain.

4. How many more people live in Fort Lauderdale than in Tallahassee?

Fort Lauderdale

MiamiHialeah

••

•

•

•

••

•

St. Petersburg

Tampa Orlando

TallahasseeJacksonville

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LESSON 4.1

Par for the CourseIn golf the par for a hole is the number of strokes, or hits, it takes an average golfer to put the ball in the hole.

If a golfer is under par, it means that he or she took fewer than the par number of strokes to put the ball in the hole.

If a golfer is over par, it means that he or she took more than the par number of strokes to put the ball in the hole.

For 1–6, find the golfer’s score for each hole.

1. 2. 3.

Par: 3 Par: 4 Par: 3Strokes: 1 under par Strokes: 1 under par Strokes: 1 over par

Score: Score: Score:

4. 5. 6.

Par: 2 Par: 3 Par: 5Strokes: par Strokes: 2 over par Strokes: 2 under par

Score: Score: Score:

7. a. Add the par numbers for the holes to find the par for the course. Par for the course:

b. Add the golfer’s scores for the holes to find her or his score for the course. Score for the course:

c. Was the golfer over or under par for the course? By how much?

par for the hole: 4golfer’s strokes: 1 under pargolfer’s score: 4 � 1 � 3

par for the hole: 4golfer’s strokes: 2 over pargolfer’s score: 4 � 2 � 6

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LESSON 4.2

Parentheses Fun

Place the parentheses to make the expression equal 4.

1. 6 � 4 � 2 2. 2 � 4 � 2 3. 5 � 4 � 2 � 1

4. 5 � 3 � 3 � 1 5. 7 � 6 � 5 � 2 6. 6 � 4 � 2 � 4

7. 4 � 3 � 5 � 2 � 4 8. 3 � 1 � 4 � 2 � 2 � 2

Use the rules below to play the Parentheses Game with a partner.

A. Use only the numbers 0–5.

B. Use only addition and subtraction.

C. Use as many parentheses as possible.

D. The expression should equal 2.

The winner is the one that writes the most examples.

Make up your own parentheses game. Write the rules and writeyour own examples.

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LESSON 4.3

Whose Number is Closer to 10?The object of this game is to write a number that is closer to10 than your partner’s number.

• You name any 2 numbers, for example, 9 and 4. Yourpartner names any 2 numbers, for example, 6 and 2.

• Each of you must write an expression using all 4 numbersin any order. You must use at least one set of parentheses.You may use only the � and � symbols.

• Find the value of your expression and compare it to your partner’s number. The one whose result is closer to 10gets a point. For example:

You write: (9 � 6) � (4 � 2). The value of your expression is 9.Your partner writes: 4 � (6 � 2) � 9. The value of your partner’sexpression is 17.9 is closer to 10, so you get a point.

• The first to get 10 points is the winner.

• Remember, you may use 2-digit or 3-digit numbers.

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LESSON 4.4

Another Look at Variables

Write an expression for each of the following. Use n for theunknown number.

Write and solve an equation for each of the following. Choose avariable for the unknown number.

7. There are 20 channels available on the TV. Five are local.How many are not local?

8. There are 17 children in the class. Five more students jointhe class. How many students are in the class?

9. Eight books were removed from the shelf. Three booksare still on the shelf. How many books were on the shelfto start?

1. four less than a number

3. ten more than a number plus 3

5. a number increased by the samenumber

2. two more than a number andfour

4. three increased by a numberminus 5

6. six and a number decreased byseven

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LESSON 4.5

Find a Rule

Complete the table using the given rule.

1. a � b � 7 2. a � 5 � b 3. 3 � a � b

Find a rule for the output values. Write the rule as an equationthat includes variables a and b.

4. Output b: 5, 7, 9, 11

5. Output b: 10, 7, 4, 1

6. Output b: 6, 12, 24, 48

Write a sequence for the rule.

7. a � 4 � b

8. a � (2 � 1) � b

9. a � (3 � 3) � b

10. a � (4 � 3) � b

11. (a � 2) � 2 � b

12. (a � 4) � (2 � 1) � b

a b

7

3

5

4

a b

5

19

11

51

a b

2

4

15

0

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LESSON 4.6

Balance It

Write the expressions from the box below above the pans of thebalances so that the two amounts on a balance are the same.

1. 2.

3. 4.

5. 6.

7. 8.

8 � 9 7 � 7 3 � 8 20 � 6

5 � 6 12 � 4 15 � 0 9 � 1

11 � 6 18 � 3 9 � 9 14 � 2

11 � 7 6 � 6 17 � 8 13 � 4

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LESSON 4.7

Deciphering the King’s Numbers

You and your friends visit the ruins of an ancient civilization.There are many stone tablets carved with English words, but thenumbers are in strange symbols. So far, no one can decode thesymbols. Can you?

There are four number symbols: ♦, �, ○, and �.

1. What number does ♦ represent?

2. Which digit is greater, ○ or �?

3. What is (♦ � ○) – (♦ � �)?

4. How many horses does the Prince have?

5. What is �?

Make up your own code of symbols for the digits 0, 1, 2, 3, 4,5, 6, 7, 8, and 9. Write 3 of your symbols in several differentexpressions. Ask a friend to decode your 3 symbols.

Passage 1: “The Kinghas ♦ grandsons,together they have 6 knees.”

Passage 2: “Everybirthday the King giveshis daughter ♦ moreflowers compared to theprevious year. This yearhe gave her ♦ � ○flowers. Last year shegot ♦ � � flowers.”

Passage 3: “The Kinghas ♦ � ♦ horses. Thatis ♦ more than thePrince’s ♦ � � horses.”

Find the Missing DataThe Lane family drove their car on vacation. At the end ofeach day, Mr. Lane recorded the number of miles thatthey had driven.

1. Complete the table to find out how far the Lanestraveled each day.

Matt took a notebook on the trip. He used the notebook to draw pictures and play games with his sister.

2. Look at the table below. How many notebook pages did

Matt use by the end of the trip?

3. Complete the table to find out how many pages Mattused on each day of the trip.

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LESSON 5.1

Total MilesDay Miles in One Day (Cumulative Frequency)

Monday 150 miles

Tuesday 225 miles

Wednesday 368 miles

Thursday 378 miles

Friday 500 miles

Saturday 575 miles

Total PagesDay Pages in One Day (Cumulative Frequency)

Monday 20 pages

Tuesday 33 pages

Wednesday 45 pages

Thursday 73 pages

Friday 80 pages

Saturday 80 pages

Find the Median and the Mode

1. What numbers are missing from this group?The mode is 10, and the median is 9.

4, 4, 6, 8, , 10, 10, , 11

For 2–7, use the table below.

2. What is the median grade of students in the recycling club?

3. What grade is the mode?

4. Would the median grade change if one new second-grader and one fifth-grader joined the recycling club?

5. If two second-grade students quit the recycling club,and three fifth-graders and one fourth-grader joinedthe club, what would the median grade be?

6. Change the data in the table so that you have twomodes.

7. What is the median for your new data?

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LESSON 5.2

RECYCLING CLUB MEMBERS

Grade Number of Students

2 7

3 6

4 5

5 3

Line PlotStephanie is comparing the number of letters in her classmates’ first names. She printed each student’s name on a piece of paper. She then began to count and recordthe number of letters in each name.

1. Complete Stephanie’s line plot by recording the number ofletters in the first names of the other students in her class.

Jennifer Zachary Lee Elizabeth DimitriTed Inderjeet Trudi Malcolm LaurenCarl Koko Matthew Moe KathleenJuan Joanie Christopher Oscar RamonaPaul Siri Mercedes Kevin Alan

For 2–5, use the completed line plot.

2. How many first names have 7 letters?

3. What is the most frequent number of letters in a first

name in Stephanie’s class?

4. What is the range of this data?

5. Would the data be different if you made a line plot for the number of letters in the first names of students in your class? Make a list of names and a line plot for your classmates.

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LESSON 5.3

3 4 5 6 7 8 9 10 11Number of Letters in First Name

3 4 5 6 7 8 9 10 112

How Many Marbles in a Jar?Mr. Murphy asked each of the students in his class to estimate the number of marbles in a jar. He organized theestimates in a stem-and-leaf plot.

For 1–4, use the stem-and-leaf plot.

1. What number was estimated by the greatest number of students?

2. What is the median in this set of estimates?

3. What is the difference between the highest estimate and

the lowest estimate?

4. Use the following clues and the stem-and-leaf plot todetermine the exact number of marbles in the jar.

• Only one student guessed the exact number.

• The exact number is not a multiple of 5.

• The exact number has 7 tens.

There are exactly marbles in the jar.

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LESSON 5.4

Stem Leaves

6 3 5 5 6 7

7 0 0 0 4 4 5 8 9 9

8 0 3 3 6 6

9 0 5

Marble Estimates

6 | 3 means 63 marbles.

Did You Know?The table shows the oldest recorded age of some animals.

Use the data in the table above to complete the graph. Draw barsacross the graph to show the age of each animal.

1. What interval is used in the scale of the graph?

2. For which animals do the bars end exactly on the scale lines?

3. If the graph had a scale with intervals of 2, how manybars would end exactly on the scale lines?

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LESSON 5.5

Animal Age (in years)

Cat 28

Dog 20

Goat 18

Rabbit 13

Guinea Pig 8

Mouse 6

4 80 12 16 20 24

Ani

mal

Oldest Recorded Ages of Animals

Age (in years)

28

Cat

Dog

Goat

Rabbit

Guinea Pig

Mouse

Use Graphic AidsStudents collected empty soda cans.The amounts collected are shown in the table.

1. What is the range of the data in

the table?

2. On a bar graph of this data, what

scale, other than 1, would allow the

most bars to end exactly on a scale line?

3. Using your answers to 1 and 2, make a bar graph of thedata in the table.

4. On which two consecutive days did the studentscollect the most cans?

5. When would it be easier to use a graph instead of atable to find an answer?

6. When would it be easier to use a table instead of agraph to find an answer?

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LESSON 5.6

SODA CANS COLLECTED

Monday 41

Tuesday 37

Wednesday 30

Thursday 25

Friday 20

Strike Up the Band

1. Use the clues to fill in the missing information on thisdouble-bar graph.

• The same number of boys and girls play the trombone.

• More boys than girls play the trumpet.

• Two more boys than girls play the drums.

• More girls play the flute than any other instrument.

• The same number of boys play the flute and the trombone.

• Twice as many girls as boys play the clarinet.

For 2–5, use the completed graph.

2. Which instruments are played by more boys than girls?

3. Do more students play the flute or the trumpet?

4. Are there more boys or more girls in the band?

5. How many students are in the band?

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LESSON 6.1

INSTRUMENTS PLAYED IN THE SCHOOL BAND

Num

ber

of S

tude

nts

Instrument

0

2

4

6

8

10

12

Trumpet

Drums

Key:

Clarinet

Temperature Patterns

This line graph shows the normal temperatures inBoston and San Francisco for each month of the year.

1. What does the dashed line represent?

2. What is normally the coldest month in Boston?

3. What is normally the warmest month in San Francisco?

4. In which city is the difference in temperature betweenthe summer months and the winter months greater?

5. During which months is the normal temperature in thetwo cities the same?

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LESSON 6.2

MONTHLY NORMAL TEMPERATURES IN BOSTON AND SAN FRANCISCO

60

50

40

30

20

10

0 Jan Feb Mar Apr Jun JulMay

70

80

Aug Sep Oct Nov Dec

Key:

Boston

San Francisco

•• • • •

••

•

• ••

• •• •

•

•

•••

••

Tem

pera

ture

(in

°F)

Month

Find the Missing Scales

The line graphs below show the number of sales of several itemsin The Red Balloon Toy Shop during one week.

1. Use the following information to fill in the missingscales in each graph.• There were 10 more puzzles sold on Monday than on Tuesday.• The number of models sold on Wednesday was 5.• There were 60 paint sets sold during the week.• There were 8 more games sold on Thursday than on Friday.

For 2–5, use the graphs.

2. How many models were sold in all during the week?

3. On which day was the greatest number of paint sets sold?

4. Were there more sales of models or games on Monday?

5. Write two more similar questions using the data in the graphs.

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LESSON 6.3

0

40

M T W Th F S

30

20

10

0

8

6

4

2

M T W Th F S

PUZZLE SALES MODEL SALES

•

• •

• •

•

•

•

•• •

•

Day

Num

ber

Sold

Num

ber

Sold

Day

0

20

15

16

12

10

5

0

8

4

M T W Th F S M T W Th F S

PAINT SET SALES GAME SALES

• • • •

•

•

• ••

•

•

•Num

ber

Sold

Num

ber

Sold

Day Day

Data DisplayCorina recorded the grades that she got on her spellingtest each week for nine weeks. She displayed the data intwo different ways.

A B

Circle the letter of the graph or plot you would use to answereach question. Then answer the question.

1. What grade did Corina get most often? A B

2. What grade did Corina get in Week 5? A B

3. Did Corina’s grades improve or decline between Weeks 5 and 8?

A B

4. What is the range of Corina’s grades? A B

5. By how many points did Corina’s grade improve between Weeks 2 and 3?

A B

6. What is the median of Corina’s grades? A B

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LESSON 6.4

75 80 85 90 95 100

✗ ✗ ✗ ✗ ✗✗ ✗ ✗✗

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9

•• •

••

••

• •

70

80

90

100

Week

Grad

eSpelling Test Grades

SPELLING TEST GRADES

What’s the Reason?The graph at the right shows the number of studentsenrolled at Kensington Elementary in 7 different years.

When we read a graph, wecan make conclusions aboutwhat happened, then try tothink of reasons why thosethings might have happened.

For example:

Conclusion: The number of students enrolled atKensington Elementary rosesteadily between 1940, 1950,and 1960.

Possible Reason: The community around the school was growing steadily, meaning that there were more children to attend Kensington Elementary.

Give a possible reason for each of the following conclusions.

1. Conclusion: There was a sharp increase in the numberof students between 1960 and 1970.

Possible Reason:

2. Conclusion: The number of students enrolled atKensington Elementary began to decrease steadilyafter 1980.

Possible Reason:

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LESSON 6.5

Enrollment at Kensington Elementary

Year

Num

ber o

f Stu

dent

s

Stop That Watch!

Work with a partner to estimate and then check how many timesyou can do different activities in one minute.

You need a watch with a second hand.

1. Record your estimates and findings in the tables.

Partner 1 Name �� Partner 2 Name ��

2. How close are the actual numbers to your estimated numbers? Write a paragraph to explain.

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LESSON 7.1

Estimated Actual

Activity Number of Number of

Repetitions Repetitions

Write yourname.

Hop onone foot.

Draw astar andcolor it.

Walk aroundyour desk or table.

Count to 200.

Estimated Actual

Activity Number of Number of

Repetitions Repetitions

Write yourname.

Hop onone foot.

Draw astar andcolor it.

Walk aroundyour desk or table.

Count to 200.

What Time Is It?Each clock shows a time in the morning or the afternoon. Each clock has a letter that you will use to find the secret message.

1. Find the 4:00 A.M. clock. Write that clock’s letter in the firstbox. Continue matching the times, with the clocks. Writethe letter next to the clock in the box above the time.

What is the secret message?

2. Use the letters above the clocks at the top of the pageto write the longest word you can in the spaces below.Also write the time for each letter.

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LESSON 7.2

4 A.M. 7 A.M. 9 A.M. 11 A.M.

5 P.M. 9 P.M. 1 hour 1 hour 1 hour �12� hour

after before before before

1 P.M. 5 A.M. midnight midnight

1 P.M. 1:55 P.M. 2 P.M.

4 P.M.

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

M Y E A P

F I A T RA.M.

A.M. A.M.

A.M.P.M. P.M. P.M.

8910

11 12

7 6 543

21

O

P.M.

P.M. P.M. P.M.

8910

11 12

7 6 543

21

!

P.M.

Replace the Batteries

Mr. Smith went into his clock shop on Monday morning.Several of his clocks were running slow. He realized that he needed to replace the batteries in those clocks andreset the time.

The exact time is 8:10. Write how much time each clock has lost.Use the abbreviations hr and min.

1. 2.

3. 4.

5. 6.

7. 8.

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

5:107:51

8:056:28

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

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LESSON 7.3

Trina’s Tuesday

Read the following story about Trina’s Tuesday. Then make anordered list of the 15 things that happened to Trina, starting at2:00 A.M. Tuesday and continuing until 11:00 P.M. Wednesday.

Trina woke up to the sound of her alarm clock at 6:00A.M. She felt tired because a thunder storm woke her up at2:00 A.M. She ate breakfast at 7:00 A.M. and took the bus at8:00 A.M. On the bus Trina studied for her Math test,which was at 2:00 P.M.

She arrived at school at 9:00 A.M. The teacher told Trinathat there was an assembly at 1:00 P.M. Trina did Social Studies at 10:00 A.M., and at 12:00 P.M., she ate lunch.

At 3:00 P.M. she took the bus home. Dinner was at 6:00 P.M.Trina was happy that she had done all of her homework at 4:00 P.M. so she was able to play outside at 7:00 P.M. At 9:00 P.M., Trina went to sleep. She heard her baby brother cryat 11:00 P.M. but went right back to sleep.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

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LESSON 7.4

LESSON 7.5Name

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Hatching Eggs

The table shows the average incubation time for eggs of differentkinds of birds. Incubation time is the number of days between thetime an egg is laid and the time it hatches.

For Problems 1–6, use the table and a calendar.

1. How much longer does it usually take a duck’s egg to

hatch than a chicken’s egg?

2. If a chicken lays an egg on June 1, on about what date

should the egg hatch?

3. If a duck lays an egg on June 21, on about what date

should the egg hatch?

4. A turkey egg hatches on July 4. On about what date was

the turkey egg laid?

5. A goose egg hatches on the last day in July. On about

what date was the goose egg laid?

6. A chick is 3 days old on July 31. On what date did the

chicken egg hatch?

On about what date was the egg laid?

INCUBATION TIME FOR EGGS

Kind of BirdAverage Number

of Days

Chicken 21

Duck 30

Turkey 26

Goose 30

Fact Family BingoMaster basic multiplication facts with a friendly game of Fact Family Bingo. Play with several students.

To play:• Have one player call out one equation from the

Fact Family of his or her choice.• The other players look for another equation

from that Fact Family on their bingo board. If a player finds one, he or she places a scrap of paper on that equation.

• The first player to complete a row across, down, or diagonally says “Fact Family Bingo.”

CARD A CARD B

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LESSON 8.1

4��12� 3��18�

5��25� 2��16� 2��4�

2��10� FREE 1��2� 3��15�

8��40� 9��18� 6��48�

12��60� 6��72� 9��90� 6��30�6

� 9

9� 9

7� 8

3� 1

7� 2

5� 4

3� 3

4� 2

2� 3 12��14�4� 4��8� 3��9�

9��45� 8��80� 12��96�

9��99� 3��9� FREE 1��3� 12��10�8�

7��63�10

� 107

� 105

� 75

� 9

12� 7

2� 7

6� 7

2� 12

5� 6

8� 9

2� 6

1� 1

11� 11

584

1016

2126

Math MachineryEach machine in Mariko’s Machinery Shop does differentthings with the numbers put into it.

Complete the In and Out columns for each machine.

1. 2.

3. 4.

5. The machine in Problem 4 needs to be reprogrammedto do the same job in one step instead of two. How canthis be done?

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CW40 Challenge

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LESSON 8.2

Fingers and Factors

Mickey’s mother taught him how to multiply by using hisfingers. She said this is a very old method. It only workswhen the factors are greater than 5. Here are the stepsMickey followed to find the product of 7 � 8.

Step 1 7 is 2 more than 5. Turn down 2 fingers of the left hand.

Step 2 8 is 3 more than 5. Turn down 3 fingers of the right hand.

Step 3 Multiply the number of 5 � 10 � 50turned-down fingers by 10.

Step 4 Multiply the number of not 3 � 2 � 6turned-down fingers of one hand by the number of notturned-down fingers of the other hand.

Step 5 Add the products. 50 � 6 � 56So, 7 � 8 � 56.

Use the above method to find the product.

1. 6 � 8 � 2. 6 � 6 � 3. 7 � 7 �

4. 7 � 9 � 5. 9 � 8 � 6. 6 � 7 �

7. 9 � 9 � 8. 6 � 9 � 9. 8 � 8 �

10. 7 � 6 � 11. 8 � 7 � 12. 9 � 6 �

13. 8 � 6 � 14. 9 � 7 � 15. 8 � 9 �

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LESSON 8.3

Hand-y MultiplicationA handy method for multiplying with facts with 9s is finger multiplication.

Use both hands with fingers spread apart. Label the fingers consecutively from 1 to 10, as shown.

To multiply, bend the “multiplier finger.” For the basicfact 3 � 9, you bend finger number 3, as shown below.

3 � 9 � 27

The fingers to the left of the multiplier give the tens in theproduct. The fingers to the right of the multiplier give theones in the product.

Solve by using finger multiplication. Draw a picture of what eachhand looks like.

1. 7 � 9 � 2. 5 � 9 �

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LESSON 8.4

multiplier

2 tens7 ones

Up, Down, or Diagonal

Find three numbers in a row that have the given product. Draw aline through the three numbers. You may draw the line across, upand down, or diagonally.

1. product: 36 2. product: 120 3. product: 90




13. Make your own puzzle. Exchange with a partner to solve.

product:

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LESSON 8.5

1 2 5

6 3 0

7 6 2

2 9 5

3 5 7

5 6 4

7 2 9

3 5 1

2 4 9

4 3 6

2 5 7

0 8 2

7 4 5

2 8 6

6 4 3

3 8 6

6 3 4

9 6 2

5 3 4

4 2 8

7 9 3

4 6 2

9 7 4

3 2 8

7 6 2

1 4 7

9 5 8

3 7 3

2 4 6

7 4 12

4 5 3

8 0 7

6 9 4

6 5 3

6 2 4

7 8 9

Birthday Greetings

Grandma Gallagher will soon be 75 years old. Her ten grandchildren made a card to give her on her birthday. They will sign their names in order from oldest to youngest.

Use the clues below to find the age of each grandchild. Record thenames in the chart.

1. Ryan is 8 years old.

2. Nadia is 5 years younger than Ryan.

3. Nick is 6 times as old as Nadia.

4. Mary Kate is 4 years older than Ryan.

5. Emma is 2 years older than Nadia.

6. Charlotte is half as old as Mary Kate.

7. Jack is 4 times as old as Emma.

8. Margaret is 4 years older than Charlotte.

9. Laura is 7 years younger than Nick.

10. Michael is twice as old as Ryan.

For Problems 11–12, use the chart.

11. Who will sign the card first? last?

12. Who will be the fifth person to

sign the card?

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LESSON 8.6

20 yr

19 yr

18 yr

17 yr

16 yr

15 yr

14 yr

13 yr

12 yr

11 yr

10 yr

9 yr

8 yr

7 yr

6 yr

5 yr

4 yr

3 yr

Parentheses PuzzlesLook at the array. See how the numbers on the outside arethe result of multiplying the expressions and numbers onthe inside from left to right or top to bottom.

21

44

33 28

Arrange the inside expressions and numbers in the ParenthesesPuzzle so that the top-to-bottom and left-to-right products equalthe outside numbers.

1. Inside: 2, (6 � 4), (8 � 2), 5 2. Inside: (2 � 7), (12 � 5), 4, 6

Outside: 10, 12, 50, 60 Outside: 28, 42, 54, 36

50

Arrange the inside expressions and numbers in the ParenthesesPuzzle so that the top-to-bottom and left-to-right differencesequal the outside numbers.

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LESSON 9.1

3 (5 � 2)

(2 � 9) 4

5

(8 � 2)

(4 � 5) 5

3. Inside: (4 � 5), (2 � 2), 18, 5

Outside: 1, 2, 14, 15

4. Inside: (7 � 4), (2 � 9),(6 � 3), (2 � 10)

Outside: 2, 10, 8, 0

15

What’s the Problem?

Write a problem that matches the expression. Then find the value ofthe expression to solve your problem.

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LESSON 9.2

1. 10 � (2 � 4)

3. 3 � (5 � 4)

5. 22 � (2 � 8)

2. (9 � 5) � 4

4. (6 � 9) � 7

6. (3 � 12) � 10

Keep It EqualWhen the same amount of weight is oneach side of a scale, the scale is balanced.If there is more weight on one side, thescale will tip to that side.

Use the information to balance the scale.

1 weighs one pound.

1 weighs two pounds.

1 weighs three pounds.

1 � 4 � 7 pounds and 3 � 1 � 7 pounds.

So the scale is balanced.

Tell how to make the scales balance?

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LESSON 9.3

1.

3.

2.

4.

Variable Grab BagPractice finding the value of an expression by playingVariable Grab Bag. Copy the table below onto a piece ofpaper and cut out the numbers 1 through 12. These arevalues for the variable b. Put the pieces into a bag or hat.

Without looking, Player A grabs one number out of thebag, uses it to find the value of the first expression, andrecords the result as points in the correct column. If theresult is not a whole number, the player gets 5 points.

After replacing the number, it is Player B’s turn. Playerscontinue taking turns. Find the total number of points forthe 10 rounds. The player with more points is the winner.

Round Expression Player A Player B

1 4 � b points points


3 b � 8 points points








TOTAL POINTS points points

1 2 3 4 5 6 7 8 9 10 11 12

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LESSON 9.4

Say It Again, SamWhen writing equations to match words, there is usuallymore than one correct answer.

Example Write an equation using a variable.

5 towels in each of 7 stacks is the total number of towels.

Kris’s equation: 5 � 7 � t

Deb’s equation: t � 7 � 5

In both equations, t is the total number of towels.

One equation is given. Give another possible equation.

Write 2 possible equations.

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LESSON 9.5

1. A total number of eggs, n, in 5cartons is 3 eggs in each carton.

n � 5 � 3

2. 6 pages each in 4 baby books isthe total number of pages, p.

6 � 4 � p

3. 12 players on each of 8basketball teams is the totalnumber of players, p.

5. 2 socks in each of some numberof pairs, p, is 24 socks.

4. 50 campers split among 10cabins is the number ofcampers, c, in each cabin.

6. 100 pieces of firewood dividedinto 5 piles is some number, f,in each pile.

Play by the RulesAn input/output table can have any kind of rule.Sometimes a rule is one step, like multiply by 4.

Sometimes a rule is two steps. Can you find a rule for theinput/output table?

Think: What operations on 3 give a value of 10?

Idea: Multiply by 3, then add 1.

Test your idea for input 5. Does (5 � 3) � 1 � 14?

Try again: Multiply by 2, then add 4.




So, a rule for the input/output table is multiply by 2, thenadd 4.

Find a rule for each input/output table. Remember, you must testyour rule on each row!

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LESSON 9.6

Input Output

3 10

5 14

6 16

10 24

1. 2. Input Output

20 14

16 12

8 8

10 9

Input Output

3 9

4 11

8 19

10 23

Flying AroundMarty the Fly is standing on the grid below. When he flies,it is always one whole space either straight up, straightdown, directly left, or directly right.

Follow Marty’s moves and tell where he lands.

Marty makes the following moves:

Starting in space D8, Marty moves 2 spaces up, 3 spacesright, 4 spaces left, 5 spaces up, 3 spaces right, 2 spacesdown, 3 spaces right, 1 space up and 2 spaces left.

1. Where does Marty land?

2. Make up your own moves for Marty and have a friendplay your game.

A B C D E F G H I J

1

2

3

4

5

6

7

8

9

10

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LESSON 9.7

The Powers That Be

You can write some large numbers in a shorter form byusing exponents. An exponent tells how many times tomultiply a number, called the base, by itself.

100 � 1 base → 100

101 � 10

102 � 10 � 10 � 100

103 � 10 � 10 � 10 � 1,000

As you can see, the exponent also tells how many zerosfollow the number 1.

Many scientists round large numbers and use exponents.

One million equals 106. 18 million equals 18 � 106.

Draw a line to the matching number.

1. 32,000 • • 89 � 105

2. 48,000,000 • • 17 � 100

3. 560 • • 9 � 106

4. 7,700 • • 77 � 102

5. 8,900,000 • • 32 � 103

6. 690,000 • • 44 � 105

7. 9,000,000 • • 16 � 107

8. 28,000 • • 48 � 106

9. 17 • • 98 � 106

10. 4,400,000 • • 28 � 103

11. 160,000,000 • • 56 � 101

12. 98,000,000 • • 69 � 104

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LESSON 10.2Name

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About the SameIn each large box, circle all the sets of factors whose estimatedproduct is the number in the center box.

4�581 6�487 5�531

8�304 2,400 3�894

3�815 8�256 6�356

2�599 6�212 3�395

4�304 1,200 2�673

3�444 4�256 6�184

3�999 5�555 6�456

6�601 3,000 5�499

5�648 6�666 3�1,845

6�524 4�888 9�444

4�973 3,600 6�555

9�381 6�631 4�918

4�999 8�487 5�765

8�592 4,000 4�1,846

2�1,815 5�825 8�456

4�5,081 6�4,875 8�2,931

8�3,704 24,000 3�8,132

3�7,777 4�5,555 6�3,925

2�8,344 4�3,456 8�1,793

4�4,444 16,000 2�7,891

8�2,468 2�8,500 4�4,567

5�6,872 3�9,999 6�4,721

6�4,382 30,000 5�5,734

6�5,377 5�6,294 3�10,388

1.

3.

5.

7.

2.

4.

6.

8.

Doubling and HalvingOne of the earliest methods of multiplying was accomplishedthrough doubling and halving. This method can be traced to the early Egyptians.

Here is how to multiply 7 � 35.

Double Halve

7 � 35

14 17 ← Half of 35 is 17�12

�; use only 17.

28 8 ← Half of 17 is 8�12

�; use only 8.

56 4

112 2

224 1

• Halve the numbers in the second column until you reachthe number 1.

• Double the numbers in the first column.

• Cross out the even numbers in the Halve column: 2, 4,and 8. Then cross off numbers in the Doublecolumn that are opposite the crossed-off numbers.

• Add the numbers in the Double column that are notcrossed out: 7 � 14 � 224 � 245.

So, 7 � 35 is 245.

Multiply, using the doubling and halving method. Show your work.

1. 2. 3. 4 � 513 � 276 � 42

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LESSON 10.3

Multiply 3-Digit NumbersComplete the multiplication puzzle.

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LESSON 10.4

246

�

3

�

�7 �

157 ��

314 ��3

� 4 � 621

�

4

555

�

�

476

2

�

4

�

� �

�401

�

8

�

229

�

�

2

�

4257 ��

7 ��

345 ��

�

�

�

361

�

�

2

6

�

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Napier’s Rods

John Napier, a Scottish mathematician, lived about 400years ago. He invented the series of multiplication rodsshown below.

You can use Napier’s rods to multiply 4 � 537.

• Line up the guide rod and therods for 5, 3, and 7.

• Look at the numbers in thefourth row. Start at the right;add the numbers as shown.Then write them as shown.

• The answer is 2,148.

Copy or cut out the rods above. Use them to find the products.

1. 6 � 549 � 2. 4 � 375 �

3. 3 � 627 � 4. 2 � 125 �

5. 7 � 194 � 6. 5 � 431 �

Guide�

1

2

3

4

5

6

7

8

9

0

00

00

00

00

00

00

00

00

00

1

01

02

03

04

05

06

07

08

09

2

02

04

06

08

10

12

14

16

18

3

03

06

09

12

15

18

21

24

27

4

04

08

12

16

20

24

28

32

36

5

05

10

15

20

25

30

35

40

45

6

06

12

18

24

30

36

42

48

54

7

07

14

21

28

35

42

49

56

63

8

08

16

24

32

40

48

56

64

72

9

09

18

27

36

45

54

63

72

81

Guide�

1

2

3

4

5

05

10

15

20

3

03

06

09

12

7

07

14

21

28

2 1 4 8

� �

LESSON 10.5

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LESSON 10.6

Comparison ShoppingThe music store offers CDs at $10.99 each or 5 for $44.95. Which is the better deal?

• You can multiply the individual CD price by 5 to compare.$10.99 � 5 � $54.95 compared to 5 for $44.95.

The package deal for 5 CDs is the better buy.

Determine the better buy.

1. Fancy chocolate candies––14-piece box for $24.92 oreach piece for $2.00?

3. Eggs––$0.79 for 6 or$1.49 for 12?

5. Coffee cups––1 for $0.89 or 12 for $9.00?

7. Colored pencils––1 for $0.66 or6 for $4.10?

9. Spring water––1.5 liter for $1.69 or3.0 liter for $2.99?

2. Batteries––2 for $1.57 or8 for $6.42?

4. Ice cream––1 half gallon for $1.89 or3 half gallons for $5.76?

6. Butter––1 stick for $0.49 or4 sticks for $1.96?

8. Laundry detergent––64 oz for $2.99 or128 oz for $5.99?

10. Candy bars––4 for $2.96 or12 for $8.40?

Moving DayThe Barretts are moving. Help them color code their boxes. Solve the problems. Look at the number of zeros in the product.Use the table below to color code the Barretts’ boxes.

90,000� 20��

800� 3��

700� 30��

60,000� 50��

80,000� 4��

500� 300��

4,000� 4��

400� 30��

900� 6��

200� 4��

1,000� 500��

700� 300��

500� 60��

300� 40��

6,000� 300��

20,000� 40��

400� 20��

40� 20��

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LESSON 11.1

Number ofZeros in Product

Color red blue orange yellow green

2 3 4 5 6

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LESSON 11.2

Multiple Wheels

The factor in the outer circle times the factor in the innercircle equals the product in the center.

Write the missing multiple of 10.

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LESSON 11.3

Target Practice

Practice your estimation skills in this challenging game.

The object of the game is to choose a factor that produces a product closer to the chosen target.

Work with a partner to solve.

Step 1 One player chooses a number from List A as the target and circles it.

Step 2 The partner chooses a number from List B and circles it.

Step 3 Each player secretly estimates the other factor. Eachplayer multiplies that factor by the circled factor.

The player whose product is closer to the circled target gets 1 point. If both players choose the same factor, then they eachreceive 1 point. The first player to reach 6 points wins. For eachround players circle new numbers.

List A List BProduct Factor

473 698 5,444 23 72 49

541 237 629 41 61 27

812 1,010 303 18 36 54

349 421 568 32 15 45

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Cross-Number Puzzle

A cross-number puzzle is a way to model multiplication.

Solve the puzzle 23 � 16 � n this way.• Put the factors in the boxes.• Break each factor into 2 of its addends. Record the

addends along the top and right side of the drawing.

• Multiply the addends. Record the products in the insideboxes.

• Add the products horizontally and vertically.• Record the sums along the bottom and left side of the

drawing.• Add the sums. The sum of the 2 numbers at the bottom

should equal the sum of the 2 numbers on the left side.• Put this number in the circle; this is the product of the

original factors.

So, n � 368.

Complete the cross-number puzzles.

1. 18 � 27 � n 2. 14 � 36 � n

23

�

20

�

36

1016

23138230368

�

20120200320 �

3183048

6

1016

18

�

10

�

820

727

14

�

� 36

LESSON 11.5

Use the Word!Sometimes it is difficult to work with large numbersbecause they have so many digits. You can use placevalue and word form to help find products of some greaternumbers.

Find 4 � 2,000,000. Think: 4 � 2 million � 8 million.

So, 4 � 2,000,000 � 8,000,000.

Find 7 � 60,000. Think: 7 � 60 thousand � 420 thousand.

So 7 � 60,000 � 420,000.

Use this strategy to find the products.

1. 7 � 1,000,000

Think: 7 � 1 � .

So, 7 � 1,000,000 � .

2. 8 � 10,000

Think: � � .

So, 8 � 10,000 � .

3. 5 � 40,000

Think: � � .

So, 5 � 40,000 � .

4. 9 � 30,000

Think: � � .

So, 9 � 30,000 � .

5. 4 � 6,000,000

Think: � � .

So, 4 � 6,000,000 � .

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LESSON 12.1Name

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Digit Detective

Complete the problem by finding the missing digits.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. Use the space below to create your own multiplicationproblems with missing digits. Ask a classmate to complete them.

5

� 7

5, 2 5 05, 6 2 5

3 2

� 4

2 4

1, 2 8 0

1, 0 4

5� 3 3

1 7 4

1, 4 0

1, 1 4

6

� 4

2 5

1, 2 0

1, 5 3 6

7

� 5

1

, 5 0

2, 4 9 1

5 4

� 3

1, 6 2 01, 9 4 4

8

� 5

4 1 54, 9 8 05, 3 9 5

7 3

� 4

2

3, 6 0

3, 9

3

� 3

1 5

, 5 0

1, 8 5 5

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The Bigger, the Better

Players: 3 or more

Materials: Index cards numbered 1–9

Rules:

• One player draws six cards and pauses after each draw so that other players have time to decide where to writeeach digit.

• Players write the digits to make factors that give thegreatest possible product. In every round, each playermay throw out one digit.

• Once a player has written a digit, he or she cannot move the digit to another position.

• When the six cards have been drawn, players multiply to find their products. The player who has the greatestproduct wins the round.

Number NumberThrown Out Thrown Out

↓ ↓

Round 1 Round 2

Round 3 Round 4

Round 5 Round 6

Lattice Multiplication

An early method of multiplying is the lattice method. Thisdescribes how it works.

Multiply 2,781 � 26.

• Write one factor along the top of the lattice and the otherfactor along the right side.

• Multiply each digit of the factors. Record the productsinside the lattice so that the ones and tens are separatedby a diagonal. (See Figure 1.)

• Add the numbers in the grid along the diagonals, startingfrom the lower right corner. Record each sum at the endof its diagonal—just as you do when adding columns.(See Figure 2.)

• Read the digits down the left and across the bottom. Thisis the product.

Figure 1 Figure 2

So, 2,781 � 26 � 72,306.

Use lattice grids to find the product.

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LESSON 12.3

04

12

14

42

16

48

02

06 6

2

2 7 8 10

41

2

14

42

16

48

02

06 6

2

2 7 8 1

0

7

2 3 0 6

1 11

1. 2,531 � 81 � 2. 6,491 � 34 �

Doubling Tales

An ancient story tells of a clever traveling storyteller. Hepromised to entertain the king, and at a price that seemedunbeatable. For the first day the storyteller wanted only 1¢,and for each day after that the rate would double. The kingthought about it briefly: 1¢ on day 1, 2¢ on day 2, and 4¢on day 3. The king assumed that the price was reasonable.

How much will the storyteller charge the king on day 26?

Complete the table to find out.

Do you think the storyteller charged a reasonable price? Explain.

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LESSON 12.4

Day Price

1 1¢

2 2¢

3

4

5

6

7

8

9

10

11

12

13

Day Price

14

15

16

17

18

19

20

21

22

23

24

25

26

LESSON 12.5Name

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Letter Go!

Each letter stands for a 1-digit number. Find a value for each letter.

1. 2. 3.

4. 5. 6. XX� YY

��XX

XX��

XZX

EEE� F F F��

EEEEEE

EEE��EGHGE

J J J� KK��

J J JJ J J

��JLLJ

TTT� S��

RRR

MMMN N N

�P P P��

Q Q Q

AAA�B B B��

CCC

Number RiddlesTo solve the riddles on this page, you will need to know the name for each part of a division problem. Use the example at the right as a reminder.

Complete to make a true equation.

9. ( � ) � 2 � 27 10. ( � ) � 5 � 26

11. ( � ) � 3 � 52 12. ( � ) � 1 � 36

13. Write your own number riddle below.

9 r14��3�7�

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1. My divisor is 5.I am greater than 4 � 5.I am less than 5 � 5.My remainder is 1.

What dividend am I?

3. My divisor is 8.I am less than 30.I am greater than 3 � 8.My remainder is 5.

What dividend am I?

5. My dividend is 50.My remainder is 1.I am an odd number.

What divisor am I?

7. My remainder is 8.My dividend is 80.I am a 1-digit number.

What divisor am I?

2. My divisor is 9.I am greater than 7 � 9.I am less than 8 � 9.My remainder is 7.

What dividend am I?

4. My divisor is 6.I am less than 60.I am greater than 8 � 6.I have no remainder.

What dividend am I?

6. My dividend is 8 times as largeas my divisor.

I am an even number less than 15.

What quotient am I?

8. My dividend is 24.I am 2 more than

my quotient.I have no remainder.

What divisor am I?

remainderdividenddivisor

quotient

Cookie Coordinating

Joe and Melissa are organizing cookies to sell at a bakesale. They are making equal groups of each kind of cookie.

Complete the chart.

Total Number � Number of Plates � Number of Cookies on Each Plate

1.

2.

3.

4.

5.

6. How many plates in all did Joe and Melissa use?

NameLESSON 13.2

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Kind of Cookie Total Number Number on Each Plate Number of Plates

Chocolate chip 96 1212 � 8 � 9696 � 12 � 8

Oatmeal 42

� 3 � 42

42 � � 3

Peanut butter 13

13 � 7 �

� 13 � 7

Butterscotch 19

19 � 4 �

� 19 � 4

Sugar 90 18

� �

� �

Ginger 36 12

� �

� �

Remainders GameNumber of players: 2, 3, or 4

Materials: game boardmarkers (24 small pieces of paper)number cube labeled 3, 4, 5, 6, 7, and 8

Rules:

• Take turns placing a marker on one of the numberson the board and rolling the number cube. Divide thenumbers. For example, if you choose 92 on the boardand roll a 3 on the number cube, you then write theproblem 92 � 3 � 30 r2.

• Your score is equal to your remainder.

• After all the numbers on the board have been coveredwith markers, find the sum of your remainder scores.The winner is the player who has the greatest total score.

NameLESSON 13.3

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32 51 53 46 22 18

92 19 36 41 11 47

42 68 72 13 25 61

43 71 64 61 36 75

Grouping Possibilities

Complete each table by finding For example, works in table 1,different ways to divide a number into groups while always having the same remainder. but does not work.

1.

2.

3.

21 r23��6�5�

32 r12��6�5�

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Total Number of Groups Number in Each(less than 10) Group Remainder

74 2

74 2

74 2

74 2

74 2


99 3

99 3

99 3

99 3

99 3


65 2 32 1

65 1

65 1

Riddle-jamRiddle: What do geese do in a traffic jam?

Find each quotient. Then write the quotients in order from leastto greatest at the bottom of the page. Write the matching letterbelow each quotient.

1. 450 � 5 � Y 2. 270 � 9 � T

3. 3,600 � 9 � O 4. 42,000 � 7 � L

5. 2,100 � 7 � H 6. 7,200 � 8 � K

7. 36,000 � 9 � A 8. 280 � 7 � H

9. 3,500 � 7 � N 10. 240 � 4 � E

11. 56,000 � 7 � T 12. 49,000 � 7 � O

Riddle Answer:

NameLESSON 13.5

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30

!

What’s the Problem?

Write a problem that could be solved by using the division sentence. Then write a pair of compatible numbers, and estimate the quotient.

NameLESSON 13.6

Challenge CW73

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1. 1,489 � 5 � n

Problem:

Compatible numbers:

3. 63,147 � 9 � n

Problem:

Compatible numbers:

5. 758 � 4 � n

Problem:

Compatible numbers:

2. 7,100 � 9 � n

Problem:

Compatible numbers:

4. 276 � 4 � n

Problem:

Compatible numbers:

6. 41,797 � 6 � n

Problem:

Compatible numbers:

Name

CW74 Challenge

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LESSON 14.1

Break the CodeIn the division problems below, each letter stands for a digit.The same letter stands for the same digit in all of the problems.

The table shows that H � 2 and T � 8. Use the division problems to find out what each of the other letters stands for.

Once you have broken the code, use the letters and digits toanswer the riddle at the bottom of this page.

1. 2. 3.

4. 5. 6.

7. 8.

HOW DID THE RIVER HURT ITSELF?Code Letter

Digit6 8 2 0 4 0 9 0 8 5 3 7 0 1 1

HH rHD��W�A�

I rLF��D�R�

LHE��IA�

TD��R�H�

HTH��E�I�

TI��D�T�

LHD��D�T�2��8�8�

DDH��T�T�

0 1 2 3 4 5 6 7 8 9

H T

Name

Challenge CW75

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LESSON 14.2

Remainders GameNumber of players: 2, 3, or 4

Materials: game boardmarkers (24 small pieces of paper)number cube with the numbers 3, 4, 5, 6, 7, and 8

Rules:

• Take turns placing a marker on one of the numbers onthe board and rolling the number cube. Divide thenumbers. For example, if you choose 923 on the boardand roll a 3 on the number cube, you then write theproblem 923 � 3 � 307 r2.

• Your score is equal to your remainder.

• After all the numbers on the board have been coveredwith markers, find the sum of your remainder scores. Thewinner is the player who has the greatest total score.

295 561 350 923 174 532

718 895 473 624 596 407

499 744 303 255 936 577

800 131 652 729 348 210

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LESSON 14.3

Super Checker!

Solve each division problem. Then complete the number sentencethat can be used to check the answer. Draw a line from the division problem to the related number sentence.

1. A. ( � 160) �

2. B. ( � 105) � 1 �

3. C. ( � 309) � 1 �

4. D. ( � 120) � 2 �

5. E. ( � 207) � 3 �7��8�4�2�

2��6�1�9�

4��8�3�1�

5��8�0�0�

3��3�1�6�

Name

Challenge CW77

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LESSON 14.4

Create a Problem

Write a word problem that could be solved with each division sentence given. Then solve your creation!

1. 237 � 4 �

Problem

3. 4,822 � 8 �

Problem

5. $97.35 � 3 �

Problem

2. 637 � 6 �

Problem

4. 3,207 � 9 �

Problem

6. 2,517 � 2 �

Problem

Name

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LESSON 14.5

Diagram Division

Complete the division number sentence for each of the illustrations.

1. Cookies

98 � 4 � r

2. Eggs

� � 12 r5

3. Marbles

145 � 3 � r

4. Crayons

� � 36 r2

5. Pennies in Piñatas

� � $3.29

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LESSON 14.6

Find the Missing ScoresMr. Murphy gave a math quiz to his students each day fora week. The highest possible score was 12 points.

A group of 4 students kept a record of their scores for the week.

1. Complete the chart by filling in the missing numbers.

2. Which student had the highest average score?

3. On which days was the average score for the 4 studentsthe highest?

4. What is the difference between Corina’s average scoreand the lowest average score?

5. What does the number in the box at the lower right-hand corner of the chart represent?

Average Mon. Tues. Wed. Thu. Fri. score for

eachstudent

Hank 8 pts 9 pts 9 pts 12 pts 12 pts

Jim 6 pts 9 pts 8 pts 9 pts 8 pts

Sarah 5 pts 6 pts 7 pts 8 pts 9 pts

Corina 9 pts 12 pts 12 pts 11 pts 11 pts

Average 9 ptsscore on each quiz

Cookie Giveaway

You have 210 cookies to give equally to friends. There can be no cookies left over. How many different groups can you make?

Write your groupings in the table. Fact families can help you.

Name

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LESSON 15.1

Groupings Table

210 � 2 � 105 210 � 3 � 70

2 friends each get 105 3 friends each get 70 friends each get

friends each get friends each get friends each get




LESSON 15.2Name

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Puzzled

Trace and cut out each of the figures below. See if you can buildan 8-by-8 square. Record your final square on the grid below.

LESSON 15.3Name

CW82 Challenge

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Evenly Divided

How many ways can you divide a square into four equal pieces? Try to find at least six different ways.

LESSON 15.4Name

Challenge CW83

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Division Cipher

Each shape in the exercises below represents a number 0–9. Use your multiplication and division skills to find what numbereach shape represents. Then fill in the key.

1.

2.

Solve.

3. 4.

5. 6.

Key� 0, � 1, � 2, � 3, � 4,

� 5, � 6, � 7, � 8, � 9

�

�

r

�

�

�

�

�

�

r

LESSON 15.5Name

CW84 Challenge

What’s for Lunch?

Joe’s Lunch Shop

Hot dog $1.09 Juice, small $0.39 Cookie $0.50

Hamburger $1.59 Juice, medium $0.59 Brownie $0.75

Slice of pizza $1.25 Juice, large $0.69 Ice cream bar $1.25

Lunch Special $2.19Hamburger, medium juice, cookie

1. Lucas bought a hot dog, a largejuice, and an ice cream bar.How much money did he spendon lunch?

3. Tom bought 2 hamburgers anda medium juice. What was hischange from a $5 bill?

5. In one week, the shop sold 246 hot dogs. The shop is open6 days a week. What was theaverage number of hot dogssold each day?

7. During one week, the shop sold 272 slices of pizza. If eachwhole pizza is cut into 8 slices,how many whole pizzas did theshop sell during the week?

2. Mr. Torres bought 4 lunch specials for his family. Howmuch money did he spend?

4. How much more does a hotdog, small juice, and a browniecost than the lunch special?

6. On Monday, the cook made 6 whole pizzas. He cut eachpizza into 8 slices. At the end ofthe day, there were 3 slices leftover. How many slices of pizzadid the shop sell that day?

8. The shop sold 4 dozen brown-ies on Tuesday. How muchmoney did the shop take infrom brownie sales?

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Birthday Party MathShruti is planning a birthday party for her friends. Foreach situation, circle Factor if she should use factors tosolve the problem or Multiple if she should use multiples.

1. Shruti is setting up tables for her guests. If thereare 18 people coming, how many tables shouldshe set, and how many people will be at eachtable?

2. Shruti’s mother is buying birthday candles for hercake. Candles come in boxes of 4. How manyboxes of candles does Shruti’s mother need to buyin order to have 10 candles?

3. Shruti is going to give away purple pencils as partyfavors. She has to order the pencils in sets of 10.How many sets of pencils should she order so thateach guest can have two?

4. The guests will be playing some games. Shrutiwants to form equal-sized teams. How can she formteams?

5. The guests are playing a game in a circle. Theycount off, starting with 1. Every 4th person wins aprize from the grab bag. Celia wants to know if shewill win a prize. How can she figure out if she willwin?

6. Shruti wants to write thank-you notes for her gifts.She wants to write the same number of notes eachday. How many notes should she write each day?

Name

Challenge CW85

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LESSON 16.1

Factor Multiple

Factor Multiple

Factor Multiple

Factor Multiple

Factor Multiple

Factor Multiple

Name

CW86 Challenge

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LESSON 16.2

Shipping BasketballsThe Best Basketball Factory ships basketballs to sportinggoods stores. The factory can ship basketballs in cartons ofdifferent sizes that hold either 1, 2, 4, or 8 basketballs.

1. Complete the chart to show 6 different ways that theBest Basketball Factory can ship 30 basketballs.

The factory saves money when it ships basketballs in thefewest number of cartons possible.

2. What is the fewest number of boxes that the factory canuse to ship 30 basketballs?

3. Complete the chart below to show how the factory can use the fewestnumber of cartons to ship the different numbers of basketballs.

Number of Number of Number of Number of Total NumberCartons for 1 Cartons for 2 Cartons for 4 Cartons for 8 of Basketballs

2 0 7 0 30

30

30

30

30

30

Number of Number of Number of Number of Total NumberCartons for 1 Cartons for 2 Cartons for 4 Cartons for 8 of Basketballs

1 1 1 1 15

31

63

122

251

300

LESSON 16.3Name

Challenge CW87

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Number Pyramids

The numbers in the pyramids are found by using one of thesesimple formulas:

A � B � C or C � A � B or C � B � A

If you know some of the numbers, you can find the rest.

To find the top number, add. 14 � 16 � 30

To find the lower number, subtract. 16 � 9 � 7

Find the missing numbers in each pyramid.

1. 2.

3. 4.

Now, make your own number pyramids. Exchange them with apartner, and test each other’s math skills.

41

9

7 7

23

9

35

67

17

10 12 6

9

26

10

15

9 14

14 16

5 9

C

A B

LESSON 16.4

Something in CommonFor each pair of numbers, write the prime factors. Then listany prime factors that the pair has in common. If the pairhas no prime factors in common, write none.

Use the common prime factors to solve the puzzle.

1. 81

18

Common Prime Factors:

3. 8

12


5. 55

66


7. 51

34


2. 25

60


4. 21

56


6. 39

52


8. 65

12


What does a bee use to do his hair?

A _____ _____ _____ _____ _____ _____ _____ _____ _____ !!!!

2 13 17 5 3 7 13 11 none

Name

CW88 Challenge

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EY

H

M

N

C

O

B

LESSON 16.5Name

Challenge CW89

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Pascal’s Triangle1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

The first row contains only one number, 1.

The second row contains 1 and 1.

1. Find the sum of the numbers in the third row.

2. Find the sum of the numbers in the fourth row.

3. Find the sum of the numbers in the fifth row.

4. Do you notice a pattern? What is it?

5. Use the pattern to guess the sum of the numbers in theseventh row.

6. What are the numbers in the seventh row?

7. What other patterns do you notice in Pascal’s Triangle?

This triangle is calledPascal’s Triangle. To get the next row ofnumbers in the triangle,add the two numbersabove.

Name

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LESSON 17.1

A Fraction of a Message

Decode the message. Find the fraction in the boxes below thatrepresents each letter on the number line. Write the letter of that fraction in the message boxes.

The message:

Make up your own coded message or riddle using the number lines above. Add extra letters if you need them.

�14� �

57� �

45� �

34��

27� �

68��

26� �

45� �

57� �

56� �

34� �

27� �

38� �1

30�

�38� �

26� �

57�

�57��

57�

�12� �1

60� �

38� �

15� �

13�

• •

• •

• •

• •

• •

• •

• •• •halves

•0 �

22�

••• • •sixths0

0

0

0

0

0

0

thirds• •

W

F C

�66�

�11

00�

�33�

•

E

• • • • •

•

sevenths �77�

• •P T

fourths �44�

eighths• • • • • • •

�88�

• • • •fifths �

55�

O S

L R

tenths• • • • • • • • •

N HI A

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Challenge CW91

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LESSON 17.2

Equivalent Fraction Bingo!

Use your math skills with equivalent fractions to play bingo!

Materials:

2 number cubes, counters to cover gameboard, fraction bars

To Play:

• The object of the game is to cover a row—horizontally,vertically, or diagonally—with counters.

• Toss a number cube two times. Using one number asthe numerator and one number as the denominator,write a fraction less than or equal to one. Place acounter on a space with a fraction that is equivalent tothe one you made.

For example, if you toss a 6 and a 4, the fraction youwrite is �

46�. Look for an equivalent fraction such as �

23�.

Cover the space marked �23� on the gameboard. (Use

fraction bars to help find equivalent fractions.)

Gameboard

�14� �

15� �

66� �

35� �

12�

1 �23� �

56� �

45� �

14�

�34� �

13� FREE �

12� 1

�35� 1 �

16� �

14� �

25�

�12� �

34� �

23� 1 �

13�

Name

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LESSON 17.3

Colorful Fractions

Follow the directions. Color each part. Then write the numerators in the fraction to describe the group.

1. Color �13� red. �

13� �

Color �23� green. �

23� �

2. Color �25� red. �

25� �

Color �25� blue. �

25� �


15� �

3. Color �14� blue. �

14� �

Color �24� red. �

24� �


14� �

4. Color �18� blue. �

18� �

Color �38� red. �

38� �


48� �

9

9

15

15

15

12

12

16

16

16

12

Name

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LESSON 17.4

Estimating Fractional Parts

You can estimate the part of a whole that is shaded bythinking about benchmark fractions.

Example About what part of this rectangle is shaded? Is �

13� or �

12� the better estimate?

The part shaded is closer to �12� than to �

13�. So, �

12� is the better estimate.

What part of the figure is shaded?Circle the fraction that is the closer estimate.

1. 2. 3.

�78� or �

34� �

23� or �

56� �

13� or �

14�

4. 5. 6.

�46� or �1

52� �

23� or �

56� �

23� or �

1112�

7. 8. 9.

�34� or �

58� �

14� or �

38� �

14� or �

13�

�23

��13

�

�12

�

Name

CW94 Challenge

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LESSON 17.5

Language Exploration

Use a dictionary to help you complete this page.

A centimeter is one hundredth of a meter or �1100� m.

1. How many centimeters are in a meter?

2. List several words that contain the root word “cent,” and give

their meanings.

A triangle has three angles.

3. How many sides has a triangle?

4. List several words that begin with “tri,” and give their meanings.

A milliliter is one thousandth of a liter or �1,0

100� L.

5. How many milliliters are in a liter?

6. List several words that begin with “mill,” and give their meanings.

7. What does “bicycle” mean?

8. Name other common words that begin with “bi,” where “bi”

means “two.”

Name

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LESSON 17.6

A Mixed-Number Challenge

Work together with a partner to write a mixed number that tellshow much is shaded.

1. 2.

Write a mixed number for each of the following figures. The figureat the right stands for 1.

3. 4.

5. 6. 7.

Shade parts of the following figures. Have a partner write a mixednumber that tells how much is shaded.

8. 9.

Amazing Maze

Find the path from the beginning to the end of the maze. Start with �1

12� and add each fraction along your path. Your goal is to

end at the finish with 6�11

02�.

START

FINISH

Name

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LESSON 18.1

�112�

�142�

�112�

�132�

�132�

�112�

�112�

�172�

�152�

�112�

�122�

�142�

�112�

�132�

�112�

�132�

�132�

�122�

�132�

�122�

�112�

�142�

�112�

�112�

�122�

�182�

�112�

�122�

�112�

�122�

�122�

�122�

�112�

�132�

�142�

�132�

�142�

�122�

�162�

�192�

�11

02� �1

52�

�122�

�122�

What’s Left?

Color each picture as directed. Colors do not overlap. When you are finished coloring, answer each question.

1. Color �13� of the cake red.

Color �13� of the cake brown.

How much of the cake is not

colored?

How much of the cake is

colored?

2. Color �165� of the figure brown.

Color �165� of the figure orange.

What fraction of the figure is

not colored?

What fraction of the figure is

colored?

3. Color �188� of the flag red.

Color �128� of the flag green.

Color �128� of the flag blue.

Color �168� of the flag orange.

What fraction of the flag is not

colored?

What fraction of the flag is

colored?

Name

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LESSON 18.2

All Mixed Up!

Draw a line to connect the problem with the correct answer.

S. 5�18� � 3�

18� � ?• • 7�1

30�

E. 6�13� � 5�

13� � ?• • 9

E. 10�12� � 1�

12� � ?• • 13�

58�

N. 4�25� � 3�

15� � ?• • 11�

16�

V. 15�68� � 2�

18� � ?• • 4�

14�

T. 10�34� � 6�

24� � ?• • 8�

14�

I. 8�37� � 2�

27� � ?• • 2�

29�

A. 7�56� � 6�

36� � ?• • 7�

35�

E. 5�120� � 2�1

10� � ?• • 8�

12�

N. 10�112� � 1�1

12� � ?• • 11�

23�

E. 6�14� � 2�

14� � ?• • 1�

13�

N. 10�79� � 8�

59� � ?• • 10�

57�

To solve the riddle, match the letters above with the answersbelow the boxes.

Riddle: Why was six afraid of seven?

Answer: because

8�14� 8�

12� 13�

58� 7�1

30� 2�

29� 1�

13� 4�

14� 11�

23� 11 10�

57� 7�

35� 91

�6

Name

CW98 Challenge

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LESSON 18.3

What Breed Is Each Dog?There are 48 dogs at the dog show.

Clue 1 Every dog is a specific breed.

Clue 2 The different breeds of dogs are: German shepherds, cairn terriers, poodles, golden retrievers, and Labradors.

Clue 3 Half of the dogs are German shepherds.

Clue 4 There are an equal number of cairn terriers and poodles.

Clue 5 There are twice as many cairn terriers as Labradors.

Clue 6 There are four golden retrievers.

1. List how many of each breed of dog there are.

2. What fraction of the group does each breed of dog represent?

Name

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LESSON 18.4

Name

CW100 Challenge

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LESSON 18.5

Total CostEach coin of United States currency can be thought of as afraction of a dollar.

1. Use coin values to help you find the sum. Use what youknow about adding money to find the sum in simplest form.

2. �210� � �1

10� � 3. �1

100� � �1

10� � 4. �1

300� � �1

40� �

5. �220��

1300� � 6. �

1100� � �

160� � 7. �

230� � �

1400� �

8. �210� � �

24

� � 9. �13010

� � �140� � 10. �

1600� � �

14010

� �

11. �11090

� � �1220� � 12. �

14

� � �260� � 13. �

150� � �

230� �

One quarter is equal to �

14� dollar.

One dime isequal to �1

10�

dollar.

One nickel isequal to �2

10� dollar.

One penny isequal to �1

100�

dollar.

Problem: Think: Steps:

�14� � �110� � One quarter � one dime Write each coin as a fraction.

25¢ � 10¢ � 35¢ Use what you know about money to write an equation.

35¢ � �13050� � �2

70� Write the sum in simplest form.

So, �14� � �1

10� � �2

70� .

Cut Up!You can subtract unlike fractions only after they havebeen renamed with like denominators.

Find �12� � �

14�. �

�12

� �14

�

Divide each half of the first figure in half. Both figures nowhave equal parts. Subtract the like fractions.

� �

�24� �14� �14�

So, �12� � �

14� � �

14�.

For each pair of figures, find a way to divide one of them so thatboth have equal parts. Explain. Then subtract.

1. 2.

3. 4.

912

23

34

58

34

916

23

16

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LESSON 18.6

Riddlegram!

Answer this riddle. Write the letter that matches each fraction or decimal. You will use some models more than once.

Riddle: What did one Math book say to the other Math book?

� � � � � � � � � �0.2 0.6 5 8 6 0.01 49 0.52 0.9 0.35

� � � �10 10 10 100

!� � � � � � � �0.3 1 0.6 2 0.12 35 0.7 15

� � � �10 10 100 100

Name

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LESSON 19.1

T E Y

N OH

A

V

F

,

MATH

MATH

Decimal DriftLarge numbers are often written with both whole numbersand words. This can make the numbers easier to read.

Example: 34,000,000 may be written as 34 million.

Large numbers can also be written with words and decimals.

Examples: 34,500,000 � 34.5 million

1,400,000 � 1.4 million

4,800,000 � 4.8 million

The table below shows the areas of the continents in square miles.

1. Complete the table by writing the missing numbers.

Use the table to answer 2–5.

2. Which continent has the greatest area?

3. Which continent has the least area?

4. How many continents have a greater area than North America?

5. Which 2 continents together have about the same area as NorthAmerica?

Name

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LESSON 19.2

Continent Area (in square miles) Area (in square miles)

North America 9,400,000 9.4 million

South America 6,900,000

Europe 3.8 million

Asia 17.4 million

Africa 11,700,000

Oceania, including3.3 million

Australia

Antarctica 5,400,000

Designing with Decimals

Shade in the decimal amount in each model.

1. 2. 3.

0.2 0.4 0.8

4. 5. 6.

0.35 0.24 0.52

Complete. You may look at the shaded models above.

7. 2 tenths � hundredths

8. tenths � 40 hundredths

9. 35 hundredths � tenths and 5 hundredths

10. 2 tenths and 4 hundredths � hundredths

Use colored pencils to make a design or picture on the grid. Color the numbers of small squares needed to model the decimals shown below.

Red � 0.25

Yellow � 0.30

Blue � 0.15

Black � 0.10

Green � 0.20

Name

CW104 Challenge

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LESSON 19.3

First-Second-ThirdAt the recent Number Olympics, people were confused bywho was in first, second, or third place. (HINT: First wasalways the least number and third the greatest number.)

For each event listed, put the numbers in their proper places onthe medals stand. The first stand has been completed.

Number Put Fraction Jump

Decimal Hurdles Area Swim

High Number Number Beam

Freestyle Numbers Perimeter Sprint

1ST

2ND 3RD

1ST

2ND 3RD

1ST

2ND 3RD

1ST

2ND 3RD

1ST

2ND 3RD

0.620.6

1.01ST

2ND 3RD

0.360.23

0.45

1ST

2ND 3RD

0.96

0.8

1.531ST

2ND 3RD

0.3

0.2

0.4

Name

Challenge CW105

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LESSON 19.4

Event Scores

Number Put 0.3, 0.4, 0.2

Decimal Hurdles 0.23, 0.45, 0.36

High Number 0.3, 0.28, 0.4

Freestyle Numbers 1.23, 0.84, 1.1

Event Scores

Fraction Jump 0.96, 1.53, 0.8

Area Swim 0.6, 0.62, 1.0

Number Beam 3.5, 3.05, 3.47

Perimeter Sprint 2.34, 2.4, 2.05

Money Combos

Show three different coin combinations that equal each amountbelow. Use quarters, dimes, nickels, and pennies—at least one ofeach coin—in each combination.

1. $0.84

2. $0.55

3. $1.37

4. $2.46

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LESSON 19.5

Missing Number Mystery

Write mixed numbers for the numbers that are missing from eachnumber line below.

1.

2.

3.

4.

5.

6.

7. Make your own number line. Include the following

numbers: 4.01, 4.12, 4.03, 4 �1900�, 4 �

225�, 4 �

230�.

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LESSON 19.6

4.10 4.20 4.25

5.4 5.7 5.8

7.32 7.34 7.36

9.40 9.44 9.4642100

2150or

48100

1225or

8 .2 8.6 8.8 9.0

3.18 3.19 3.233.21

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Super (Market) EstimationsCashiers can make errors, and scanners don’t always scan the correct prices. It is important to check your receipt.

At the left is a list of your purchases. At the right is what the cash register rang up. Match the lists and circle the errors. By how much was the receipt off?

Market Receipt

Facial tissues $1.29 4.50

Fruit drink $1.79 1.96

Rice $1.69 0.65

Soap $0.89 1.99

Apples—3 lbs. at $1.50 lb. 2.98

Light bulbs $2.89 0.97

Carrots $0.65 1.29

Cereal $3.49 3.49

Milk $1.39 4.39

Butter $1.99 8.90

Sugar $0.79 1.56

Flour $0.75 1.79

Soda $3.49 0.30

Oatmeal $1.56 1.39

Bagels $3.00 0.75

Bread $1.59 4.79

Mustard $3.10 2.75

Cookies $2.75 3.10

Chicken $4.97 1.59

Total Total

The receipt was off by .

Shop Till You Drop!

Estimate the cost of the items on each list. Circle the list that comes closer without going over your spending limit.

1. Your spending limit is $400.

Estimated cost: Estimated cost:

Actual cost: Actual cost:

2. Your spending limit is $2,000.

Estimated cost: Estimated cost:

Actual cost: Actual cost:

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List 1

Suit

Shirt

Shoes

Coat

Gloves

List 2

Coat

Hat

Shirt

Suit

Belt

Suit $185.40 Belt $32.00

Shirt $35.65 Coat $115.40

Shoes $43.75 Hat $46.00

Tie $27.65 Pants $28.90

Gloves $12.99 Suspenders $34.81

Socks $7.00

List 1

Computer

CD-ROM drive

Printer

Software

Speakers

List 2

LaptopComputer

Printer

Software

Computer $1,199.99 Joystick $59.25

Laptop Desk $79.42Computer $1,499.95

CD-ROM drive$238.75 Speakers $138.60

Printer $318.66

Software $179.25

Play Ball

Place the numbers on the balls in the correct place in the diagram below so that the sum of these positions is the same:

• All of the outfield � b

• Catcher � Pitcher � Third Base � Left field � b

• Catcher � Pitcher � Shortstop � Center field � b

• Catcher � Pitcher � Second Base � Right field � b

• Catcher � Pitcher � First Base � b

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0.14

Catcher

Pitcher

Third base

Second base

First base

Shortstop

Left field

Center fieldRight field

0.9 1.04 1.3 1.16 1.48 2.200.72

Amazing Mazes

Use the number patterns to complete the empty boxes.

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2.4

2.16 2.17

3.34

3.6

Addition and Subtraction Puzzles

Put the numbers in the boxes so that when you either add or subtract from left to right or top to bottom the answers at the right are the same and the answersbelow are the same.

Example:

0.2, 0.3, 0.7, 0.2

1. 1.1, 0.5, 0.2, 0.8 2. 1.7, 0.5, 0.6, 0.6

3. 0.2, 0.2, 1.3, 0.9 4. 0.9, 1.1, 1.3, 0.7

5. 0.9, 0.3, 1.2, 1.8 6. 0.6, 0.6, 1.2, 1.2

7. 0.2, 0.2, 0.3, 0.3 8. 1.3, 1.1, 0.7, 0.5

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0.7 0.3

0.2 0.2

0.4 0.7 � 0.3 � 0.4

0.5 0.5

0.4 0.2 � 0.2 � 0.4

0.3 � 0.2 � 0.5

0.7 � 0.2 � 0.5

Think About It

The decimal point is missing from each of the numbers in Exercises 1–8. Place the decimal point where it belongs in each number.

1. number of seconds it takes Tony to write his name

2. length of a new pencil in centimeters

3. length of a bee in centimeters

4. record speed in seconds for the 200-meter run

5. cost of a fancy helium-filled balloon

6. number of miles walked in one hour

7. number of miles driven in one hour

8. height of an average fourth-grade student in centimeters

For 9–14, arrange the digits shown to make the described number.

9. Least number possible .

10. Greatest number possible .

11. Number nearest to 30 .

12. Greatest number that is less than 35 .

13. Least number that is greater than 20 .

14. Number nearest to 10 .

15. What would your answers to Exercises 9–14 be if the 5 card wasreplaced with a zero card?

1 3 7 1

3 4 0

3 4 0

$ 1 2 5

2 0 3 6

1 7 7

1 7 7

3 5

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LESSON 21.1

Pathfinder1. Measure every path to the nearest inch or half inch.

Write the length on the path.

2. List four ways to drive from home to school, followingthese guidelines. Always travel down and to the right orleft. Do not retrace your path.

3. What is the longest route? How many miles is it?

4. What is the shortest route? How many miles is it?

5. About how long would it take you to walk the shortest route

to school? HINT: It takes about 20 minutes to walk a mile.

Home

StoreFred's House

School

Park

1 inch � 1 mile

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LESSON 21.2

Biking Adventure1. Sammy is going on a week-long bicycle trip with his dad.

They plan to ride from Acton to Halpine by goingthrough Brattle, Capeville, Dawson, Easton, Foxboro, andGrafton. Then they will go straight back to Acton fromHalpine. They made a detailed map of the route. Use theinformation below to find about how far they will ride.

2. If Sammy and his dad bicycle the same distance each dayfor five days, how many miles will they travel in one day?

3. Make dash marks on the map to show about how farSammy and his dad rode each day.

Acton Brattle

Dawson

Easton Foxboro

Grafton

Capeville

Halpine

Scale:1 inch � 8 miles

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LESSON 21.3

Cap This!MATERIALS string 24 inches long, customary ruler

What’s your cap size?

• Take a string and carefully measure around your head.

• Mark the string, and then lay it down along a ruler. Read the measure to the nearest quarter inch.

• Record your cap size.

• Take a survey to find the cap size of ten of your classmates.

What is the average cap size for the ten classmates in yoursurvey? Explain.

Name Cap Size

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LESSON 21.4

Half Full or Half Empty?

The pitchers below are the same size. They are arranged from barely full to completely full. Each pitcher can be labeled withtwo equal measurements. Use the measures in the box to write in the missing measurement for each pitcher.

8 cups, 3 quarts, 4 quarts,6 pints, 1 gallon, 1 quart, 6 cups

1. 2.

1 pint or 2 cups 2 pints or

3. 4.

3 pints or 4 pints or

5. 6.

or or

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LESSON 21.5

Which Weight?

The weights below belong on the balance scales. Some of thescales are unbalanced. Match each weight listed below with one ofthe problems to make a true statement. Use each weight once.

16 ounces, 32 ounces, 48 ounces, 52 ounces, 96 ounces, 5 pounds, 4,000 pounds, 8 tons

1. 2.

2 pounds � 24 ounces >

3. 4.

4 pounds > 2 tons �

5. 6.

6 pounds � 6 tons <

7. 8.

24 ounces < 3 pounds �

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LESSON 21.6

Atlas StonesAt the annual “World’s Strongest Person” competition, noevent tests athletic strength better than the Stones of Atlas.Competitors must lift six progressively larger round stonesonto 3-foot platforms. The stones are huge—about 2–3 feet indiameter. Their weight is staggering.

The weight of the Stones of Atlas is given in the ancient measurement of stones. A stone is about 14 pounds.

Convert the weight of the 6 Atlas Stones into pounds.

1. 10 stones � lb

2. 13 stones � lb

3. 15 stones � lb

4. 18 stones � lb

5. 20 stones � lb

6. 23 stones � lb

7. In the 1995 event, one competitor executed a dead lift of952 pounds. How many stones would that be?

8. Some of the competitors in the “World’s StrongestPerson” competition weigh 30 stones. What is theirweight in pounds?

9. Figure out how much the following people in Doreen’s family weigh in stones. Complete the chart. Round to the nearest tenth.

Name Weight in Pounds Weight in Stones

Doreen 76

Natalie 92

Jake 105

Mrs. Snell 146

Mr. Snell 207

Point A to Point B

1. Measure and record the length of each line to the nearest centimeter and decimeter.

2. Start at A and measure clockwise until you are back at A.

a. How many centimeters is this measure?

b. How many decimeters is this measure?

c. How many times would you need to measure around

this figure to have a measure of 5 meters?

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A

B

C

DE

F

cm dm

cm dm

cm dm

cm dm

cm dm

cm dm

Wedding Fun

Sam and Sarah are getting married. Their friends are tyingcans to the back of their car. How many meters long is therope they are using?

To find out:

• Place the measures in order from least to greatest in the cake.

• Complete the squares from left to right and frombottom to top.

• Add the measures in the starred boxes to find how long the rope is.

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★

★

7 dm, 250 cm, 1 m, 5 cm, 0.6 m, 1 dm, 180 cm, 14 dm, 0.28 m, 20 dm, 88 cm, 32 cm, 3 dm, 120 cm, 15 cm, 210 cm, 2 cm, 9.0 dm, 0.01 m, 2.15 m, 4.8 dm

Punch All Around

1. List the recipe ingredients from the least to the greatestamount.

2. How much punch will the recipe make in milliliters?

in liters?

3. A punch glass holds about 300 mL. About how many

glasses does the recipe make?

4. You sell a glass of punch for $0.50. How much money will you take in if you sell all the punch one

recipe makes?

5. It costs $4.87 for all the punch ingredients. How much

money will you make?

6. Your punch is so popular, you are asked to makeenough for 100 glasses. How many times will you

need to make the recipe?

7. You charge $0.75 a glass. How much money will

you take in?

8. Your cost for all the ingredients is $38.96. How

much money will you make?

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Fruity-Tutty Punch Recipe

1 liter orange juice250 milliliters pineapple juice500 milliliters apple juice100 milliliters kiwi juice50 milliliters lemon juice2 liters seltzer water

Sweet Enough

How many sugar packs would it take to balance each mass?

1. 2.

1 gram � 2.3 kg �

3. 4.

80 kg � 25 g �

Write the mass in grams and kilograms.

5. 100 sugar packs � 6. 300 sugar packs �

7. 250 sugar packs � 8. 1,000 sugar packs �

9. 3,000 sugar packs � 10. 5,000 sugar packs �

Find the number of sugar packs in each box.

11. 12. 13.

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Ring-A-LingWhen you graph your phone number, does it make a geometric pattern?

YOU WILL NEED grid paper

On a piece of grid paper, follow these directions.

• Start in the center of the grid paper.

• Use the digits in your phone number to decide how farto move in each direction. Write your phone numberfour times in a row.

• Move up (↑ ), then right (→), then down (↓ ), then left(←). Continue this process until there are no more digits.

For example:

The phone number 321-4123 would make the following moves:

• 3 up, 2 right, 1 down, 4 left, 1 up, 2 right, 3 down, 3 left, and so on.

• The result is the figure at the right.

Write your phone number 4 times. Graph your numbers. Compareyour completed geometric pattern with the one shown above andwith one of your classmates’.

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↑ → ↓ ← ↑ → ↓

3 2 1 4 1 2 3

← ↑ → ↓ ← ↑ →

3 2 1 4 1 2 3

↓ ← ↑ → ↓ ← ↑

3 2 1 4 1 2 3

→ ↓ ← ↑ → ↓ ←

3 2 1 4 1 2 3

•start

↑ → ↓ ← ↑ → ↓

3 2 1 4 1 2 3

← ↑ → ↓ ← ↑ →

3 2 1 4 1 2 3

↓ ← ↑ → ↓ ← ↑

3 2 1 4 1 2 3

→ ↓ ← ↑ → ↓ ←

Fahrenheit Match-up

Match the temperature on the thermometer with the event bydrawing a line to connect them.

A

B

C

D

E

F

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LESSON 23.1

Heating UpTemperature is measured indegrees Fahrenheit (°F) in theUnited States. Temperature ismeasured in degrees Celsius (°C)in countries that use the metricsystem and by scientists.

To estimate degrees °F, use this rule.(2 � Celsius temperature) � 32 � � °F

To estimate 25°C in degrees Fahrenheit,replace 25 with the Celsius temperature and solve.

(2 � 25) � 32 50 � 32 � 82

So, 25°C is about 82°F.

Write the temperature that is a better estimate for each activity.

1. ice hockey, 30°C or 30°F 2. running, 50°C or 50°F

3. surfing, 40°C or 40°F 4. swimming, 30°C or 30°F

For 5–6, use the rule above.

5. Your pen pal in Japan writes that it is 20°C outside.Estimate the temperature in °F. Does she need to wear ajacket?

6. You write to your pen pal in Nebraska where it is 9°C.Estimate the temperature in °F. Does your pen pal need ajacket?

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LESSON 23.2

°F

–10 0

10 20 30 40 50 60 70 80 90

100 110 120 130 140 150 160 170 180 190 200 210 220 230

–20

–10

0

10

20

30

40

50

60

70

80

90

100

110 °C

water212 °F boils 100 °C

room68 °F temp 20 °C

water32 °F freezes 0 °C

Number Riddles

Use a number line to help answer these number riddles.

1. I am greater than �20 and less than �18.

2. I am halfway between �2 and �8.

3. I am between �10 and �4. I am 5 units away from 0.

4. I am less than �5 and greater than �20. My two digits

are the same.

5. I am between �11 and �18. The sum of my digits is 5.

6. I am between �20 and �20. My two digits read thesame forward and backward. On the number line, I am

to the left of 0.

7. I am between �16 and �8. I am twice as far away from

0 as 6 is.

8. Make up your own number riddle. Give enough clues sothere can be only one answer.

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LESSON 23.3

-16 -14 -12 -10 -8 -6 -4-18-20 +2 +4 +6 +8 +10 +12 +14 +16 +18 +200-2

Logical ConclusionsYou use inductive reasoning when you make a generalstatement about particular pieces of information.

For example: You know a poodle has 4 legs, a terrierhas 4 legs, a beagle has 4 legs, and a chihuahua has 4 legs. You use inductive reasoning to come to thisconclusion: All dogs have 4 legs.

If you do not use enough information, you may jump to a conclusion.

For example: Joy ate a steak that was tough. She usedinductive reasoning to conclude that all steak is tough.Kent’s steak was tender. He told Joy she jumped to thewrong conclusion.

You use deductive reasoning when you use a general statement to draw a conclusion about a particular situation.

Kayla learned all insects have 6 legs. She counts 8 legs on a spider.She comes to the conclusion that a spider is not an insect.

Write inductive or deductive to tell what kind of reasoning wasused to arrive at each conclusion. If the conclusion is incorrect,write jumped to a conclusion.

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LESSON 23.4

1. Tyrone hears the bell chime onceat 1:00, twice at 2:00, and 3 timesat 3:00. He concludes the bell willchime the number of the hour.

3. Ted looks at this pattern: 1, 4, 7,10, 13, . . . . He concludes thatthe rule for the pattern is � 3.

5. Jedd learned that prime numbershave only 2 factors: 1 and thenumber itself. He concluded that51 is a prime number.

2. In math Merri learned that theproduct of 0 and any number isalways zero. She concludes theproduct of 234,687 and 0 is 0.

4. Ron wrote these multiples of 4:4, 8, 12, 16, 20, and 24. He concluded that the multiples of 4 are even numbers.

6. Lien read that a quadrilateral isa figure that has 4 sides. Sheconcluded that a square is aquadrilateral.

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LESSON 24.1

Checkmate!Materials: colored pencils

The game of chess was invented more than 1,300 years ago. Today it is played in all parts of the world. Eachpiece has its own ways to move. For example:

The king can move onesquare at a time. It can move up, down, left, right, or diagonally.

For 1–4, use the drawing shown at the right.

1. Which chess piece is in g4?

2. Which piece is in c2?

3. Can the king move to h6?

4. Can the bishop move to d8?

The queen is the most powerful chess piece. It can moveany number of squares up, down, left, right, or diagonally.Suppose the queen is in b7. Can it move from b7 to eachof the following squares? Write yes or no.

5. d7 6. d6 7. a4 8. g2

For Exercises 9–11, use colored pencils to color squares on the chess board.

9. Color blue all the squares to which the king can move.

10. Color red all the squares to which the bishop can move.

11. Color yellow all the squares to which the rook can move.

K R

B

A rook can move up, ordown, left, or right. It can move any number of squares.

A bishop can move diagonally any number of squares.

B

R

K87654321

a b c d e f g h

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LESSON 24.2

Length on the Coordinate Grid

On each coordinate grid, graph 2 different rectangles with theperimeter given. Then name the endpoints and find the length of each side.

1. Perimeter: 12 units

Rectangle A:

width:

length:

Rectangle B:

width:

length:

2. Perimeter: 26 units

Rectangle A:

width:

length:

Rectangle B:

width:

length:

3. Explain how you chose your rectangles in Problems 1 and 2.

y-ax

isx-axis

0y-

axis

x-axis

0

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LESSON 24.3

Use an Equation

Play with a partner.

Materials: 1 number cube labeled 2–7

Directions:

Step 1: The first player should write an equation with 2 variables, such as 2x � 1 � y or x � 3 � y, in thetable below and then toss the number cube. Thevalue on the number cube is the value for x.

Step 2: The second player should use this value to find the value for y.

Step 3: Trade roles and repeat steps 1 and 2 until you have 10 equations.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Equation Value for x Value for y

x � y �

x � y �

x � y �

x � y �

x � y �

x � y �

x � y �

x � y �

x � y �

x � y �

Graph an Equation

Complete each table of values. Then graph both equations on the coordinate grid.

1. x � 2 � y 3x � 2 � y

What is the ordered pair of the point where your lines intersect?

This ordered pair contains the only values of x and y that make both equations true.

2. x � 2 � y �12

�x � 1 � y

What is the ordered pair of the point where your linesintersect?

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LESSON 24.4

Input, x Output, y12345678910

Input, x Output, y12345678910

y-ax

is

x-axis

Input, x Output, y2 03 14 25 36 47 58 69 710 8

Input, x Output, y2 24 36 48 510 6

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LESSON 24.5

Identify Relationships

Write the fractions as ordered pairs. Use the numerator as the xvalue and the denominator as the y value. Graph the ordered pairson the coordinate grid and connect the points with a line.

1. �23

�, �24

�, �25

�, �26

�

a. Ordered pairs:

b. If the pattern continued, whatwould be the next ordered pair?

c. If the pattern continued, whatwould be the next fraction?

2. �31

�, �62

�, �93

�, �142�

a. Ordered pairs:

b. If the pattern continued, whatwould be the next ordered pair?

c. If the pattern continued, whatwould be the next fraction?

3. What would be the next fraction in this pattern? �34

�, �68

�, �192�

4. Explain how you solved Problem 3.

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LESSON 25.1

Semaphore Code

The Semaphore Code was used by the United States Navy to send short-range messages. The message sender holds twoflags in various positions to represent the letters of the alphabet.

To make a number, give the “numeral” sign first. Then use A � 1,B � 2, C � 3, and so on for the digits 1–9. Use J for zero.

1. The Semaphore Code makes use of angles. Choose a letter and explain what kind of angle is shown.

2. Write your name by using the Semaphore Code. Forexample, Mark would be

M A R K

3. Now, write the year in Semaphore Code.

A B C D E F G

JI

H

K L M N O

RQ

P

S T U V W

ZY

X

ATTENTION INTERVAL NUMERAL

acute right

straight obtuse

R

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LESSON 25.2

Mapmaker, Mapmaker, Make Me a Map!

Use your knowledge of lines and angles and the following instructions to complete the map. Use a pencil and a ruler.

1. Draw River Road to the north of and parallel to Main Street.

2. Draw High Street to the north of and parallel to River Road.

3. Draw West Lane to the east of the bank and perpendicular to Main Street. West Lane is a line segment from Main Street to High Street.

4. Draw Pine Street to the west of the school and perpendicular to River Road.

5. Draw Hope Ave. to the east of the school and west of the store. Hope Ave. is parallel to West Lane.

6. Draw Devine Drive as a ray beginning at the intersection of West Lane and High Street. It movessouthwest and intersects Main Street east of the store.

7. Draw Last Road perpendicular to Devine Drive, intersecting Main Street west of the bank.

School Store BankMain Street

N

W E

S

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LESSON 25.3

Shapes in MotionHere is your chance to practice flipping, turning, andsliding figures to make a design.

Step 1 Read the numbers in the 4-by-4 grid.

Step 2 Replace the numbers with the matching symbols.

Step 3 Use two colors to make any design in the 4-by-4 grid.

Complete using the steps above. 1.

2.

Use the puzzles above to help you make your own design.

3.

� �

1 2 3 4

3 4 1 2

2 3 4 1

4 1 2 3

�

3 3 3 3

3 3 3 3

1 1 1 1

1 1 1 1

�

1 3 3 1

3 1 1 3

4 2 4 2

1 3 3 1

�

1 �

2 �

3 �

4 �

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LESSON 25.4

a. Start with asquare piece of paper.

d. Fold in half again, along the diagonal.

b. Fold the square in half.

e. Cut out variouspolygons to makea design.

c. Fold in half again.

f. Open the paper and find a symmetricalsnowflake pattern.

Let It Snow!Snowflakes are symmetrical ice crystals, showing both line symmetry and rotational symmetry. You can experimentwith symmetry by making your own snowflakes.

1. Use square pieces of paper to cut out five differentsnowflakes.

2. Test each snowflake. Mark a central point in the middle of the snowflake.

3. Place the snowflake on a sheet of paper. Trace aroundthe snowflake. Shade in the holes of the snowflake.

4. Place a pencil on the central point. Rotate thesnowflake.

Do your snowflakes have rotational symmetry?

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LESSON 25.5

Problem Solving Strategy

Make a Model

Activity: Enlarge a picture.

Directions:

Step 1: Draw a square around the figure you wish to enlarge.

Step 2: Use your ruler to draw a 1-cmgrid on your picture.

Step 3: Draw your figure on the gridbelow. Since the grid you drew on the picture is smallerthan the grid below, you will enlarge your picture.

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LESSON 26.1

Polygons in ArtModern art is often based on geometric figures. Here is a sample.

For 1–4, use the sketch.

1. Label the triangle with the greatest perimeter Triangle 2.Label the other triangle Triangle 1.

2. Are their angles acute, obtuse, or right?

3. Label the gray background rectangle, which is partiallycovered, Rectangle 1.

4. Now, create your own art in this style. Cut geometricshapes from colored paper. Put them together in a creative way.

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LESSON 26.2

Block It Out!

Read the directions for making each figure. Draw, number, and color the figure on the grid below.

1. Figure 1: Draw a square figurewith a perimeter of 4, using 1 square. Color it red.

3. Figure 3: Draw a square figurewith a perimeter of 12, using 9 squares. Color it blue.

5. Figure 5: Draw a figure with a perimeter of 12, using 5squares. Color it yellow.

7. Figure 7: Draw a figure with a perimeter of 16, using 16squares. Color it brown.

2. Figure 2: Draw a rectangularfigure with a perimeter of 10,using 6 squares. Color it green.

4. Figure 4: Draw a figure with a perimeter of 14, using 9squares. Color it black.

6. Figure 6: Draw a figure with a perimeter of 24, using 11squares. Color it purple.

8. Figure 8: Draw a figure with a perimeter of 20, using 21squares. Color it orange.

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LESSON 26.3

Unusual MeasuresA very long time ago, people used body units to measurelengths.

Span length from the end of the thumbto the end of the little fingerwhen the hand is stretched fully

Cubit length from the elbow to thelongest finger

Fathom length from fingertip to fingertipwhen arms are stretched fully inopposite directions

Pace length of a walking step, measured from toe of back foot to toe of front foot

You can use body measures to find the perimeters and areas of objects at school. Record your results in the chart below.

1.

2.

3.

4.

5. Measure the length and the width of your classroom infathoms and in paces.

length of classroom: fathoms; paces

width of classroom: fathoms; paces

Object MeasuredMeasured in Spans Measured in Cubits

Perimeter Area Perimeter Area

Desk Top 14 spans 12 sq spans 9 cubits 4�12� sq cubits

1. Jasmine wrote a story about aflying carpet ride to PlumeIsland. She flew 4,638 milesnorth. Then she flew twice asmany miles east. Finally, Jasmineflew south and reached PlumeIsland. She traveled 15,690 milesin all. How many miles was thelast part of her trip?

3. Two Islanders offered to buy Jasmine’s carpet. Tirianoffered her $500. Miraz offeredher $7.50 per square foot. If theperimeter of the square carpetequals 32 feet, who offeredmore money? How much more?

5. Flying carpets give prizes if youtravel more than 25,000 miles.Can Jasmine get a prize? Howmany miles did she fly? (Hint:See Problems 1 and 4.)

2. Jasmine’s flying carpet not onlyflies—it also changes shape.The perimeter is always 32 feet.Jasmine needs the greatest areato take her new Plume Islandfriends for a ride. What polygonwill give her the greatest possible area? What are thelengths of the sides?

4. Jasmine flew home by a more direct path. Her returnflight was 5,555 miles shorterthan her trip to Plume Island.How far was Jasmine’s returnflight? (Hint: See Problem 1.)

6. Write your own multistep problem about an adventurewith a flying carpet. Show thesolution upside down at thebottom of column 1.

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LESSON 26.4

Flying Carpet Ride

Solve.

Answer:

Relate Formulas and Rules

Find the length and width of each figure.

7. Explain the strategy you used to solve Problems 1–6.

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LESSON 26.5

1. Area � 4 square inches

Perimeter � 8 inches

3. Area � 36 square feet








6. Area � 144 square centimeters

Perimeter � 48 centimeters

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LESSON 26.6

Problem Solving Strategy

Find a Pattern

What if? Use the figures below to give examples that agree withyour answers to the “What If” question.

5. What do you think would happen to the area of a rectangle whose width is multiplied by 4?divided by 4?

1. What if the width of a rectanglewas doubled? What would happen to the area of the rectangle?

3. What if the width of a rectanglewas tripled? What would happento the area of the rectangle?

2. What if the width of a rectanglewas divided by 2? What wouldhappen to the area of therectangle?

4. What if the width of a rectanglewas divided by 3? What wouldhappen to the area of therectangle?

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LESSON 27.1

Riddle, Riddle

Name the plane or solid figure described by each riddle.

1. When you trace one face of a cone or a cylinder, you seeme. What am I?

2. I have 6 flat faces that all look exactly the same. Whatam I?

3. You see two sizes of me when you trace a rectangularprism. What am I?

4. If you trace me six times, you make a cube. What figure am I?

5. I am a solid figure with one round face. What am I?

6. If you trace my 5 faces, you will find a square and triangles. What am I?

7. I have 9 edges, 6 vertices, and 5 faces. What figure am I?

8. I am a solid figure with no vertices or edges. What am I?

9. All 4 of my faces are identical. What solid figure am I?

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LESSON 27.2

Puzzle Watch

Here are two puzzles to solve.

1. A supermarket worker wants to know how many wayshe can stack four cube-shaped boxes. He can stackthem in 1, 2, 3, or 4 layers. Help by finding as manyarrangements as you can. Draw the arrangementsbelow. How many did you find?

2. Use the five points shown below. Connect each pointto all the other points. When you connect the five points,how many triangles can you find in the figure?

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LESSON 27.3

Estimate and Find Volume of PrismsCircle the box in each row that has the greatest volume.

1.

2.

3.

4. Which of the three boxes you circled has the greatest volume?

5. Is it easy to judge the volume of a box by looking at it? Explain.

2 in.

10 in.1 in.

1 in.

1 in.

1 in.

8 in.

2 in.

3 in.

2 in.

3 in.

3 in.

2 in.

8 in.

2 in.

2 in.

2 in.

2 in.

2 in.

2 in.

3 in.

6 in.5 in.

5 in.

4 in.

4 in.

6 in.

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LESSON 27.4

Problem Solving Skill

Too Much/Too Little Information

Each of these problems has too little information. Supply each problem with reasonable data. Solve.

1. Marion wants to build a wooden box that is 20 centimeters long and 15 centimeters high. What is the volume of the box?

2. Rebecca wants to build a box too. She wants it to have the same volume as Marion’s, but a different width. Rebecca wants the box to be 20 centimeters long. What is the height and width of the box?

3. Michael bought some wood to build a box. He wants to build a box that is 10 inches long and 4 inches high. What is the volume of the box?

Pentomino TurnsA pentomino is a figure made of 5 congruent squaresjoined edge to edge. Each square in a pentomino mustshare a side with its neighbor.

These sides do not line up.

These are pentominoes. These are not pentominoes.

In the first column, draw as many pentominoes as you can.In the next 3 columns draw each of your pentominoes as itwould look after a �

14

�, �12

�, and �34

� turn.

Pentomino �41

� turn �21

� turn �43

� turn

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LESSON 28.1

Angle Analogies

Measure the angles in each exercise. Write the measures of the first 3angles in the spaces provided. Then circle the angle that best finishesthe sentence and write the measure of that angle in the last space pro-vided.

Example:

is to as is to .

1.

is to as is to .

2.

is to as is to .

3.

is to as is to .

4.

is to as is to .

40°20°60°30°

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LESSON 28.2

Circles

Help the athletes by choosing the correct plates to put onthe weight-lifting dumbbell bar.

Remember the following:

• The dumbbell bar weighs 45 pounds.

• Plates weigh 5, 10, 25, 35, or 45 pounds.

• A matching plate must be added to both sides tobalance the bar.

• It is quicker to use heavier plates. So, adding one 10-pound plate to a side is better than adding two 5-pound plates to a side.

1. Anna wants to lift 135 pounds. Which plates should she use?

2. Anna wants to increase the weight from 135 pounds to 185 pounds. Which plates should she add?

3. The world record for weight-lifting is 765 pounds.Which plates would be needed for such a task?

4. Mark wants to lift about 300 pounds. What would you suggest he use?

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LESSON 28.3

45 35 25 10 5

Circumference

Each figure below is made from parts of circles and rectangles. Tellhow many circles are in the figure, and then estimate the distancearound each figure.

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LESSON 28.4

1.

2.

3.

4.

5.

a. Number of circles:

b. Estimated distance around:








b. Estimated distance around:10 ft

10 ft

10 ft

6 cm

6 cm

2 yd

2 yd

3 yd

3 yd

2 m2 m

2 m

6 m

2 m

4 m 4 m

9 ft

5 ft

Classify Triangles1. How many different isosceles triangles can you

find and name in the figure below?

equilateral triangles?

scalene triangles?

2. How many different isosceles triangles can youfind and name in the figure below?

equilateral triangles?

scalene triangles?

3. How many triangles are formed when any parallelogramand its diagonals are drawn?

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LESSON 28.5

A B

D

E

C

A

B

D

C

E

A Scavenger HuntQuadrilaterals are all around you. Here is your chance to find them. By yourself or in a small group, find theshapes listed below. Search for shapes in your classroom, on the playground, or at home. Use the chart to record your findings.

Give yourself the following points for each shape.Challenge yourself to find the harder shapes—and score more points!

Rectangle 1 point

Square 2 points

Rhombus 3 points

Trapezoid 4 points

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LESSON 28.6

Shape Found Description Points

rectangle cafeteria table 1

Diagram Detective

It is time for you to be a Diagram Detective. Look at the Venn diagrams in 1 and 2. Choose the labels that best describe each Venn diagram, and write them on the lines provided. You will not use all of the labels.

1.

2.

Think about how these months are related. Then write your own labels for the Venn diagram.

3.

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LESSON 28.7

Venn Diagram LabelsFactors of 12Odd Numbers Between 0 and 20Even Numbers Between 0 and 20Multiples of 3 Less Than 20Multiples of 5 Between 0 and 28Numbers Divisible by 2Factors of 10

A

B

A

B

A B

A B

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LESSON 29.1

Three Coins in a Fountain

When you toss a coin, there are just two possible outcomes:heads or tails.

If you toss two coins at once, there are three possible outcomes:

• 2 heads

• 1 head and 1 tail

• 2 tails

For Problems 1–2, complete the sentence.

1. If you toss three coins at once, there are four possibleoutcomes: 3 heads, 2 heads and 1 tail,

and .

2. If you toss four coins at once, how many possibleoutcomes are there? What are they?

For Problems 3–4, use the table.

Try this experiment. Toss two coins at once,and tally the results of the tosses. Repeat for atotal of 20 tosses.

3. Of the 20 tosses, how many times did youget 2 heads? 1 head and 1 tail? 2 tails?

4. Compare your results with those of your classmates.Which outcome seems more likely: 2 tails or 1 head and 1 tail?

2 Heads 1 Headand 1 Tail 2 Tails

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LESSON 29.2

The Path of Probability

Toss a coin 5 times to follow a probability path from the startto the end boxes.

Rules a. Toss the coin. If it is heads, follow the heads path tothe next oval. If it is tails, follow the tails path.

b. Put a tally mark in an oval for each toss.

c. After 5 tosses, record the letter of the box in whichyou land.

d. Repeat the process 20 times.

1. In which lettered boxes did you finish most often?

2. In which boxes did you finish least often?

Start

Toss 2

tails

tails tails

tailstailstails

tails tails tails tails

tailstailstailstailstailstailstailstails

heads

heads

heads

heads

heads heads

heads

heads

heads

heads

heads

heads heads

heads

heads

A B C D E F

Toss 3

Toss 4

Toss 5

Toss 1

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LESSON 29.3

Mystery CubeYancy wrote 6 different one-digit numbers on a cube.Then he made an identical cube. The line plot shows thesums and the number of ways he could get each sum if hewere to toss his two number cubes.

HINT: If Yancy wrote the numbers 4 and 5 on each cube, he would count

getting 4 � 5 and 5 � 4 as two different ways to toss.

Answer the question.

1. If 1 were the least number on each cube, what would be

the least sum that could be marked on a line plot?

Use the line plot. Complete the table below to find the 6 one-digit numbers Yancy wrote on each cube.

2.

3. The numbers Yancy wrote on each cube are .

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19Sums

? ??

? ??

? � ? � ?

Number ofSum Ways to Toss Ways to Toss the Sum

8 1 4 � 4

9 2 4 � 5, 5 � 4

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LESSON 29.4

A Likely Story

A single dart can land anywhere on this dart board. The player’sscore is the number in the area the dart hits. Tell whether eachevent is likely or unlikely.

1. The score is an odd number.

2. The score is an even number in a shaded section.

3. The score is less than 100.

4. The score is a number divisible by 50.

5. The score is a number divisible by 10.

6. The score is 25 or 50.

7. The score is 10.

8. The dart lands exactly in the center of the board.

9. The dart lands in a shaded section.

10. The dart lands in a section that is not shaded.

10

531

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LESSON 30.1

Certainly Not!

Remember, if an event is certain, it will always happen. Ifan event is impossible, it will never happen.

1. Write numbers in the spinner so that each of the followingevents is certain.

The pointer stopping on a number

A. that is greater than 25

B. that has 12 as a factor

C. that is divisible by 3

D. that has the sum of 8 or more when its two digits are added together

2. Write numbers in the spinner so that each of the eventsabove is impossible.

3. Look at the spinner in Problem 2. Write two more eventsthat would be impossible if you were to use the spinner.

Impossible

Certain

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LESSON 30.2

Heads or Tails?

A coin should land on heads about half of the time.

What if you toss a coin 10 times? Are you likely to get 5 headsand 5 tails?

What if you toss a coin 50 times? Are you likely to get 25heads and 25 tails?

Try these experiments before you answer.

1. Toss a coin 10 times. Record your tallies in the table.

2. Toss a coin 50 times. Record your tallies in the table.

3. Compare your results with those of yourclassmates. How many students got exactly 5 heads and 5 tails? How many students got exactly 25 heads and 25 tails?

4. Find the fraction (in simplest form) of heads for both experiments, as follows.

Experiment 1: number of heads �10

Experiment 2: number of heads �

50

Compare the fractions in Problem 4 with those of your classmates.Then complete 5–7. Write likely or unlikely.

5. If you toss a coin 10 times, you are to getexactly 10 heads.

6. If you toss a coin 50 times, you are to getexactly 50 heads.

7. If you toss a coin 50 times, you are to getbetween 20 and 30 heads.

Heads Tails Total

10

50

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LESSON 30.3

Word WondersThe words and, or, not are small words, but they are veryimportant to the meanings of sentences.

Circle the shape that has 4 sides and has sides thatare the same length.

Circle the shapes that have 3 sides or a consonant.

Circle the shapes that are not triangles.

Use the shapes with the numbers. Write a sentence of your own for each of the words and, or, not. Draw the answer.

4.

5.

6.

A BC D

A BC D

A BC D

For 1–3, use the shapes at the right.

1. Draw the shapes that have exactly4 sides and the number 1.

2. Draw the shapes that are trianglesor have the number 2.

3. Draw the shapes that do nothave exactly 4 sides.

1 2 1 2

1 2 1 21

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LESSON 30.4

Name Mix-Up

Read the clues given. They describethe probabilities of pulling specificstudents’ names from a bag. The sixnames at right were not put intoeither bag. Use the information todecide into which bag each nameshould go. Write the correct nameson the cards below.

GinaErrol

Otis Mia

Javier

Merrilee

Laurence Jamie Kim

Ava Miguel Eddie

Elise Chu Stan

Candace Pearl Bob

Ms. Simon’s Class Bag

The probability of pulling a name

a. beginning with a vowel is �39�, or �

13�.

b. ending in the letter l is �29�.

c. beginning with the letter J, K,L, or M is �

69�, or �

23�.

Mrs. Kipp’s Class Bag

The probability of pulling a name

a. ending in a vowel is �59�.

b. with 5 or more letters is �39�, or �

13�.

c. beginning with the letter V is �09�.

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