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Challenge Workbook PUPIL EDITION Grade 5 Orlando • Boston • Dallas • Chicago • San Diego www.harcourtschool.com

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Page 1: Challenge Workbook, Grade 5 (PE) - Selamat datang di kelas Ibu …kelas-ibu-yudith.weebly.com/uploads/3/2/1/2/32121015/5th... · 2019-09-01 · The Chinese Abacus An abacus is one

ChallengeWorkbook

P U P I L E D I T I O NGrade 5

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

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Copyright © by Harcourt, Inc.

All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy,recording, or any information storage and retrieval system, without permission in writing from the publisher.

Permission is hereby granted to individual teachers using the corresponding student’stextbook or kit as the major vehicle for regular classroom instruction to photocopycomplete pages from this publication in classroom quantities for instructional use andnot for resale.

Duplication of this work other than by individual classroom teachers under theconditions specified above requires a license. To order a license to duplicate this work in greater than classroom quantities, contact Customer Service, Harcourt, Inc.,6277 Sea Harbor Drive, Orlando, Florida 32887-6777. Telephone: 1-800-225-5425. Fax: 1-800-874-6418 or 407-352-3445.

HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc.

Printed in the United States of America

ISBN 0-15-320432-X

2 3 4 5 6 7 8 9 10 082 2004 2003 2002 2001

©H

arco

urt

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Unit 1: USE WHOLE NUMBERS ANDDECIMALS

Chapter 1: Place Value of WholeNumbers1.1 The Chinese Abacus . . . . . . . . . . . . . . 11.2 Some Solar Sums . . . . . . . . . . . . . . . . 21.3 Busy Airports . . . . . . . . . . . . . . . . . . . . 31.4 Number Detective . . . . . . . . . . . . . . . 41.5 Languages of the World . . . . . . . . . . 5

Chapter 2: Place Value of Decimals2.1 About the Abacus . . . . . . . . . . . . . . . 62.2Find the Message! . . . . . . . . . . . . . . . 72.3 The Equalizer . . . . . . . . . . . . . . . . . . . . 82.4Place the Values . . . . . . . . . . . . . . . . . 92.5 Mystery Numbers . . . . . . . . . . . . . . . . 10

Chapter 3: Add and Subtract WholeNumbers3.1 Rounding Fun . . . . . . . . . . . . . . . . . . . 113.2 Find the Missing Numbers . . . . . . . . 123.3 Mystery Message . . . . . . . . . . . . . . . . 133.4 A Path of Greater Numbers . . . . . . . 143.5 Logical Reasoning . . . . . . . . . . . . . . . . 15

Chapter 4: Add and Subtract Decimals4.1 Traveling Gum . . . . . . . . . . . . . . . . . . . 164.2Estimate . . . . . . . . . . . . . . . . . . . . . . . . 174.3 Around the World . . . . . . . . . . . . . . . 184.4How Much Farther? . . . . . . . . . . . . . . 194.5 Super (Market) Estimations . . . . . . . 20

Unit 2: ALGEBRA, DATA, ANDGRAPHING

Chapter 5: Algebra: Use Addition5.1 Secret Message . . . . . . . . . . . . . . . . . . 215.2 Distance Dilemma . . . . . . . . . . . . . . . 225.3 Veterinary Wonders . . . . . . . . . . . . . . 235.4 Closure Property . . . . . . . . . . . . . . . . 245.5 In the Hole . . . . . . . . . . . . . . . . . . . . . . 25

Chapter 6: Algebra: Use Multiplication6.1 What’s My Pattern? . . . . . . . . . . . . . . 266.2Mystery Triangles. . . . . . . . . . . . . . . . 276.3 Flying Away . . . . . . . . . . . . . . . . . . . . . 286.4Cross-Number Puzzle . . . . . . . . . . . . 29

Chapter 7: Analyze Data and Graphs7.1 Home on the Range . . . . . . . . . . . . . . 307.2 Hungry Hamster. . . . . . . . . . . . . . . . . . 317.3 Pick One! . . . . . . . . . . . . . . . . . . . . . . . 327.4 Don’t LEAVE Me Out!! . . . . . . . . . . . . 337.5 Camp Out . . . . . . . . . . . . . . . . . . . . . . 34

Chapter 8: Make Graphs8.1 Selective Scales . . . . . . . . . . . . . . . . . 358.2Dollar Data . . . . . . . . . . . . . . . . . . . . . 368.3 What’s the Biggest

Animal? . . . . . . . . . . . . . . . . . . . . . . . . 378.4Find the Error! . . . . . . . . . . . . . . . . . . . 388.5 Matt’s Bike Log . . . . . . . . . . . . . . . . . . 398.6Which Is Which? . . . . . . . . . . . . . . . . . 40

CONTENTS

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Unit 3: MULTIPLY WHOLE NUMBERSAND DECIMALS

Chapter 9: Multiply Whole Numbers9.1 Zeroing In on an Answer . . . . . . . . . . 419.2 Crossing Numbers . . . . . . . . . . . . . . . 429.3 The Case of the

Lost Digits . . . . . . . . . . . . . . . . . . . . . . 439.4 Letter Go! . . . . . . . . . . . . . . . . . . . . . . 449.5 On the River . . . . . . . . . . . . . . . . . . . . 45

Chapter 10: Multiply Decimals10.1 A Trip to the Grocery Store . . . . . . 4610.2 Windy Conditions . . . . . . . . . . . . . . 4710.3 Mystery Triangles . . . . . . . . . . . . . . . 4810.4 Tiny Numbers . . . . . . . . . . . . . . . . . . 4910.5 The Distributive Property

and Decimals . . . . . . . . . . . . . . . . . . . 5010.6 Decisions, Decisions . . . . . . . . . . . . 51

Unit 4: DIVIDE WHOLE NUMBERS AND DECIMALS

Chapter 11: Divide by 1-Digit Divisors11.1 Division Spiral . . . . . . . . . . . . . . . . . . 5211.2 Math Tip . . . . . . . . . . . . . . . . . . . . . . . 5311.3 How High Can You Climb? . . . . . . . 5411.4 Digit Discovery . . . . . . . . . . . . . . . . . 5511.5 Number Pyramids . . . . . . . . . . . . . . . 5611.6 Create a Problem . . . . . . . . . . . . . . . 57

Chapter 12: Divide by 2-Digit Divisors12.1 Division Puzzles . . . . . . . . . . . . . . . . 5812.2 What’s the Problem? . . . . . . . . . . . . 5912.3 Number Pyramids . . . . . . . . . . . . . . . 6012.4 Division Designs . . . . . . . . . . . . . . . . 6112.5 Division Tip . . . . . . . . . . . . . . . . . . . . 6212.6 Number Patterns . . . . . . . . . . . . . . . 63

Chapter 13: Divide Decimals by Whole Numbers13.1 Riddle Jumble . . . . . . . . . . . . . . . . . . 6413.2Share and Share Alike! . . . . . . . . . . . 6513.3 Right to Left and Left to Right . . . . 6613.4Tricky Tickets! . . . . . . . . . . . . . . . . . . 6713.5 Calculating Fractions . . . . . . . . . . . . 68

Chapter 14: Divide Decimals by Decimals14.1 Circular Patterns . . . . . . . . . . . . . . . . 6914.2 Number Maze . . . . . . . . . . . . . . . . . . 7014.3 Number Puzzle . . . . . . . . . . . . . . . . . 7114.4 Food for Thought . . . . . . . . . . . . . . . 72

Unit 5: FRACTIONS, RATIO, AND PERCENT

Chapter 15: Number Theory15.1 Divisibility Rules! . . . . . . . . . . . . . . . 7315.2 What’s Next? . . . . . . . . . . . . . . . . . . . 7415.3 Math Puzzles . . . . . . . . . . . . . . . . . . . 7515.4 It’s All Relative . . . . . . . . . . . . . . . . . 7615.5 Number Pyramids . . . . . . . . . . . . . . . 7715.6 Take 10 (� 10, � 10, � 10. . . .) . . . . 7815.7 Equal Powers . . . . . . . . . . . . . . . . . . . 7915.8 Factor Phone . . . . . . . . . . . . . . . . . . . 80

Chapter 16: Fraction Concepts16.1 Riddlegram! . . . . . . . . . . . . . . . . . . . . 8116.2 Fix the Pattern . . . . . . . . . . . . . . . . . 8216.3 Batter Up! . . . . . . . . . . . . . . . . . . . . . 8316.4 Riddle Time . . . . . . . . . . . . . . . . . . . . 8416.5 Greater Than One! . . . . . . . . . . . . . . 8516.6 Use Models . . . . . . . . . . . . . . . . . . . . 86

Chapter 17: Ratio17.1 Word Ratios . . . . . . . . . . . . . . . . . . . 8717.2 Winning Ratios . . . . . . . . . . . . . . . . . 88

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17.3 Ratio Art . . . . . . . . . . . . . . . . . . . . . . . 8917.4 Solar Ratios . . . . . . . . . . . . . . . . . . . . 9017.5 Rate the Ratios . . . . . . . . . . . . . . . . . 91

Chapter 18: Percent18.1 Percents with Style . . . . . . . . . . . . . 9218.2 Understanding Standings . . . . . . . . 9318.3 Find the Match! . . . . . . . . . . . . . . . . 9418.4 Sale!! . . . . . . . . . . . . . . . . . . . . . . . . . . 9518.5 Strange Dimensions . . . . . . . . . . . . . 9618.6 Fast-Food Facts . . . . . . . . . . . . . . . . . 9718.7 Town Budgets . . . . . . . . . . . . . . . . . . 98

Unit 6: OPERATIONS WITHFRACTIONS

Chapter 19: Add and Subtract Fractions19.1 Guess Where I Go . . . . . . . . . . . . . 9919.2 Missing Parts . . . . . . . . . . . . . . . . . . 10019.3 Mystery Fraction . . . . . . . . . . . . . . 10119.4 Cut Me Up! . . . . . . . . . . . . . . . . . . . 10219.5 The Race Is On! . . . . . . . . . . . . . . . 10319.6 Hal’s Hat Store . . . . . . . . . . . . . . . . 10419.7 Model Fractions . . . . . . . . . . . . . . . 105

Chapter 20: Add and Subtract Mixed Numbers20.1 And the Answer Is . . . . . . . . . . . . . 10620.2Subtraction Madness . . . . . . . . . . . 10720.3 Fraction Fill-in . . . . . . . . . . . . . . . . . 10820.4Add or Subtract? . . . . . . . . . . . . . . 10920.5Unfolding! . . . . . . . . . . . . . . . . . . . . 110

Chapter 21: Multiply Fractions21.1 Parts of Wholes! . . . . . . . . . . . . . . . 11121.2 3-D Fractions . . . . . . . . . . . . . . . . . . 11221.3 Which Model? . . . . . . . . . . . . . . . . . 11321.4 Four Square . . . . . . . . . . . . . . . . . . . 11421.5 Fraction Triangles . . . . . . . . . . . . . . 115

Chapter 22: Divide Fractions22.1 Division Detective . . . . . . . . . . . . . 11622.2Find My Reciprocal . . . . . . . . . . . . 11722.3 Dividing Fractions Rule . . . . . . . . . 11822.4Rule Tables . . . . . . . . . . . . . . . . . . . . 11922.5 Make It Simpler . . . . . . . . . . . . . . . 120

Unit 7: ALGEBRA AND GEOMETRY

Chapter 23: Algebra: Integers23.1 Puzzle Me This . . . . . . . . . . . . . . . . 12123.2 Riddle Me This . . . . . . . . . . . . . . . . 12223.3 Sum It Up . . . . . . . . . . . . . . . . . . . . . 12323.4 Write the Problem . . . . . . . . . . . . . 12423.5 Integer Adds and Subtracts . . . . . 12523.6 Going the Distance . . . . . . . . . . . . 126

Chapter 24: Geometry and theCoordinate Plane24.1 Fraction Functions . . . . . . . . . . . . . 12724.2 A Fish Story . . . . . . . . . . . . . . . . . . . 12824.3 Changing Intervals . . . . . . . . . . . . . 12924.4 Making a Duplicate . . . . . . . . . . . . 130

Chapter 25: Plane Figures25.1 What’s the Point? . . . . . . . . . . . . . . 13125.2 A Star Is Born! . . . . . . . . . . . . . . . . . 13225.3 Measure Me . . . . . . . . . . . . . . . . . . . 13325.4 Divide and Conquer! . . . . . . . . . . . 13425.5 Find the Congruent Shapes! . . . . . 13525.6 Finish the Pictures . . . . . . . . . . . . . 13625.7 Other Tessellations . . . . . . . . . . . . 137

Chapter 26: Classify Plane and Solid Figures26.1 Triangle Land . . . . . . . . . . . . . . . . . . 13826.2Venn Diagrams . . . . . . . . . . . . . . . . 13926.3 How Did I Get Here? . . . . . . . . . . . 14026.4Crossed Words . . . . . . . . . . . . . . . . 141

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26.5 What a View! . . . . . . . . . . . . . . . . . . 14226.6Elementary, My Dear Watson . . . 143

Unit 8: MEASUREMENT

Chapter 27: Customary and Metric Systems27.1 Can You Measure Up? . . . . . . . . . . 14427.2 Can You Still Measure Up? . . . . . . 14527.3 It Doesn’t Add Up . . . . . . . . . . . . . 14627.4 The Stones of Atlas . . . . . . . . . . . . 14727.5 How Full Is It? . . . . . . . . . . . . . . . . . 14827.6 One Life to Live . . . . . . . . . . . . . . . 14927.7 Metric Dominoes . . . . . . . . . . . . . . 150

Chapter 28: Perimeter and Area28.1 Perimeter Puzzle . . . . . . . . . . . . . . 15128.2 A Slice of Pi . . . . . . . . . . . . . . . . . . . 15228.3 Castle Creations . . . . . . . . . . . . . . . 15328.4 Rectangle Challenge . . . . . . . . . . . 15428.5 Triangle Match-Up . . . . . . . . . . . . . 15528.6 Parallelograms Large

and Small . . . . . . . . . . . . . . . . . . . . . 15628.7 Go Team . . . . . . . . . . . . . . . . . . . . . 157

Chapter 29: Surface Area and Volume29.1 Create a Package . . . . . . . . . . . . . . . 15829.2 Paint the Barn . . . . . . . . . . . . . . . . . 15929.3 Boxed In . . . . . . . . . . . . . . . . . . . . . . 16029.4 Stack ’em Up . . . . . . . . . . . . . . . . . . 16129.5 Operation 45 . . . . . . . . . . . . . . . . . . 162

Unit 9: PROBABILITY

Chapter 30: Probability30.1 Don’t Flip Out! . . . . . . . . . . . . . . . . 16330.2 Summing It Up . . . . . . . . . . . . . . . . 16430.3 The Path of Probability . . . . . . . . . 16530.4 Three Coins in a Fountain . . . . . . . 16630.5 Presidential Probability . . . . . . . . . 167

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The Chinese AbacusAn abacus is one of the first calculating tools. The best knownChinese abacus, called the suan pan, is shown in this lesson.

To make and read numbers, move beads toward the center bar and add. For example:

4 7 0 9 5 � 47,095 2 3 8 4 6 1 � 238,461

Write the number shown on the abacus.

1. 2.

Name

Challenge CW1

©H

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LESSON 1.1

← Each bead above the bar represents 5 units.

← center bar

← Each bead below the bar represents 1 unit.

← The abacus is arranged like a place-value chart.

hu

nd

red

th

ousa

nd

s

ten

th

ousa

nd

s

thou

san

ds

hu

nd

red

s

ten

s

ones

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Some Solar SumsThe table lists the average distances between planets.

Use the information in the table above to write how many mileseach planet is from the sun.

1.

2.

3.

4.

5.

6.

7.

8.

9.

Name

CW2 Challenge

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LESSON 1.2

DISTANCES BETWEEN PLANETSPlanets Distance Between (in miles)

Sun to Mercury 35,960,000Mercury to Venus 31,040,000Venus to Earth 25,900,000Earth to Mars 48,700,000Mars to Jupiter 341,700,000Jupiter to Saturn 403,100,000Saturn to Uranus 899,600,000Uranus to Neptune 1,007,000,000Neptune to Pluto 871,000,000

DISTANCES FROM SUN TO PLANETS

Planet Distance from Sun (in miles)

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

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Busy AirportsHartsfield International Airport in Atlanta, Georgia is the

world’s busiest airport for passenger travel, based on 2000data. The table lists cities with the number of passengersserved each year.

Keep the table in order from greatest number of passengers to leastnumber of passengers and number these cities where they belong:

1. Between which two cities would you place Tokyo with54,338,212 passengers?

2. Where would you place Paris with 43,596,943 passengers?

3. Which airports have about the same number of passengers?

4. Which city’s airport is ranked number 2? Explain.

Name

Challenge CW3

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LESSON 1.3

Rank City Passengers

1 Atlanta 77,939,536

3 Los Angeles 63,876,561

5 Dallas/Ft. Worth 60,000,125

7 San Francisco 40,387,422

Frankfurt 45,858,315 passengers

Chicago 72,568,076 passengers

London 62,263,710 passengers

Denver 38,034,231 passengers

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Number DetectiveUse the clues to figure out the mystery numbers. Select your answers from the list on the right.

1. This number is greater than 35,897. It is different in only the thousands place. It is less than 39,000.

2. This number is 100,000 less than1,327,495.

3. This number is the same as 437,876except for the digit in the thousands place. This number is greater than437,000.

4. This number is the same as 28,987 inthe thousands place and the tens place.

5. This number is between the numbers1,567,435 and 1,568,227.

6. This number is the same as 43,675 in the hundreds place. It is the same as 575,098 in the ones place. It is the same as 684,521 in the hundred thousands place.

Name

CW4 Challenge

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LESSON 1.4

a. 1,078,482

b.637,608

c. 37,897

d.434,876

e. 1,568,300

f. 439,876

g.656,758

h.1,567,932

i. 1,227,495

j. 39,897

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Languages of the WorldRead the following facts about languages.

Use the facts to answer the questions.

Did you know that there are over 2,700 languages spoken in the world? Over 1,000 languages are spoken just on the continent of Africa. Today many Americans speak two languages, English and the language of theirancestors. The most widely spoken language in the world in2000 is Mandarin Chinese, with 1,034 million speakers.Some of the other most common languages are English, with508 million speakers; Spanish, with 392 million speakers;and Arabic, with 246 million speakers. Other widely spokenlanguages include Hindi, spoken by 497 million people;Bengali, spoken by 211 million people; and Russian, spokenby 277 million people.

On the lines below, list the world’s most widely spoken languages in order from greatest to least. The first line iscompleted for you. List the numbers in standard form.

LANGUAGE NUMBER OF SPEAKERS

1. Mandarin Chinese 1,034,000,000

2.

3.

4.

5.

6.

7.

8. How many languages are spoken by your classmates?

Name

Challenge CW5

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LESSON 1.5

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About the AbacusThe abacus is a calculating machine that has been used for thousands of years. In ancient times, the abacus consisted of rows of grooves in sand into which pebbles were placed. Today’s abacus, known as the Chinese suan pan, consists of beads strung on parallel wires. Each wire represents a place value.

Each bead above the bar represents 5.The beads move next to the bar to count 5s.

Each bead below the bar represents 1.The beads move up to the bar to count 1s.

Write the number represented by the abacus.

1. 2. 3.

4. 5. 6.

Draw beads on the abacus to represent the number.

7. 2,358.41 8. 8,642.09 9. 3,962.15

Name

CW6 Challenge

©H

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LESSON 2.1

thou

sand

shu

ndre

dste

nson

este

nths

hund

redt

hs

7 6 5 4.3 2

bar →

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Find the Message!

Write each number in standard form. Use your answers to breakthe code.

A. eight thousandths U. 0.90 � 0.10 C. �1,

10400�

D. sixty-five ten thousandths E. 1.0 � 0.2 � 0.007 R. 0.2 � 0.02

T. seven hundredths H. �13,02070

� I. one hundred onethousandths

Y. 0.1 � 0.02 X. �160,3,04050

� L. 0.053 � 0.07

M. 0.43 � 0.03 O. fifty-two P. sixteen thousandths hundredths

Name

Challenge CW7

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LESSON 2.2

0.12

0.008

1.207

0.052

0.6345

1.000

0.0065

0.16

1.207

1.207

0.008

0.014

0.22

0.22

0.101

0.07

1.207

0.4 0.008 0.123

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The Equalizer

Each number in the column at the right is a decimal equal to anumber in a circle. Write the letter of the decimal next to itsequivalent in a circle. You may use some letters more than once.

A � 0.002

B � 16.02

C � 40.0100

D � 36.450

E � 0.060

F � 81.6

G � 6.14

H � 31.0

I � 21.220

J � 29.000

K � 11.61

L � 25.25

M � 445.450

N � 21.7

O � 76.67000

P � 8.210

Q � 4.0100

R � 97.41

S � 0.12

T � 0.00200

U � 16.0200

Make three words using the letters in eachcircle.

Name

CW8 Challenge

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LESSON 2.3

76.6

7 0.120

25.250 16.02081.60

4.01

8.21

29

11.6100

97.4100 6.140021.70

0.0020

40.01

16.0

200 0.06

0.002000 445.4531.00

21.22

36.45

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Place the ValuesYou can make several different numbers that all use thesame digits.

The following numbers all use the digits 0, 2, 5, 6, 7, and 9.

205.679; 5,076.92; 592.067; 620.597

Complete the tables. There are many different correct answers.

1. Use the numbers 0, 1, 2, 5, 6, 7, 9. Create four 7-digit numbers of increasing value.

2. Use the numbers 0, 2, 3, 4, 6, 8, 9. Create four 7-digitnumbers of decreasing value.

3. Use the numbers 0, 1, 2, 4, 5, 7, 8. Create four 7-digitnumbers of increasing value.

Name

Challenge CW9

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LESSON 2.4

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

Thousands Hundreds Tens Ones Tenths Hundredths Thousandths

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Mystery NumbersUse the clues below to draw conclusions and find each person’s mystery number.

Clue 1: All numbers have place values to the thousandths.

Clue 2: Vince’s number is the greatest number.

Clue 3: Holly’s number is the least number of the group.

Clue 4: Jennifer’s number is five thousandths less than Robert’s.

Clue 5: Jane’s number is the same as Lynn’s number except for the ones place.

Clue 6: Glenn’s number has the same digits as Lynn’s, with onesand hundredths having the same value.

Clue 7: The least number is Lynn’s number minus 0.136.

Clue 8: The digit in the tenths place of Glenn’s number is 1 lessthan the digit in the hundredths place.

Clue 9: The ones digit in Jane’s number is 2 less than the onesdigit in the greatest number.

Name

CW10 Challenge

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LESSON 2.5

Name Mystery Number

Jane

Lynn 1.154

Jennifer

Robert 4.019

Holly

Vince 4.021

Glenn

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Rounding FunFind three numbers that would round to

1. 45,900 when rounding to the nearest hundred.

2. 53,980 when rounding to the nearest ten.

3. 120,000 when rounding to the nearest ten thousand.

Find three numbers that when rounded to the nearest ten are

4. greater than 34,720 but less than 34,740.

5. less than 235,430 but greater than 235,400.

Name

Challenge CW11

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LESSON 3.1

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Name

CW12 Challenge

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LESSON 3.2

Find the Missing NumbersFind the missing number to make the problem correct.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12. 21,000����

19,000� 51,000���

37,000

36,000����

14,000

11,000����

2,000

� 60,000���

10,000

11,000����

8,000

8,800

4,2003,300

����

22,300

112,000

212,000333,000

�����

957,000

24,000

22,00033,000

�����

114,000

1,000

4,000� 5,000����

16,000

2,5001,4003,200

�����

80,000

1,000

2,000� 3,000����

10,000

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Mystery MessageWhy did the astronaut throw a plate out the window?

To find the answer, subtract.

1.

T

2.

G

3.

L

4.

O

5.

U

6.

A

7.

F

8.

I

9.

Y

10.

E

11.

N

12.

C

13.

S

14.

R

15.

!

Locate each of your answers below. Put the letter that correspondsto it in the matching box to solve the riddle.

98,312� 6,172����

48,314� 12,386����

4,280� 1,699���

7,224� 3,568���

6,976� 2,697���

8,251� 4,627���

4,593� 2,646���

463475

� 366���

1,465� 876��

398987

� 628���

74,460� 12,143����

8,266� 5,380���

63,947� 14,138����

4,636� 2,564���

14,136� 10,024����

Name

Challenge CW13

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LESSON 3.3

4,112 2,886 2,581 3,624 3,624 2,013

589 78,085 1,947 1,304 4,279 2,072

2,581 2,013 86,603 3,656 3,624 35,928 92,140

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A Path of Greater Numbers

Complete each path so that each expression is correct.

PATH A

PATH B

PATH C

Create your own path.

��

��

451,341�

�35,613,500�716,678

153,872�

450,970�52,098�

��103,130,713

��

789,927,888�

�335,613,500�456,716,678

Name

CW14 Challenge

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LESSON 3.4

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Use Logical Reasoning

1. Fran, Kate, Nick, Louis, and Ray all ride bicycles. In one year, Kate traveled twice as far as Fran and half as much asNick. Nick traveled 1,000 miles.Louis traveled three times as faras Kate, and Ray traveled twice as far as Nick. Fill in the table at the right.

2. Fran, who just turned 24, is theyoungest of the group. Ray is twoyears older than Fran and half theage of Nick. Louis is thirty yearsold and two years younger thanKate. Fill in the table at the right.

3. The five cyclists represent twofamilies: the Smiths and theBrowns. The Smith family has two males and no females. Ray isKate’s brother. Place the correctnames in the table at the right.

Name

Challenge CW15

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LESSON 3.5

Name Miles Traveled

Name Age

Name Family Name

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Traveling GumWhy did the gum cross the road?

To find the solution, round each number to the specifiedplace value. Then write the letter of the correct answer inthe space above the problem number.

Round each to the nearest one.

1. 3.18 (A) 4 (E) 3 (O) 3.2 2. 7.61 (T) 8 (S) 7 (P) 7.5

3. 18.43 (O) 19 (E) 18.4 (I) 18 4. 7.02 (L) 7.1 (B) 8 (C) 7

Round each to the nearest tenth.

5. 3.18 (C) 3 (G) 3.1 (K) 3.2 6. 7.61 (E) 7.5 (O) 7.6 (I) 7.7

7. 18.43 (S) 18 (T) 18.4 (R) 18.5 8. 7.02 (A) 7 (U) 7.0 (O) 7.1

Round each to the nearest hundredth.

9. 0.76314 (K) 0.75 (C) 0.76 10. 14.246 (R) 14.246 (T) 14.24

(S) 0.763 (H) 14.25

11. 9.1725 (U) 9.173 (O) 9.17 12. 7.406 (M) 7.407 (C) 7.40

(A) 9.18 (S) 7.41

Round each to the nearest thousandth.

13. 0.76314 (L) 0.7631 (C) 0.763 14. 14.2463 (B) 14.25 (K) 14.246

(N) 0.7632 (H) 14.24

15. 9.1725 (N) 9.173 (R) 9.172 16. 7.4067 (D) 7.406 (F) 7.407

(S) 9.17 (G) 7.41

It was to the ’s

!

Name

CW16 Challenge

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LESSON 4.1

12 2 8 13 5 4 10 3 9 14 1 15

16 6 11 7

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Estimate

Round each number to the place value noted on the card. Thenadd or subtract. Circle the estimate for each sum or difference.

Name

Challenge CW17

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LESSON 4.2

1.

3.

5.

2.

4.

6.

To the nearesttenth29.76

�37.21���?

67

67.1

66.9

66.8

To the nearesttenth23.24

�11.58���?

11.7

11.4

11.5

11.6

111.59 111.6To the nearest

hundredth48.357

�63.248���?

To the nearest

hundredth67.361

�28.475���?

111.61 111.6538.88 38.85

38.87 38.86

To the nearest

hundredth84.309

�51.266���?

135.57 135.56

135.58 135.59

To the nearest

hundredth156.826

�73.994���?

82.86 82.83

82.85 82.84

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Around the World

Begin at start. Add or subtract clockwise. In each box write anumber to add or subtract. Write each answer on the line withthe equal sign. Be sure that your answer at the end equals the starting number.

1.

2.

Name

CW18 Challenge

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LESSON 4.3

15.8 0.04

6.0567.2

� �

Start:

End:

� 83.0

� 82.96

� 76.91

67.2 �

45.3

� �

Start:

End:

45.3 �

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How Much Farther?

Freddy Four is traveling from Count City to Problem Solver’sLanding. He knows the distance between Problem Solver’sLanding and Count City is 297 miles.

The distance between each town is marked on the map. Ateach town, write down the distance remaining for Freddy totravel.

Name

Challenge CW19

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LESSON 4.4

Start

Finish

County City 297 mi

23.9 mi

Tally Town

19.4 mi

Chart City

42.18 mi

Total Town

25.8 mi

Curve City

16.41 miTable Town

23.85 miCalculator City

8.04 mi

Tax Town

Centimeter

City

6.72 mi

3.8 mi

Time Town

32.14 miCircle City

56.3 mi

Triangle

Town

23.26 mi

CompassCity

Problem Solver'sLanding

15.2 mi

Page 26: Challenge Workbook, Grade 5 (PE) - Selamat datang di kelas Ibu …kelas-ibu-yudith.weebly.com/uploads/3/2/1/2/32121015/5th... · 2019-09-01 · The Chinese Abacus An abacus is one

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 .

Name

CW20 Challenge

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LESSON 4.5

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Secret Message

Write an expression for each problem. Use the extra informationgiven in each problem to find the value of the variable. Matchthe value of the variable to values in the message below. Placethe first initial of the person’s name in the problem on the spaceabove the value.

Name

Challenge CW21

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urt

LESSON 5.1

1. Glynis had 8 dolls inher collection. Shereceived some moredolls as gifts. (Nowshe has 11 dolls.)

4. Ramon mowed 3lawns in the morning,and more in theafternoon. (He mowed7 lawns that day.)

7. Linda bicycled 5 miles. Then shewent farther. (Sherode 12 miles in all.)

10. Fred had 22 coloredpencils. He lostsome. (Then he hadonly 5 left.)

2. Salvatore had 15houseplants and thensome died. (Now hehas only 4 plantsleft.)

5. Ursula had 55 ceramictiles to install. Shedropped a box andbroke some. (She had35 tiles left.)

8. Alejandro boughta breeding pair ofgerbils. They had alitter. (Now Alejandrohas 8 gerbils.)

11. Nick made 12 modelairplanes. His sisterbroke some. (Now hehas only 10 left.)

3. Al planted 16 rosebushes. Then hebought some more.(He now has 22 rosebushes.)

6. Egbert had 64 stampsin his collection. Hebought some more.(Then he had 72stamps.)

9. Betty practiced pianofor 15 minutes. Afterdinner she practicedsome more. (Shepracticed for a totalof 27 minutes.)

12. Ivan’s puppy weighed 8 pounds. Then hegained weight. (Now thepuppy weighs 13pounds.)

6

5

7

11

3 8

17

12

20

4

2

6

!

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Distance DilemmaDr. Jacquelinemust travelbetween citiesduring the weekto explain hernew invention.

Use the schedule to answer the questions. Write an equationwith a variable.

1. What distance did Dr. Jacqueline travel on

Monday? Thursday?

Tuesday? Friday?

Wednesday?

2. What is the difference between the miles from Chart Townto Tax Town and from Tax Town to Compass Town?

3. On what two days does Dr. Jacqueline’s travel equal themiles traveled on Wednesday?

Name

CW22 Challenge

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LESSON 5.2

Dr. Jacqueline’s ScheduleFrom To Total Distance

Mon. Home Town Chart Town to Triangle Town 250 milesTues. Triangle Town Circle Town to Chart Town 150 miles Wed. Chart Town Tax Town to Compass Town to Edgar Town 400 milesThurs. Edgar Town Tax Town to Mill Town to Grove Town 90 milesFri. Grove Town Time Town to Home Town 200 miles

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Veterinary WondersThe Veterinary Clinic in Giant Springs schedules patientsduring the week.

Use the schedule to write an equation. Then solve it.

1. The veterinarian saw 30 birds during the week. Howmany birds did he see on Monday?

2. Noah groomed all of the dogs for the veterinarian. Ifthere were 21 dogs at the clinic on Thursday and Friday,how many dogs did he groom on Friday?

3. The veterinarian goes to the farm each week to see 18horses. This week, he had to cancel Wednesday’sappointments. How many horses did he see this Friday?

4. How many more dogs were seen on Thursday than onWednesday and Monday?

5. All of the cats on Tuesday and Friday received a rabiesshot. How many cats did not receive a rabies shot?

Name

Challenge CW23

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LESSON 5.3

Veterinary ClinicMonday Tuesday Wednesday Thursday Friday

Dogs 6 4 10 dCats 3 6 7 4Turtles 4 1Snakes 3 4 1Lizards 1Birds b 14Cows 10Horses 6 3 4 h

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Closure PropertyYou have learned different properties of addition likethe Communative Property, Associative Property, andProperty of Zero.

Another property is called the Closure Property.

If a set of numbers is closed under an operation, or satisfiesthe Closure Property, then when you perform the operationon any number in the set, you will always get anothernumber in that set.

If you add two numbers in the set of even numbers, you willalways get another even number.

2 � 4 � 6

2 � 8 � 10

So, the set of even numbers is closed under addition.

Test to see if each set of numbers and the operation satisfy theClosure Property.

1. Odd numbers and addition.

2. Even numbers and multiplication.

3. Odd numbers and multiplication.

4. Odd numbers and subtraction.

Name

CW24 Challenge

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LESSON 5.4

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In the HoleA formula can be used to find the perimeter of a rectangle.You can also use a formula to find the area of a rectangle.

The area of a rectangle is equal to the product of the lengthand the width of the rectangle. If A represents the area, lrepresents the length, and w represents the width, the formula would look like this: A � l � w. Find the perimeterand area of each figure.

1. 2.

Perimeter: Perimeter:

Area: Area:

Hint: Think of the differencein the areas of the tworectangles.

3. 4.

Perimeter: Perimeter:

Area: Area:

20 ft

20 ft

30 ft

130 ft

100 ft

100 ft

30 ft

70 ft

40 ft30 ft 70 ft

60 ft30 ft

20 ft

40 ft

20 ft

30 ft

60 ft

90 ft

30 ft

50 ft90 ft

50 ft

50 ft50 ft

10 ft

10 ft

50 ft30 ft

30 ft

20 ft

20 ft

90 ft

Name

Challenge CW25

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LESSON 5.5

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Name

CW26 Challenge

LESSON 6.1

What’s My PatternWrite an expression to explain the pattern.

1. 2.

3. 4.

5. 6.

7. 8. 542, 533, 524, 515, 50646, 43, 40, 37, 34

2, 5, 11, 23, 473, 6, 12, 24, 48

86, 74, 62, 50, 387, 14, 21, 28, 35

13, 24, 35, 46, 5726, 36, 46, 56, 66

9. (n � 4)

156, 160, , ,

10. (n � 18)

253, 235, , ,

11. (n � 2) � 5

23, 51, , ,

12. (n � 10) � 3

21, 93, , ,

Create your own pattern. Use at least 5 numbers to show your pattern. Write theexpression that describes your pattern.

Write the next three numbers in the pattern.

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Mystery TrianglesThe numbers in the boxes are the products of thenumbers in the circles. Write an equation for each side andfind the missing numbers.

1.

3.

5.

2.

4.

6.

Name

Challenge CW27

LESSON 6.2

a

b2 10

6 15

c d

h

g

k l

j

i

f

e

24 28

42 7

24 14

784

36

4

72

32

9

15 45

27

18

48

8

24

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Name

CW28 Challenge

LESSON 6.3

Flying Away

Sharon has let go of her balloons. The only way they won’t fly away is if you solve the equations. Then use the directions below to color the balloons.

1. Color red the balloons that use the Zero Property of multiplication.

2. Color blue the balloons that use the Property of One.

3. Color green the balloons that use the Associative Property.

4. Color orange the balloons that are left. Write somethingabout the factors in these balloons.

5. Why do the equations in the red balloons equal 0?

4 � (5 � 6) �(4 � n) � 6

n � 1 � 7

3 � n �0

9 � n � 0

3 � 6 � n 5 � n � 0

n � 1 � 5

4 � 2 �2 � n

8 � (3 � 4) �(8 � 3) � n

(3 � 2) � 6 �3 � (2 � n)

9 � 2 �n � 9n � 1 � 8

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Name

Challenge CW29

LESSON 6.4

Cross-Number Puzzle

This cross-number puzzle is a multiplication puzzle thatillustrates the Distributive Property.

Solve the puzzle 9 � 8 � n this way.• Put the factors in the rectangles as shown.• Break each factor into 2 of its addends. Record the

addends along the top and right side of the drawing.

9 � 5 � 4

• 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, 9 � 8 � 72.

Complete the cross-number puzzles.

1. 8 � 7 � n 2. 14 � 36 � n

9

5

43

58 8 � 5 � 3

9274572

5152540 �

4122032

3

58

8

4

45

27

14

� 36

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Home on the Range

Ranger Kate keeps track of antelope herdsize each month for a year.

This year the range in the numberof antelopes in the herd is 86 � 23 � 63.

Find the range for each of these other herd counts:

1. 2.

For 3-4, use the clipboard below.

Herd SizeJan- 125Feb- 106

Mar- 138Apr- 1 1 1

May- 148Jun - 156

Jul- 1 4 1Aug- 192

Sept- 167Oct - 1 73

Nov- 145Dec- 132

Herd SizeJan-35Feb-42

Mar-50Apr-55

May-72Jun -64

Jul-68Aug-36

Sept-75Oct -84

Nov-52Dec-32

Name

CW30 Challenge

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LESSON 7.1

Herd SizeJan-35Feb-42

Mar-60Apr-55

May-72Jun - 74

Jul-68Aug-86

Sept-75Oct-64

Nov-52Dec-23

Herd SizeJan-103Feb-?

Mar-1 1 1Apr-1 14

May-125Jun -137

Jul-122Aug-93

Sept-87Oct-98

Nov-96Dec-91

3. Find the range of the herd counts from Julythrough December.

4. The range for the whole year was 55. Find twopossible values for the herd count for February.Which answer do you think was the actualherd count? Why?

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Hungry HamsterMrs. Morgan’s class recorded the temperature in a table fourtimes a day for five days. Unfortunately, the class hamsterchewed some holes in the paper containing the table. Usethe information provided to fill in the missing data.

1. The mean temperature at 9:00 A.M. was 32°. Fill in the

temperature at 9:00 A.M. on Thursday.

2. Find the mean of the temperatures recorded on

Thursday. Mean �

3. The mean temperature on Tuesday was 23°. Fill in the

temperature at 1:00 P.M. on Tuesday.

4. The mean temperature on Wednesday was 45°. Fill in the

temperature at 11:00 A.M. on Wednesday.

5. The mean temperature at 1:00 P.M. was 35°. Fill in the

temperature at 1:00 P.M. on Friday.

6. Find the mean temperature at 3:00 P.M. Mean �

7. If the actual temperature at 3:00 P.M. on Monday was 41°,what would be the new mean for 3:00 P.M.? How much

would the mean change? Mean �

TEMPERATURE (° Fahrenheit)

DAY 9:00 A.M. 11:00 A.M. 1:00 P.M. 3:00 P.M.

MONDAY 31 33 37 31

TUESDAY 25 22 24

WEDNESDAY 42 47 47

THURSDAY 38 40 43

FRIDAY 27 28 30

Name

Challenge CW31

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LESSON 7.2

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LESSON 7.3Name

CW32 Challenge

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urt

Pick One!Once there were three rats called Mean, Median, and Mode.They were given their names because the numbers they atewere best described by the mean, median, or mode of thenumbers.

Find the mean, median, and mode for each rat. Decide if the mean,median, or mode best describes most of the numbers inside the rat.Then name each rat Mean, Median, or Mode.

Name:

Name:

2

214

16

15

74 20

16 17 15

76 19

18

2

12

83

56

2

Name:

527

361

1006

12101

6102

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Don’t LEAVE Me Out!!Angela keeps track of her math test scores by keeping a list.To organize her scores, she started to make a stem-and-leafplot but stopped before she was finished. Use the factsbelow to finish Angela’s plot.

Stem Leaves

7 8 9

8 2 4 7 9

9 1 3 6

For 1–3, use the information given to fill in the numbers missingfrom Angela’s chart. Explain how you found the missing number.

1. The mode of Angela’s test score data is 84.

2. The range of the test scores is 21.

3. The mean of Angela’s test scores is 86.

4. What is Angela’s median test score?

5. Angela studied hard for her next test and got a perfect100! How can you add this score to her stem-and-leaf plot?

Name

Challenge CW33

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arco

urt

LESSON 7.4

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Camp OutJacob’s family has justreturned from theirannual camping trip.Jacob recorded the hightemperature each dayand made this line graphto display the temperatures.

For each statement, tellwhether it is a conclusion that can be drawn from the graph.Explain your answer in the space provided.

1. It was cloudy most of the week.

2. It got warmer toward the end of the trip.

3. Jacob did not pack enough warm clothes.

4. The best weather was on Friday.

5. Monday was colder than Thursday.

Name

CW34 Challenge

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LESSON 7.5

Tues Wed Thurs Fri

DAILY TEMPERATURE

DayTe

mpe

ratu

re (d

egre

es F

)

0

20

40

60

80

Mon

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Selective ScalesNajuma wants to display thenumber of phone calls she getseach day for a week.

Use the data in the table to complete each graph. Use theintervals noted below each graph.

For Problems 1–3, use the graphs above.

1. Which graph uses an interval that makes the best use ofthe space? Explain.

���������������������������������������������������������������������������������������������������������

2. On which graph were points more difficult to graph? Explain.

���������������������������������������������������������������������������������������������������������

3. What is similar and what is different about graphs B and C?

Name

Challenge CW35

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LESSON 8.1

Phone CallsMon Tue Wed Thu Fri

2 10 8 7 24

01234

567

8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

M T W Th F

Phone Calls

By 1's

024

6

8 10

12

14

16

18 20

22 24 26

M T W Th F

Phone Calls

By 2's

0

2

4

6

8

10

12

14

16

18

20

22

24

26

M T W Th F

Phone Calls

By 2's

0

5

10

15

20

25

M T W Th F

Phone Calls

By 5's

A B C D

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Dollar DataThe U.S. Treasury Department is responsible for makingsure there are enough of each type of bill in circulation.

1. Complete the table.

*Not printed since 1977.

2. Complete the bar graph using the data from the table above.

3. About how many trillion dollars were in circulation?

4. Compare the number of $10 and $20 bills in circulation.

Name

CW36 Challenge

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urt

LESSON 8.2

NUMBER OF U.S. BILLS IN CIRCULATION IN 1999

Type of Bill Amount in Circulation Number of Bills in Circulation

$1 bills $6.7 trillion 6.7 trillion

$2 bills* $1.2 trillion 0.6 trillion

$5 bills trillion 1.5 trillion

$10 bills trillion 1.5 trillion

$20 bills trillion 4.35 trillion

$50 bills trillion 1.0 trillion

$100 bills trillion 3.26 trillion

NUMBER OF U.S. BILLS IN CIRCULATION IN 1999

Num

ber

of B

ills

(in t

rilli

ons)

0

1.0

2.0

3.04.0

5.0

6.0

7.0

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What’s the Biggest Animal?What animal is the biggest? How big is it?

To find the answer, use the coordinate grid below. On theblank above the ordered pairs, put the letter of the point towhich the ordered pair refers.

Name

Challenge CW37

©H

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LESSON 8.3

0

2

4

6

8

10

2 4 6 8 10

U

G

LE

OI

T

H

RW

NM

A

BS

P

(5,6)

(9,7)

(9,7)

(9,4)

(2,4)

(4,3)

(4,3)

(2,4)

(1,2)

(0,5)

(2,4)

(7,3)

(2,1)

(7,8)

(2,4)

(0,5)

(1,9)

(2,4)

(9,0)

(6,1)

(2,4)

(4,3)

(4,3)

(0,5)

(10,2)

(5,6)

(7,3)

(3,7)

(4,3)

(8,5)

(2,4)

(7,3)

(5,6)

(8,5)

(10,2)

16

.

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Find the Error!

Mike would like to use a double-line graph to display thedata in the table.

There are 8 errors in Mike’s double-line graph above. Find each error and explain how each should be fixed.Then draw an accurate double-line graph using the data table above.

Name

CW38 Challenge

©H

arco

urt

LESSON 8.4

4-MONTH SALES RECORD

Month Company A Company B

January $120 million $140 million

February $160 million $180 million

March $100 million $100 million

April $140 million $120 million

SALES IN THOUSANDS OF $

Months

4-Ye

ar S

ales

Rec

ord

0Jan Feb Mar Apr

20406080

100120140160180200

Company 1 Company 2

1.

2.

3.

4.

5.

6.

7.

8.

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Matt’s Bike Log

Using Matt’s Bike Trips information above, create the log bookthat could be represented by the histogram.

Matt’s Bike Log

Name

Challenge CW39

©H

arco

urt

LESSON 8.5

Date Miles Date Miles Date Miles

MATT’S BIKE TRIPS

10–19 20–29 30–39 40–49 50–59

10

8

6

4

2

0

Num

ber o

f Trip

s

Miles Traveled

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Which Is Which?

Graphs A and B were made using the same data.

Graph A Graph B

1. You are an employee of the Kazam Toy Company. Which graph would you use to convince others how well your company is doing compared with the competition? Explain.

2. You are an employee of Multimedia Games. Which graph would you use to show how well your company is doing compared with the competition? Explain.

3. Why do the two graphs look so different? Explain.

4. What interval would more honestly represent both companies’ sales?

Name

CW40 Challenge

©H

arco

urt

LESSON 8.6

70

50

01999 2000

Sale

s in

Mill

ions

($)

Year

130

110

90

Toy Company Sales

Kazam Toy CompanyMultimedia Games

120

80

40

01999 2000

Toy Company Sales

Sale

s in

Mill

ions

($)

YearKazam Toy CompanyMultimedia Games

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Zeroing In on an AnswerCity budgets have very large figures. This chart gives one figure for each cityfor each type of expenditure. Estimate the answers to complete the chart.

Name

Challenge CW41

©H

arco

urt

LESSON 9.1

General Police Public EducationGovernment Works

Nottingham 45,955 120,980

Circleville 178,555

Stanfordshire 55,280

1. Circleville spent 10 times as much asNottingham for its General Government.

2. Stanfordshire spent 8 times as much asCircleville for its Police protection.

3. Nottingham spent 24 times as much asStanfordshire on Public Works.

4. Circleville spent twice as much asNottingham on Education.

5. Stanfordshire spent three times as much asNottingham on Education.

6. Circleville spent 18 times as much asStanfordshire on Public Works.

7. Nottingham spent 5 times as much asCircleville for Police protection.

8. Stanfordshire spent 4 times as much onGeneral Government as did Nottingham.

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LESSON 9.2Name

CW42 Challenge

©H

arco

urt

31,246

3

93,738�7 �

81,328 ��

60,996 ��3

� 4 � 9,621124,984

4

4,555

18,220

476

2

4

38,484

� �

�401

1,203

8

17,229

137,832

2

487,968 6,4257 �� 44,975

243,984

656,166

7 �� 120,603

6,345 25,380��

� 27,330

1,361

9,527

2

50,760

6

365,976

952

Crossing NumbersFind the products.

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LESSON 9.3Name

Challenge CW43

©H

arco

urt

The Case of the Lost Digits

Some numbers are missing. Be a math detective and find the missing digits.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

� ,

, 4191

0471

4

3

8

,

� ,

, 4901

29

841

832

,

� ,

, 771

1041

73

8

764

,

� ,

, 890

0312

83

4

45

� ,

, 002

0051

6

82

7

� ,

, 1882

08

02

4

7

,

� ,

, 86004

6183

801

36 �

� ,

, 57422

72

52

3

57

,

� ,

, 05733

003

53

5

57

,

� ,

, 420

0521

0

626

,

� ,

, 145

074

131

1

5

,

� ,

, 032

0411

81

5

83

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LESSON 9.4Name

CW44 Challenge

©H

arco

urt

Letter Go!

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

1. 2. 3.

There are 32 There are 42 There are 4possible solutions. possible solutions. possible solutions.

4. 5. 6.

There are 3 There are 2 There are 2possible solutions. possible solutions. possible solutions.

��

��

��

��

��

��

��

��

��

��

��

��

��

��

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

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Up the RiverThe chart below tells the length of the four rivers.

1. A barge working on the Mackenzie River traveled up anddown the river 22 times. How many miles did the barge travel? Show the reasonableness of your exact answer byestimating to nearest thousand.

2. If a barge on the Missouri traveled 50 miles an hour for 12hours, how many more miles would the driver need to completehis way down the river?

3. Because he worked on river barges for a living, Mr. Mac hadmade 130 round trips up and down the Missouri River. Mr. Macsaid that he traveled over 1 million miles. Is his answer reason-able? Explain.

4. A team of 12 huskies made 3 round trips up and down the banksof the Yukon. How many miles did each husky travel? Estimateyour answer for reasonableness.

5. Mike, being an outdoor person, took it upon himself to travel thelength of all four rivers. How far did he travel? Estimate youranswer for reasonableness.

Name

Challenge CW45

©H

arco

urt

LESSON 9.5

Name of River Length of River in Miles

Mackenzie 1,120

Mississippi 2,348

Missouri 2,315

Yukon 1,990

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A Trip to the Grocery Store

Use the price table to answer the following questions.

5. Make a grocery list for the Richardson family using the price table above. Find the total amount spent on groceries.

Total cost:

Name

CW46 Challenge

©H

arco

urt

LESSON 10.1

Item Price Item Price

Bread $0.89 Milk $2.88Pizza $6.20 Cheese $2.50Orange Juice $3.19 Butter $1.05Salad $1.50 Spaghetti Noodles $0.56Tortilla Shells $1.84 Spaghetti Sauce $1.95

1. Mr. Stolz wants to buy bread,milk, two pizzas, and three pack-ages of tortilla shells. How muchwill it cost to buy these groceries?

3. Which costs more, 4 containersof milk, or 3 containers of orangejuice? How much more?

2. Mrs. Lee wants to buy 2 pack-ages of noodles, a jar of sauce,and 5 salads. How much will itcost to buy these groceries?

4. How many packages of cheesecan you buy with a twenty-dollarbill?

Item to Buy Price Quantity Total Price for Items

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Windy Conditions

For 1–8, find the product. Then write the product in words.

1. 0.03 � 1,000

2. 0.1 � 10

3. 0.0068 � 10

4. 0.134 � 1,000

5. 100 � 0.0057

6. 0.0248 � 100

7. 0.0083 � 100

8. 10 � 0.00097

Use the first letter from the written products aboveto complete the sentence.

Since it was so windy yesterday, Wendy wore her windbreaker

the blow.

Name

Challenge CW47

©H

arco

urt

LESSON 10.2

1 2 3 4 5 6 7 8

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Name

CW48 Challenge

©H

arco

urt

LESSON 10.3

Mystery Triangles

The numbers in the squares are the products of the numbers inthe circles. Find the missing numbers.

1. 2.

3. 4.

5. 6.

0.3

0.06 0.15

0.2 0.1 0.5

0.8

0.48 0.24

0.6 0.18 0.3

0.4

0.24 0.28

0.6 0.42 0.7

0.5

0.15 0.45

0.3 0.27 0.9

0.2

0.04 0.06

0.2 0.06 0.3

0.1

0.08 0.02

0.8 0.16 0.2

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Name

Challenge CW49

©H

arco

urt

LESSON 10.4

Tiny Numbers

What comes after the ten-thousandths place? Use the pattern tocomplete the table.

Complete the next 2 rows of the table.

Write the place value of the product if you multiplied:8. tenths � tenths

10. tenths � ten-thousandths

12. hundredths � hundred-thousandths

9. hundredths � tenths

11. tenths � millionths

13. thousandths � thousandths

2 � 0.1 � 0.2two � one tenth �two tenths

2 � 0.01 � 0.02two � one hundredth �two hundredths

2 � 0.001 � 0.002 two � one thousandth �two thousandths

2 � 0.0001 �two � one ten-thousandth �two ten-thousandths

2 � 0.00001 �two � one hundred-thousandth �two hundred-thousandths

2 � 0.000001 �two � one millionth �two millionths

2 � 0.0000001 �two � one ten-millionth �two ten-millionths

2 � 0.00000001 �two � one hundred-millionth �two hundred-millionths

1.

2.

3.

4.

5.

2 � � 0.000000002two � �

two billionths

2 � 0.0000000001 �two � one ten-billionth �

6.

7.

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The Distributive Property and DecimalsSuppose you wanted to find the product 53 � 39. One way tofind the product is to use place value and the DistributiveProperty. Since 39 � 30 � 9, you can write the product 53 � 39as 53 � (30 � 9) � (53 � 30) � (53 � 9). So, now you can find theproduct by finding 53 � 30 and adding this to 53 � 9. The sameidea can be used for multiplying two decimals. For example, tofind the product 0.32 � 0.084, you can write 0.084 � 0.08 �0.004. So, the product 0.32 � 0.084 can be found by solving(0.32 � 0.08) � (0.32 � 0.004) � 0.0256 � 0.00128 � 0.02688.

Use place value and the Distributive Property to find the products.

10. Describe a way to find the product 0.189 � 0.0436 using placevalue and the Distributive Property. Then find the product.

Name

CW50 Challenge

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LESSON 10.5

1. 28 � 0.072

4. 0.041 � 0.19

7. 0.12 � 0.12

2. 1.3 � .091

5. $1.20 � 0.025

8. 0.77 � 0.099

3. 0.52 � 0.062

6. 7.9 � 0.0037

9. 0.55 � 0.033

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Decisions, DecisionsWe make decisions every day, and we often use severalpieces of information to make these decisions.

Describe four decisions that you made during the past weekthat involved numbers as part of the information you used tomake the decision. Those numbers might have been price,time, or distance.

Now, describe two decisions that you made during the past weekthat involved numbers but were not the best decision to make.

Name

Challenge CW51

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LESSON 10.6

Decision Information Used

Decision What Information Would Have Helped YouMake the Best Decision?

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Division SpiralChoose the correct divisor. Start with 480,000 and carry out a division operation at each step to follow the spiral to the center.Write the divisor in each circle.

Name

CW52 Challenge

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LESSON 11.1

480,000

4,000

500

2,000

100

20,000

60,000

25

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Name

Challenge CW53

©H

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LESSON 11.2

Math Tip

Write the letter of the correct quotient from Column 2. Then,in the box at the bottom of the page, write the letter above thematching problem number. You will discover the math tip!

Column 1 Column 2

1. 351 � 3 A. 70

2. 747 � 9 B. 29

3. 156 � 6 C. 63

4. 210 � 3 D. 117

5. 256 � 8 E. 67

6. 133 � 7 I. 83

7. 74 � 2 L. 47

8. 116 � 4 M. 22

9. 448 � 8 N. 56

10. 315 � 5 O. 32

11. 486 � 6 P. 97

12. 188 � 4 R. 19

13. 477 � 9 S. 53

14. 194 � 2 T. 26

15. 201 � 3 U. 81

16. 176 � 8 V. 78

17. 468 � 6 Y. 37

10

9

15

5

11

17

16

16

15

14

8

9

4

15

12

3

6

7

2

13

8 12

1

15

2 17 2 1 15

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LESSON 11.3

How High Can You Climb?

Can you get to the top of these steps? Solve the division problem at the bottom. Then put that answer on the next step and solve the problem. Continue to the top.

� � 9

� 3 �

1. 540 � 5 �

� � 3

� 5 �

2. 960 � 8 �

� � 8

� 6 �

3. 720 � 3 �

� � 11

� 4 �

4. 616 � 2 �

� � 1

� 5 �

5. 860 � 4 �

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�����������

����������������

Name

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LESSON 11.4

Digit Discovery

Write the missing digits.

1. 2. 3.

4. 5.

8 �4 4 8� 4 0

�4 80

4 2

7 3 7 9

9

�2 8

�1 40

3 8 r

6 2 5 7

3

�3 05

�4 8

5

������������5 6 2 r

9 1 3

� 4

3

�������������5 r

3 7 5 5 6� 6

1 5

0

� 32 6

2

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Name

CW56 Challenge

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LESSON 11.5

Number Pyramids

The numbers in the pyramids are found by using one ofthese simple formulas:

A � B � C orC � A � B orC � B � A

If you know some of the numbers, you can find the ones thatare missing.

To find the top number, multiply12 � 14 � 168.

To find the number on thelower right, divide 14 � 2 � 7.

Fill in the missing numbers.

1. 2.

3. 4.

C

A B

14 16

5 9

15

9 14

9

26

10

35

67

17

10 12 6

72

6

7 3

84

4

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LESSON 11.6

Create a Problem

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

1. 237 � 4 �

Problem

3. 822 � 8 �

Problem

5. 735 � 4 �

Problem

2. 637 � 6 �

Problem

4. 207 � 8 �

Problem

6. 517 � 2 �

Problem

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LESSON 12.1

Division Puzzles

Solve the equations.Then complete the puzzle.

1 0

0

6 0

5

0

0

7 0 0

0

5 0 0

0 04

3

14

11

9

7

4

3

5

6

8

10

12

15

17

16

13

1

29

0

0 04

0005

0

00003

8

001

0

0 0 0

8

0

02 0 0

7

02

0 0

Across

1. 150 � 50 �

2. 72,000 � 80 �

3. 36,000 � 90 �

4. 10,000 � 20 �

5. 24,000 � 60 �

6. 30,000 � 6 �

7. 63,000 � 90 �

8. 1,600 � 200 �

9. 2,500 � 50 �

10. 900,000 � 30 �

11. 42,000 � 70 �

12. 8,000 � 80 �

13. 560 � 70 �

14. 200 � 20 �

15. 100,000 � 5 �

16. 140 � 20 �

17. 12,000 � 6 �

Down

1. 9,000 � 30 �

2. 810,000 � 90 �

3. 800 � 20 �

4. 35,000 � 70 �

5. 1,600 � 40 �

6. 45,000 � 90 �

7. 42,000 � 60 �

8. 400,000 � 5 �

9. 3,000 � 60 �

10. 180 � 6 �

11. 18,000 � 30 �

13. 560,000 � 70 �

16. 4,900 � 70 �

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LESSON 12.2

What’s the Problem?

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

1. 1,489 � 28 � n

Problem:

Compatible numbers:

3. 63,147 � 879 � n

Problem:

Compatible numbers:

5. 758 � 42 � n

Problem:

Compatible numbers:

2. 7,100 � 93 � n

Problem:

Compatible numbers:

4. 276 � 37 � n

Problem:

Compatible numbers:

6. 41,797 � 561 � n

Problem:

Compatible numbers:

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Number Pyramids

The numbers in the puzzles are found by using one of these formulas:

A � B � C or C � A � B or C � B � A

To find the top number, multiply:12 � 14 � 168.

To find the number in the lowerright box, divide: 14 � 2 � 7.

Fill in the missing numbers.

1. 2.

3. 4.

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LESSON 12.3

A

C

B

12 14

6 2

168

7

15

73 2

648

36

16

81

3

9

3,888

72

6

7 3 4

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LESSON 12.4

Division DesignsThe number in the center of each design is an estimate of the four division exercises.

If the estimate is just right, color the problem red.If the estimate is too low, color the problem green.If the estimate is too high, color the problem blue.

1. 2.

3. 4.

� 19037 4 � 9623

� 26083

� 25061

� 10119 6 � 29542

� 24137

� 31551

� 6,70095 70 � 4,45074

� 3,00036

� 5,89083

800

� 24,00029

� 15,70016

� 32,00038

� 17,80026

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LESSON 12.5

Division Tip

Write the letter of the correct answer from Column 2 on the linein Column 1. Then write the letter on the line or lines with thematching problem number in the box at the bottom of the page.

Column 1

1. 842 � 41

2. 19,432 � 22

3. 119 � 16

4. 367 � 26

5. 14,820 � 19

6. 758 � 65

7. 496 � 92

8. 34,339 � 51

9. 613 � 72

10. 547 � 86

11. 1,932 � 35

12. 60,140 � 97

13. 3,721 � 46

14. 5,745 � 71

15. 11,780 � 23

16. 2,602 � 44

Column 2

A. 14 r3

B. 5 r36

C. 6 r31

D. 883 r6

E. 80 r41

H. 673 r16

I. 780

M. 620

N. 512 r4

O. 7 r7

P. 59 r6

R. 8 r37

S. 20 r22

T. 80 r65

V. 55 r7

W. 11 r43

9 13 12 13 12 7 13 9 14 3 10 3 12 16 4 9 13 14 8 13

9 13 12 4 5 15 2 13 9 6 5 14 8 14 8 13 2 5 11 5 1 3 9

.4 14 13 4 10 8 1 14 13 16

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LESSON 12.6

Number Patterns

Write a rule. Then find the next three numbers in the pattern.

1. 26, 33, 47, 68, , ,

Rule:

2. 7.6, 9.1, 11.6, 15.1, , ,

Rule:

3. 631, 620, 610, 601, , ,

Rule:

4. 87, 91, 99, 111, 127 , ,

Rule:

5. 396, 391, 381, 366, , ,

Rule:

6. 17, 68, 34, 136, 68, , ,

Rule:

7. 23, 46, 138, 552, , ,

Rule:

Try making your own pattern. See if a classmate can figure it out.

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Riddle JumbleComplete the division patterns to answer the riddle.

Riddle: What do strawberries do when they feel crushed?

Order your answers from least to greatest. Write thematching letters in the boxes.

!

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LESSON 13.1

30,000 � 6 � A

3,000 � 6 � 500

300 � 6 � K

3 � 6 � H

56,000 � 7 � 8,000

5,600 � 7 � J

56 � 7 � M

5.6 � 7 � Y

54,000 � 9 � 6,000

5,400 � 9 � E

540 � 9 � 60

5.4 � 9 � E

320,000 � 8 � M

32,000 � 8 � 4,000

320 � 8 � A

3.2 � 8 � T

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LESSON 13.2

Share and Share Alike!

A granola company advertisesthat its new dog-shaped bar isbig enough to share.

There are many ways for 2people to share 1 bar equally.Here are two ways.

Each person will get 7.5 chunks.

Show 2 ways to share 1 bar equally. Tell how many chunks each person gets.

1. if 3 people share

3. if 5 people share

2. if 4 people share

4. if 6 people share

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LESSON 13.3

right armleft arm

left footright foot

4.05

4.12

9.2 6.84

23.65 2.5 9.18

1.3

72.24 59.5 0.56 418.4

3 4

5 6

7 8

Right to Left and Left to RightThe persons below are missing the decimals in their handsor feet. The missing numbers are

Place the numbers in their hands and feet so that

1. when you divide the left arm by the number in the bellyyou get the right foot.

2. when you divide the right arm by the number in the bellyyou get the left foot.

1.53

0.07

2.3

10.32

0.5

4.73

1.35

8.5

1.71

52.3

7.8

12.36

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LESSON 13.4

Tricky Tickets!Eight groups of people bought tickets to different events.The envelopes containing the tickets got mixed up. Usethe clues below to help match the envelopes with theamount of money each group paid.

Clues:

1. Each group’s total amount paid was evenly divisibleby the number of people in the group. For example, $9.45 � 9 � $1.05 each.

2. Each group has a different number of people in it. Thegroups have 2, 3, 4, 5, 6, 7, 8, and 9 people in them.

3. Each group paid a different price for its tickets.

4. The group with 2 people in it got a better ticket pricethan the group with 3 people in it.

5. The group of 4 people got a better ticket price than thegroup of 6 people.

6. The prices paid were: $5.67, $7.14, $9.20, $10.92, $12.57,$13.75, $14.21, and $19.14.

Tota l :

EachTicketPr i ce :

Enve lope wi th2 t i ckets

Tota l :

EachTicketPr i ce :

Enve lope wi th3 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th4 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th5 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th9 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th8 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th7 t i c kets

Tota l :

EachTicketPr i ce :

Enve lope wi th6 t i c kets

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Name

CW68 Challenge

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LESSON 13.5

Calculating Fractions

You can see if two fractions are equivalent by changing them todecimals.

Divide the numerator by the denominator in each fraction.Round the answer to the nearest hundredth where necessary.Does �

14� � �

28� ?

1 � 4 � 0.25 �14

� � 0.25

2 � 8 � 0.25 �28

� � 0.25

So, �14

� � �28

�. They are equivalent.

Are the fractions equivalent? Use a calculator to find out. Roundto the nearest hundredth where necessary. Write yes or no.

1. �68

� �

�3400� �

4. �12

� �

�4998� �

7. �187� �

�14082

� �

10. �78

� �

�112562

� �

13. �23

� �

�2485� �

2. �79

� �

�7979� �

5. �1270� �

�4550� �

8. �5684� �

�1136� �

11. �35

� �

�16160

� �

14. �1201� �

�139909

� �

3. �56

� �

�1156� �

6. �1241� �

�2323� �

9. �34

� �

�6868� �

12. �1260� �

�6860� �

equal

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Circular Patterns

Each circle holds four numbers. Choose from these numbersto complete each division pattern. The first one has beendone for you.

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Challenge CW69

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LESSON 14.1

1. 360� 4 � 90

36 � 0.4 � 90

3.6�0.04 � 90

3. �5 � 27

� 0.5 � 27

� � 27

5. � � 19

� � 19

� � 19

7. � � 33

� � 33

� � 33

9. � � 40

� � 40

� � 40

2. 120� �

12 � � 3

1.2 � � 3

4. 126� � 21

� � 21

1.26� � 21

6. � � 4

� � 4

� � 4

8. � .65 �

� 6.5 �

� 65 �

0.04

40

3.6

4

0.05

1.35

13.5

1.35

0.0595

9.55

0.5

0.95

4,6200.14

462

4.62

.014

141.4

46.2

.01950.03

19.50.03

0.195

0.06

1.95

0.03

480

0.001248

12

36

0.12

4.8

1.2

0.4

40

4

3

0.06

12.6

6

0.6

0.0936

93.6

0.36

0.9

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LESSON 14.2

Number Maze

Solve.

1. 36 � 0.6 � 2. 30 � 0.06 � 3. 3 �0.006 �

4. 0.2 � 0.01 � 5. 20 � 0.05 � 6. 0.02 � 0.05 �

7. 0.4 � 8 � 8. 40 � 0.8 � 9. 0.04 � 0.8 �

10. 0.8 � 0.02 � 11. 0.08 � 0.02 � 12. 0.008 � 0.02 �

13. 0.1 � 0.4 � 14. 10 � 0.4� 15. 1 � 0.4 �

Find the numbers for division sentences in the maze. Problems canbe written horizontally, vertically, and diagonally left to right.One is done for you.

0.04 500 0.8 50 0.8 0.02 40 60 0.4 0.4

0.8 2 0.08 40 500 300 30 0.02 20 8

0.05 0.2 30 0.06 20 40 0.008 0.08 25 0.05

5 30 0.6 0.02 0.05 0.4 400 0.5 10 0.4

0.08 80 50 0.06 400 100 0.1 50 0.4 500

300 0.02 2.5 3 4 0.04 0.8 600 25 0.02

0.08 250 4 0.006 0.5 40 0.8 80 400 0.04

100 30 0.06 500 0.1 0.01 0.04 0.25 0.02 0.5

0.4 2.5 0.2 0.05 4 400 500 0.1 0.4 0.25

500 0.04 0.08 0.8 300 1 0.4 2.5 0.8 0.06

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LESSON 14.3Name

Challenge CW71

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Number Puzzle

Find the quotients. Then find the sum of the quotients for each set of 3 circles by following the arrows.

1.

2.

0.14���0�.2�9�1�2� 0.15��0�.2�6�7�

0.16���0�.2�8�0.08��0�.3�1�1�2� 0.15��0�.0�5�4�

0.13���0�.3�2�1�1�

0.2��0�.2�08��

0.2��0�.7�7�2�

0.23��0�.5�8�4�2�

0.26��0�.9�3�6� 0.25��1�.2�7�5�

0.12���0�.2�6�0�4�

0.25��1�.0�1�7�5� 0.29��.6�0�0�3�

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Food for ThoughtLisa kept a log of what supplies were delivered to her grocery store last week.

Complete the table by using the clues below.

Groceries to Lisa’s Store

Clue 1

She will receive the same amount of food this week as shedid last week.

Clue 2

A total of 500 pounds of food came in for 2 weeks.

Clue 3

The number of pounds of potatoes is twice the amount of salt.

Clue 4

Combined, the number of pounds of frozen food and flour is105.25.

Clue 5

The total of Wednesday’s, Thursday’s, and Friday’s deliverieswas 149.25 pounds.

Clue 6

Friday’s delivery is equal to Monday’s delivery minus21.4 pounds.

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CW72 Challenge

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LESSON 14.4

Date Food Pounds of Food

Monday Potatoes

Tuesday Tomato Sauce 12.75

Wednesday Salt

Thursday Flour

Friday Frozen Foods

Total Pounds of foodper week

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LESSON 15.1

Divisibility Rules!

Use the digits in the circles to form numbers that are divisible bythe given divisors.

1. Numbers divisible by 2:

Numbers divisible by 5:

2. Numbers divisible by 3:

Numbers divisible by 5:

3. Numbers divisible by 2:

Numbers divisible by 9:

4. Numbers divisible by 4:

Numbers divisible by 6:

5. Numbers divisible by 3:

Numbers divisible by 4:

0

3 6

2

4 6

3

7 8

0

3 9

1

2 5

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LESSON 15.2

What’s Next?Draw the next figure in each pattern.

1.

2.

3.

4.

5.

6.

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

8910

11 12

7 6 543

21

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LESSON 15.3

Math Puzzles

Try these math puzzles. Have fun!

1. Try to figure out the pattern. What is the next line? Explainthe pattern.

3 4 1 2 2

4 5 2 0 0

5 6 3 0 0

6 7 4 2 8

7 8 5 6 3 0

2. From the starting square, trace a path by moving onesquare to a 1, then two squares to a 2, then three squaresto a 3, and so on. Your last move is eight squares, endingon 8. You may move horizontally, vertically, or both oneach move, but you may not move diagonally. There ismore than one solution.

Start 1 3 2 5 4 4 6

2 4 5 3 4 6 7 4

5 2 3 5 3 5 6 5

4 3 6 3 5 4 7 4

3 4 7 6 5 7 6 5

5 6 5 3 7 6 4 7

4 7 4 5 6 5 5 7

6 5 7 7 5 6 4 8

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LESSON 15.4

It’s All RelativeFinding a relationship can be challenging, whether you’redealing with numbers or people.

Geneaologists are people who study the relationships infamilies.

To show their work, geneaologists often make family trees.

Each level of the tree is a generation of a family. The oldestknown generation is at the top of the tree (Generation 1).The newest generation is at the bottom. Circles stand forwomen and squares stand for men.

Generation 1

Generation 2

You can use ideas of the family tree to explore relationshipsof numbers.

To make a family tree using numbers, first put the numberat the top. Then travel down through the generations. Forexample:

Now it’s your turn. Take a number and make a “family tree”for it.

10

5

2 3+

5

3 2+

1 1+ + 1 2+ 1 2+ + 1 1+

1 1+

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LESSON 15.5

Number Pyramids

The numbers in the pyramids are found by using one ofthese simple 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 upper number, multiply.

To find the lower number, divide.

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.

6,048

72

14 6

7 2 4

84

12

3

48

3

9 1

81

368

2,944

8

4 2 184

18

9

1,944

108

122

10

80

4

8

5 2

C

A B

10 � 8 � 80

8 � 4 � 2

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Take 10 (x 10, x 10, x 10....)We seldom have to count in numbers that are greaterthan one trillion. That number is

1012. You can write it as:

1,000,000,000,000

But there are numbers much higherthan a trillion. One of them is agoogol.

A googol is 10100. It’s easier towrite “googol” than it is to writeout this number mathematically!

The greatest number we have aname for is a googolplex. That’s agoogol to the 100th power or:

10100100

Now it’s your turn:

• What can you call the powers of ten that are between a trillion and a googol?

• What can you call the powers of ten between a googol and a googolplex?

• What can you call the powers often that are greater than a googolplex?

Create a new “math language” of your own. Combine theterms you know with terms you invent. Write some mathexpressions using your new terms.

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LESSON 15.6

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LESSON 15.7

Equal PowersWrite the equal factors to find the value of each expression. Draw lines to match numbers in the columns.

Puzzle

What numbers are represented by A and B in AB � BA?

1. 26

2. 54

3. 44

4. 36

5. 64

6. 104

7. 34

8. 15

9. 74

10. 106

a. 252

b. 362

c. 1,0002

d. 92

e. 82

f. 272

g. 1002

h. 162

i. 492

j. 19

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LESSON 15.8

Factor PhoneDid you ever play the game Telephone? There’s a version of the game that’s a lot like finding exponents and factors.

In this version, one person says a word to two other people. Those people each tell two more people. Each of those people tells two more. Each of those tells two more. Although each person in the game tells the word to only two people, the number of people who hear the word keeps growing.

If you made a diagram of the game it would look like this:

The same is true with numbers that are multiplied by them-selves.

The above pattern shows how many people have heard theword given by the first person after 3 rounds.

2 � 2 � 2 � 23 � 8

Create your own Telephone game where one person tells 3

people, and each person after that tells another three people.

How many people will have heard the word after 4 rounds?

Start

Round 1

Round 2Round 3

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LESSON 16.1

Riddlegram!

Answer this riddle. Write the letter that matches each fraction or decimal. You will use some models several times.

Riddle: Why do you measure snakes in inches?

�0.7

� �0.5

� �0.52

� �0.35

� �0.2

� �0.9

�0.49

� �0.12

� �0.3

� �0.35

� �0.35

� ! �

�120�

�160�

�180�

�13050

�15020

�13050

�14090

�11050

�110�

�13050

T E Y

N OH

A

V

F

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LESSON 16.2

Fix the Pattern

Each series is supposed to create a pattern of equivalent fractions.One fraction in each series does not follow the pattern. Cross outthat fraction. Write the fraction that belongs in its place. The firstone is done for you.

1. �23

� �47

� �69

� �182�

3. �126� �

234� �

340� �

450�

5. �34

� �68

� �1102� �

1126�

7. �2258� �

1251� �

1104� �

57

9. �2302� �

1254� �

1106� �

68

11. �140� �

280� �

1300� �

1460�

13. �15

� �125� �

135� �

240�

15. �2871� �

1227� �

39

� �13

2. �146� �

122� �

28

� �14

4. �24

� �48

� �166� �

1362�

6. �27

� �144� �

281� �

1566�

8. �14

� �130� �

396� �

12078

10. �191� �

1282� �

2343� �

3464�

12. �16

� �234� �

792� �

22176

14. �79

� �1158� �

2217� �

2386�

16. �12

� �24

� �35

� �48

�46�

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LESSON 16.3

Batter Up!The bases are loaded, and the next batter is supposed tocome up to the plate. But who is the next batter?

Each fraction represents a person on base, the batter, or the batter on deck. Starting with the batter on deck, then the batter,and then each base in order, the fractions should be orderedfrom least to greatest. Put them in the correct order.

1st

Batter

On Deck

2nd

3rd

�16

�158�

�29

�14

�112�

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LESSON 16.4

Riddle Time

What has locks but no keys? To find out, write each fraction insimplest form. Then match the letter with the fraction in one ofthe boxes at the bottom of the page. These boxes will spell outthe answer.

�13

� �45

� �56

� �78

� �35

� �23

� �14

� �38

� �12

�18

� �34

� �15

� �58

� �25

1. �1255� � A

3. �684� � C

5. �3468� � A

7. �2500� � L

9. �110200

� � E

11. �255� � N

13. �1264� � N

2. �45

� � H

4. �14250

� � M

6. �2450� � A

8. �142� � T

10. �1664� � A

12. �1224� � A

14. �7878� � P

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LESSON 16.5

Greater Than One!

In figure A if each triangle represents the number 1, the hexagon represents the number 6.

If the hexagon represents 1, each triangle represents �16�.

In figure B if the parallelogram represents thenumber 1, each triangle represents the fraction �

12�

and figure B represents 1�12�.

Each figure represents the given number. Determine which shaperepresents the number 1.

1.

2�13�

3.

2�26�

2.

10�12�

4.

9�13�

A

B

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LESSON 16.6

Use ModelsThe shaded part of each figure represents a fraction. Write the fraction. Order the fractions in each rowfrom least to greatest.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

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LESSON 17.1Name

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Word Ratios

Just as ratios can be used to compare numbers, analogies canbe used to compare words.

An analogy sets up two word ratios for comparison.

Here’s an example of a part-to-whole analogy.

ducks�birds � poodles�dogs

This analogy is read “ducks are to birds as poodles are to dogs.”

Remember that the words in an analogy must be in the correctorder.

ducks�birds � dogs�poodles Incorrect

Circle the letter of the choice that best completes the analogy.

1. general�army

a. gardener�garden

b. teacher�class

c. school�principal

d. chef�kitchen

3. taco�dinner

a. cream cheese�bagel

b. cereal�breakfast

c. dessert�ice cream

d. popcorn�movie

5. pianist�musician

a. bird�feathered

b. boat�canoe

c. ant�insect

d. airplane�flight

2. water�ocean

a. dam�river

b. Jupiter�solar system

c. ocean�sea

d. sand�beach

4. Houston�Texas

a. Berlin�Germany

b. Mississippi�state

c. Nevada�Las Vegas

d. mountain�Everest

6. pencil�writing

a. building�hammer

b. pan�cooking

c. horse�seeing

d. house�flying

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Winning Ratios

Contest promoters are oftenrequired to tell you your chanceof winning.

Here, the chance of winning isexpressed as the ratio 1:100,000.This means that, for every100,000 people who enter thecontest, there will be one winner.

The following data concern a cereal-box contest.

Prize Value of Prize Chance of Winning

Grand Prize $20,000 1�2,500,000

Second Prize $300 1�42,000

Third Prize $20 1�3,000

Fourth Prize $1 1�50

Use the data about the cereal-box contest to solve each problem.

1. Which prize is awarded most often? least often?

2. What is your chance of winning second prize?

3. What is your chance of winning a $20 prize?

4. If everyone in your town or city entered the contest, what

results would you expect?

5. The promoters of the contest advertise that the chance of winning a prize is “better than 1 in 50.” Is this accurate? Is it misleading?

Explain.

Enter Contest!Win a Fabulous Prize!

Chance of winning 1:100,000

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LESSON 17.3

Ratio Art

You can use ratios to draw the same piece of art in differentsizes. Redraw the following piece of art on the grid belowusing the ratios 1�2, 1�3, and 1�4.

Color your drawings.

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LESSON 17.4

Solar Ratios

You’ve been assigned to help build a model of the solar system for a local park. Your job is to figure out how far fromthe sun to place the planets. Here’s some useful information.

Since the sculptor wants the Earth to be 10 feet from the sun,you need to convert the planet distances into Earth units andthen multiply by 10.

Earth units �

Earth units for Mercury ��3963,,000000,,000000

mm

iilleess

�� 0.387

Mercury’s distance in model � 0.387 � 10 � 3.87 feet

Complete the chart.

planet’s distance from the sun����Earth’s distance from the sun

Distance from Sun to Each Planet

Mercury—36,000,000 mi Saturn—886,400,000 mi

Venus—67,000,000 mi Uranus—1,786,000,000 mi

Earth—93,000,000 mi Neptune—2,794,000,000 mi

Mars—141,000,000 mi Pluto—3,660,000,000 mi

Jupiter—483,300,000 mi

Planet Distance in Earth Units Distance in Model

Mercury 0.387 3.87 ft

Venus 0.720 7.2 ft

Earth 1.000 10 ft

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

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Rate the Ratios

Regulations state that the United States flag have a width-to-length ratio of 1�1.9.

Find the length of each flag.

1. width � 3 yards, length �

2. width � 5 meters, length �

3. width � 12 feet, length �

4. width � 26 inches, length �

Ratios state the relationship between two quantities. For a ratio to be in simplest form, both terms must have the same units.

Find the ratios in simplest form. Change the units when necessary.

5. 12 feet to 6 inches 6. 6 quarts to 12 gallons

7. 7 miles to 18 miles 8. 4 feet to 5 inches

9. 3�12

� days to 10 hours 10. 144 ships to 18 ships

11. 3 pints to 9 quarts 12. 6 minutes to 20 seconds

13. 18 feet to 9 yards 14. a leap year to 61 days

15. 4 cups to 2 gallons 16. 1 mile to 440 yards

17. 4 feet to 76 feet 18. 2 weeks to 1 year

19. $30.00 to $0.75 20. 2 years to 13 weeks

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Percents with Style

There are many different ways you can shade a 10 � 10 gridto show a percent. Here are three different models for 24%.The first model is familiar. The second and third models arefun.

Show each percent by shading an interesting pattern.

1. 36% 2. 80% 3. 40%

4. 28% 5. 60% 6. 72%

7. 18% 8. 44% 9. 66%

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Understanding Standings

Check the sports section of your newspaper. Teams areranked according to “winning percentage.” This may beabbreviated as “pct.” The team with the highest winning percentage is in first place.

To find a team’s winning percentage, divide. Here is anexample that shows you how.

Suppose the Rams won 17 and lost 11. That’s 28 gamesplayed in all.

pct � wins � games � 17 � 28 � 0.6071

Winning percentage is usually expressed as a decimal rounded to three decimal places.

So, the Rams’ pct is 0.607, or .607.

Find each winning percentage to three decimal places.Then rank the following teams from highest to lowest winning percentages.

Wins Losses Pct Rank

Cubs 34 20

Rams 22 29

Timberwolves 25 26

Dodgers 27 24

White Sox 22 31

Giants 28 25

Cardinals 20 23

Pacers 27 27

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Find the Match!

Write the letter of the percent or decimal that matches eachfraction. Then place the letter above each problem numberbelow to solve the riddle.

1. �11070

� B. 76% Q. 0.30

2. �130�

3. �1295� D. 22% R. 20%

4. �12

5. �15

� F. 17% S. 4%

6. �215�

7. �1510� H. 0.50 T. 35%

8. �270�

9. �1225� I. 3% V. 0.48

10. �170�

11. �18010

� K. 0.07 W. 0.81

12. �34

13. �1700� M. 40% X. 70%

14. �1300�

15. �25

� O. 0.75

What must have four wings to fly?

8 11 12 3 14 5 7 6

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Sale!!

Pilar is a clerk at a women’s clothing store. Her boss wantsher to mark each price tag with the sale price. Can youhelp her?

On each tag, cross off the regular price and write in the sale price.

25% OFF 30% OFF 40% OFF

Storewide Sale!!

Sweater$72

$54.00

Jacket$149

$111.75

Pajamas$37

$27.75

Pants$44

$33.00

Sneakers$82

$57.40

Coat$184

$128.80

Hat$59

$41.30

Scarf$21

$12.60

Raincoat$53

$31.80

Dress$209

$125.40

Boots$107

$64.20

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Strange Dimensions

Change the percents to fractions or decimals. Then find theperimeter of each rectangle.

1. 2.

3. 4.

5. 6.

�130�

10%

25%

0.25

32%

�35

80%

0.3

15%

�45

40%

�215�

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LESSON 18.6

Fast-Food Facts

What percent of the calories you consume are from fat? Ifyou want to keep fat below 30%, go light on the fast food!

To calculate the percent of calories from fat, use this equation:

(Calories from fat � total calories) � 100 �percent of calories from fat.

Suppose a slice of bread has 90 calories, and 12 caloriescome from fat.

(12 � 90) � 100 � 13.3

So, about 13% of the calories in this bread come from fat.

For each of the following fast foods, calculate the percent of calories from fat. Round to the nearest whole percent.

Fast Foods Total Calories Calories from Fat Percent Fat

Harry’s Hamburger 420 180

Harry’s Hamburger with Cheese 520 260

Big Bun Burger 640 350

Big Bun Burger with Cheese 730 410

Teresa’s Taco 180 100

Teresa’s Taco Light 140 50

Charlie’s Cheese Pizza (slice) 344 90

Bob’s Big Bacon Burger 610 290

Crispy Chicky 360 180

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Town BudgetsHow Two Towns Spent Their Incomes

1. If the total yearly budget for Steel Town was $50,000,how much did Steel Town spend on schools?

2. If the total yearly budget for Coal Town was $50,000,how much did Coal Town spend on schools?

3. How much money did Steel Town spend on interest ondebt, if the total yearly budget was $50,000?

4. How much money did Coal Town spend on interest ondebt, if the total yearly budget was $40,000?

5. The town council for Steel Town voted to increase thebudget from $50,000 to $60,000 per year. How much willSteel Town spend on safety?

6. The town council for Coal Town voted to increase thebudget from $50,000 to $60,000 per year. How much willCoal Town spend on safety?

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LESSON 18.7

STEEL TOWN

Schools30%

Intereston Debt

25%

Safety15%

Health &Welfare12%

Other Services8%

PublicWorks

10%

COAL TOWN

Safety10%

Health & Welfare15%

OtherServices

7.5%

PublicWorks

7.5%

Schools40%

Interest on Debt

20%

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LESSON 19.1

Missing PartsSome of the numerators are missing from the fractions below. Write the missing numerators.

1. �140� � �

10� � �

35

� 2. �35

� � �375� � �

17

� 3. �1118� � �

18� � �

89

4. �1821� � �

81� � �

19

� 5. �48

� � �458� � �

12

� 6. �20

� � �270� � �

34

7. �36

� � �386� � �

34

� 8. �32

� � �352� � �

38

� 9. �1247� � �

27� � �

13

10. �281� � �

21� � �

23

� 11. �49

� � �2419� � �

27

� 12. �6767� � �

77� � �

17

13. How did you find the missing numerators in the additionproblems?

14. How did you find the missing numerators in the subtraction problems?

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LESSON 19.2

Mystery FractionPick a fraction from the list below. Write that fraction in thecircle that has exact spaces for it. Continue until you fill bothcircles. Then answer the questions below.

One fraction, the mystery fraction, should go into both circles.All other fractions belong in only one circle.

�18

� �14

� �112� �

38

� �136� �

162� �

116� �

16

Circle 1 Circle 2(sixteenths) (twelfths)

1. What is the mystery fraction?

2. Write the fractions that fill circle 1.

What is their sum?

3. Write the fractions that fill circle 2.

What is their sum?

4. What is the least fraction listed?

5. What is the greatest fraction listed?

14

112

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Name

Challenge CW101

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LESSON 19.3

Cut Me Up!You can subtract only like fractions.

Find �12� � �

14�. �

�12

� �14

Divide each half of the first figure in half. The figures willthen have equal parts. Subtract like fractions.

� �

�24� �14� �14�

So, �12� � �

14� � �

14�.

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

1. 2.

3. 4.

912

23

34

58

34

916

23

16

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Name

CW102 Challenge

LESSON 19.4

Guess Where I Go

Is each fraction closest to 0, to �12�, or to 1?

Write 0, �12�, or 1 on the line.

Then write the fraction in the correct circle.

1. �1225� 2. �

2410� 3. �

187� 4. �

1330�

5. �1189� 6. �

2224� 7. �

136� 8. �

191�

9. �112� 10. �

321� 11. �

1256� 12. �

1272�

0 112

13. How many fractionsare closest to 0?

14. How many fractionsare closest to �

12�?

15. How many fractionsare closest to 1?

16. Make up your own fractions, and tell which circle theybelong in.

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Name

Challenge CW103

LESSON 19.5

The Race Is On!Sierra Elementary School is having its annual race day. Solve theproblem in the first hurdle. Write the answer in simplest form.Then write that answer in the first space of the next hurdle, and solve the problem. Continue in this way to the finish line. Get ready! Get set! Go!

1.

2.

3.

4.

START

FINISH

�34

� � �18

� � � �12

� � � � �156�

START

FINISH

�152� � �

14

� � � �12

� � � � �158�

START

FINISH

�12

� � �130� � � �

13

� � � � �23

START

FINISH

�56

� � �23

� � � �14

� � � � �34

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Name

CW104 Challenge

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LESSON 19.6

Hal’s Hat StoreFind the sum or difference of the fractions in each hat. Writeyour answers in simplest form. Then color the hats to match thetable of denominators below.

6913�

13

251

10�

12

51216�

14

11124

12� �

712

341

1223

2923�

89

3614�

34

6102

10�

25

1525�

35

green pink red

purple green brown

red blue blue

1. How many hats are purple?

2. How many hats have answers that could bewritten as equivalent fractions with adenominator of 12?

3. List the answers that are in these hats.

Denominator of the Answer

Color

2 pink

3 green

4 red

5 blue

9 brown

12 purple

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Name

Challenge CW105

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LESSON 19.7

Model FractionsPlace one fraction from the list below in each circle. Arrange thefractions so that the sum for one diagonal is the same as the sumfor the other diagonal.

�12

�, �13

�, �23

�, �34

�, �36

�, �58

�, �112�, �

142�, �

244�

412

58

12

13

23

424

34

112

36

What is the sum for each diagonal?

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LESSON 20.1Name

CW106 Challenge

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And the Answer IsFor each problem below, arrange the numbers in the circles so that both diagonals have the same sum.

1. �12

�, 2�38

�, 3�14

�, 4�12

�, 5�18

� 2. 2�14

�, 2�56

�, 3�13

�, 4, 4�12

� 3. 1�16

�, 2�12

�, 3�23

�, 3�56

�, 5�16

Sum � Sum � Sum �

4. 1�58

�, 2�13

�, 2�12

�, 3�34

�, 3�1112� 5. 2�

15

�, 2�35

�, 2�12

�, 3�12

�, 3�35

� 6. 1�79

�, 2�29

�, 2�13

�, 2�79

�, 3�19

Sum � Sum � Sum �

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LESSON 20.2Name

Challenge CW107

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Subtraction Madness

Fill each with the correct mixed number: 2�16

�, 5�56

�, 2�12

�, or 5�13

�.

1. 2.

Fill each with the correct mixed number: 4�78

�, 4�38

�, 1�12

�, or 1�14

�.

3. 4.

Fill each with the correct mixed number: 3�25

�, 6�35

�, 6�170�, or 3�

110�.

5. 6.

Fill each with the correct mixed number: 2�14

�, 1�112�, 4�

12

�, or 5�12

�.

7. 8.

Fill each with the correct mixed number: 6�79

�, 2�13

�, 3�13

�, or 5�34

�.

9. 10.

� � � �

� � � �

� � � �

� � � �

� � � �

3�16

� 3�13

3�18

� 3�38

3�12

� 3�130�

3�14

� 3�152�

3�49

� 3�152�

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LESSON 20.3Name

CW108 Challenge

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Column 1

Row 1

Row 2

Column 2

Column 1

Row 1

Row 2

Column 2

Fraction Fill-In

1. Fill in each box with one of the following fractions:

�56

�, 4�13

�, 4�23

�, 5�29

Follow these rules:

• The difference for Row 1 is �89

�.

• The difference for Row 2 is 3�56

�.

• The difference for Column 1 is �59

�.

• The difference for Column 2 is 3�12

�.

2. Fill in each box with one of the following fractions:

2�12

�, 3�25

�, 3�12

�, 2�23

Follow these rules:

• The difference for Row 1 is �56

�.

• The difference for Row 2 is �190�.

• The difference for Column 1 is �110�.

• The difference for Column 2 is �16

�.

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LESSON 20.4Name

Challenge CW109

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Add or Subtract?Decide if you should add or subtract each mixed number to gofrom the start to the finish. Put � or � in each circle.

1. Start Finish

5�34

� 1�12

� 2�14

� 3�38

� � 8�38

2. Start Finish

7�23

� 3�16

� 1�14

� 1�38

� � 4�58

3. Start Finish

2�39

� 1�19

� 4�49

� 3�16

� � 2�12

4. Start Finish

10�1112� 3�

34

� 4�13

� 1�16

� � 1�23

5. Start Finish

7�45

� 2�110� 3�

25

� 4�35

� � 4�12

6. Start Finish

3�13

� 2�14

� 1�16

� 2�12

� � 4�14

7. Start Finish

11�79

� 2�23

� 1�13

� 7�19

� � 3�13

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LESSON 20.5Name

CW110 Challenge

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Unfolding!The piece of paper below was folded three times. Unfoldingit shows its original dimensions.

The original dimensions were 5 in. by 5 in.

Unfold each piece of paper three times to find the originaldimensions. Give the dimensions of each unfolding.

1.

The original dimensions were .

2.

The original dimensions were .

5 in.

5 in.5 in. in.212

in.114

in.212

in.212

in.212

2�12

� in. by 1�14

� in. 2�12

� in. by 2�12

� in.

5 in. by 2�12

� in. 5 in. by 5 in.

10 in.

7 in.

5 in.

7 in.

5 in.

in.

in.

in. 31231

2

212

118 in.

118 in.

118 in.

2 in.14

2 in.14

2 in.14

2 in.14

in.124

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Parts of Wholes!

Each figure in the picture shows a fraction of a whole. Write thenumber sentence for each picture.

Name

Challenge CW111

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LESSON 21.1

1.

3.

5.

2.

4.

6.

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3-D Fractions

You can use a cube to create a 3-dimensional model to multiply

�14� � �

13� � �

12�.

There are 24 blocks in the cube. There is only 1 blockwith all 3 colors.

So, �14� � �

13� � �

12� � �2

14�.

Color the 3-dimensional model to find the product.

Name

CW112 Challenge

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LESSON 21.2

Show �14

�.

Cut the width into 4equal parts.

Color 1 part blue.

Show �13

�.

Cut the height into 3equal parts.

Color 1 part red.

Show �12

�.

Cut the length into 2equal parts.

Color 1 part yellow.

blue

red

yellow

1. �13

� � �12

� � �12

� �

3. �13

� � �13

� � �13

� �

2. �14

� � �12

� � �12

� �

4. �14

� � �23

� � �12

� �

Lower-right front blockhas all 3 colors.

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Which Model?

In each exercise, the fraction model shows a multiplication sentence. Choose a fraction and a mixed number from the list above the row of the fraction model. Write the multiplication sentence that is modeled.

1. 2�12

� �34

� 2�15

� �35

� 1�270� 2�

35

� 2�14

2. �13

� 2�59

� �36

� 3�56

� �23

� 3�59

� �56

3. Choose a mixed number from the list in Exercise 1 and a fraction from the list in Exercise 2. Make a model to multiply.

Name

Challenge CW113

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LESSON 21.3

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Four Square

Multiply in all four directions in each square. Record theproducts, in simplest form, in the circles.

Name

CW114 Challenge

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LESSON 21.4

23

69

121

4811

1

1

1

1820

910

263

133

3

3

3

3

1618

89

124

244

4

4

4

4

810

45

8162

122

2

2

2

2

3.

4.

2.

1.

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Fraction Triangles

Each triangle contains two multiplication sentences. Fill in themissing numbers to complete each multiplication sentence. Write your fractions in simplest terms.

1. 2.

3. 4.

5. 6.

14

132

120

� �

� �

18

15

79

314

911

� �

� �

16

711

34

25

47

� �

� �

310

37

13

118

124

� �

� �

16

18

15

135

130

� �

� �

17

16

56

34

45

58

� �

� �

23

Name

Challenge CW115

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LESSON 21.5

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Division DetectiveFollow the path below to find the number in the cloud.

Name

CW116 Challenge

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LESSON 22.1

� �94

� �23

� �98

3

� 3

� 4

� �23

� 2

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Find My Reciprocal

Use the clues below to find the reciprocal for each number.

1. If you divide me by 2, I am �32

�. What is my reciprocal?

2. I am a multiple of 5. When I am multiplied by �34

�, I am 3greater than 12. What is my reciprocal?

3. When you add �12

� to me, I am �34

�. What is my reciprocal?

4. When you divide me by �12

�, I am 4 more than 6. What ismy reciprocal?

5. When you add �38

� to me, I am 1. What is my reciprocal?

6. When you multiply me by 2, I am �43

�. What is my reciprocal?

7. When you divide me by �34

�, I am �23

�. What is my reciprocal?

Name

Challenge CW117

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LESSON 22.2

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Dividing Fractions Rule

Find the quotients. Then match them to the letters below tocomplete the sentence.

1. 4 � �12

� E 2. 7 � �47

� I 3. 9 � �38

� C 4. 12 � �29

� R

5. 7 � �172� A 6. 2 � �

45

� T 7. 8 � �27

� H 8. 10 � �48

� P

9. 6 � �15

� O 10. 35 � �112� L 11. 6 � �

78

� F 12. 48 � �26

� N

Dividing a whole number by a fraction is the same asmultiplying the whole number by .

Name

CW118 Challenge

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LESSON 22.3

2�12

� 28 8 54 8 24 12�14

� 20 54 30 24 12 420

30 6�67

� 2�12

� 28 8 6�67

� 54 12 24 2�12

� 12�14

� 30 144

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Name

Challenge CW119

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LESSON 22.4

n n � �51

3

10

�16

3�34

�78

p � �21

� p p � �21

8

�12

�38

5

7

n n � �53

15

�59

8

3�35

5�56

p � �41

� p � �41

� p

32

16

�230�

�47

2�12

Rule Tables

Find the missing numbers in each rule table.

1. 2.

3. 4.

Make your own rule tables. Leave some blanks and challenge aclassmate to complete.

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Make it Simpler

Explain what you need to know to answer each question. Solve.

Mary is catering a large party. There will be 100 guests.

Chicken was ordered by �12

� of the guests, and �34

� of the guests

will be having dessert. Each dessert will cost $2.50. Each

serving of prepared chicken weighs about �14

� pound. A pound

of prepared chicken costs $3.65. Each table will seat 8 people.

1. How many tables are needed?

2. How much will be spent on chicken?

3. How much will be spent on dessert?

Name

CW120 Challenge

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LESSON 22.5

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Puzzle Me This

1. I am the opposite of �5.

2. I am the absolute value of �9.

3. I am the absolute value of �4.

4. I am 3 feet underground.

5. I am a multiple of 2, and I am greater than 2 and less than 6.

6. I am a multiple of 3, and I am greater than 6 and less than 10.

7. I am a multiple of 3, and I am less than �6 and greater than �10.

8. I am 3 units less than �3.

9. I am 10 units less than 0.

10. I am 10 units greater than 0.

11. Follow me through the maze. Think of a number line.

a) Go to the opposite of �5.

b) Go left 2 units.

c) Go to the opposite of �1.

d) Go left 2 units.

e) How many units are between answer a and answer d?

12. Make up your own number-line maze. Give plenty of clues, so there canonly be one correct answer.

Name

Challenge CW121

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LESSON 23.1

�1 0�2�3��4���5���6�7�8�9�10 �1 �2 �3 �4 �5 �6 �7 �8 �9 �10

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Name

CW122 Challenge

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LESSON 23.2

Riddle Me This

Name the integer.

1. I am greater than �2 and less than �6, and I am a multiple of 5.

2. I am 8 less than �2 and 1 greater than �11.

3. I am less than �18, greater than �21, and an odd number.

4. I am the first two-digit number greater than 0 that has the same digits.

5. I am the first number greater than �15 that is a multiple of 5.

6. I am a negative number between �5,000 and �5,000. All of

my digits are the same, and they total 12.

7. I am 1 more than �3,000.

8. I am 2 less than �4,099.

9. I am a multiple of 500. I am greater than �3,500 and less

than �4,500.

10. I am a multiple of 1,000. I am less than �2,000 and greater

than �5,000. My first digit is odd.

11. Make up your own riddle. Give plenty of clues, so there can be only one correct answer.

0�1,000�2,000�3,000�4,000�5,000 �1,000 �2,000 �3,000 �4,000 �5,000

�2 0�4�6��8���10�12�14�16�18�20 �2 �4 �6 �8 �10�12�14�16�18�20

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Name

Challenge CW123

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LESSON 23.3

Sum It UpThe integer at the top of each rectangle is the sum of four addendscontained in the rectangle. Shade the boxes containing the addendsyou use to get the sum. You will use one addend in each row.

1. 2. 3.

4. 5. 6.

7. 8. 9.

�3 0

�9 �1

�10 �7

�16 �4

�4

�3 0

�8 �2

�10 �6

�3 �13

�9 �6

�5 �7

�1 �6

�12 0

�2

�1 �4

�4 �3

�9 �2

�6 0

�4

�5 �8

�3 �6

�2 �9

�7 �10

�8

�7 �2

�1 �5

�2 �4

�9 �4

�6

�5 �4

0 �12

�6 �9

�4 �1

0

�10 �6

�2 �12

�6 �5

�9 �14

�3

�6 �2

�7 0

�9 �8

�8 �2

�2 �5

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Name

CW124 Challenge

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LESSON 23.4

Write the ProblemWrite a word problem that can be solved with each subtractionproblem below. Then trade problems with a classmate, and solve each other’s problems.

1. �12 � �7 �

3. �25 � �17 �

5. 0 � �23 �

2. �15 � �9 �

4. �32 � �14 �

6. �78 � �19 �

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Name

Challenge CW125

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LESSON 23.5

Integer Adds and Subtracts

1. Rules:

Add across the boxes to get A and B, and subtract down the boxes to get C and D.

2. Rules:

This second puzzle is filled in with the A, B, C, and D answers from the first puzzle. Add across the boxes to get E and F, and subtract down theboxes to get G and H.

3. Rules:

This third puzzle is filled in with the E, F, G, and H answers from the second puzzle. Addacross the boxes to get I and J, and subtractdown the boxes to get K and L.

4. In each puzzle, the sum of your answers for rows should equal the difference of your answersfor columns. See if your answers are correct.

1st puzzle: C � D � M

A � B � M

2nd puzzle: G � H � O

E � F � O

3rd puzzle: K � L � R

I � J � R

�4 �2

�3 �1

A �

B �

C � D �

A B

C D

G � H�

E F

G H

I �

J �

K � L �

E �

F �

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LESSON 23.6

Going the Distance

The map below is special. Instead of showing distances, the locationsare separated by positive and negative integers. Add the numbersbetween locations to find the total score for a given route.Remember, different routes between locations have different scores.

1. What is the score for a trip from thescience lab to the cafeteria, throughthe library, your locker, math class,and language arts?

3. What is the score for a trip from thelibrary to the nurse’s office, throughyour homeroom, math class, and thecafeteria?

5. Find the trip from the cafeteria to thegym with the lowest total score.

7. Find the trip from your homeroom tothe principal’s office with the lowesttotal score.

2. What is the score for a trip from yourhomeroom to the track, throughmath class, English, and the lobby?

4. What is the score for a trip from thenurse’s office to the library, throughthe football field, the gym, and theplayground?

6. Find the trip from language arts to theplayground with the lowest total score.

8. Find the trip from the teacher’slounge to the lobby with the lowesttotal score.

�5Gym

�6Lobby �9

�17Track �6

Principal's Office

Playground

Science Lab

Library

Teacher's LoungeYourHomeroom

RestroomLanguageArts Cafeteria

Nurse's Office

YearbookRoom

WaterCooler

Your Locker

English

MusicRoom

Football Field

Math Class

Bus Stop History�4

�1�5

�5

�4

�5�5

�6

�6

�8

�2�3

�8�10

�15

�15�11

�12

�11�1

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Fraction FunctionsEquivalent fractions can be shown on a graph. Choose anyfraction. Think of several equivalent fractions. Make a tablewith the numerator, x, and the denominator, y. Then writethe ordered pairs and graph them. What discovery did youmake about equivalent fractions?

Predict what will happen with several other equivalent fractions.Test your prediction. Make a table for each; write the orderedpairs and graph. Does your theory hold for all your examples?Can you think of equivalent fractions that will not followyour theory?

What generalization can you make about equivalentfractions?

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LESSON 24.1

+6

+4

+2

+12

+10

+16

+14

+8

0 +2 +4 +6 +8 +10 +12 +14 +16

y

x

Numerator

Den

omin

ator

Equivalent Fractions

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A Fish Story

Solve this riddle.

Where do fish like to sleep?

Hint:

On the line above each ordered pair, write the letter namingthat point on the coordinate plane.

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LESSON 24.2

(�6,�3) (�7,0) (�3,�3) (�5,�5) (�6,�7) (�2,�4) (�6,�4)

(�7,�6) (�2,�4) (�4,0) (�7,�8)

-6 -2

-2

- 10 -8 -4

-4

-8

-6

x

y

WR

A

S

D

+2 +4 +8+6

+100

+2

+4

+6 B

N

EI

T

+8

+10

-10

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Changing IntervalsDraw a coordinate plane withintervals of 2. Each interval willinclude an integer which fallsbetween the interval lines. Apoint with one of these integersas a coordinate will go betweenthe labeled lines. See the illustration of (�2,�3).

Graph these equations on acoordinate plane with intervalsgreater than 1. Write at least fourordered pairs for each equation.Use integers greater than 5.

y � 2x � 3

y � x � 20

y � ��12

�x

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LESSON 24.3

x

y

x

y

x

y

-6 -2

-2

- 10 -8 -4

-4

-10

-8

-6

x

y

(2,3)

+2

+2 +4 +8+6

+8

+4

+100

+10

+6

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Making a Duplicate

To make a duplicate of a drawing, you can use a coordinateplane and describe the ordered pairs at each corner.

Look at the illustration and give directions to a partner onhow to duplicate it.

Write an ordered pair for each corner of the drawing. Have yourpartner connect the points with line segments according to yourdirections.

-2 -1-5

-2

-1

-5

-4 -3

-4

-3

x

y

+2+3

+5

+1

+2 +4+3+1 +5

+4

0

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LESSON 24.4

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LESSON 25.1

What’s the Point?

Draw line segments from 1 to 2, 2 to 3, 3 to 4, and 4 to 1.

Draw line segments from 5 to 6, 6 to 7, 7 to 8, and 8 to 5.

Draw line segments from 9 to 10, 10 to 11, 11 to 12, and 12 to 9.

Continue in this pattern until all the numbers have been used.

What shape appears in the center?

1 5 9 1317

2125

2933

4137

45

49

53

2

610

18

2630

3438

4246505437111519

14

22

2327

3135

3943

47

51

55

48

12

1620

2428

3236

4044

48 52 56

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LESSON 25.2

A Star Is Born!

Name every acute angle and obtuse angle in the star.

Acute Angles

Obtuse Angles

A

B C

D

E

F

G

H

I J

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LESSON 25.3

Measure Me

On the planet Trianglium, there are three different speciesof triangles. They are Obtusiums, Acutiums, and Rightiums.Obtusiums have one obtuse angle and never smile.Acutiums always smile and have all acute angles. Rightiumsfeel they are always right because they have a right angle.They always smirk. The one thing they all have in commonis that the sum of their angles is always 180°.

Name each creature. Write Obtusium, Acutium, or Rightium, anddraw the matching faces. Measure each angle of the triangle.

20˚38˚

122˚

56˚ 48˚

76˚

37˚90˚

53˚

67˚

51˚

62˚

44˚ 32˚

104˚

43˚

47˚

90˚

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LESSON 25.4

Divide and Conquer!The enemy forces are upon you. They are rapidly approaching in the shape of a wedge. Your goal is to divide them by finding a line between their advancing forces. Study the step-by-stepprocess for bisecting an angle to accomplish your goal.

Bisect each angle.

Step 1

Draw an angle. Placethe compass on the vertex, M. Draw an arc.

Step 2

Label the points wherethe arc intersects theangle as points L and N.

Step 3

Place the point of thecompass on point L.Draw an arc with thepencil toward point N.

Step 4

Then place the point ofthe compass on point N.Draw another arc withthe pencil to intersectthe arc drawn from point L.

Step 5

Use a straightedge todraw a line from the vertex, M, through thetwo arcs at the pointwhere they intersect.

M

80˚ angle

M

80˚ angle

N

L

L

M N

L

M N

L

M N

1. 2.

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LESSON 25.5

Find the Congruent Shapes!

List below all the shapes that are congruent to each other.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

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LESSON 25.6

Finish the Pictures

Each figure has one or two lines of symmetry. Only part of the figure is drawn. Use the lines of symmetry to finish drawing each picture.

1. 2.

3. 4.

5. 6.

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LESSON 25.7

Other Tessellations

You can create figures that tessellate by changing the figuresthat you know tessellate.

Trace your new figure to show that it tessellates.

Trace and cut out each figure. Change it in the manner describedabove to create a new figure. Trace it to show that it tessellates.

1.

2.

3.

4. Pick one of the above figures and create an amusingcreature.

The rectangle below tessellates.Cut out two triangles from one side.

Attach the two triangles to theopposite side.

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LESSON 26.1

Triangle Land

Triangle Land is divided into three counties. They are IsoscelesCounty, Scalene County, and Equilateral County. Measure the sides ofeach triangle. Use a centimeter ruler. Decide which county it belongsin. Then draw an arrow from the triangle to the correct county.

How many triangles are there in each county?

3.5 cm

3.2 cm

1.5 cm

2.3 cm

1.8 cm2.9 cm

2.5 cm

2.5

cm 2.5 cm

3 cm

3.9 cm

3.9 cm

1.7 cm 1.7 cm

3 cm

4.5 cm

2.2 cm2.9 cm

1.7 cm

2.4 cm3 cm

2.3

cm

2.5 cm

1.6 cm

2.2 cm3.2 cm

2.2 cm1.5 cm

2.5 cm

2.3 cm

0.7 cm1 cm

1 cm

Isosceles County

ScaleneCounty

Equilateral County

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LESSON 26.2

Venn Diagrams

Venn diagrams are used to show how objects are related to one another.

In a group of 10 pet owners, 5 own fish and birds, 2 own fish only, and 3 own birds only.

In the Venn diagram, the box represents all 10 pet owners. The area where the two circles overlap represents pet owners who own both fish and birds.

In another group of 10 pet owners, 6 own horses and4 own pigs.

In the Venn diagram, the box represents all 10 petowners. The circles do not overlap because no petowner owns both horses and pigs.

Use the definitions of the different quadrilaterals to construct aVenn diagram.

Trapezoid1 pair of parallel sides

Parallelogram2 pairs of congruentsides 2 pairs ofcongruentangles2 pairs ofparallel sides

Rectangle2 pairs of congruentsides4 congruentangles2 pairs ofparallel sides

Rhombus4 congruentsides 2 pairs ofcongruentangles2 pairs of parallel sides

Square4 congruentsides 4 congruentangles2 pairs ofparallel sides

Pet Owners

25

3Birds

BothFish

Pet Owners

6 4PigsHorses

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How Did I Get Here?

Use the clues to trace the movements of each figure. Draw the figure as it is transformedfrom one position to the next.

1. I know that I was reflected so that my vertex at (4,1) went to (6,1). I was then translated 3 up and 3 to the right. Finally, Iwas rotated 90° to theright around my bottomright point. Where am I?

2. I know that I started outby rotating, keeping thepoint (12,7) steady. Thepoint (10,7) became(12,5). I was thenreflected so that thepoint (12,5) became(12,2). Then I wastranslated so that thepoint (12,2) became(6,4). Where am I?

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LESSON 26.3

0

123456789

10

1 2 3 4 5 6 7 8 9 10

(4,4)

1112

11 12 13 14 15

(1,1) (4,1)

13

1415

y

x

0

123456789

10

1112

(12,7)

(9,9)

(10,9)

(10,7)

(9,12) (12,12)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

x

y

13

1415

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LESSON 26.4

Crossed Words

ACROSS

2. solid figure that has two congruent polygons in parallelplanes

5. All 6 faces of this solid figure arerectangles.

6. where two faces of a solid figuremeet

7. The base of this solid figure has 4equal sides. The faces are triangles.

9. five-sided polygon

10. formed where three or moreedges of a solid figure meet

11. The faces of a triangular pyramidare these.

12. solid figure with triangular basesand rectangular faces

DOWN

1. flat surface of a solid figure

2. solid figure with a pentagon for abase and triangular faces

3. solid figure with one polygonbase and triangular faces

4. faces by which a solid figure isnamed

8. These form the bases of a prism.

5

1

7

9

10 11

8

12

2

6

3

4

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LESSON 26.5

What a View!Some everyday objects are sketched below. Draw a top view,a side view, and a front view of each.

1.

2.

3.

4.

Front viewSide viewTop view

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“Elementary, My Dear Watson”Sherlock Holmes, the fictional detective, used his powers ofdeduction to solve crimes. Deduction is a type of reasoning.This is how it works:

1. Use facts at hand.

2. Make generalizations from those facts.

3. Eliminate other possibilities.

4. Make a deduction to find the answer.

Sherlock Holmes is visiting Maple Avenue Middle School.The fifth graders have a mystery. They have found a figurebut can’t identify it.

First, Holmes gathers the clues. The figure is 6 feet long and2 feet high. Looking at it from the front, the figure seems likea rectangle. Holmes picks it up and sees that the base is asquare. The students move the figure several different waysand every view is a rectangle or square.

What facts can Holmes work with? Draw a table to show thefacts on one side.

What information can he generalize? Use another column on the table to make generalizations.

What possibilities can he eliminate? Do his generalizationshelp with this?

What deduction can he reach?

Now it’s your turn. Make up a mathematical mystery. Then share your mysterywith another student. Can he or she make a deduction?

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LESSON 26.6

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LESSON 27.1

Can You Measure Up?

Estimate the lengths in inches of the following objects. Then

measure, to the nearest �116� inch. Write both your estimate and

exact measurement.

1. 2. 3.

Estimate

Measure

4. 5.

Estimate

Measure

Measure the length and width of each figure to the nearest �116� inch.

6. 7. 8.

length length length

width width width

wid

th

lengthwidth

leng

thwid

th

length

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LESSON 27.2

Can You Still Measure Up?

Estimate the lengths of the following objects. Then measure to the nearest millimeter. Write both your estimate and exact measurement.

1. 2. 3.

Estimate

Measure

4. 5.

Estimate

Measure

Measure the length and width for each figure to the nearest millimeter.

6. 7. 8.

length length length

width width width

wid

th

lengthwidth

leng

thwid

th

length

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LESSON 27.3

It Doesn’t Add UpEach of the following exercises has an error. Your mission isto find and correct the error. The answer is always correct.The first one is done for you.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10. 12 ft 3 in.� 8 ft 11 in.

�����������20 ft 2 in.

19 yd 2 ft� 13 yd 2 ft

�����������5 yd 2 ft

7 yd 2 ft� 7 yd 2 ft�����������

14 yd 1 ft

8 ft 4 in.� 5 ft 6 in.

�����������4 ft 10 in.

36 ft 11 in.� 10 ft 6 in.�����������

46 ft 5 in.

10 ft 7 in.� 9 ft 8 in.

�����������2 ft 11 in.

26 yd 5 ft� 19 yd 6 ft

�����������49 yd 1 ft

10 yd 1 ft� 7 yd 2 ft�����������

1 yd 2 ft

7 yd 4 ft� 4 yd 5 ft�����������

3 yd 2 ft

8 ft 4 in. 5 in.� 2 ft 10 in.

�����������11 ft 2 in.

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LESSON 27.4

The Stones of AtlasAt 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 feetin diameter. Their weight is staggering.

The weight of the Stones of Atlas is given in the ancient measurement of stones. A stone is about 13.5 pounds.

Change the weights of the Atlas Stones to 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 liftof 960 pounds. How many stones would that be?

8. Some of the competitors in the “World’s Strongest Person”competition weigh 30 stones. What is their weight inpounds?

9. Figure out how much the following people in Doreen’sfamily weigh in stones. Complete the table. Round tothe nearest tenth.

Name Weight in Pounds Weight in Stones

Doreen 76

Natalie 92

Jake 105

Mrs. Snell 146

Mr. Snell 207

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LESSON 27.5

How Full Is It?

Each of the containers below holds a certain amount when full.Shade each container to show about the number of mL or L shownbelow. The first container is shaded for you.

This vase holds 1 liter.

300 mL 1L 800 mL 200 mL

1. A large glass will hold 500 milliliters.

250 mL 400 mL 375 mL 300 mL

2. An olive oil bottle holds 750 milliliters.

187.5 mL 750 mL 375 mL 250 mL

3. A soda bottle holds 2 liters.

1L 1.5 L 500 mL 1,000 mL

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LESSON 27.6

One Life to LiveThe life span of the average American is now about 76 years.

Complete the table. Use a calculator.

Calculate how long you have lived to seconds. Round your age inyears to the nearest month. Round your answers to the nearestwhole number.

Average American Life Span

Number of years 76

Number of months

Number of days

Number of hours

Number of minutes

Number of seconds

My Life So Far

Number of years

Number of months

Number of days

Number of hours

Number of minutes

Number of seconds

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LESSON 27.7

30 3dm km

3 3dm cm

0.03 30m cm

3 30,000m dm

3,000 0.3m m

30 3,000mm mm

Metric Dominoes

Play this game with a partner.

Make four copies of each domino below.

To play: 1. Give each player six dominoes. Place the remaining dominoes in a pile.

2. Player 1 puts down a domino.

3. Player 2 puts down a domino with a metric equivalent. For example, 30 dm and 3 m are equivalents.

4. If a player does not have a metric equivalent,that player draws from the pile until a match ispossible.

5. The first player to use all of his or her dominoeswins!

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Perimeter Puzzle

Find the perimeter. Fill in the crossword puzzle with thecorrect answers to the problems. Don’t use units of measurein the puzzle.

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LESSON 28.1

Down

1. A square, each side measures 33

3. A polygon, sides measure 25, 25,20, 15, 18, 27, 20

4. A parallelogram, base and heightmeasure 27 and 54

6. A triangle, sides measure 450,200, 150

7. An equilateral triangle, each sidemeasures 11

Across

2. A regular pentagon, each sidemeasures 75

4. An equilateral triangle, each sidemeasures 544

5. A rectangle, length and widthmeasure 370 and 670

7. A regular pentagon, each sidemeasures 61

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A Slice of PiThe quotient of the circumference andthe diameter of a circle (C � d) is calledpi (�). Pi has been used throughout history.You have used 3.14 as an approximation ofpi. The ancient Chinese culture used 3for the value of pi. The value of pi was more preciselydetermined by a Greek scientist named Archimedes, wholived around 200 B.C. He calculated that the value of pi wasa mixed number close to 3�

17�. When the decimal system

started to be used in the 1600’s, mathematicians wanted tofind an exact value for pi. It turned out to be impossible! Pi isan irrational number—a decimal that goes on forever withoutrepeating or ending. Computers can calculate pi to a numberthat is thousands of decimal places long. When pi is shownto five decimal places, it is 3.14159.

Calculate the circumference of each circle three times.

a. Use 3 as the value of pi, as in ancient China.

b. Use 3�17

� for the value of pi, as Archimedes did.

c. Use a modern estimate of pi, 3.14159.

1. 2.

a. a.

b. b.

c. c.

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LESSON 28.2

diameter � 10 in.

diameter � 6 ft

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Castle Creations

Mark and Jennifer have made this castle for a school project.

How many square feet of cardboard did Mark and Jenniferuse to make the castle? Hint: The castle is made of squares andrectangles. (Remember to subtract the area of the door opening.)

square feet of cardboard

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LESSON 28.3

19 ft

16 ft

6ft

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Rectangle Challenge

There are 7 different rectangles with a perimeter of 28 feet and whole-number dimensions. Sketch and label each rectangle, and then list the perimeter and area of each.

8. What is the average area of these rectangles?

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LESSON 28.4

Sketch Perimeter Area

1. 28 ft

2. 28 ft

3. 28 ft

4. 28 ft

5. 28 ft

6. 28 ft

7. 28 ft

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Triangle Match-Up

Each set of triangle measurements in Column A is missing onenumber. Find the missing number in Column B. Write the letterof the correct answer in the blank. Not all of the answers inColumn B will be used.

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LESSON 28.5

COLUMN A

1. b � 12.5

h � 5

A �

2. b �

h � 67

A � 1,072

3. b � 0.6

h � 1.2

A �

4. b � 10.2

h �

A � 17.85

5. b � 12

h � 56

A �

6. b � 20

h �

A � 310

COLUMN B

a. 3.3

b. 30

c. 336

d. 0.36

e. 0.036

f. 31

g. 35

h. 390

i. 32

j. 31.25

k. 3.5

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Parallelograms Large and Small

1. Draw and label a parallelogram with an area equal toexactly twice the area of the rectangle drawn above.

2. Draw and label a parallelogram with an area equal toexactly half the area of the parallelogram you drew above.

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LESSON 28.6

3cm

15 cm

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Go Team

The fifth grade students designed a banner to cheer on thesoccer team. The letters will be cut from red paper and gluedto the background. How much red paper will be needed to makeeach letter of the word “team” ?

1. The letter T

2. The letter E

3. The letter A

4. The letter M

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LESSON 28.7

base = 3 in.height = 2 in.

15 in. 15 in. 15 in.

7 in. 7 in. 7 in.7 in.

7 in.

15 in.3 in.

3 in.

3 in.3 in.

3 in.

3 in.

3 in.

3 in.

12 in.

3 in.

10 in.

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LESSON 29.1

Create a PackageDesign a net that could be made into a container for each of thefollowing gifts. Use crayons or markers to create a colorful patternon your net.

1.

2.

3.

4.

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Paint the BarnThe Bradleys are going to paint their barn. In order to knowhow much paint to buy, they need to calculate the surfacearea of the barn.

Help them find the barn’s surface area by adding the areas of each of the barn’s faces. You may wish to use a calculator.

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LESSON 29.2

17 ft

47 ft

75 ft

12 ft high26 ft

Face Shape Problem Area

front rectangle 47 � 17 � 799 sq ft

back

left side

right side

left part of roof

right part of roof

front part of roof triangle

back part of roof (hidden)

TOTAL

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LESSON 29.3

Boxed InEach of the figures below is made up of cubic boxes which measure 1 unit on each side. Find the volume and surface area of each figure.

1. 2.

Volume: Volume:

Surface area: Surface area:

3. 4.

Volume: Volume:

Surface area: Surface area:

5. 6.

Volume: Volume:

Surface area: Surface area:

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Stack ‘em upMaterials: 10 connecting cubes

Use 10 connecting cubes to make different figures. For each different figure you make, record its volume, surface area, andthe perimeter of its base.

Sketch Volume Surface Area Perimeter of Base

10 cubic units 34 square units 12 units

1.

2.

3.

4.

5.

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LESSON 29.4

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LESSON 29.5

1.

3.

5.

2.

4.

6.3

8

15

5

0

5

9

1

1

8

50

3

2

6

10

3

5

8

35

7

44 � 1 � 45

54 � 10 � 44

6 � 9 � 541

9

10

6

Operation 45Start with 2 numbers in the circle. Add, subtract, multiply, ordivide. Use the answer and a different number in the circle with adifferent operation. Then use that answer and the last number inthe circle with an operation you have not used yet. Your finalanswer must be 45.

The first one has been done for you!

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LESSON 30.1

Don’t Flip Out!

A coin will land heads up 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 your classmates. Howmany students got exactly 5 heads and 5 tails? How manystudents got exactly 25 heads and 25 tails?

4. Divide to find the percent of heads for both experiments,as follows.

Experiment 1: number of heads 10 100 � %

Experiment 2: number of heads 50 100 � %

Compare the percents in Problem 4 with those of your classmates.Then complete Problems 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 40% and 60% heads.

Heads Tails Total

10

50

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LESSON 30.2

Summing It Up

What happens when you roll two cubes, each numbered 1–6?

To find out, answer the following questions.

1. Make a list of all possible outcomes of rolling the two number cubes.

2. List the sums of each possible outcome in problem 1. For example, the sum for the outcome 1 and 4 is 5.

3. Which sums are most likely to occur?

4. Which sums are least likely to occur?

5. Predict the number of times each sum will occur if you roll the num-ber cubes 50 times. Then test your prediction by rolling the cubes 50 times. Use tally marks to recordthe results in the table.

6. Did your actual results match your predicted outcomes?Explain.

Sum 2 3 4 5

Predicted frequency

Actual frequency

13 2

54 1

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LESSON 30.3

The Path of Probability

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

Rules 1. Toss the coin. If it lands heads up, follow the headspath to the next oval. If it lands tails up, follow thetails path.

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

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

4. Repeat the process 20 times.

1. In which boxes did you land most often?

2. In which boxes did you land 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 30.4

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 possible out-comes are there? What are they?

For Problems 3–4, use the table.

Try this experiment. Toss twocoins at once, and tally theresults of the tosses. Repeatfor a total of 20 tosses.

3. Of the 20 tosses, howmany times did you get 2heads? 1 head and 1 tail?2 tails?

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

2 Heads 1 Headand 1 Tail 2 Tails

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LESSON 30.5

First Letter of U.S. Presidents’ First Names

A B C D E F G H I J K L M

3 1 2 1 0 2 5 2 0 10 0 1 2

N O P Q R S T U V W X Y Z

0 0 0 0 3 0 2 1 0 6 0 0 1

Presidential Probability

Does the President’s first name help him get elected?

Certain first initials, such as J, W, and G, seem to suggest an answer to this question. Of the first 42 Presidents of theUnited States, half of them had first names beginning withone of these letters. Here are the data.

1. List the top 10 letters for the Presidents’ first initial in orderfrom greatest to least.

2. You pick a president at random among the first 42Presidents. What is the probability that his name beginswith J? W? E?

3. Why do you think so many Presidents have the first initial J?

4. Two candidates are running for the office of President.One has the first name Barbara, and the other Geraldine.Explain whether you think one has an advantage based on her first initial.