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ChallengeWorkbook
P U P I L E D I T I O NGrade 5
Orlando • Boston • Dallas • Chicago • San Diegowww.harcourtschool.com
Copyright © by Harcourt, Inc.
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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
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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
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
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
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
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
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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
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
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
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
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
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
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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 →
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
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
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
•
•
•
•
•
•
•
•
•
•
•
•
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
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
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
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
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
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
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
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
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:
�
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45.3 �
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
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
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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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
!
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
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
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
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
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?
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
LESSON 7.3Name
CW32 Challenge
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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
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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LESSON 7.4
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
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.
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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
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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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
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
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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
.
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
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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.
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
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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
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
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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
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
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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.
LESSON 9.2Name
CW42 Challenge
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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.
LESSON 9.3Name
Challenge CW43
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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
LESSON 9.4Name
CW44 Challenge
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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.
��
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XX� YY
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XZX
EEE� F F F���
EEEEEE
EEE���EGHGE
J J J� KK���
J J JJ J J
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TTT� S���
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MMMN N N
�P P P��
Q Q Q
AAA�B B B��
CCC
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
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LESSON 9.5
Name of River Length of River in Miles
Mackenzie 1,120
Mississippi 2,348
Missouri 2,315
Yukon 1,990
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
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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
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
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LESSON 10.2
1 2 3 4 5 6 7 8
Name
CW48 Challenge
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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
Name
Challenge CW49
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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.
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
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?
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
Name
Challenge CW53
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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
Name
CW54 Challenge
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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 �
�����������
����������������
Name
Challenge CW55
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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
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
Name
Challenge CW57
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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
Name
CW58 Challenge
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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 �
Name
Challenge CW59
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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:
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.
Name
CW60 Challenge
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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
Name
Challenge CW61
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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
Name
CW62 Challenge
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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
Name
Challenge CW63
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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.
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.
!
Name
CW64 Challenge
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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
Name
Challenge CW65
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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
Name
CW66 Challenge
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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
Name
Challenge CW67
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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
Name
CW68 Challenge
©H
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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
Circular Patterns
Each circle holds four numbers. Choose from these numbersto complete each division pattern. The first one has beendone for you.
Name
Challenge CW69
©H
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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
Name
CW70 Challenge
©H
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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
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�
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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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+
Name
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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
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
Name
CW82 Challenge
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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�
Name
Challenge CW83
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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
Name
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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.
LESSON 17.1Name
Challenge CW87
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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
LESSON 17.2Name
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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
LESSON 17.5Name
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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
LESSON 18.1Name
CW92 Challenge
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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%
LESSON 18.2Name
Challenge CW93
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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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CW94 Challenge
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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
LESSON 18.4Name
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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
LESSON 18.5Name
CW96 Challenge
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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�
Name
Challenge CW97
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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
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?
Name
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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%
Name
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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?
Name
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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
Name
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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
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.
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
�
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
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?
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 �
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�
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
�.
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
�
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
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.
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.
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
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.
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
©H
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LESSON 21.5
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
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
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
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.
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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arco
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LESSON 22.5
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
Name
CW122 Challenge
©H
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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
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
Name
CW124 Challenge
©H
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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 �
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 �
Name
CW126 Challenge
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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
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?
Name
Challenge CW127
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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
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.
Name
CW128 Challenge
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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
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
Name
Challenge CW129
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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
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
Name
CW130 Challenge
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LESSON 24.4
Name
Challenge CW131
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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
Name
CW132 Challenge
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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
Name
Challenge CW133
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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˚
Name
CW134 Challenge
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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
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
“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
Name
CW146 Challenge
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!
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
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
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
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
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
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
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.
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:
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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CW162 Challenge
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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.