Challenge
Workbook
PUPIL EDITION
G ra d e 4
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ISBN 0-15-320431-1
2 3 4 5 6 7 8 9 10
082
2002 01 00
© Harcourt
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CONTENTS
Unit 2: DATA, GRAPHING, AND TIME
Unit 1: UNDERSTAND NUMBERS
AND OPERATIONS
Chapter 1: Place Value and
Number Sense
1.1 Just Down the Road a Bit . . . . . . . . .
1.2 Broken Records . . . . . . . . . . . . . . . . . .
1.3 Spin That Number . . . . . . . . . . . . . . .
1.4 Sun to Planet . . . . . . . . . . . . . . . . . . . .
1.5 The Complete Picture . . . . . . . . . . . .
Chapter 2: Compare and
Order Numbers
2.1 The Number Machine . . . . . . . . . . . .
2.2 In Between . . . . . . . . . . . . . . . . . . . . .
2.3 Miles to Go . . . . . . . . . . . . . . . . . . . . .
2.4 Basketball Bonanza . . . . . . . . . . . . . .
Chapter 3: Add and Subtract
Greater Numbers
3.1 Estimating Populations . . . . . . . . . . .
3.2 Number Pyramids . . . . . . . . . . . . . . .
3.3 Money Math . . . . . . . . . . . . . . . . . . . .
3.4 Daily Cross-Number Puzzle . . . . . . .
3.5 My Balance! . . . . . . . . . . . . . . . . . . . .
3.6 Popular Hot Spots . . . . . . . . . . . . . . .
Chapter 4: Algebra: Use Addition
and Subtraction
4.1 Par for the Course . . . . . . . . . . . . . . .
4.2 Parentheses Fun . . . . . . . . . . . . . . . . .
4.3 Whose Number is Closer to 10? . . .
4.4 Another Look at Variables . . . . . . . .
4.5 Find a Rule . . . . . . . . . . . . . . . . . . . . .
4.6 Balance It . . . . . . . . . . . . . . . . . . . . . . .
4.7 Deciphering the King’s Numbers . . .
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Chapter 5: Collect and Organize Data
5.1 Find the Missing Data . . . . . . . . . . . .
5.2 Find the Median and the Mode . . .
5.3 Line Plot . . . . . . . . . . . . . . . . . . . . . . . .
5.4 How Many Marbles in a Jar? . . . . . .
5.5 Did You Know? . . . . . . . . . . . . . . . . . .
5.6 Use Graphic Aids . . . . . . . . . . . . . . . .
23
24
25
26
27
28
Chapter 6: Analyze and Graph Data
6.1 Strike Up the Band . . . . . . . . . . . . . .
6.2 Temperature Patterns . . . . . . . . . . . .
6.3 Find the Missing Scales . . . . . . . . . . .
6.4 Data Display . . . . . . . . . . . . . . . . . . . .
6.5 What’s the Reason? . . . . . . . . . . . . . .
29
30
31
32
33
Chapter 7: Understand Time
7.1 Stop That Watch! . . . . . . . . . . . . . . . .
7.2 What Time Is It? . . . . . . . . . . . . . . . . .
7.3 Replace the Batteries . . . . . . . . . . . .
7.4 Trina’s Tuesday . . . . . . . . . . . . . . . . . .
7.5 Hatching Eggs . . . . . . . . . . . . . . . . . . .
34
35
36
37
38
Unit 3: MULTIPLICATION AND
DIVISION FACTS
Chapter 8: Practice Multiplication and
Division Facts
8.1 Fact Family Bingo . . . . . . . . . . . . . . . . 39
8.2 Math Machinery . . . . . . . . . . . . . . . . . 40
8.3 Fingers and Factors . . . . . . . . . . . . . . 41
8.4 Hand-y Multiplication . . . . . . . . . . . 42
8.5 Up, Down, or Diagonal . . . . . . . . . . . 43
8.6 Birthday Greetings . . . . . . . . . . . . . . . 44
Chapter 9: Algebra: Use Multiplication
and Division Facts
9.1 Parentheses Puzzles . . . . . . . . . . . . . . 45
9.2 What’s the Problem? . . . . . . . . . . . . . 46
9.3 Keep It Equal . . . . . . . . . . . . . . . . . . . . 47
9.4 Variable Grab Bag . . . . . . . . . . . . . . . . 48
9.5 Say It Again, Sam . . . . . . . . . . . . . . . . 49
9.6 Play by the Rules . . . . . . . . . . . . . . . . 50
9.7 Flying Around . . . . . . . . . . . . . . . . . . . 51
Unit 4: MULTIPLY BY 1- AND 2-DIGIT
NUMBERS
Chapter 10: Multiply by 1-Digit
Numbers
10.1 The Powers That Be . . . . . . . . . . . . .
10.2 About the Same . . . . . . . . . . . . . . . .
10.3 Doubling and Halving . . . . . . . . . . .
10.4 Multiply 3-Digit Numbers . . . . . . . .
10.5 Napier’s Rods . . . . . . . . . . . . . . . . . .
10.6 Comparison Shopping . . . . . . . . . . .
52
53
54
55
56
57
Chapter 11: Understand Multiplication
11.1 Moving Day . . . . . . . . . . . . . . . . . . . . 58
11.2 Multiply Wheels . . . . . . . . . . . . . . . . 59
11.3 Target Practice . . . . . . . . . . . . . . . . . 60
11.4 Cross-Number Puzzle . . . . . . . . . . . 61
11.5 Use the Word! . . . . . . . . . . . . . . . . . 62
13.3 Remainders Game . . . . . . . . . . . . . .
13.4 Grouping Possibilities . . . . . . . . . . .
13.5 Riddle-jam . . . . . . . . . . . . . . . . . . . . .
13.6 What’s the Problem? . . . . . . . . . . . .
70
71
72
73
Chapter 14: Divide by 1-Digit Divisors
14.1 Break the Code . . . . . . . . . . . . . . . . .
14.2 Remainders Game . . . . . . . . . . . . . .
14.3 Super Checker! . . . . . . . . . . . . . . . . .
14.4 Create a Problem . . . . . . . . . . . . . . .
14.5 Diagram Division . . . . . . . . . . . . . . .
14.6 Find the Missing Scores . . . . . . . . .
74
75
76
77
78
79
Chapter 15: Divide by 2-Digit Divisors
15.1 Cookie Giveaway . . . . . . . . . . . . . . .
15.2 Puzzled . . . . . . . . . . . . . . . . . . . . . . . .
15.3 Evenly Divided . . . . . . . . . . . . . . . . .
15.4 Division Cipher . . . . . . . . . . . . . . . . .
15.5 What’s for Lunch? . . . . . . . . . . . . . . .
80
81
82
83
84
Chapter 16: Patterns with Factors
and Multiples
16.1 Birthday Party Math . . . . . . . . . . . .
16.2 Shipping Basketballs . . . . . . . . . . . .
16.3 Number Pyramids . . . . . . . . . . . . . . .
16.4 Something in Common . . . . . . . . . .
16.5 Pascal’s Triangle . . . . . . . . . . . . . . . .
85
86
87
88
89
Unit 6: FRACTIONS AND DECIMALS
Chapter 12: Multiply by 2-Digit
Numbers
12.1 Digit Detective . . . . . . . . . . . . . . . . . 63
12.2 The Bigger, the Better . . . . . . . . . . . 64
12.3 Lattice Multiplication . . . . . . . . . . . 65
12.4 Doubling Tales . . . . . . . . . . . . . . . . . 66
12.5 Letter Go! . . . . . . . . . . . . . . . . . . . . . 67
Unit 5: DIVIDE BY 1-AND 2-DIGIT
DIVISORS
Chapter 13: Understand Division
13.1 Number Riddles . . . . . . . . . . . . . . . . 68
13.2 Cookie Coordinating . . . . . . . . . . . . 69
Chapter 17: Understand Fractions
17.1 A Fraction of a Message . . . . . . . . .
17.2 Equivalent Fraction Bingo! . . . . . . .
17.3 Colorful Fractions . . . . . . . . . . . . . .
17.4 Estimating Fractional Parts . . . . . . .
17.5 Language Exploration . . . . . . . . . . .
17.6 A Mixed-Number Challenge . . . . .
90
91
92
93
94
95
Chapter 18: Add and Subtract Fractions
and Mixed Numbers
18.1 Amazing Maze . . . . . . . . . . . . . . . . . 96
18.2 What’s Left? . . . . . . . . . . . . . . . . . . . . 97
18.3 All Mixed Up! . . . . . . . . . . . . . . . . . . 98
18.4 What Breed Is Each Dog? . . . . . . . . 99
18.5 Total Cost . . . . . . . . . . . . . . . . . . . . . 100
18.6 Cut Up! . . . . . . . . . . . . . . . . . . . . . . . 101
Chapter 19: Understand Decimals
19.1 Riddlegram! . . . . . . . . . . . . . . . . . . . 102
19.2 Decimal Drift . . . . . . . . . . . . . . . . . . 103
19.3 Designing with Decimals . . . . . . . . 104
19.4 First-Second-Third . . . . . . . . . . . . . 105
19.5 Money Combos . . . . . . . . . . . . . . . . 106
19.6 Missing Number
Mystery . . . . . . . . . . . . . . . . . . . . . . . 107
Chapter 20: Add and Subtract Decimals
20.1 Super (Market) Estimations . . . . . . 108
20.2Shop Till You Drop! . . . . . . . . . . . . 109
20.3 Play Ball . . . . . . . . . . . . . . . . . . . . . . . 110
20.4Amazing Mazes . . . . . . . . . . . . . . . . 111
20.5 Addition and Subtraction
Puzzles . . . . . . . . . . . . . . . . . . . . . . . . 112
20.6Think About It . . . . . . . . . . . . . . . . . 113
Unit 7: MEASUREMENT, ALGEBRA,
AND GRAPHING
Chapter 21: Customary Measurement
21.1 Pathfinder . . . . . . . . . . . . . . . . . . . . . 114
21.2 Biking Adventure . . . . . . . . . . . . . . . 115
21.3 Cap This! . . . . . . . . . . . . . . . . . . . . . . 116
21.4 Half Full or Half
Empty? . . . . . . . . . . . . . . . . . . . . . . . 117
21.5 Which Weight? . . . . . . . . . . . . . . . . 118
21.6 Atlas Stones . . . . . . . . . . . . . . . . . . . 119
Chapter 22: Metric Measurement
22.1 Point A to Point B . . . . . . . . . . . . . . 120
22.2 Wedding Fun . . . . . . . . . . . . . . . . . . 121
22.3 Punch All Around . . . . . . . . . . . . . . 122
22.4 Sweet Enough . . . . . . . . . . . . . . . . . 123
22.5 Ring-A-Ling . . . . . . . . . . . . . . . . . . . 124
Chapter 23: Algebra: Explore
Negative Numbers
23.1 Fahrenheit Match-Up . . . . . . . . . . . 125
23.2 Heating Up . . . . . . . . . . . . . . . . . . . . 126
23.3 Number Riddles . . . . . . . . . . . . . . . 127
23.4 Logical Conclusions . . . . . . . . . . . . 128
Chapter 24: Explore the Coordinate Grid
24.1 Checkmate! . . . . . . . . . . . . . . . . . . . 129
24.2 Length on the
Coordinate Grid . . . . . . . . . . . . . . . 130
24.3 Use an Equation . . . . . . . . . . . . . . . 131
24.4 Graph an Equation . . . . . . . . . . . . . 132
24.5 Problem Solving Skill: Identify
Relationships . . . . . . . . . . . . . . . . . . 133
Unit 8: GEOMETRY
Chapter 25: Plane Figures
25.1 Semaphore Code . . . . . . . . . . . . . . 134
25.2 Mapmaker, Mapmaker,
Make Me a Map! . . . . . . . . . . . . . . . 135
25.3 Shapes in Motion . . . . . . . . . . . . . . 136
25.4 Let it Snow! . . . . . . . . . . . . . . . . . . . 137
25.5 Problem Solving Strategy:
Make a Model . . . . . . . . . . . . . . . . . 138
Chapter 26: Perimeter and Area of
Plane Figures
26.1 Polygons in Art . . . . . . . . . . . . . . . . 139
26.2 Block It Out! . . . . . . . . . . . . . . . . . . 140
26.3 Unusual Measures . . . . . . . . . . . . . . 141
26.4 Flying Carpet Ride . . . . . . . . . . . . . 142
26.5 Relate Formulas and Rules . . . . . . 143
26.6 Problem Solving Strategy:
Find a Pattern . . . . . . . . . . . . . . . . . . 144
Chapter 27: Solid Figures and Volume
27.1 Riddle, Riddle . . . . . . . . . . . . . . . . . 145
27.2 Puzzle Watch . . . . . . . . . . . . . . . . . . 146
27.3 Estimate and Find Volume
of Prisms . . . . . . . . . . . . . . . . . . . . . . 147
27.4 Problem Solving Skill: Too Much/
Too Little Information . . . . . . . . . . 148
Chapter 28: Measure and Classify
Plane Figures
28.1 Pentamino Turns . . . . . . . . . . . . . . . 149
28.2 Angle Analogies . . . . . . . . . . . . . . . . 150
28.3 Circles . . . . . . . . . . . . . . . . . . . . . . . . 151
28.4 Circumference . . . . . . . . . . . . . . . . . 152
28.5 Classify Triangles . . . . . . . . . . . . . . . 153
28.6 A Scavenger Hunt . . . . . . . . . . . . . . 154
28.7 Diagram Detective . . . . . . . . . . . . . 155
Unit 9: PROBABILITY
Chapter 29: Outcomes
29.1 Three Coins in a Fountain . . . . . . . 156
29.2 The Path of Probability . . . . . . . . . 157
29.3 Mystery Cube . . . . . . . . . . . . . . . . . 158
29.4 A Likely Story . . . . . . . . . . . . . . . . . 159
Chapter 30: Probability
30.1 Certainly Not! . . . . . . . . . . . . . . . . . 160
30.2 Heads or Tails? . . . . . . . . . . . . . . . . . 161
30.3 Word Wonders . . . . . . . . . . . . . . . . 162
30.4 Name Mix-up . . . . . . . . . . . . . . . . . . 163
LESSON 1.1
Name
Just Down the Road a Bit
Hancock
•
Black Creek
•
Dover
•
• Belmont
Rye
•
Taylorville
•
•
North Adams
•
Bristol
The distance from Taylorville to Rye is 10 miles.
Use the map. Estimate the distances.
Taylorville to North Adams
2.
Hancock to Black Creek
3.
Bristol to Dover
4.
Belmont to Black Creek
5.
Taylorville to Hancock
6.
The distance between Taylorville and North Adams is about
the same as the distance between which other two towns?
7.
The distance between which two towns is about 2 times
as great as the distance between Rye and Taylorville?
8.
It takes Don longer to bicycle from Bristol to North
Adams than to bicycle from Bristol to Dover, although
the distance is shorter. Explain why this might be so.
© Harcourt
1.
Challenge
CW1
LESSON 1.2
Name
Broken Records
Read each world record for the largest collection. Write the missing digit.
Then place the letter over the digit at the bottom of the page to answer
the question.
1.
Ties: ten thousand, four hundred fifty-three
10,4
2.
Refrigerator magnets: twelve thousand
3.
Pens: fourteen thousand, four hundred ninety-two
4.
Parking meters: two hundred sixty-nine
26
5.
Get-well cards: thirty-three million
,000,000 (M)
6.
Four-leaf clovers: seven thousand, one hundred sixteen
1
3
3 (W)
,000 (A)
1
, 492 (G)
(S)
,116 (R)
7.
Earrings: eighteen thousand, seven hundred fifty
8.
Credit cards: one thousand, three hundred eighty-four
1,3
10.
4 (P)
Soda bottles: six thousand, five hundred ten
Miniature bottles: twenty-nine thousand, five hundred eight
29,5
11.
, 510 (E)
8 (B)
© Harcourt
9.
8,750 (U)
What does John collect?
L
0
1
0
CW2 Challenge
0
6
4
1
3
5
7
2
8
8
6
7
9
LESSON 1.3
Name
Spin That Number
Work Together
Use a pencil and a paper clip to
make a spinner like the one shown.
Play this game with a partner.
Each player spins the paper clip
six times. The player’s score is
the number that the paper clip
points to. The other player
keeps score, using tally marks.
After each round, find the total
value for each player. The player
with the higher value wins. Play
three rounds.
Sample Scorecard
Name
1.
100,000 10,000 1,000
100
10
1
Total Value
10
1
Total Value
Scorecard
Name
100,000 10,000 1,000
100
© Harcourt
2.
3.
4.
What is the highest possible total value for one round?
Challenge
CW3
LESSON 1.4
Name
Sun to Planet
For Problems 1–7, use the table.
Distance from the Sun in Miles
Mercury
36,000,000
Venus
67,000,000
Earth
93,000,000
Mars
141,000,000
Jupiter
486,000,000
Saturn
892,000,000
1.
Which two planets are closest together?
2.
Which planet is about twice as far from the sun as Mercury is?
3.
What is the distance between Earth and Saturn?
4.
Which planet is closest to Earth?
5.
Which planet is closest to Jupiter?
6.
Which two planets are 856,000,000 miles apart?
7.
Which planet is about ten times as far from the sun as Earth is?
CW4 Challenge
© Harcourt
Planet
LESSON 1.5
Name
The Complete Picture
Complete the pictograph and the chart using the information
provided.
The Five Most Populated States in the U.S.A. and their Estimated Populations
30,000,000
California:
Florida:
New York:
20,000,000
Pennsylvania:
10,000,000
Texas:
The Five Most Populated States in the U.S.A.
California
Florida
New York
Pennsylvania
Texas
Key: Each
=
people.
Explain how you completed your chart and pictograph.
2.
Could the sixth most populated state have an estimated
population of fourteen million? Explain.
© Harcourt
1.
Challenge
CW5
LESSON 2.1
Name
The Number Machine
How can the number machine
change the number
2,744 to 2,044 in one step?
Subtract 700.
Tell how the number machine can change one number to the
other in one step.
1.
3,825 → 3,805
2.
1,649 → 649
3.
4,646 → 4,006
4.
421,715 → 420,715
5.
893,686 → 893,286
6.
57,237 → 50,007
7.
54,764,823 →
54,764,826
8.
1,335 → 1,835
9.
738,231 → 739,231
12.
914,695 → 914,700
10.
77,123 → 77,723
11.
50,234 → 50,555
Find the numbers that are described.
6,314 a. 2,000 greater
b.
15.
17.
2,000 less
16,802 a. 10,000 greater
b.
1,000 less
CW6 Challenge
5,967 a. 5,000 greater
b.
16.
10,000 less
99,999 a. 1,000 greater
b.
14.
81,043 a. 500 greater
b.
18.
5,000 less
500 less
20,000 a. 1,000 greater
b.
1,000 less
© Harcourt
13.
LESSON 2.2
Name
In Between
For 1–8, fill in the blanks by choosing one of the numbers from the box.
1,335
349
5,160
57 2,015,675
498 3,145,000
15,721
5,289
615,460
1,672
4,900
3,456
572
1,020
365
29 3,450,000
43
15,440
1.
Heights of mountains in feet:
1,535 2.
Temperatures in degrees Celsius:
25 3.
Populations of cities:
615,450 4.
Lengths of tunnels in feet:
5,280 5.
Ages of trees in years:
241 6.
Lengths of rivers in miles:
3,710 7.
Numbers of stamps in collections:
490 8.
Numbers of mosquitoes in swamps: 2,500,000 1,025
36
615,490
5,046
356
2,980
563
3,300,000
For 9–14, circle the number that is between the greatest
number and the least number.
Depths of lakes in feet:
328
230
390
10.
Heights of mountains in feet:
20,320
14,573
14,730
11.
Heights of volcanic eruptions in feet:
9,991
9,175
9,003
12.
Numbers of Kennel Club collies
registered:
14,025
14,281
14,073
112
115
© Harcourt
9.
13.
Highest recorded Alaska temperatures: 107
14.
Daily log-ons to the internet
3,673,471 3,841,391 3,897,100
Challenge
CW7
LESSON 2.3
Name
Miles to Go
Wash
.
n, D.C
ingto
e, FL
hasse
Talla
781
764
281
404
525
546
940
455
165
702
1,324
860
390
1,085
492
1,105
238
615
256
, NY
C
Y o rk
gh , N
Ralei
New
A
ans, L
Orle
239
New
le, FL
C
S
ston,
Charleston, SC
onvil
Jacks
le
Char
Mileage Chart
Jacksonville, FL
239
New Orleans, LA
781
546
New York, NY
764
940
1,324
Raleigh, NC
281
455
860
492
Tallahassee, FL
404
165
390
1,105
615
Washington, D.C.
525
702
1,085
238
256
868
868
Follow these steps to find the driving distance between
New York, NY, and Tallahassee, FL.
• Locate New York along the top of the chart.
Locate Tallahassee along the side of the chart.
• Follow the column down, and the row across.
• The number at which they intersect is the driving
distance, in miles, between them.
So, the driving distance between New York and
Tallahassee is 1,105 miles.
The Coronado family traveled from New York to Charleston, SC,
in 3 days. Use the mileage chart to find the number of miles they
traveled each day.
2.
DAY 1
New York, NY
to
Washington, D.C.
4.
3.
DAY 2
Washington, D.C.
to
Raleigh, NC
On which day did they travel the greatest distance?
the least distance?
CW8
Challenge
DAY 3
Raleigh, NC
to
Charleston, SC
© Harcourt
1.
LESSON 2.4
Name
Basketball Bonanza
The basketball club held a contest to guess the number of
points famous players scored in their career. Winners got
a basketball autographed with the player’s name.
Guesses closest to the players’ scores won. These are the
winning guesses.
Billy guessed 27,300.
Antoine guessed 38,400.
Shaun guessed 29,300.
Samantha guessed 26,700.
Terry guessed 26,500.
Pat guessed 27,400.
Willie guessed 31,400.
Jon guessed 26,400.
Place the name of the winner on the basketball.
1.
2.
10.
© Harcourt
4.
Oscar
Robertson
Dominique
Wilkins
Moses
Malone
John
Havlicek
26,710
26,534
27,409
26,395
5.
9.
3.
6.
7.
8.
Michael
Jordan
Elvin
Hayes
Wilt
Chamberlin
Kareem
Abdul Jabbar
29,277
27,313
31,419
38,387
If you round the scores to the nearest thousand, which
four players would have the same score?
Who scored the most points in his career?
Challenge
CW9
LESSON 3.1
Name
Estimating Populations
State
POPULATIONS: 1790 – 1820
1790
1800
1810
1820
Connecticut
237,655
251,002
261,942
275,248
Massachusetts
378,556
422,845
472,040
523,287
New Hampshire
141,899
183,858
214,460
244,161
69,112
69,122
76,931
83,059
Rhode Island
The table shows how the populations of four New England states changed
from 1790–1820. Use the table to answer the questions. Estimate each
answer to the nearest ten thousand.
About how many people lived in either New Hampshire or
Connecticut in 1790?
2.
About how many people lived in either Connecticut or
Massachusetts in 1820?
3.
About how many more people lived in Massachusetts than
New Hampshire in 1820?
4.
About how many more people lived in New Hampshire in 1820
than in 1790?
5.
About how many people lived in the four New England states in 1790?
6.
About how many people lived in the four New England states in 1820?
7.
About how many more people lived in the four New England states
in 1820 than in 1790?
© Harcourt
1.
CW10
Challenge
LESSON 3.2
Name
Number Pyramids
Number pyramids gain new squares by adding together the
two numbers in the squares beneath. Use this simple pattern:
C
A
B
10
ABC
For example, given
6
4
6 4 10. So,
6
4 .
Depending on which numbers are given, you may also use
subtraction: C B A or C A B.
Solve the number pyramids using mental math.
1.
2.
130
170
90
3.
120
80
20
80
4.
240
190
90
© Harcourt
80
5.
260
60
30
6.
350
180
80
70
100
7. Make two of your own pyramids.
Challenge
CW11
LESSON 3.3
Name
Money Math
Write each amount from the box below in a money bag to make
the number sentences true.
$2,107
$448
$1,310
$1,099
$2,306
$893
1.
$1,685 3.
$690 $409 =
4.
5.
$923 $1,184 =
6.
$456 = $1,850
7.
$1,945 8.
$1,163 = $2,795
9.
If you put the money from each money bag into one
large money bag, will you be putting in an amount that
is greater than or less than $10,000?
CW12
Challenge
= $792
= $1,497
$576 = $1,886
2.
$2,257 = $1,612
© Harcourt
$645
$1,632
LESSON 3.4
Name
Daily Cross-Number Puzzle
Find the difference. Enter your answers in the cross-number puzzle.
Across
1.
7.
300
158
4.
2,000
1,177
8.
284
102
1,400
1,113
10,000
9,925
800
685
10.
11.
5,001
2,438
14.
1,710
189
15.
10,201
2,238
18.
501
402
9.
2
1
3
4
7
5
6
12
13
8
9
10
11
14
15
16
17
18
19
19.
9,007
4,789
20
20.
324
226
© Harcourt
Down
1.
3,008
1,191
2.
5,200
985
3.
5.
1,280
1,192
6.
1,000
973
11.
13.
8,907
5,709
15.
104
30
16.
700
465
4.
25,000
12,245
4,003
1,865
12.
10,106
3,807
9,001
8,909
17.
3,114
3,053
Challenge
CW13
LESSON 3.5
Name
My Balance!
Ted forgot to enter all of his checks and deposits into his check
register. Fill in the missing information from these checks to help
Ted find the balance in his account.
Check
Number
Date
Description
Amount of
Check
Amount of
Deposit
Balance
$897.54
645
1/17
Shirts Galore
$38.75
646
1/18
Newton News
$16.88
1/18
paycheck
647
1/18
Burger Buster
648
1/19
Snipper Salon
649
1/20
Ring-A-Ling
650
1/20
Walkin’ Wear
651
1/20
Harry’s Hats
652
1/21
Auto Al
1/21
bonus check
CW14
Challenge
$325.76
$13.67
$144.91
© Harcourt
$478.23
$30.99
$675.25
LESSON 3.6
Name
Popular Hot Spots
Many people like the warm weather in the state of Florida.
Listed below are the populations for major cities in Florida.
Florida Cities
City Population
Fort Lauderdale
149,377
Hialeah
188,004
Jacksonville
635,230
Miami
358,548
Tampa
Orlando
164,693
St. Petersburg
St. Petersburg
238,629
Tallahassee
124,773
Tampa
280,015
• Tallahassee •
•
•
Jacksonville
•
Orlando
Fort Lauderdale
Hialeah
• •
• Miami
Tell if an estimate or exact answer is needed. Solve.
What is the difference in population between Hialeah and Orlando?
2.
Which three cities have a total population about the same as
Jacksonville?
3.
The cities of Tampa and St. Petersburg share an airport. Do you think
that the Tampa-St. Petersburg airport would be larger than the
Jacksonville airport? Explain.
4.
How many more people live in Fort Lauderdale than in Tallahassee?
© Harcourt
1.
Challenge
CW15
LESSON 4.1
Name
Par for the Course
In golf the par for a hole is the number of
strokes, or hits, it takes an average golfer
to put the ball in the hole.
If a golfer is under par, it means that he
or she took fewer than the par number of
strokes to put the ball in the hole.
par for the hole: 4
golfer’s strokes: 1 under par
golfer’s score: 4 1 3
If a golfer is over par, it means that he or
she took more than the par number of
strokes to put the ball in the hole.
par for the hole: 4
golfer’s strokes: 2 over par
golfer’s score: 4 2 6
For 1–6, find the golfer’s score for each hole.
2.
3.
Par: 3
Strokes: 1 under par
Par: 4
Strokes: 1 under par
Par: 3
Strokes: 1 over par
Score:
Score:
Score:
4.
5.
6.
Par: 2
Strokes: par
Par: 3
Strokes: 2 over par
Par: 5
Strokes: 2 under par
Score:
Score:
Score:
7. a.
b.
c.
CW16
Add the par numbers for the
holes to find the par for the course.
Par for the course:
Add the golfer’s scores for the holes
to find her or his score for the course.
Score for the course:
Was the golfer over or under par for
the course? By how much?
Challenge
© Harcourt
1.
LESSON 4.2
Name
Parentheses Fun
Place the parentheses to make the expression equal 4.
1.
64 2
2.
2 42
4.
53 31
5.
76 52
7.
4352 4
8.
31 42 22
3.
6.
54 21
6 42 4
Use the rules below to play the Parentheses Game with a partner.
A. Use only the numbers 0–5.
B. Use only addition and subtraction.
C. Use as many parentheses as possible.
D. The expression should equal 2.
© Harcourt
The winner is the one that writes the most examples.
Make up your own parentheses game. Write the rules and write
your own examples.
Challenge
CW17
LESSON 4.3
Name
Whose Number is Closer to 10?
The object of this game is to write a number that is closer to
10 than your partner’s number.
• You name any 2 numbers, for example, 9 and 4. Your
partner names any 2 numbers, for example, 6 and 2.
• Each of you must write an expression using all 4 numbers
in any order. You must use at least one set of parentheses.
You may use only the and symbols.
• Find the value of your expression and compare it to your
partner’s number. The one whose result is closer to 10
gets a point. For example:
You write:
(9 6) (4 2). The value of your expression is 9.
Your partner writes: 4 (6 2) 9. The value of your partner’s
expression is 17.
9 is closer to 10, so you get a point.
• The first to get 10 points is the winner.
© Harcourt
• Remember, you may use 2-digit or 3-digit numbers.
CW18
Challenge
LESSON 4.4
Name
Another Look at Variables
Write an expression for each of the following. Use n for the
unknown number.
1.
four less than a number
2.
two more than a number and
four
3.
ten more than a number plus 3
4.
three increased by a number
minus 5
5.
a number increased by the same
number
6.
six and a number decreased by
seven
© Harcourt
Write and solve an equation for each of the following. Choose a
variable for the unknown number.
7.
There are 20 channels available on the TV. Five are local.
How many are not local?
8.
There are 17 children in the class. Five more students join
the class. How many students are in the class?
9.
Eight books were removed from the shelf. Three books
are still on the shelf. How many books were on the shelf
to start?
Challenge
CW19
LESSON 4.5
Name
Find a Rule
Complete the table using the given rule.
1.
ab7
a
2.
a5b
b
a
b
5
7
11
5
4
51
3ab
a
b
2
19
3
3.
4
15
0
Find a rule for the output values. Write the rule as an equation
that includes variables a and b.
4.
Output b: 5, 7, 9, 11
5.
Output b: 10, 7, 4, 1
6.
Output b: 6, 12, 24, 48
7.
a4b
8.
a (2 1) b
9.
a (3 3) b
10.
a (4 3) b
11.
(a 2) 2 b
12.
(a 4) (2 1) b
CW20
Challenge
© Harcourt
Write a sequence for the rule.
LESSON 4.6
Name
Balance It
© Harcourt
Write the expressions from the box below above the pans of the
balances so that the two amounts on a balance are the same.
89
77
38
20 6
56
12 4
15 0
91
11 6
18 3
99
14 2
11 7
66
17 8
13 4
1.
2.
3.
4.
5.
6.
7.
8.
Challenge
CW21
LESSON 4.7
Name
Deciphering the King’s Numbers
You and your friends visit the ruins of an ancient civilization.
There are many stone tablets carved with English words, but the
numbers are in strange symbols. So far, no one can decode the
symbols. Can you?
There are four number symbols:
Passage 1: “The King
has ♦ grandsons,
together they have
6 knees.”
Passage 2: “Every
birthday the King gives
his daughter ♦ more
flowers compared to the
previous year. This year
he gave her ♦ ○
flowers. Last year she
got ♦ flowers.”
Passage 3: “The King
has ♦ ♦ horses. That
is ♦ more than the
Prince’s ♦ horses.”
♦, , ○, and .
♦ represent?
1.
What number does
2.
Which digit is greater,
3.
What is (♦ 4.
How many horses does the Prince have?
5.
What is
○) – (♦
○ or ?
)?
?
© Harcourt
Make up your own code of symbols for the digits 0, 1, 2, 3, 4,
5, 6, 7, 8, and 9. Write 3 of your symbols in several different
expressions. Ask a friend to decode your 3 symbols.
CW22
Challenge
LESSON 5.1
Name
Find the Missing Data
The Lane family drove their car on vacation. At the end of
each day, Mr. Lane recorded the number of miles that
they had driven.
1.
Complete the table to find out how far the Lanes
traveled each day.
Day
Miles in One Day
Total Miles
(Cumulative Frequency)
Monday
150 miles
Tuesday
225 miles
Wednesday
368 miles
Thursday
378 miles
Friday
500 miles
Saturday
575 miles
Matt took a notebook on the trip. He used the notebook
to draw pictures and play games with his sister.
2.
Look at the table below. How many notebook pages did
Matt use by the end of the trip?
3.
Complete the table to find out how many pages Matt
used on each day of the trip.
© Harcourt
Day
Pages in One Day
Total Pages
(Cumulative Frequency)
Monday
20 pages
Tuesday
33 pages
Wednesday
45 pages
Thursday
73 pages
Friday
80 pages
Saturday
80 pages
Challenge
CW23
LESSON 5.2
Name
Find the Median and the Mode
1.
What numbers are missing from this group?
The mode is 10, and the median is 9.
4, 4, 6, 8,
, 10, 10,
, 11
For 2–7, use the table below.
RECYCLING CLUB MEMBERS
2.
Grade
Number of Students
2
7
3
6
4
5
5
3
What is the median grade of students in the recycling club?
What grade is the mode?
4.
Would the median grade change if one new secondgrader and one fifth-grader joined the recycling club?
5.
If two second-grade students quit the recycling club,
and three fifth-graders and one fourth-grader joined
the club, what would the median grade be?
6.
Change the data in the table so that you have two
modes.
7.
What is the median for your new data?
© Harcourt
3.
CW24
Challenge
LESSON 5.3
Name
Line Plot
Stephanie is comparing the number of letters in her
classmates’ first names. She printed each student’s name
on a piece of paper. She then began to count and record
the number of letters in each name.
1.
Complete Stephanie’s line plot by recording the number of
letters in the first names of the other students in her class.
Jennifer
Ted
Carl
Juan
Paul
Zachary
Inderjeet
Koko
Joanie
Siri
Lee
Trudi
Matthew
Christopher
Mercedes
Elizabeth
Malcolm
Moe
Oscar
Kevin
Dimitri
Lauren
Kathleen
Ramona
Alan
3 4 5 6 7 8 9 10 11
Number of Letters in First Name
For 2–5, use the completed line plot.
2.
How many first names have 7 letters?
3.
What is the most frequent number of letters in a first
© Harcourt
name in Stephanie’s class?
4.
What is the range of this data?
5.
Would the data be different if you
made a line plot for the number of
letters in the first names of students
in your class? Make a list of names
and a line plot for your classmates.
2 3 4 5 6 7 8 9 10 11
Challenge
CW25
LESSON 5.4
Name
How Many Marbles in a Jar?
Mr. Murphy asked each of the students in his class to
estimate the number of marbles in a jar. He organized the
estimates in a stem-and-leaf plot.
Marble Estimates
Stem
Leaves
6
35567
7
000445899
8
03366
9
05
6 | 3 means 63 marbles.
For 1–4, use the stem-and-leaf plot.
1.
What number was estimated by the greatest number
of students?
2.
What is the median in this set of estimates?
3.
What is the difference between the highest estimate and
4.
Use the following clues and the stem-and-leaf plot to
determine the exact number of marbles in the jar.
• Only one student guessed the exact number.
• The exact number is not a multiple of 5.
• The exact number has 7 tens.
There are exactly
CW26
Challenge
marbles in the jar.
© Harcourt
the lowest estimate?
LESSON 5.5
Name
Did You Know?
Animal
The table shows the
oldest recorded age
of some animals.
Age (in years)
Cat
28
Dog
20
Goat
18
Rabbit
13
Guinea Pig
8
Mouse
6
Use the data in the table above to complete the graph. Draw bars
across the graph to show the age of each animal.
Oldest Recorded Ages of Animals
Cat
Animal
Dog
Goat
Rabbit
Guinea Pig
Mouse
0
4
8
12
16
20
24
28
© Harcourt
Age (in years)
1.
What interval is used in the scale of the graph?
2.
For which animals do the bars end exactly on the scale lines?
3.
If the graph had a scale with intervals of 2, how many
bars would end exactly on the scale lines?
Challenge
CW27
LESSON 5.6
Name
Use Graphic Aids
Students collected empty soda cans.
The amounts collected are shown in
the table.
1.
2.
SODA CANS COLLECTED
Monday
41
Tuesday
37
What is the range of the data in
Wednesday
30
the table?
Thursday
25
Friday
20
On a bar graph of this data, what
scale, other than 1, would allow the
most bars to end exactly on a scale line?
Using your answers to 1 and 2, make a bar graph of the
data in the table.
4.
On which two consecutive days did the students
collect the most cans?
5.
When would it be easier to use a graph instead of a
table to find an answer?
6.
When would it be easier to use a table instead of a
graph to find an answer?
© Harcourt
3.
CW28
Challenge
LESSON 6.1
Name
Strike Up the Band
INSTRUMENTS PLAYED IN THE SCHOOL BAND
Number of Students
12
Key:
10
8
6
4
2
Cl
ar
in
et
s
um
Dr
Tr
u
m
pe
t
0
Instrument
1.
Use the clues to fill in the missing information on this
double-bar graph.
• The same number of boys and girls play the trombone.
• More boys than girls play the trumpet.
• Two more boys than girls play the drums.
• More girls play the flute than any other instrument.
• The same number of boys play the flute and the trombone.
• Twice as many girls as boys play the clarinet.
© Harcourt
For 2–5, use the completed graph.
2.
Which instruments are played by more boys than girls?
3.
Do more students play the flute or the trumpet?
4.
Are there more boys or more girls in the band?
5.
How many students are in the band?
Challenge
CW29
LESSON 6.2
Name
Temperature Patterns
MONTHLY NORMAL TEMPERATURES IN BOSTON AND SAN FRANCISCO
80
Temperature (in °F)
70
60
50
•
•
40
30
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Key:
20
Boston
San Francisco
10
0
Jan
Feb Mar Apr May Jun Jul
Month
Aug Sep Oct Nov Dec
1.
What does the dashed line represent?
2.
What is normally the coldest month in Boston?
3.
What is normally the warmest month in San Francisco?
4.
In which city is the difference in temperature between
the summer months and the winter months greater?
5.
During which months is the normal temperature in the
two cities the same?
CW30
Challenge
© Harcourt
This line graph shows the normal temperatures in
Boston and San Francisco for each month of the year.
LESSON 6.3
Name
Find the Missing Scales
The line graphs below show the number of sales of several items
in The Red Balloon Toy Shop during one week.
Use the following information to fill in the missing
scales in each graph.
• There were 10 more puzzles sold on Monday than on Tuesday.
• The number of models sold on Wednesday was 5.
• There were 60 paint sets sold during the week.
• There were 8 more games sold on Thursday than on Friday.
PUZZLE SALES
•
30
20
•
10
0
M
•
•
T
W Th
Day
•
F
10
•
•
•
•
•
5
0
M
T
W Th
Day
F
4
•
•
S
•
M
T
W
Th
Day
F
GAME SALES
12
S
•
•
8
4
•
•
2
16
•
15
•
6
0
S
PAINT SET SALES
20
Number Sold
•
MODEL SALES
8
Number Sold
Number Sold
40
Number Sold
1.
•
•
M
T
•
•
0
W Th
Day
F
S
© Harcourt
For 2–5, use the graphs.
2.
How many models were sold in all during the week?
3.
On which day was the greatest number of paint sets sold?
4.
Were there more sales of models or games on Monday?
5.
Write two more similar questions using the data in the graphs.
Challenge
CW31
LESSON 6.4
Name
Data Display
Corina recorded the grades that she got on her spelling
test each week for nine weeks. She displayed the data in
two different ways.
A
SPELLING TEST GRADES
B
✗
✗
✗
✗
100
✗
✗
✗
✗
✗
90
80
Spelling Test Grades
60
Grade
75 80 85 90 95 100
70
•
•
•
•
•
•
•
•
•
8
9
50
40
30
20
10
0
1
2
3
4
5
6
7
Week
Circle the letter of the graph or plot you would use to answer
each question. Then answer the question.
1.
What grade did Corina get most often? A B
2.
What grade did Corina get in Week 5? A B
3.
Did Corina’s grades improve or decline between Weeks 5 and 8?
4.
What is the range of Corina’s grades? A B
5.
By how many points did Corina’s grade improve between Weeks 2 and 3?
A B
6.
What is the median of Corina’s grades? A B
CW32 Challenge
© Harcourt
A B
LESSON 6.5
Name
What’s the Reason?
The graph at the right shows the number of students
enrolled at Kensington Elementary in 7 different years.
For example:
Conclusion: The number of
students enrolled at
Kensington Elementary rose
steadily between 1940, 1950,
and 1960.
Enrollment at Kensington Elementary
Number of Students
When we read a graph, we
can make conclusions about
what happened, then try to
think of reasons why those
things might have happened.
Year
Possible Reason: The community around the school
was growing steadily, meaning that there were more
children to attend Kensington Elementary.
Give a possible reason for each of the following
conclusions.
1.
Conclusion: There was a sharp increase in the number
of students between 1960 and 1970.
Possible Reason:
© Harcourt
2.
Conclusion: The number of students enrolled at
Kensington Elementary began to decrease steadily
after 1980.
Possible Reason:
Challenge
CW33
LESSON 7.1
Name
Stop That Watch!
Work with a partner to estimate and then check how many times
you can do different activities in one minute.
You need a watch with a second hand.
1.
Record your estimates and findings in the tables.
Partner 1 Name Activity
Estimated
Number of
Repetitions
Actual
Number of
Repetitions
Partner 2 Name Activity
Write your
name.
Write your
name.
Hop on
one foot.
Hop on
one foot.
Draw a
star and
color it.
Draw a
star and
color it.
Walk
around
your desk
or table.
Walk
around
your desk
or table.
Count
to 200.
Count
to 200.
Actual
Number of
Repetitions
How close are the actual numbers to your estimated
numbers? Write a paragraph to explain.
© Harcourt
2.
Estimated
Number of
Repetitions
CW34
Challenge
LESSON 7.2
Name
What Time Is It?
Each clock shows a time in the morning or the afternoon.
Each clock has a letter that you will use to find the secret message.
M
Y
11 12 1
2
10
9
3
4
8
7 6 5
E
11 12 1
2
10
9
3
4
8
7 6 5
A.M.
P.M.
F
I
O
11 12 1
2
10
9
3
4
8
7 6 5
P.M.
T
11 12 1
2
10
9
3
4
8
7 6 5
A.M.
P.M.
P
11 12 1
2
10
9
3
4
8
7 6 5
A.M.
A
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
1.
A
11 12 1
2
10
9
3
4
8
7 6 5
P.M.
R
11 12 1
2
10
9
3
4
8
7 6 5
P.M.
!
11 12 1
2
10
9
3
4
8
7 6 5
A.M.
P.M.
11 12 1
2
10
9
3
4
8
7 6 5
11 12 1
2
10
9
3
4
8
7 6 5
P.M.
P.M.
Find the 4:00 A.M. clock. Write that clock’s letter in the first
box. Continue matching the times, with the clocks. Write
the letter next to the clock in the box above the time.
What is the secret message?
4 A.M.
4 P.M.
© Harcourt
2.
7 A.M.
5 P.M.
9 A.M.
9 P.M.
11 A.M.
1 P.M.
1:55 P.M.
2 P.M.
1 hour
1 hour
1 hour
1
hour
2
after
before
before
before
1 P.M.
5 A.M.
midnight
midnight
Use the letters above the clocks at the top of the page
to write the longest word you can in the spaces below.
Also write the time for each letter.
Challenge
CW35
LESSON 7.3
Name
Replace the Batteries
Mr. Smith went into his clock shop on Monday morning.
Several of his clocks were running slow. He realized that
he needed to replace the batteries in those clocks and
reset the time.
The exact time is 8:10. Write how much time each clock has lost.
Use the abbreviations hr and min.
1.
2.
11 12 1
2
10
9
3
4
8
7 6 5
5.
6:28
4.
8:05
7:51
6.
5:10
7.
8.
11 12 1
2
10
9
3
4
8
7 6 5
CW36
© Harcourt
3.
11 12 1
2
10
9
3
4
8
7 6 5
Challenge
11 12 1
2
10
9
3
4
8
7 6 5
LESSON 7.4
Name
Trina’s Tuesday
Read the following story about Trina’s Tuesday. Then make an
ordered list of the 15 things that happened to Trina, starting at
2:00 A.M. Tuesday and continuing until 11:00 P.M. Wednesday.
Trina woke up to the sound of her alarm clock at 6:00
A.M. She felt tired because a thunder storm woke her up at
2:00 A.M. She ate breakfast at 7:00 A.M. and took the bus at
8:00 A.M. On the bus Trina studied for her Math test,
which was at 2:00 P.M.
She arrived at school at 9:00 A.M. The teacher told Trina
that there was an assembly at 1:00 P.M. Trina did Social
Studies at 10:00 A.M., and at 12:00 P.M., she ate lunch.
At 3:00 P.M. she took the bus home. Dinner was at 6:00 P.M.
Trina was happy that she had done all of her homework at
4:00 P.M. so she was able to play outside at 7:00 P.M. At
9:00 P.M., Trina went to sleep. She heard her baby brother cry
at 11:00 P.M. but went right back to sleep.
1.
2.
3.
4.
5.
6.
7.
8.
© Harcourt
9.
10.
11.
12.
13.
14.
15.
Challenge
CW37
LESSON 7.5
Name
Hatching Eggs
The table shows the average incubation time for eggs of different
kinds of birds. Incubation time is the number of days between the
time an egg is laid and the time it hatches.
INCUBATION TIME FOR EGGS
Kind of Bird
Average Number
of Days
Chicken
21
Duck
30
Turkey
26
Goose
30
For Problems 1–6, use the table and a calendar.
1.
How much longer does it usually take a duck’s egg to
hatch than a chicken’s egg?
2.
If a chicken lays an egg on June 1, on about what date
should the egg hatch?
3.
If a duck lays an egg on June 21, on about what date
should the egg hatch?
4.
A turkey egg hatches on July 4. On about what date was
5.
A goose egg hatches on the last day in July. On about
what date was the goose egg laid?
6.
A chick is 3 days old on July 31. On what date did the
chicken egg hatch?
On about what date was the egg laid?
CW38
Challenge
© Harcourt
the turkey egg laid?
LESSON 8.1
Name
Fact Family Bingo
Master basic multiplication facts with a friendly game of
Fact Family Bingo. Play with several students.
To play:
• Have one player call out one equation from the
Fact Family of his or her choice.
• The other players look for another equation
from that Fact Family on their bingo board. If a
player finds one, he or she places a scrap of paper
on that equation.
• The first player to complete a row across, down,
or diagonally says “Fact Family Bingo.”
© Harcourt
CARD A
CARD B
318
4
2
525
5
4
216
7
2
24
945
210
3
1
FREE
12
315
999
39
FREE
13
1210
8
840
7
8
648
9
9
5
6
2
12
6
7
2
7
12
7
630
6
9
5
9
763
5
7
7
10
10
10
2
3
412
1260
672
918
990
3
3
11
11
1
1
1214
4
48
39
880
2
6
8
9
1296
Challenge
CW39
LESSON 8.2
Name
Math Machinery
Each machine in Mariko’s Machinery Shop does different
things with the numbers put into it.
Complete the In and Out columns for each machine.
1.
2.
3.
4.
5
8
4
10
16
© Harcourt
6
12
2
5.
The machine in Problem 4 needs to be reprogrammed
to do the same job in one step instead of two. How can
this be done?
CW40
Challenge
LESSON 8.3
Name
Fingers and Factors
Mickey’s mother taught him how to multiply by using his
fingers. She said this is a very old method. It only works
when the factors are greater than 5. Here are the steps
Mickey followed to find the product of 7 8.
Step 1
7 is 2 more than 5. Turn down 2 fingers of
the left hand.
Step 2
8 is 3 more than 5. Turn down 3 fingers of
the right hand.
Step 3
Multiply the number of
turned-down fingers by 10.
5 10 50
Step 4
Multiply the number of not
turned-down fingers of one
hand by the number of not
turned-down fingers of the
other hand.
326
Step 5
Add the products.
So, 7 8 56.
50 6 56
© Harcourt
Use the above method to find the product.
1.
68
2.
66
3.
77
4.
79
5.
98
6.
67
7.
99
8.
69
9.
88
10.
76
11.
87
12.
96
13.
86
14.
97
15.
89
Challenge
CW41
LESSON 8.4
Name
Hand-y Multiplication
A handy method for multiplying with facts with 9s is
finger multiplication.
Use both hands with fingers spread apart.
Label the fingers consecutively from 1 to 10, as shown.
To multiply, bend the “multiplier finger.” For the basic
fact 3 9, you bend finger number 3, as shown below.
multiplier
7 ones
2 tens
3 9 27
The fingers to the left of the multiplier give the tens in the
product. The fingers to the right of the multiplier give the
ones in the product.
Solve by using finger multiplication. Draw a picture of what each
hand looks like.
79
2.
59
© Harcourt
1.
CW42 Challenge
LESSON 8.5
Name
Up, Down, or Diagonal
Find three numbers in a row that have the given product. Draw a
line through the three numbers. You may draw the line across, up
and down, or diagonally.
1.
4.
7.
10.
© Harcourt
13.
product: 36
2.
product: 120
3.
product: 90
1
2
5
2
9
5
7
2
9
6
3
0
3
5
7
3
5
1
7
6
2
5
6
4
2
4
9
product: 40
5.
product: 96
6.
product: 108
4
3
6
7
4
5
3
8
6
2
5
7
2
8
6
6
3
4
0
8
2
6
4
3
9
6
2
product: 96
8.
product: 108
9.
product: 84
5
3
4
4
6
2
7
6
2
4
2
8
9
7
4
1
4
7
7
9
3
3
2
8
9
5
8
product: 144
11.
product: 84
12.
product: 48
3
7
3
4
5
3
6
5
3
2
4
6
8
0
7
6
2
4
7
4
12
6
9
4
7
8
9
Make your own puzzle.
Exchange with a partner
to solve.
product:
Challenge
CW43
LESSON 8.6
Name
Birthday Greetings
Grandma Gallagher will soon be 75 years old. Her ten
grandchildren made a card to give her on her birthday.
They will sign their names in order from oldest to youngest.
Use the clues below to find the age of each grandchild. Record the
names in the chart.
1.
Ryan is 8 years old.
2.
Nadia is 5 years younger than Ryan.
3.
Nick is 6 times as old as Nadia.
4.
Mary Kate is 4 years older than Ryan.
5.
Emma is 2 years older than Nadia.
17 yr
6.
Charlotte is half as old as Mary Kate.
16 yr
7.
Jack is 4 times as old as Emma.
8.
Margaret is 4 years older than Charlotte.
9.
Laura is 7 years younger than Nick.
10.
Michael is twice as old as Ryan.
For Problems 11–12, use the chart.
11.
Who will sign the card first? last?
20 yr
19 yr
18 yr
15 yr
14 yr
13 yr
12 yr
11 yr
10 yr
Who will be the fifth person to
sign the card?
9 yr
8 yr
7 yr
6 yr
5 yr
4 yr
3 yr
CW44
Challenge
© Harcourt
12.
LESSON 9.1
Name
Parentheses Puzzles
Look at the array. See how the numbers on the outside are
the result of multiplying the expressions and numbers on
the inside from left to right or top to bottom.
3
(5 2)
21
(2 9)
4
44
33
28
Arrange the inside expressions and numbers in the Parentheses
Puzzle so that the top-to-bottom and left-to-right products equal
the outside numbers.
1.
Inside: 2, (6 4), (8 2), 5
Outside: 10, 12, 50, 60
2.
Inside: (2 7), (12 5), 4, 6
Outside: 28, 42, 54, 36
5
(8 2)
50
Arrange the inside expressions and numbers in the Parentheses
Puzzle so that the top-to-bottom and left-to-right differences
equal the outside numbers.
3.
Inside: (4 5), (2 2), 18, 5
© Harcourt
Outside: 1, 2, 14, 15
(4 5)
5
4.
Inside: (7 4), (2 9),
(6 3), (2 10)
Outside: 2, 10, 8, 0
15
Challenge
CW45
LESSON 9.2
Name
What’s the Problem?
Write a problem that matches the expression. Then find the value of
the expression to solve your problem.
1.
10 (2 4)
3. 3 (5
4)
8)
(9 5) 4
4. (6
9) 7
6. (3
12) 10
© Harcourt
5. 22 (2
2.
CW46
Challenge
LESSON 9.3
Name
Keep It Equal
When the same amount of weight is on
each side of a scale, the scale is balanced.
If there is more weight on one side, the
scale will tip to that side.
Use the information to balance the scale.
1
weighs one pound.
1
weighs two pounds.
1
weighs three pounds.
1
4
7 pounds and 3
1
7 pounds.
So the scale is balanced.
Tell how to make the scales balance?
2.
3.
4.
© Harcourt
1.
Challenge
CW47
LESSON 9.4
Name
Variable Grab Bag
Practice finding the value of an expression by playing
Variable Grab Bag. Copy the table below onto a piece of
paper and cut out the numbers 1 through 12. These are
values for the variable b. Put the pieces into a bag or hat.
1
2
3
4
5
6
7
8
9
10
11
12
Without looking, Player A grabs one number out of the
bag, uses it to find the value of the first expression, and
records the result as points in the correct column. If the
result is not a whole number, the player gets 5 points.
After replacing the number, it is Player B’s turn. Players
continue taking turns. Find the total number of points for
the 10 rounds. The player with more points is the winner.
Expression
1
4b
points
points
2
20 b
points
points
3
b8
points
points
4
7b
points
points
5
60 b
points
points
6
b9
points
points
7
12 b
points
points
8
48 b
points
points
9
b2
points
points
10
b2
points
points
points
points
TOTAL POINTS
CW48
Challenge
Player A
Player B
© Harcourt
Round
LESSON 9.5
Name
Say It Again, Sam
When writing equations to match words, there is usually
more than one correct answer.
Example Write an equation using a variable.
5 towels in each of 7 stacks is the total number of towels.
Kris’s equation: 5 7 t
Deb’s equation: t 7 5
In both equations, t is the total number of towels.
One equation is given. Give another possible equation.
1.
A total number of eggs, n, in 5
cartons is 3 eggs in each carton.
2.
6 pages each in 4 baby books is
the total number of pages, p.
64p
n53
© Harcourt
Write 2 possible equations.
3.
12 players on each of 8
basketball teams is the total
number of players, p.
4.
50 campers split among 10
cabins is the number of
campers, c, in each cabin.
5.
2 socks in each of some number
of pairs, p, is 24 socks.
6.
100 pieces of firewood divided
into 5 piles is some number, f,
in each pile.
Challenge
CW49
LESSON 9.6
Name
Play by the Rules
An input/output table can have any kind of rule.
Sometimes a rule is one step, like multiply by 4.
Sometimes a rule is two steps. Can you find a rule for the
input/output table?
Input
Output
3
10
5
14
6
16
10
Think: What operations on 3 give a value of 10?
Idea: Multiply by 3, then add 1.
Test your idea for input 5.
Does (5 3) 1 14?
Try again: Multiply by 2, then add 4.
Test your idea for input 5.
Does (5 2) 4 14?
24
Test your idea for input 6.
Does (6 2) 4 16?
Test your idea for input 10.
Does (10 2) 4 24?
So, a rule for the input/output table is multiply by 2, then
add 4.
1.
Input
Output
3
CW50
2.
Input
Output
9
20
14
4
11
16
12
8
19
8
8
10
23
10
9
Challenge
© Harcourt
Find a rule for each input/output table. Remember, you must test
your rule on each row!
LESSON 9.7
Name
Flying Around
Marty the Fly is standing on the grid below. When he flies,
it is always one whole space either straight up, straight
down, directly left, or directly right.
Follow Marty’s moves and tell where he lands.
Marty makes the following moves:
Starting in space D8, Marty moves 2 spaces up, 3 spaces
right, 4 spaces left, 5 spaces up, 3 spaces right, 2 spaces
down, 3 spaces right, 1 space up and 2 spaces left.
A
B
C
D
E
F
G
H
I
J
1
2
3
4
5
6
7
© Harcourt
8
9
10
1. Where does Marty land?
2. Make up your own moves for Marty and have a friend
play your game.
Challenge
CW51
LESSON 10.1
Name
The Powers That Be
You can write some large numbers in a shorter form by
using exponents. An exponent tells how many times to
multiply a number, called the base, by itself.
base → 100
100 1
101 10
102 10 10 100
103 10 10 10 1,000
As you can see, the exponent also tells how many zeros
follow the number 1.
Many scientists round large numbers and use exponents.
One million equals 106. 18 million equals 18 106.
1.
32,000
•
• 89 105
2.
48,000,000
•
• 17 100
3.
560
•
• 9 106
4.
7,700
•
• 77 102
5.
8,900,000
•
• 32 103
6.
690,000
•
• 44 105
7.
9,000,000
•
• 16 107
8.
28,000
•
• 48 106
9.
17
•
• 98 106
10.
4,400,000
•
• 28 103
11.
160,000,000 •
• 56 101
12.
98,000,000
• 69 104
•
CW52 Challenge
© Harcourt
Draw a line to the matching number.
LESSON 10.2
Name
About the Same
In each large box, circle all the sets of factors whose estimated
product is the number in the center box.
2.
1.
4581
6487
5531
3999
5555
6456
8304
2,400
3894
6601
3,000
5499
3815
8256
6356
5648
6666
31,845
4.
3.
2599
6212
3395
6524
4888
9444
4304
1,200
2673
4973
3,600
6555
3444
4256
6184
9381
6631
4918
6.
5.
4999
8487
5765
8592
4,000
41,846
21,815
5825
8456
44,444
16,000
27,891
82,468 28,500 44,567
8.
7.
© Harcourt
28,344 43,456 81,793
45,081 64,875 82,931
56,872 39,999 64,721
83,704
64,382
24,000
38,132
37,777 45,555 63,925
30,000
55,734
65,377 56,294 310,388
Challenge
CW53
LESSON 10.3
Name
Doubling and Halving
One of the earliest methods of multiplying was accomplished
through doubling and halving. This method can be traced
to the early Egyptians.
Here is how to multiply 7 35.
Double
7
Halve
35
14
17
28
8
56
4
112
2
224
1
← Half of 35 is 1712; use only 17.
← Half of 17 is 812; use only 8.
• Halve the numbers in the second column until you reach
the number 1.
• Double the numbers in the first column.
• Cross out the even numbers in the Halve column: 2, 4,
and 8. Then cross off numbers in the Double
column that are opposite the crossed-off numbers.
• Add the numbers in the Double column that are not
crossed out: 7 14 224 245.
So, 7 35 is 245.
1.
CW54
6 42
Challenge
2.
3 27
3.
4 51
© Harcourt
Multiply, using the doubling and halving method. Show your work.
LESSON 10.4
Name
Multiply 3-Digit Numbers
Complete the multiplication puzzle.
246
4
621
3
157
7
4
361
3
314
401
6
476
2
2
7
555
425
345
8
2
229
7
4
© Harcourt
Challenge
CW55
LESSON 10.5
Name
Napier’s Rods
John Napier, a Scottish mathematician, lived about 400
years ago. He invented the series of multiplication rods
shown below.
Guide
0
1
0
2
0
3
0
4
0
5
0
0
6
0
7
0
8
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
4
5
6
7
8
9
0
0
0
0
1
1
1
1
1
3
2
4
6
8
0
2
4
6
8
0
0
0
1
1
1
2
2
2
4
3
6
9
2
5
8
1
4
7
0
0
1
1
2
2
2
3
3
5
4
8
2
6
0
4
8
2
6
0
1
1
2
2
3
3
4
4
6
5
0
5
0
5
0
5
0
5
You can use Napier’s rods to multiply 4 537.
• Line up the guide rod and the
rods for 5, 3, and 7.
• Look at the numbers in the
fourth row. Start at the right;
add the numbers as shown.
Then write them as shown.
0
1
1
2
3
3
4
4
5
7
6
2
8
4
0
6
2
8
4
0
1
2
8
3
5
4
2
4
9
5
6
6
3
Guide
0
0
2
1
3
1
4
2
0
1
6
2
2
4
3
3
2
4
4
0
4
5
8
5
6
6
6
7
4
7
8
2
3
5
0
5
0
0
0
9
8
7
6
5
4
3
2
1
7
3
6
0
1
7
4
2
9
1
1
2
0 2 8
4
8
© Harcourt
1
9
8
1
5
1
1.
6 549 2.
4 375 3.
3 627 4.
2 125 5.
7 194 6.
5 431 Challenge
4
2
Copy or cut out the rods above. Use them to find the products.
CW56
7
1
2
• The answer is 2,148.
8
LESSON 10.6
Name
Comparison Shopping
The music store offers CDs at $10.99 each or 5 for $44.95.
Which is the better deal?
• You can multiply the individual CD price by 5 to compare.
$10.99 5 $54.95 compared to 5 for $44.95.
The package deal for 5 CDs is the better buy.
© Harcourt
Determine the better buy.
1.
Fancy chocolate candies––
14-piece box for $24.92 or
each piece for $2.00?
2.
Batteries––
2 for $1.57 or
8 for $6.42?
3.
Eggs––
$0.79 for 6 or
$1.49 for 12?
4.
Ice cream––
1 half gallon for $1.89 or
3 half gallons for $5.76?
5.
Coffee cups––
1 for $0.89 or
12 for $9.00?
6.
Butter––
1 stick for $0.49 or
4 sticks for $1.96?
7.
Colored pencils––
1 for $0.66 or
6 for $4.10?
8.
Laundry detergent––
64 oz for $2.99 or
128 oz for $5.99?
9.
Spring water––
1.5 liter for $1.69 or
3.0 liter for $2.99?
10.
Candy bars––
4 for $2.96 or
12 for $8.40?
Challenge
CW57
LESSON 11.1
Name
Moving Day
The Barretts are moving. Help them color code their boxes.
Solve the problems. Look at the number of zeros in the product.
Use the table below to color code the Barretts’ boxes.
2
red
Color
40
20
5
6
blue
orange
yellow
green
20,000
40
700
300
500
60
900
6
CW58
4
400
20
300
40
80,000
4
3
400
30
60,000
50
Challenge
6,000
300
1,000
500
4,000
4
700
30
200
4
500
300
800
3
90,000
20
© Harcourt
Number of
Zeros in Product
Name
LESSON 11.2
Multiple Wheels
The factor in the outer circle times the factor in the inner
circle equals the product in the center.
© Harcourt
Write the missing multiple of 10.
Challenge
CW59
LESSON 11.3
Name
Target Practice
Practice your estimation skills in this challenging game.
The object of the game is to choose a factor that produces
a product closer to the chosen target.
Work with a partner to solve.
List A
Product
List B
Factor
473
698
5,444
23
72
49
541
237
629
41
61
27
812
1,010
303
18
36
54
349
421
568
32
15
45
Step 1 One player chooses a number from List A as the
target and circles it.
Step 2 The partner chooses a number from List B and circles it.
Step 3 Each player secretly estimates the other factor. Each
player multiplies that factor by the circled factor.
© Harcourt
The player whose product is closer to the circled target gets
1 point. If both players choose the same factor, then they each
receive 1 point. The first player to reach 6 points wins. For each
round players circle new numbers.
CW60
Challenge
LESSON 11.4
Name
Cross-Number Puzzle
A cross-number puzzle is a way to model multiplication.
Solve the puzzle 23 16 n this way.
• Put the factors in the boxes.
• Break each factor into 2 of its addends. Record the
addends along the top and right side of the drawing.
23
20
3
6
10
16
• Multiply the addends. Record the products in the inside
boxes.
• 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.
23
138
230
368
20
3
120 18
200 30
320 48
6
10
16
So, n 368.
© Harcourt
Complete the cross-number puzzles.
1. 18 27 n
18
2. 14 36 n
10
8
14
20
7
27
Challenge
36
CW61
LESSON 11.5
Name
Use the Word!
Sometimes it is difficult to work with large numbers
because they have so many digits. You can use place
value and word form to help find products of some greater
numbers.
Find 4 2,000,000.
Think: 4 2 million 8 million.
So, 4 2,000,000 8,000,000.
Find 7 60,000.
Think: 7 60 thousand 420 thousand.
So 7 60,000 420,000.
Use this strategy to find the products.
7 1,000,000
Think: 7 1
.
So, 7 1,000,000 2.
8 10,000
Think:
So, 8 10,000 3.
.
.
.
.
.
So, 5 40,000 .
9 30,000
Think:
So, 9 30,000 5.
5 40,000
Think:
4.
.
.
4 6,000,000
Think:
So, 4 6,000,000 CW62 Challenge
.
© Harcourt
1.
LESSON 12.1
Name
Digit Detective
Complete the problem by finding the missing digits.
5
1.
3
4
2
2
4
1, 2 8
1,
0
0
4
2.
7
5, 2 5
5, 6 2
0
5
6
4.
7
5.
1, 2
0
1, 5 3
6
8
5
5
0
4 9
1
,
2,
7
8.
4 1 5
4, 9 8 0
5, 3 9 5
1,
1
4
5
3
4
1, 6 2
1, 9 4
0
4
3
4
3
9.
2
3, 6
3, 9
3
1
0
,
1,
5
5
0
8 5
5
Use the space below to create your own multiplication
problems with missing digits. Ask a classmate to
complete them.
© Harcourt
10.
1,
1 7 4
4 0
1
2 5
7.
6.
5
4
5
3 3
3.
Challenge
CW63
LESSON 12.2
Name
The Bigger, the Better
Players: 3 or more
Materials: Index cards numbered 1–9
Rules:
• One player draws six cards and pauses after each draw
so that other players have time to decide where to write
each digit.
• Players write the digits to make factors that give the
greatest possible product. In every round, each player
may throw out one digit.
• Once a player has written a digit, he or she cannot move
the digit to another position.
• When the six cards have been drawn, players multiply
to find their products. The player who has the greatest
product wins the round.
Number
Thrown Out
↓
Number
Thrown Out
↓
Round 2
Round 3
Round 4
Round 5
Round 6
© Harcourt
Round 1
CW64
Challenge
LESSON 12.3
Name
Lattice Multiplication
An early method of multiplying is the lattice method. This
describes how it works.
Multiply 2,781 26.
• Write one factor along the top of the lattice and the other
factor along the right side.
• Multiply each digit of the factors. Record the products
inside the lattice so that the ones and tens are separated
by a diagonal. (See Figure 1.)
• Add the numbers in the grid along the diagonals, starting
from the lower right corner. Record each sum at the end
of its diagonal—just as you do when adding columns.
(See Figure 2.)
• Read the digits down the left and across the bottom. This
is the product.
Figure 1
2
0
1
7
4
2
1
4
Figure 2
8
4
2
1
4
2
1
6
8
0
2 2
0
6 6
7
8
1
1
1
1
0 0 4 1 4 1 6 0 2 2
7 1 2 4 2 4 8 0 6 6
2
3
0
6
So, 2,781 26 72,306.
Use lattice grids to find the product.
2,531 81 2.
6,491 34 © Harcourt
1.
Challenge
CW65
LESSON 12.4
Name
Doubling Tales
An ancient story tells of a clever traveling storyteller. He
promised to entertain the king, and at a price that seemed
unbeatable. For the first day the storyteller wanted only 1¢,
and for each day after that the rate would double. The king
thought about it briefly: 1¢ on day 1, 2¢ on day 2, and 4¢
on day 3. The king assumed that the price was reasonable.
How much will the storyteller charge the king on day 26?
Complete the table to find out.
Price
Day
1
1¢
14
2
2¢
15
3
16
4
17
5
18
6
19
7
20
8
21
9
22
10
23
11
24
12
25
13
26
Price
Do you think the storyteller charged a reasonable price? Explain.
CW66
Challenge
© Harcourt
Day
LESSON 12.5
Name
Letter Go!
Each letter stands for a 1-digit number. Find a value for each
letter.
AAA
B B B
CCC
2.
MMM
NNN
P P P
QQQ
3.
TTT
S
RRR
4.
JJJ
KK
JJJ
JJJ
JLLJ
5.
EEE
FFF
EEE
EEE
EEE
EGHGE
6.
XX
YY
XX
XX
XZX
© Harcourt
1.
Challenge
CW67
LESSON 13.1
Name
Number Riddles
To solve the riddles on this page, you
will need to know the name for each
part of a division problem. Use the
example at the right as a reminder.
1.
My divisor is 5.
I am greater than 4 5.
I am less than 5 5.
My remainder is 1.
quotient
divisor
2.
What dividend am I?
3.
My divisor is 8.
I am less than 30.
I am greater than 3 8.
My remainder is 5.
4.
My divisor is 6.
I am less than 60.
I am greater than 8 6.
I have no remainder.
What dividend am I?
My dividend is 50.
My remainder is 1.
I am an odd number.
6.
My dividend is 8 times as large
as my divisor.
I am an even number less than 15.
What quotient am I?
What divisor am I?
7.
My divisor is 9.
I am greater than 7 9.
I am less than 8 9.
My remainder is 7.
What dividend am I?
What dividend am I?
5.
remainder
9 r1
7
dividend
43
My remainder is 8.
My dividend is 80.
I am a 1-digit number.
8.
My dividend is 24.
I am 2 more than
my quotient.
I have no remainder.
What divisor am I?
What divisor am I?
9.
(
) 2 27
10.
(
) 5 26
11.
(
) 3 52
12.
(
) 1 36
13.
Write your own number riddle below.
CW68
Challenge
© Harcourt
Complete to make a true equation.
LESSON 13.2
Name
Cookie Coordinating
Joe and Melissa are organizing cookies to sell at a bake
sale. They are making equal groups of each kind of cookie.
Complete the chart.
Total Number Number of Plates Number of Cookies
on Each Plate
1.
Kind of Cookie
Total Number
Chocolate chip
96
Oatmeal
42
Number on Each Plate
Number of Plates
12
12 8 96
96 12 8
3 42
42 2.
Peanut butter
3
13
13 7 13 7
3.
Butterscotch
19
19 4 19 4
© Harcourt
4.
5.
6.
Sugar
Ginger
90
18
36
12
How many plates in all did Joe and Melissa use?
Challenge
CW69
LESSON 13.3
Name
Remainders Game
Number of players: 2, 3, or 4
Materials: game board
markers (24 small pieces of paper)
number cube labeled 3, 4, 5, 6, 7, and 8
Rules:
• Take turns placing a marker on one of the numbers
on the board and rolling the number cube. Divide the
numbers. For example, if you choose 92 on the board
and roll a 3 on the number cube, you then write the
problem 92 3 30 r2.
• Your score is equal to your remainder.
32
51
53
46
22
18
92
19
36
41
11
47
42
68
72
13
25
61
43
71
64
61
36
75
CW70
Challenge
© Harcourt
• After all the numbers on the board have been covered
with markers, find the sum of your remainder scores.
The winner is the player who has the greatest total score.
LESSON 13.4
Name
Grouping Possibilities
Complete each table by finding
different ways to divide a number
into groups while always having
the same remainder.
32 r1
5
works in table 1,
For example, 26
21 r2
5
does not work.
but 36
1.
Total
65
Number of Groups
(less than 10)
Number in Each
Group
Remainder
2
32
1
65
1
65
1
2.
Total
© Harcourt
3.
Number of Groups
(less than 10)
Number in Each
Group
Remainder
74
2
74
2
74
2
74
2
74
2
Total
Number of Groups
(less than 10)
Number in Each
Group
Remainder
99
3
99
3
99
3
99
3
99
3
Challenge
CW71
LESSON 13.5
Name
Riddle-jam
Riddle: What do geese do in a traffic jam?
Find each quotient. Then write the quotients in order from least
to greatest at the bottom of the page. Write the matching letter
below each quotient.
1.
450 5 Y
2.
270 9 T
3.
3,600 9 O
4.
42,000 7 L
5.
2,100 7 H
6.
7,200 8 K
7.
36,000 9 A
8.
280 7 H
9.
3,500 7 N
10.
240 4 E
56,000 7 T
12.
49,000 7 O
11.
Riddle Answer:
30
© Harcourt
T
!
CW72
Challenge
LESSON 13.6
Name
What’s the Problem?
Write a problem that could be solved by using the division
sentence. Then write a pair of compatible numbers, and estimate
the quotient.
1.
3.
2.
7,100 9 n
Problem:
Problem:
Compatible numbers:
Compatible numbers:
63,147 9 n
4.
276 4 n
Problem:
Problem:
Compatible numbers:
Compatible numbers:
758 4 n
6.
41,797 6 n
Problem:
Problem:
Compatible numbers:
Compatible numbers:
© Harcourt
5.
1,489 5 n
Challenge
CW73
LESSON 14.1
Name
Break the Code
In the division problems below, each letter stands for a digit.
The same letter stands for the same digit in all of the problems.
The table shows that H 2 and T 8. Use the division
problems to find out what each of the other letters stands for.
0
1
2
3
4
5
6
7
8
H
9
T
Once you have broken the code, use the letters and digits to
answer the riddle at the bottom of this page.
LH
2. DD
T
T
3. ID
T
HT
4. HE
I
T
5. DR
H
LH
6. EIA
I rL
7. FD
R
HH rH
8. DW
A
© Harcourt
DD
8
1. HT
T
28
HOW DID THE RIVER HURT ITSELF?
Code Letter
Digit
6 8
2 0 4
CW74
Challenge
0
9
0
8
5
3
7
0
1
1
LESSON 14.2
Name
Remainders Game
Number of players: 2, 3, or 4
Materials: game board
markers (24 small pieces of paper)
number cube with the numbers 3, 4, 5, 6, 7, and 8
Rules:
• Take turns placing a marker on one of the numbers on
the board and rolling the number cube. Divide the
numbers. For example, if you choose 923 on the board
and roll a 3 on the number cube, you then write the
problem 923 3 307 r2.
• Your score is equal to your remainder.
• After all the numbers on the board have been covered
with markers, find the sum of your remainder scores. The
winner is the player who has the greatest total score.
295 561 350 923 174 532
© Harcourt
718 895 473 624 596 407
499 744 303 255 936 577
800 131 652 729 348 210
Challenge
CW75
LESSON 14.3
Name
Super Checker!
Solve each division problem. Then complete the number sentence
that can be used to check the answer. Draw a line from the
division problem to the related number sentence.
33
1
6
A.
(
160) 2.
58
0
0
B.
(
105) 1 3.
48
3
1
C.
(
309) 1 4.
26
1
9
D.
(
120) 2 5.
78
4
2
E.
(
207) 3 © Harcourt
1.
CW76
Challenge
LESSON 14.4
Name
Create a Problem
Write a word problem that could be solved with each division
sentence given. Then solve your creation!
1. 237 4 2. 637 6 Problem
Problem
3. 4,822 8 Problem
5. $97.35 3 Problem
6. 2,517 2 Problem
© Harcourt
Problem
4. 3,207 9 Challenge
CW77
LESSON 14.5
Name
Diagram Division
Complete the division number sentence for each of the illustrations.
Cookies
1.
98 4 Eggs
2.
12 r5
145 3 r
36 r2
Marbles
3.
Crayons
4.
Pennies in Piñatas
CW78
Challenge
$3.29
© Harcourt
5.
r
LESSON 14.6
Name
Find the Missing Scores
Mr. Murphy gave a math quiz to his students each day for
a week. The highest possible score was 12 points.
A group of 4 students kept a record of their scores for the week.
1.
Complete the chart by filling in the missing numbers.
Mon.
Tues.
Wed.
Thu.
Fri.
Hank
8 pts
9 pts
9 pts
12 pts
12 pts
Jim
6 pts
9 pts
8 pts
9 pts
8 pts
Sarah
5 pts
6 pts
7 pts
8 pts
9 pts
Corina
9 pts
12 pts
12 pts
11 pts
11 pts
Average
score for
each
student
Average
score on
each quiz
9 pts
Which student had the highest average score?
3.
On which days was the average score for the 4 students
the highest?
4.
What is the difference between Corina’s average score
and the lowest average score?
5.
What does the number in the box at the lower righthand corner of the chart represent?
© Harcourt
2.
Challenge
CW79
LESSON 15.1
Name
Cookie Giveaway
You have 210 cookies to give equally to friends. There can be
no cookies left over. How many different groups can you make?
Write your groupings in the table. Fact families can help you.
Groupings Table
210 3 70
2 friends each get 105
3 friends each get 70
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
friends each get
CW80 Challenge
friends each get
friends each get
© Harcourt
210 2 105
LESSON 15.2
Name
Puzzled
© Harcourt
Trace and cut out each of the figures below. See if you can build
an 8-by-8 square. Record your final square on the grid below.
Challenge
CW81
Name
LESSON 15.3
Evenly Divided
© Harcourt
How many ways can you divide a square
into four equal pieces? Try to find at
least six different ways.
CW82 Challenge
LESSON 15.4
Name
Division Cipher
Each shape in the exercises below represents a number 0–9.
Use your multiplication and division skills to find what number
each shape represents. Then fill in the key.
Key
0,
1,
2,
3,
4,
5,
6,
7,
8,
9
1.
2.
Solve.
3.
4.
r
5.
6.
© Harcourt
r
Challenge
CW83
LESSON 15.5
Name
What’s for Lunch?
Joe’s Lunch Shop
Hot dog
$1.09
Juice, small
$0.39
Cookie
$0.50
Hamburger
$1.59
Juice, medium
$0.59
Brownie
$0.75
Slice of pizza
$1.25
Juice, large
$0.69
Ice cream bar
$1.25
1.
Lucas bought a hot dog, a large
juice, and an ice cream bar.
How much money did he spend
on lunch?
2.
Mr. Torres bought 4 lunch
specials for his family. How
much money did he spend?
3.
Tom bought 2 hamburgers and
a medium juice. What was his
change from a $5 bill?
4.
How much more does a hot
dog, small juice, and a brownie
cost than the lunch special?
5.
In one week, the shop sold
246 hot dogs. The shop is open
6 days a week. What was the
average number of hot dogs
sold each day?
6.
On Monday, the cook made
6 whole pizzas. He cut each
pizza into 8 slices. At the end of
the day, there were 3 slices left
over. How many slices of pizza
did the shop sell that day?
7.
During one week, the shop
sold 272 slices of pizza. If each
whole pizza is cut into 8 slices,
how many whole pizzas did the
shop sell during the week?
8.
The shop sold 4 dozen brownies on Tuesday. How much
money did the shop take in
from brownie sales?
CW84 Challenge
© Harcourt
Lunch Special $2.19
Hamburger, medium juice, cookie
LESSON 16.1
Name
Birthday Party Math
© Harcourt
Shruti is planning a birthday party for her friends. For
each situation, circle Factor if she should use factors to
solve the problem or Multiple if she should use multiples.
1.
Shruti is setting up tables for her guests. If there
are 18 people coming, how many tables should
she set, and how many people will be at each
table?
Factor
Multiple
2.
Shruti’s mother is buying birthday candles for her
cake. Candles come in boxes of 4. How many
boxes of candles does Shruti’s mother need to buy
in order to have 10 candles?
Factor
Multiple
3.
Shruti is going to give away purple pencils as party
favors. She has to order the pencils in sets of 10.
How many sets of pencils should she order so that
each guest can have two?
Factor
Multiple
4.
The guests will be playing some games. Shruti
Factor
wants to form equal-sized teams. How can she form
teams?
Multiple
5.
The guests are playing a game in a circle. They
count off, starting with 1. Every 4th person wins a
prize from the grab bag. Celia wants to know if she
will win a prize. How can she figure out if she will
win?
Factor
Multiple
6.
Shruti wants to write thank-you notes for her gifts.
She wants to write the same number of notes each
day. How many notes should she write each day?
Factor
Multiple
Challenge
CW85
LESSON 16.2
Name
Shipping Basketballs
The Best Basketball Factory ships basketballs to sporting
goods stores. The factory can ship basketballs in cartons of
different sizes that hold either 1, 2, 4, or 8 basketballs.
1.
Complete the chart to show 6 different ways that the
Best Basketball Factory can ship 30 basketballs.
Number of
Cartons for 1
Number of
Cartons for 2
Number of
Cartons for 4
Number of
Cartons for 8
Total Number
of Basketballs
2
0
7
0
30
30
30
30
30
30
2.
What is the fewest number of boxes that the factory can
use to ship 30 basketballs?
3.
Complete the chart below to show how the factory can use the fewest
number of cartons to ship the different numbers of basketballs.
Number of
Cartons for 1
Number of
Cartons for 2
Number of
Cartons for 4
Number of
Cartons for 8
Total Number
of Basketballs
1
1
1
1
15
31
63
122
251
300
CW86
Challenge
© Harcourt
The factory saves money when it ships basketballs in the
fewest number of cartons possible.
LESSON 16.3
Name
Number Pyramids
The numbers in the pyramids are found by using one of these
simple formulas:
C
A
B
A B C or C A B or C B A
If you know some of the numbers, you can find the rest.
14
5
16
9
To find the top number, add. 14 16 30
To find the lower number, subtract. 16 9 7
Find the missing numbers in each pyramid.
1.
2.
26
9
15
3.
10
14
9
4.
67
41
23
35
9
17
© Harcourt
10
12
6
9
7
7
Now, make your own number pyramids. Exchange them with a
partner, and test each other’s math skills.
Challenge
CW87
LESSON 16.4
Name
Something in Common
For each pair of numbers, write the prime factors. Then list
any prime factors that the pair has in common. If the pair
has no prime factors in common, write none.
Use the common prime factors to solve the puzzle.
3.
5.
7.
81
2.
25
18
60
Common Prime Factors:
Common Prime Factors:
Y
E
8
4.
21
12
56
Common Prime Factors:
Common Prime Factors:
H
C
55
6.
39
66
52
Common Prime Factors:
Common Prime Factors:
M
O
51
8.
65
34
12
Common Prime Factors:
Common Prime Factors:
N
B
© Harcourt
1.
What does a bee use to do his hair?
A
_____ _____ _____ _____ _____ _____ _____ _____ _____ !!!!
2
CW88
13
Challenge
17
5
3
7
13
11
none
LESSON 16.5
Name
Pascal’s Triangle
This triangle is called
Pascal’s Triangle. To
get the next row of
numbers in the triangle,
add the two numbers
above.
1
1
1
1
1
1
1
2
3
4
5
1
3
6
1
4
1
10 10 5
1
The first row contains only one number, 1.
© Harcourt
The second row contains 1 and 1.
1.
Find the sum of the numbers in the third row.
2.
Find the sum of the numbers in the fourth row.
3.
Find the sum of the numbers in the fifth row.
4.
Do you notice a pattern? What is it?
5.
Use the pattern to guess the sum of the numbers in the
seventh row.
6.
What are the numbers in the seventh row?
7.
What other patterns do you notice in Pascal’s Triangle?
Challenge
CW89
LESSON 17.1
Name
A Fraction of a Message
Decode the message. Find the fraction in the boxes below that
represents each letter on the number line. Write the letter of
that fraction in the message boxes.
P
W
•
•
2
F
•
•
0
•
•
•2
halves
0
•
•
•
sixths
•
•
•
•
6
6
0
•
thirds
•
•
•
•
• eighths
• •
•
0
• fifths •
N
•
sevenths
S
•
•8
8
•5
•
5
H
• • • • • • • • • • 1•0
•7
•
4
R
•
•
3
A
•
O
L
•3
•
•
•4
•
fourths
C
I
0
•
•
0
E
0
T
7
0
10
tenths
The message:
3
8
2
6
4
5
5
7
5
7
5
6
1
2
3
4
6
10
2
7
3
8
3
8
1
5
3
1
0
2
7
6
8
Challenge
1
4
5
7
4
5
3
4
1
3
Make up your own coded message or riddle using the
number lines above. Add extra letters if you need them.
CW90
5
7
© Harcourt
2
6
5
7
LESSON 17.2
Name
Equivalent Fraction Bingo!
Use your math skills with equivalent fractions to play bingo!
Materials:
2 number cubes, counters to cover gameboard,
fraction bars
To Play:
• The object of the game is to cover a row—horizontally,
vertically, or diagonally—with counters.
• Toss a number cube two times. Using one number as
the numerator and one number as the denominator,
write a fraction less than or equal to one. Place a
counter on a space with a fraction that is equivalent to
the one you made.
For example, if you toss a 6 and a 4, the fraction you
3.
fraction such as 2
write is 4
6. Look for an equivalent
2
Cover the space marked 3 on the gameboard. (Use
fraction bars to help find equivalent fractions.)
© Harcourt
Gameboard
1
4
1
5
6
6
3
5
1
2
1
2
3
5
6
4
5
1
4
3
4
1
3
FREE
1
2
1
3
5
1
1
6
1
4
2
5
1
2
3
4
2
3
1
1
3
Challenge
CW91
LESSON 17.3
Name
Colorful Fractions
Follow the directions. Color each part. Then write the numerators
in the fraction to describe the group.
1.
red. 1
Color 1
3
3
9
green. 2
Color 2
3
3
9
2.
2
5 red. 5 Color 2
15
2
5 blue. 5 Color 2
15
1
5 green. 5 Color 1
15
3.
1
4 blue. 4 Color 1
12
2
4 red. 4 Color 2
12
4.
blue. 1
Color 1
8
8
16
8 red. 3
8 Color 3
16
green. 4
Color 4
8
8
16
CW92 Challenge
© Harcourt
green. 1
Color 1
4
4
12
LESSON 17.4
Name
Estimating Fractional Parts
You can estimate the part of a whole that is shaded by
thinking about benchmark fractions.
Example
1
2
About what part of this rectangle
is shaded?
or 1
the better estimate?
Is 1
3
2
1
3
2
3
than to 1. So, 1
is the better estimate.
The part shaded is closer to 1
2
3
2
What part of the figure is shaded?
Circle the fraction that is the closer estimate.
1.
2.
7
3
8 or 4
4.
2
5
or 6
3
5.
4
5
6 or 1
2
© Harcourt
3.
7.
6.
5
2
3 or 6
8.
3
or 5
4
8
1
1
3 or 4
2
1
or 1
3
12
9.
1 or 3
4
8
1 or 1
4
3
Challenge
CW93
LESSON 17.5
Name
Language Exploration
Use a dictionary to help you complete this page.
1
A centimeter is one hundredth of a meter or m.
100
1. How many centimeters are in a meter?
2.
List several words that contain the root word “cent,” and give
their meanings.
A triangle has three angles.
3.
How many sides has a triangle?
4.
List several words that begin with “tri,” and give their meanings.
6.
List several words that begin with “mill,” and give their meanings.
7.
What does “bicycle” mean?
8.
Name other common words that begin with “bi,” where “bi”
means “two.”
CW94
Challenge
© Harcourt
1
A milliliter is one thousandth of a liter or L.
1,000
5. How many milliliters are in a liter?
LESSON 17.6
Name
A Mixed-Number Challenge
Work together with a partner to write a mixed number that tells
how much is shaded.
1.
2.
Write a mixed number for each of the following figures. The figure
at the right stands for 1.
3.
© Harcourt
5.
4.
6.
7.
Shade parts of the following figures. Have a partner write a mixed
number that tells how much is shaded.
8.
9.
Challenge
CW95
LESSON 18.1
Name
Amazing Maze
Find the path from the beginning to the end of the maze. Start
with 112 and add each fraction along your path. Your goal is to
end at the finish with 61102.
START
1
12
1
1
2
1
12
1
1
2
3
12
4
1
2
1
1
2
1
1
2
2
1
2
5
1
2
4
1
2
4
1
2
3
1
2
1
1
2
1
1
2
2
1
2
FINISH
1
0
12
2
12
2
12
1
1
2
Challenge
9
12
2
12
5
12
2
12
6
1
2
3
12
3
1
2
CW96
3
12
3
1
2
7
1
2
3
1
2
4
1
2
1
1
2
1
12
4
1
2
2
1
2
2
1
2
1
1
2
2
1
2
3
12
1
1
2
2
12
© Harcourt
8
1
2
2
12
Name
LESSON 18.2
What’s Left?
Color each picture as directed. Colors do not overlap.
When you are finished coloring, answer each question.
1.
of the cake red.
Color 1
3
of the cake brown.
Color 1
3
How much of the cake is not
colored?
How much of the cake is
colored?
2.
of the figure brown.
Color 165
of the figure orange.
Color 165
What fraction of the figure is
not colored?
What fraction of the figure is
colored?
3.
of the flag red.
Color 188
© Harcourt
of the flag green.
Color 128
of the flag blue.
Color 128
of the flag orange.
Color 168
What fraction of the flag is not
colored?
What fraction of the flag is
colored?
Challenge
CW97
LESSON 18.3
Name
All Mixed Up!
S.
31 ?•
51
8
8
•
7130
E.
51 ?•
61
3
3
•
9
E.
11
?•
101
2
2
•
135
8
N.
31 ?•
42
5
5
•
111
6
V.
1
8 28 ?•
156
•
4
41
T.
2
4 64 ?•
103
•
4
81
I.
2
7 27 ?•
83
•
9
22
A.
3
6 66 ?•
75
•
5
73
E.
1
2
5120
1
0 ?•
•
2
81
N.
10112 1112 ?•
•
3
112
E.
4 21
61
4 ?•
•
3
11
N.
85
?•
107
9
9
•
105
7
© Harcourt
Draw a line to connect the problem with the correct answer.
To solve the riddle, match the letters above with the answers
below the boxes.
Riddle: Why was six afraid of seven?
Answer: because
3
1
5
2
81
1
0 29
4 82 138 7
CW98
Challenge
3
11
4 112
3
41
5 3
107 75
111
6
9
LESSON 18.4
Name
What Breed Is Each Dog?
There are 48 dogs at the dog show.
Clue 1
Every dog is a specific breed.
Clue 2
The different breeds of dogs are: German shepherds,
cairn terriers, poodles, golden retrievers, and Labradors.
Clue 3
Half of the dogs are German shepherds.
Clue 4
There are an equal number of cairn terriers and poodles.
Clue 5
There are twice as many cairn terriers as Labradors.
Clue 6
There are four golden retrievers.
List how many of each breed of dog there are.
2.
What fraction of the group does each breed of dog represent?
© Harcourt
1.
Challenge
CW99
LESSON 18.5
Name
Total Cost
Each coin of United States currency can be thought of as a
fraction of a dollar.
One quarter is
dollar.
equal to 1
4
1.
One dime is
1
equal to 1
0
dollar.
One penny is
One nickel is
1
1
equal to equal to 100
2
0 dollar.
dollar.
Use coin values to help you find the sum. Use what you
know about adding money to find the sum in simplest form.
Problem:
Think:
Steps:
1
1 4 10
One quarter one dime
Write each coin as a fraction.
25¢ 10¢ 35¢
Use what you know about
money to write an equation.
35
7
35¢ 10
0
2
0
Write the sum in simplest form.
1
7
4 So, 1
1
0
2
0.
3. 2
20
6. 3
100
5. 1
2
20
4
8. 19
1220 100
11. CW100
Challenge
1
1
100 1
0
4. 1
160 100
7. 31
4
100
10
10. 1
260 4
13. 9. 12. 3
4
100 1
0
3
4
20
100
6
41
100
100
5
230 10
© Harcourt
1
1
20 10
2. LESSON 18.6
Name
Cut Up!
You can subtract unlike fractions only after they have
been renamed with like denominators.
1 1
Find 2 4.
1
2
1
4
Divide each half of the first figure in half. Both figures now
have equal parts. Subtract the like fractions.
2
4
1
4
1
4
1 1 1
So, 2 4 4.
For each pair of figures, find a way to divide one of them so that
both have equal parts. Explain. Then subtract.
1.
2.
© Harcourt
2
3
1
6
3.
3
4
9
16
4.
3
4
5
8
9
12
2
3
Challenge
CW101
LESSON 19.1
Name
Riddlegram!
Answer this riddle. Write the letter that matches each fraction or decimal.
You will use some models more than once.
Riddle: What did one Math book say to the other Math book?
,
0.2 0.6 5
10
8
6
10 10
0.01
0.3 1 0.6 2 0.12 35 0.7 15
10
10
100
100
49 0.52 0.9 0.35
100
!
T
E
A
Y
V
N
H
O
© Harcourt
F
MAT
H
MAT
H
CW102 Challenge
LESSON 19.2
Name
Decimal Drift
Large numbers are often written with both whole numbers
and words. This can make the numbers easier to read.
Example: 34,000,000 may be written as 34 million.
Large numbers can also be written with words and
decimals.
Examples: 34,500,000 34.5 million
1,400,000 1.4 million
4,800,000 4.8 million
The table below shows the areas of the continents in square miles.
1.
Complete the table by writing the missing numbers.
Continent
Area (in square miles)
North America
9,400,000
South America
6,900,000
Europe
17.4 million
11,700,000
Oceania, including
Australia
Antarctica
9.4 million
3.8 million
Asia
Africa
Area (in square miles)
3.3 million
5,400,000
© Harcourt
Use the table to answer 2–5.
2.
Which continent has the greatest area?
3.
Which continent has the least area?
4.
How many continents have a greater area than North America?
5.
Which 2 continents together have about the same area as North
America?
Challenge
CW103
LESSON 19.3
Name
Designing with Decimals
Shade in the decimal amount in each model.
1.
2.
0.2
4.
3.
0.4
0.8
5.
0.35
6.
0.24
0.52
Complete. You may look at the shaded models above.
7.
2 tenths tenths 40 hundredths
8.
9.
10.
hundredths
35 hundredths tenths and 5 hundredths
2 tenths and 4 hundredths hundredths
Use colored pencils to make a design or picture on the grid. Color the numbers
of small squares needed to model the decimals shown below.
Red 0.25
Blue 0.15
Black 0.10
Green 0.20
CW104
Challenge
© Harcourt
Yellow 0.30
LESSON 19.4
Name
First-Second-Third
At the recent Number Olympics, people were confused by
who was in first, second, or third place. (HINT: First was
always the least number and third the greatest number.)
Event
Scores
Event
Scores
Number Put
0.3, 0.4, 0.2
Fraction Jump
0.96, 1.53, 0.8
Decimal Hurdles
0.23, 0.45, 0.36
Area Swim
0.6, 0.62, 1.0
High Number
0.3, 0.28, 0.4
Number Beam
3.5, 3.05, 3.47
Freestyle Numbers
1.23, 0.84, 1.1
Perimeter Sprint
2.34, 2.4, 2.05
For each event listed, put the numbers in their proper places on
the medals stand. The first stand has been completed.
Number Put
0.3
2ND
Fraction Jump
0.2
1ST
0.4
3RD
Decimal Hurdles
0.36
2ND
0.23
1ST
0.45
3RD
High Number
0.96
2ND
0.62
2ND
© Harcourt
0.6
1ST
1.0
3RD
Number Beam
1ST
3RD
Freestyle Numbers
2ND
3RD
Perimeter Sprint
1ST
2ND
1.53
3RD
Area Swim
1ST
2ND
0.8
1ST
1ST
3RD
2ND
3RD
Challenge
CW105
LESSON 19.5
Name
Money Combos
Show three different coin combinations that equal each amount
below. Use quarters, dimes, nickels, and pennies—at least one of
each coin—in each combination.
$0.84
2.
$0.55
3.
$1.37
4.
$2.46
© Harcourt
1.
CW106
Challenge
LESSON 19.6
Name
Missing Number Mystery
Write mixed numbers for the numbers that are missing from each
number line below.
1.
4.20
4.10
4.25
2.
5.4
5.7
5.8
3.
7.32
7.34
7.36
4.
9.40
42
100 or
3.18
3.19
21
50
9.44
9.46
48
100 or
12
25
5.
3.21
3.23
6.
© Harcourt
8 .2
7.
8.6
8.8
9.0
Make your own number line. Include the following
9
2
3
, 4 , 4 .
numbers: 4.01, 4.12, 4.03, 4 100
25
20
Challenge
CW107
LESSON 20.1
Name
Super (Market) Estimations
Cashiers can make errors, and scanners don’t always scan
the correct prices. It is important to check your 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
CW108
Challenge
.
© Harcourt
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
LESSON 20.2
Name
Shop Till You Drop!
Estimate the cost of the items on each list. Circle the list that
comes closer without going over your spending limit.
1.
Your spending limit is $400.
Suit
$185.40 Belt
$32.00
Suit
Shirt
$35.65 Coat
$115.40
Coat
Shirt
Shoes
$43.75 Hat
$46.00
Hat
Shoes
Tie
$27.65 Pants
$28.90
Shirt
Coat
Gloves $12.99 Suspenders $34.81
Suit
Gloves
Socks
List 1
2.
Belt
Estimated cost:
Estimated cost:
Actual cost:
Actual cost:
Your spending limit is $2,000.
List 1
Computer
CD-ROM drive
Printer
© Harcourt
$7.00
List 2
Software
Speakers
Computer $1,199.99 Joystick
$59.25
Laptop
Desk
Computer $1,499.95
$79.42
CD-ROM drive$238.75 Speakers $138.60
Printer
$318.66
Software
$179.25
List 2
Laptop
Computer
Printer
Software
Estimated cost:
Estimated cost:
Actual cost:
Actual cost:
Challenge
CW109
LESSON 20.3
Name
Play Ball
0.72
0.9
1.04
1.3
1.16
1.48
2.20
Place the numbers on the balls in the correct place in the diagram below so that
the sum of these positions is the same:
•
All of the outfield b
•
Catcher Pitcher Third Base Left field b
•
Catcher Pitcher Shortstop Center field b
•
Catcher Pitcher Second Base Right field b
•
Catcher Pitcher First Base b
Center field
Right field
Left field
Shortstop
Second base
Third base
First base
0.72
Catcher
0.14
CW110
Challenge
© Harcourt
Pitcher
LESSON 20.4
Name
Amazing Mazes
Use the number patterns to complete the empty boxes.
2.16 2.17
2.4
3.6
© Harcourt
3.34
Challenge
CW111
LESSON 20.5
Name
Addition and Subtraction Puzzles
Put the numbers in the boxes so that when you either add or subtract from left
to right or top to bottom the answers at the right are the same and the answers
below are the same.
Example:
0.2, 0.3, 0.7, 0.2
0.7
0.3
0.4
0.7 0.3 0.4
0.2
0.2
0.4
0.2 0.2 0.4
0.5
0.5
0.3 0.2 0.5
1.
1.1, 0.5, 0.2, 0.8
2.
1.7, 0.5, 0.6, 0.6
3.
0.2, 0.2, 1.3, 0.9
4.
0.9, 1.1, 1.3, 0.7
5.
0.9, 0.3, 1.2, 1.8
6.
0.6, 0.6, 1.2, 1.2
7.
0.2, 0.2, 0.3, 0.3
8.
1.3, 1.1, 0.7, 0.5
CW112 Challenge
© Harcourt
0.7 0.2 0.5
LESSON 20.6
Name
Think About It
The decimal point is missing from each of the numbers in Exercises 1–8.
Place the decimal point where it belongs in each number.
1.
35
2.
177
length of a new pencil in centimeters
3.
177
length of a bee in centimeters
4.
2036
record speed in seconds for the 200-meter run
5.
$125
cost of a fancy helium-filled balloon
6.
340
number of miles walked in one hour
7.
340
number of miles driven in one hour
8.
1371
number of seconds it takes Tony to write his name
height of an average fourth-grade student in centimeters
For 9–14, arrange the
digits shown to make the
described number.
Least number possible
.
10.
Greatest number possible
.
11.
Number nearest to 30
.
12.
Greatest number that is less than 35
.
13.
Least number that is greater than 20
.
14.
Number nearest to 10
.
15.
What would your answers to Exercises 9–14 be if the 5 card was
replaced with a zero card?
© Harcourt
9.
Challenge
CW113
LESSON 21.1
Name
Pathfinder
1.
Measure every path to the nearest inch or half inch.
Write the length on the path.
Home
1 inch 1 mile
Park
Fred's
House
Store
School
List four ways to drive from home to school, following
these guidelines. Always travel down and to the right or
left. Do not retrace your path.
3.
What is the longest route? How many miles is it?
4.
What is the shortest route? How many miles is it?
5.
About how long would it take you to walk the shortest route
© Harcourt
2.
to school?
CW 114
HINT:
Challenge
It takes about 20 minutes to walk a mile.
LESSON 21.2
Name
Biking Adventure
1.
Sammy is going on a week-long bicycle trip with his dad.
They plan to ride from Acton to Halpine by going
through Brattle, Capeville, Dawson, Easton, Foxboro, and
Grafton. Then they will go straight back to Acton from
Halpine. They made a detailed map of the route. Use the
information below to find about how far they will ride.
Acton
Brattle
Scale:
1 inch 8 miles
Capeville
Dawson
Foxboro
Easton
Grafton
Halpine
If Sammy and his dad bicycle the same distance each day
for five days, how many miles will they travel in one day?
3.
Make dash marks on the map to show about how far
Sammy and his dad rode each day.
© Harcourt
2.
Challenge
CW115
LESSON 21.3
Name
Cap This!
MATERIALS
string 24 inches long, customary ruler
What’s your cap size?
• Take a string and carefully measure around your head.
• Mark the string, and then lay it down along a ruler.
Read the measure to the nearest quarter inch.
• Record your cap size.
• Take a survey to find the cap size of ten of
your classmates.
Name
Cap Size
© Harcourt
What is the average cap size for the ten classmates in your
survey? Explain.
CW 116
Challenge
LESSON 21.4
Name
Half Full or Half Empty?
The pitchers below are the same size. They are arranged from
barely full to completely full. Each pitcher can be labeled with
two equal measurements. Use the measures in the box to write
in the missing measurement for each pitcher.
8 cups, 3 quarts, 4 quarts,
6 pints, 1 gallon, 1 quart, 6 cups
1.
2.
1 pint or 2 cups
2 pints or
3.
4.
© Harcourt
3 pints or
4 pints or
5.
6.
or
or
Challenge
CW117
LESSON 21.5
Name
Which Weight?
The weights below belong on the balance scales. Some of the
scales are unbalanced. Match each weight listed below with one of
the problems to make a true statement. Use each weight once.
16 ounces, 32 ounces, 48 ounces, 52 ounces,
96 ounces, 5 pounds, 4,000 pounds, 8 tons
1.
2.
2 pounds 3.
24 ounces >
4.
2 tons 4 pounds >
6.
6 pounds 7.
6 tons <
8.
24 ounces <
CW 118
Challenge
3 pounds © Harcourt
5.
LESSON 21.6
Name
Atlas Stones
At the annual “World’s Strongest Person” competition, no
event tests athletic strength better than the Stones of Atlas.
Competitors must lift six progressively larger round stones
onto 3-foot platforms. The stones are huge—about 2–3 feet in
diameter. Their weight is staggering.
The weight of the Stones of Atlas is given in the ancient
measurement of stones. A stone is about 14 pounds.
Convert the weight of the 6 Atlas Stones into pounds.
1. 10 stones lb
2. 13 stones lb
3. 15 stones lb
4. 18 stones lb
5. 20 stones lb
6. 23 stones lb
7. In the 1995 event, one competitor executed a dead lift of
952 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 in pounds?
9. Figure out how much the following people in Doreen’s family
© Harcourt
weigh in stones. Complete the chart. Round to the nearest tenth.
Name
Weight in Pounds
Doreen
76
Natalie
92
Jake
105
Mrs. Snell
146
Mr. Snell
207
Weight in Stones
Challenge
CW119
LESSON 22.1
Name
Point A to Point B
1.
Measure and record the length of each line to the
nearest centimeter and decimeter.
B
cm
dm
A
cm
cm
dm
dm
F
C
cm
dm
cm
E
D
dm
Start at A and measure clockwise until you are
back at A.
a.
How many centimeters is this measure?
b.
How many decimeters is this measure?
c.
How many times would you need to measure around
this figure to have a measure of 5 meters?
CW120
Challenge
© Harcourt
cm
2.
dm
LESSON 22.2
Name
Wedding Fun
Sam and Sarah are getting married. Their friends are tying
cans to the back of their car. How many meters long is the
rope they are using?
To find out:
• Place the measures in order from least to greatest in
the cake.
• Complete the squares from left to right and from
bottom to top.
• Add the measures in the starred boxes to find how
long the rope is.
7 dm, 250 cm, 1 m, 5 cm, 0.6 m,
1 dm, 180 cm, 14 dm, 0.28 m,
20 dm, 88 cm, 32 cm, 3 dm,
120 cm, 15 cm, 210 cm, 2 cm,
9.0 dm, 0.01 m, 2.15 m, 4.8 dm
© Harcourt
★
★
Challenge
CW121
LESSON 22.3
Name
Punch All Around
Fruity-Tutty Punch Recipe
1 liter orange juice
250 milliliters pineapple juice
500 milliliters apple juice
100 milliliters kiwi juice
50 milliliters lemon juice
2 liters seltzer water
1.
List the recipe ingredients from the least to the greatest
amount.
2.
How much punch will the recipe make in milliliters?
in liters?
3.
A punch glass holds about 300 mL. About how many
glasses does the recipe make?
4.
You sell a glass of punch for $0.50. How much
money will you take in if you sell all the punch one
recipe makes?
5.
It costs $4.87 for all the punch ingredients. How much
6.
Your punch is so popular, you are asked to make
enough for 100 glasses. How many times will you
need to make the recipe?
7.
You charge $0.75 a glass. How much money will
you take in?
8.
Your cost for all the ingredients is $38.96. How
much money will you make?
CW122 Challenge
© Harcourt
money will you make?
LESSON 22.4
Name
Sweet Enough
How many sugar packs would it take to balance each mass?
1.
2.
1 gram 2.3 kg 3.
4.
80 kg 25 g Write the mass in grams and kilograms.
5.
100 sugar packs 6.
300 sugar packs 7.
250 sugar packs 8.
1,000 sugar packs 9.
3,000 sugar packs 10.
5,000 sugar packs © Harcourt
Find the number of sugar packs in each box.
11.
12.
13.
Challenge
CW123
LESSON 22.5
Name
Ring-A-Ling
When you graph your phone number, does it make a
geometric pattern?
YOU WILL NEED
grid paper
On a piece of grid paper, follow these directions.
• Start in the center of the grid paper.
• Use the digits in your phone number to decide how far
to move in each direction. Write your phone number
four times in a row.
• Move up (↑), then right (→), then down (↓), then left
(←). Continue this process until there are no more digits.
For example:
The phone number 321-4123 would
make the following moves:
• 3 up, 2 right, 1 down, 4 left,
1 up, 2 right, 3 down, 3 left, and so on.
start
↑→↓←↑→↓
←↑→↓←↑→
↓←↑→↓←↑
→↓←↑→↓←
3 2 1 4 1 2 3
3 2 1 4 1 2 3
3 2 1 4 1 2 3
3 2 1 4 1 2 3
Write your phone number 4 times. Graph your numbers. Compare
your completed geometric pattern with the one shown above and
with one of your classmates’.
↑→↓←↑→↓
←↑→↓←↑→
↓←↑→↓←↑
3 2 1 4 1 2 3
3 2 1 4 1 2 3
3 2 1 4 1 2 3
CW124
Challenge
→↓←↑→↓←
© Harcourt
•
• The result is the figure at the right.
Name
LESSON 23.1
Fahrenheit Match-up
Match the temperature on the thermometer with the event by
drawing a line to connect them.
A
B
C
D
© Harcourt
E
F
Challenge
CW125
LESSON 23.2
Name
Heating Up
°C
°F
Temperature is measured in
degrees Fahrenheit (°F) in the
United States. Temperature is
measured in degrees Celsius (°C)
in countries that use the metric
system and by scientists.
To estimate degrees °F, use this rule.
(2 Celsius temperature) 32 °F
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
–10
110
212 °F
water
100 °C
boils
100
90
80
70
60
50
40
68 °F
32 °F
room
temp
30
20 °C
water
0 °C
freezes
20
10
0
–10
–20
To estimate 25°C in degrees Fahrenheit,
replace 25 with the Celsius temperature and solve.
(2 25) 32
50 32 82
So, 25°C is about 82°F.
Write the temperature that is a better estimate for each activity.
1.
ice hockey, 30°C or 30°F
2.
running, 50°C or 50°F
3.
surfing, 40°C or 40°F
4.
swimming, 30°C or 30°F
5.
Your pen pal in Japan writes that it is 20°C outside.
Estimate the temperature in °F. Does she need to wear a
jacket?
6.
You write to your pen pal in Nebraska where it is 9°C.
Estimate the temperature in °F. Does your pen pal need a
jacket?
CW126
Challenge
© Harcourt
For 5–6, use the rule above.
LESSON 23.3
Name
Number Riddles
Use a number line to help answer these number riddles.
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2
0 +2 +4 +6 +8 +10 +12 +14 +16 +18 +20
1.
I am greater than 20 and less than 18.
2.
I am halfway between 2 and 8.
3.
I am between 10 and 4. I am 5 units away from 0.
4.
I am less than 5 and greater than 20. My two digits
are the same.
5.
I am between 11 and 18. The sum of my digits is 5.
6.
I am between 20 and 20. My two digits read the
same forward and backward. On the number line, I am
to the left of 0.
7.
I am between 16 and 8. I am twice as far away from
© Harcourt
0 as 6 is.
8.
Make up your own number riddle. Give enough clues so
there can be only one answer.
Challenge
CW127
LESSON 23.4
Name
Logical Conclusions
You use inductive reasoning when you make a general
statement about particular pieces of information.
For example: You know a poodle has 4 legs, a terrier
has 4 legs, a beagle has 4 legs, and a chihuahua has
4 legs. You use inductive reasoning to come to this
conclusion: All dogs have 4 legs.
If you do not use enough information, you may jump to a conclusion.
For example: Joy ate a steak that was tough. She used
inductive reasoning to conclude that all steak is tough.
Kent’s steak was tender. He told Joy she jumped to the
wrong conclusion.
You use deductive reasoning when you use a general
statement to draw a conclusion about a particular situation.
Kayla learned all insects have 6 legs. She counts 8 legs on a spider.
She comes to the conclusion that a spider is not an insect.
1.
Tyrone hears the bell chime once
at 1:00, twice at 2:00, and 3 times
at 3:00. He concludes the bell will
chime the number of the hour.
2.
In math Merri learned that the
product of 0 and any number is
always zero. She concludes the
product of 234,687 and 0 is 0.
3.
Ted looks at this pattern: 1, 4, 7,
10, 13, . . . . He concludes that
the rule for the pattern is 3.
4.
Ron wrote these multiples of 4:
4, 8, 12, 16, 20, and 24. He
concluded that the multiples
of 4 are even numbers.
Jedd learned that prime numbers
have only 2 factors: 1 and the
number itself. He concluded that
51 is a prime number.
6.
Lien read that a quadrilateral is
a figure that has 4 sides. She
concluded that a square is a
quadrilateral.
5.
CW128
Challenge
© Harcourt
Write inductive or deductive to tell what kind of reasoning was
used to arrive at each conclusion. If the conclusion is incorrect,
write jumped to a conclusion.
LESSON 24.1
Name
Checkmate!
Materials: colored pencils
The game of chess was invented more than 1,300
years ago. Today it is played in all parts of the world. Each
piece has its own ways to move. For example:
B
K
R
A rook can move up, or
down, left, or right. It
can move any number
of squares.
The king can move one
square at a time. It can
move up, down, left, right,
or diagonally.
A bishop can move
diagonally any
number of squares.
For 1–4, use the drawing shown at the right.
1.
Which chess piece is in g4?
2.
Which piece is in c2?
3.
Can the king move to h6?
4.
Can the bishop move to d8?
8
7
6
5
4
3
2
1
K
B
R
a b c d e f g h
© Harcourt
The queen is the most powerful chess piece. It can move
any number of squares up, down, left, right, or diagonally.
Suppose the queen is in b7. Can it move from b7 to each
of the following squares? Write yes or no.
5.
d7
6.
d6
7.
a4
8.
g2
For Exercises 9–11, use colored pencils to color squares
on the chess board.
9. Color blue all the squares to which the king can move.
10.
Color red all the squares to which the bishop can move.
11.
Color yellow all the squares to which the rook can move.
Challenge
CW129
LESSON 24.2
Name
Length on the Coordinate Grid
On each coordinate grid, graph 2 different rectangles with the
perimeter given. Then name the endpoints and find the length
of each side.
1.
Perimeter: 12 units
Rectangle A:
length:
y-axis
width:
Rectangle B:
0
x-axis
width:
length:
2.
Perimeter: 26 units
Rectangle A:
length:
Rectangle B:
y-axis
width:
width:
length:
0
3.
Explain how you chose your rectangles in
Problems 1 and 2.
CW130
Challenge
© Harcourt
x-axis
LESSON 24.3
Name
Use an Equation
Play with a partner.
Materials: 1 number cube labeled 2–7
Directions:
Step 1:
The first player should write an equation with 2
variables, such as 2x 1 y or x 3 y, in the
table below and then toss the number cube. The
value on the number cube is the value for x.
Step 2:
The second player should use this value to find
the value for y.
Step 3:
Trade roles and repeat steps 1 and 2 until you
have 10 equations.
© Harcourt
Equation
Value for x
Value for y
1.
x
y
2.
x
y
3.
x
y
4.
x
y
5.
x
y
6.
x
y
7.
x
y
8.
x
y
9.
x
y
10.
x
y
Challenge
CW131
LESSON 24.4
Name
Graph an Equation
Complete each table of values. Then graph
both equations on the coordinate grid.
x2y
Input, x
3x 2 y
Output, y
1
2
3
4
5
6
7
8
9
10
Input, x
Output, y
1
2
3
4
5
6
7
8
9
10
What is the ordered pair of the
point where your lines intersect?
y-axis
1.
This ordered pair contains the only
values of x and y that make both
equations true.
x2y
Input, x
Output, y
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
1
x 1 y
2
Input, x Output, y
2
4
6
8
10
2
3
4
5
6
© Harcourt
2.
x-axis
What is the ordered pair of the point where your lines
intersect?
CW132 Challenge
LESSON 24.5
Name
Identify Relationships
Write the fractions as ordered pairs. Use the numerator as the x
value and the denominator as the y value. Graph the ordered pairs
on the coordinate grid and connect the points with a line.
2 2 2 2
3 4 5 6
1. , , , a. Ordered pairs:
c. If the pattern continued, what
would be the next fraction?
y-axis
b. If the pattern continued, what
would be the next ordered pair?
3 6 9 12
1 2 3 4
2. , , , a. Ordered pairs:
x-axis
b. If the pattern continued, what
would be the next ordered pair?
© Harcourt
c. If the pattern continued, what
would be the next fraction?
3.
3 6 9
What would be the next fraction in this pattern? 4, 8, 12
4.
Explain how you solved Problem 3.
Challenge
CW133
LESSON 25.1
Name
Semaphore Code
The Semaphore Code was used by the United States Navy
to send short-range messages. The message sender holds two
flags in various positions to represent the letters of the alphabet.
To make a number, give the “numeral” sign first. Then use A 1,
B 2, C 3, and so on for the digits 1–9. Use J for zero.
B
C
D
F
E
G
H
acute
I
J
K
straight
Q
Y
L
N
M
O
R
S
T
U
Z
V
ATTENTION
W
INTERVAL
The Semaphore Code makes use of angles. Choose a
letter and explain what kind of angle is shown.
2.
Write your name by using the Semaphore Code. For
example, Mark would be
3.
A
R
K
Now, write the yearRin Semaphore Code.
CW134
Challenge
P
obtuse
1.
M
right
X
NUMERAL
© Harcourt
A
LESSON 25.2
Name
Mapmaker, Mapmaker, Make Me a Map!
Use your knowledge of lines and angles and the following
instructions to complete the map. Use a pencil and a ruler.
N
E
W
S
© Harcourt
School
Store
Main Street
Bank
1.
Draw River Road to the north of and parallel to
Main Street.
2.
Draw High Street to the north of and parallel to
River Road.
3.
Draw West Lane to the east of the bank and
perpendicular to Main Street. West Lane is a line
segment from Main Street to High Street.
4.
Draw Pine Street to the west of the school and
perpendicular to River Road.
5.
Draw Hope Ave. to the east of the school and west
of the store. Hope Ave. is parallel to West Lane.
6.
Draw Devine Drive as a ray beginning at the
intersection of West Lane and High Street. It moves
southwest and intersects Main Street east of the store.
7.
Draw Last Road perpendicular to Devine Drive,
intersecting Main Street west of the bank.
Challenge
CW135
LESSON 25.3
Name
Shapes in Motion
Here is your chance to practice flipping, turning, and
sliding figures to make a design.
1
Step 1 Read the numbers in the 4-by-4 grid.
2
Step 2 Replace the numbers with the matching symbols.
Step 3 Use two colors to make any design in the 4-by-4 grid.
1
2
3
4
2
3
4
1
3
4
1
2
4
1
2
3
3
4
Complete using the steps above.
1.
3
3
3
1
1
1
1
3
3
3
3
1
1
1
1
1
3
3
1
4
2
4
2
3
1
1
3
1
3
3
1
Use the puzzles above to help you make your own design.
3.
CW136
Challenge
© Harcourt
2.
3
LESSON 25.4
Name
Let It Snow!
© Harcourt
Snowflakes are symmetrical ice crystals, showing both
line symmetry and rotational symmetry. You can experiment
with symmetry by making your own snowflakes.
a.
Start with a
square piece
of paper.
b.
Fold the square
in half.
c.
Fold in half again.
d.
Fold in half
again, along
the diagonal.
e.
Cut out various
polygons to make
a design.
f.
Open the
paper and find
a symmetrical
snowflake pattern.
1.
Use square pieces of paper to cut out five different
snowflakes.
2.
Test each snowflake. Mark a central point in the
middle of the snowflake.
3.
Place the snowflake on a sheet of paper. Trace around
the snowflake. Shade in the holes of the snowflake.
4.
Place a pencil on the central point. Rotate the
snowflake.
Do your snowflakes have rotational symmetry?
Challenge
CW137
LESSON 25.5
Name
Problem Solving Strategy
Make a Model
Activity:
Enlarge a picture.
Directions:
Step 1: Draw a square around
the figure you wish to enlarge.
Step 2: Use your ruler to draw a 1-cm
grid on your picture.
© Harcourt
Step 3: Draw your figure on the grid
below. Since the grid you drew on the picture is smaller
than the grid below, you will enlarge your picture.
CW138
Challenge
LESSON 26.1
Name
Polygons in Art
Modern art is often based on geometric figures.
Here is a sample.
© Harcourt
For 1–4, use the sketch.
1.
Label the triangle with the greatest perimeter Triangle 2.
Label the other triangle Triangle 1.
2.
Are their angles acute, obtuse, or right?
3.
Label the gray background rectangle, which is partially
covered, Rectangle 1.
4.
Now, create your own art in this style. Cut geometric
shapes from colored paper. Put them together in a
creative way.
Challenge
CW139
LESSON 26.2
Name
Block It Out!
Read the directions for making each figure. Draw, number, and
color the figure on the grid below.
Figure 1: Draw a square figure
with a perimeter of 4, using
1 square. Color it red.
2.
Figure 2: Draw a rectangular
figure with a perimeter of 10,
using 6 squares. Color it green.
3.
Figure 3: Draw a square figure
with a perimeter of 12, using
9 squares. Color it blue.
4.
Figure 4: Draw a figure with
a perimeter of 14, using 9
squares. Color it black.
5.
Figure 5: Draw a figure with
a perimeter of 12, using 5
squares. Color it yellow.
6.
Figure 6: Draw a figure with
a perimeter of 24, using 11
squares. Color it purple.
7.
Figure 7: Draw a figure with
a perimeter of 16, using 16
squares. Color it brown.
8.
Figure 8: Draw a figure with
a perimeter of 20, using 21
squares. Color it orange.
© Harcourt
1.
CW140
Challenge
LESSON 26.3
Name
Unusual Measures
A very long time ago, people used body units to measure
lengths.
Span
length from the end of the thumb
to the end of the little finger
when the hand is stretched fully
Cubit
length from the elbow to the
longest finger
Fathom length from fingertip to fingertip
when arms are stretched fully in
opposite directions
Pace
length of a walking step,
measured from toe of back foot
to toe of front foot
You can use body measures to find the perimeters and areas of
objects at school. Record your results in the chart below.
Object Measured
Desk Top
Measured in Spans
Perimeter
Area
Measured in Cubits
Perimeter
Area
14 spans
9 cubits
12 sq spans
412 sq cubits
1.
2.
© Harcourt
3.
4.
5.
Measure the length and the width of your classroom in
fathoms and in paces.
length of classroom:
fathoms;
paces
width of classroom:
fathoms;
paces
Challenge
CW141
LESSON 26.4
Name
Flying Carpet Ride
Solve.
Jasmine wrote a story about a
flying carpet ride to Plume
Island. She flew 4,638 miles
north. Then she flew twice as
many miles east. Finally, Jasmine
flew south and reached Plume
Island. She traveled 15,690 miles
in all. How many miles was the
last part of her trip?
2.
Jasmine’s flying carpet not only
flies—it also changes shape.
The perimeter is always 32 feet.
Jasmine needs the greatest area
to take her new Plume Island
friends for a ride. What polygon
will give her the greatest
possible area? What are the
lengths of the sides?
3.
Two Islanders offered to
buy Jasmine’s carpet. Tirian
offered her $500. Miraz offered
her $7.50 per square foot. If the
perimeter of the square carpet
equals 32 feet, who offered
more money? How much more?
4.
Jasmine flew home by a
more direct path. Her return
flight was 5,555 miles shorter
than her trip to Plume Island.
How far was Jasmine’s return
flight? (Hint: See Problem 1.)
5.
Flying carpets give prizes if you
travel more than 25,000 miles.
Can Jasmine get a prize? How
many miles did she fly? (Hint:
See Problems 1 and 4.)
6.
Write your own multistep
problem about an adventure
with a flying carpet. Show the
solution upside down at the
bottom of column 1.
© Harcourt
1.
Answer:
CW142 Challenge
LESSON 26.5
Name
Relate Formulas and Rules
Find the length and width of each figure.
1.
Area 4 square inches
2.
Perimeter 8 inches
3.
Area 36 square feet
Perimeter 22 inches
4.
Perimeter 26 inches
5.
Area 200 square inches
© Harcourt
Perimeter 60 inches
7.
Area 24 square inches
Area 100 square inches
Perimeter 104 inches
6.
Area 144 square centimeters
Perimeter 48 centimeters
Explain the strategy you used to solve Problems 1–6.
Challenge
CW143
LESSON 26.6
Name
Problem Solving Strategy
Find a Pattern
1.
What if the width of a rectangle
was doubled? What would
happen to the area of the
rectangle?
2.
What if the width of a rectangle
was divided by 2? What would
happen to the area of the
rectangle?
3.
What if the width of a rectangle
was tripled? What would happen
to the area of the rectangle?
4.
What if the width of a rectangle
was divided by 3? What would
happen to the area of the
rectangle?
5.
What do you think would happen to the area
of a rectangle whose width is multiplied by 4?
divided by 4?
CW144
Challenge
© Harcourt
What if? Use the figures below to give examples that agree with
your answers to the “What If” question.
LESSON 27.1
Name
Riddle, Riddle
© Harcourt
Name the plane or solid figure described by each riddle.
1.
When you trace one face of a cone or a cylinder, you see
me. What am I?
2.
I have 6 flat faces that all look exactly the same. What
am I?
3.
You see two sizes of me when you trace a rectangular
prism. What am I?
4.
If you trace me six times, you make a cube. What
figure am I?
5.
I am a solid figure with one round face. What am I?
6.
If you trace my 5 faces, you will find a square and
triangles. What am I?
7.
I have 9 edges, 6 vertices, and 5 faces. What figure am I?
8.
I am a solid figure with no vertices or edges. What am I?
9.
All 4 of my faces are identical. What solid figure am I?
Challenge
CW145
LESSON 27.2
Name
Puzzle Watch
Here are two puzzles to solve.
A supermarket worker wants to know how many ways
he can stack four cube-shaped boxes. He can stack
them in 1, 2, 3, or 4 layers. Help by finding as many
arrangements as you can. Draw the arrangements
below. How many did you find?
2.
Use the five points shown below. Connect each point
to all the other points. When you connect the five points,
how many triangles can you find in the figure?
© Harcourt
1.
CW146
Challenge
LESSON 27.3
Name
Estimate and Find Volume of Prisms
Circle the box in each row that has the greatest volume.
1.
3 in.
2 in.
6 in.
2 in.
8 in.
5 in.
6 in.
4 in.
2 in.
2.
2 in.
1 in.
10 in.
1 in.
2 in.
3.
2 in.
3 in.
5 in.
1 in.
1 in.
2 in.
8 in.
4 in.
3 in.
2 in.
2 in.
3 in.
© Harcourt
2 in.
4.
Which of the three boxes you circled has the greatest volume?
5.
Is it easy to judge the volume of a box by looking at it? Explain.
Challenge
CW147
LESSON 27.4
Name
Problem Solving Skill
Too Much/Too Little Information
1.
Marion wants to build a wooden box that is 20
centimeters long and 15 centimeters high. What is the
volume of the box?
2.
Rebecca wants to build a box too. She wants it to have
the same volume as Marion’s, but a different width.
Rebecca wants the box to be 20 centimeters long. What
is the height and width of the box?
3.
Michael bought some wood to build a box. He wants to
build a box that is 10 inches long and 4 inches high.
What is the volume of the box?
CW148
Challenge
© Harcourt
Each of these problems has too little information. Supply
each problem with reasonable data. Solve.
LESSON 28.1
Name
Pentomino Turns
A pentomino is a figure made of 5 congruent squares
joined edge to edge. Each square in a pentomino must
share a side with its neighbor.
These sides do not line up.
These are pentominoes.
These are not pentominoes.
In the first column, draw as many pentominoes as you can.
In the next 3 columns draw each of your pentominoes as it
1 1
3
would look after a 4, 2, and 4 turn.
1
4
turn
1
2
turn
3
4
turn
© Harcourt
Pentomino
Challenge
CW149
LESSON 28.2
Name
Angle Analogies
Measure the angles in each exercise. Write the measures of the first 3
angles in the spaces provided. Then circle the angle that best finishes
the sentence and write the measure of that angle in the last space provided.
Example:
30°
is to
60°
as
20°
40° .
is to
1.
is to
as
is to
.
2.
is to
as
is to
.
is to
as
is to
.
is to
as
is to
.
4.
CW150
Challenge
© Harcourt
3.
LESSON 28.3
Name
Circles
Help the athletes by choosing the correct plates to put on
the weight-lifting dumbbell bar.
Remember the following:
• The dumbbell bar weighs 45 pounds.
• Plates weigh 5, 10, 25, 35, or 45 pounds.
• A matching plate must be added to both sides to
balance the bar.
• It is quicker to use heavier plates. So, adding one
10-pound plate to a side is better than adding two
5-pound plates to a side.
© Harcourt
45
35
25 10 5
1.
Anna wants to lift 135 pounds. Which plates should
she use?
2.
Anna wants to increase the weight from 135 pounds
to 185 pounds. Which plates should she add?
3.
The world record for weight-lifting is 765 pounds.
Which plates would be needed for such a task?
4.
Mark wants to lift about 300 pounds.
What would you suggest he use?
Challenge
CW151
LESSON 28.4
Name
Circumference
Each figure below is made from parts of circles and rectangles. Tell
how many circles are in the figure, and then estimate the distance
around each figure.
1.
9 ft
a.
Number of circles:
b.
Estimated distance around:
a.
Number of circles:
b.
Estimated distance around:
a.
Number of circles:
b.
Estimated distance around:
a.
Number of circles:
5 ft
2.
2m
2m
4m
4m
2m
2m
6m
3.
2 yd
2 yd
3 yd
3 yd
4.
6 cm
b. Estimated distance around:
5.
10 ft
10 ft
10 ft
CW152
Challenge
a.
Number of circles:
b.
Estimated distance around:
© Harcourt
6 cm
LESSON 28.5
Name
Classify Triangles
1. How many different isosceles triangles can you
find and name in the figure below?
equilateral triangles?
scalene triangles?
A
B
E
D
C
2. How many different isosceles triangles can you
find and name in the figure below?
equilateral triangles?
scalene triangles?
A
B
© Harcourt
E
D
C
3. How many triangles are formed when any parallelogram
and its diagonals are drawn?
Challenge
CW153
LESSON 28.6
Name
A Scavenger Hunt
Quadrilaterals are all around you. Here is your chance
to find them. By yourself or in a small group, find the
shapes listed below. Search for shapes in your classroom,
on the playground, or at home. Use the chart to record
your findings.
Give yourself the following points for each shape.
Challenge yourself to find the harder shapes—and
score more points!
Rectangle
1 point
Square
2 points
Rhombus
3 points
Trapezoid
4 points
Description
Points
rectangle
cafeteria table
1
© Harcourt
Shape Found
CW154
Challenge
LESSON 28.7
Name
Diagram Detective
It is time for you to be a Diagram Detective. Look at the Venn
diagrams in 1 and 2. Choose the labels that best describe each
Venn diagram, and write them on the lines provided. You will
not use all of the labels.
1.
Venn Diagram Labels
A
B
A
2.
B
Factors of 12
Odd Numbers Between 0 and 20
Even Numbers Between 0 and 20
Multiples of 3 Less Than 20
Multiples of 5 Between 0 and 28
Numbers Divisible by 2
Factors of 10
A
B
A
B
Think about how these months are related. Then write
your own labels for the Venn diagram.
© Harcourt
3.
Challenge
CW155
LESSON 29.1
Name
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 possible
outcomes: 3 heads, 2 heads and 1 tail,
and
.
2. If you toss four coins at once, how many possible
outcomes are there? What are they?
For Problems 3–4, use the table.
Try this experiment. Toss two coins at once,
and tally the results of the tosses. Repeat for a
total of 20 tosses.
2 Heads
1 Head
2 Tails
and 1 Tail
3. Of the 20 tosses, how many times did you
© Harcourt
get 2 heads? 1 head and 1 tail? 2 tails?
4. Compare your results with those of your classmates.
Which outcome seems more likely: 2 tails or 1 head
and 1 tail?
CW156
Challenge
LESSON 29.2
Name
The Path of Probability
Toss a coin 5 times to follow a probability path from the start
to the end boxes.
Rules a. Toss the coin. If it is heads, follow the heads path to
the next oval. If it is tails, follow the tails path.
b. Put a tally mark in an oval for each toss.
c. After 5 tosses, record the letter of the box in which
you land.
d. Repeat the process 20 times.
Start
heads tails
Toss 1
Toss 2
heads tails
Toss 3
Toss 4
Toss 5
© Harcourt
heads tails
heads tails
A
tails
heads
heads tails
heads tails
heads tails
B
tails
heads
heads tails
heads tails
heads tails
C
heads
D
heads tails
tails
heads tails
E
F
1. In which lettered boxes did you finish most often?
2. In which boxes did you finish least often?
Challenge
CW157
LESSON 29.3
Name
Mystery Cube
Yancy wrote 6 different one-digit numbers on a cube.
Then he made an identical cube. The line plot shows the
sums and the number of ways he could get each sum if he
were to toss his two number cubes.
?
?
?
? ?
?
???
HINT: If Yancy wrote the numbers 4 and
5 on each cube, he would count
getting 4 5 and 5 4 as
two different ways to toss.
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Sums
Answer the question.
1.
If 1 were the least number on each cube, what would be
the least sum that could be marked on a line plot?
Use the line plot. Complete the table below to find the
6 one-digit numbers Yancy wrote on each cube.
2.
Sum
Number of
Ways to Toss
8
1
44
9
2
4 5, 5 4
© Harcourt
Ways to Toss the Sum
3.
The numbers Yancy wrote on each cube are
CW158
Challenge
.
LESSON 29.4
Name
A Likely Story
A single dart can land anywhere on this dart board. The player’s
score is the number in the area the dart hits. Tell whether each
event is likely or unlikely.
© Harcourt
10
5
3
1
1.
The score is an odd number.
2.
The score is an even number in a shaded section.
3.
The score is less than 100.
4.
The score is a number divisible by 50.
5.
The score is a number divisible by 10.
6.
The score is 25 or 50.
7.
The score is 10.
8.
The dart lands exactly in the center of the board.
9.
The dart lands in a shaded section.
10.
The dart lands in a section that is not shaded.
Challenge
CW159
LESSON 30.1
Name
Certainly Not!
Remember, if an event is certain, it will always happen. If
an event is impossible, it will never happen.
1.
Write numbers in the spinner
so that each of the following
events is certain.
Certain
The pointer stopping on a
number
2.
A.
that is greater than 25
B.
that has 12 as a factor
C.
that is divisible by 3
D.
that has the sum of 8 or
more when its two digits
are added together
Write numbers in the spinner so that each of the events
above is impossible.
© Harcourt
Impossible
3.
Look at the spinner in Problem 2. Write two more events
that would be impossible if you were to use the spinner.
CW160
Challenge
LESSON 30.2
Name
Heads or Tails?
A coin should land on heads about half of the time.
What if you toss a coin 10 times? Are you likely to get 5 heads
and 5 tails?
What if you toss a coin 50 times? Are you likely to get 25
heads and 25 tails?
Try these experiments before you answer.
1. Toss a coin 10 times. Record your tallies
Heads
Tails
in the table.
Total
10
2. Toss a coin 50 times. Record your tallies
in the table.
50
3. Compare your results with those of your
classmates. How many students got
exactly 5 heads and 5 tails? How many students got
exactly 25 heads and 25 tails?
4. Find the fraction (in simplest form) of heads for both
experiments, as follows.
Experiment 1: number of heads 10
© Harcourt
Experiment 2: number of heads 50
Compare the fractions in Problem 4 with those of your classmates.
Then complete 5–7. Write likely or unlikely.
5. If you toss a coin 10 times, you are
to get
exactly 10 heads.
6. If you toss a coin 50 times, you are
to get
exactly 50 heads.
7. If you toss a coin 50 times, you are
to get
between 20 and 30 heads.
Challenge
CW161
LESSON 30.3
Name
Word Wonders
The words and, or, not are small words, but they are very
important to the meanings of sentences.
Circle the shape that has
4 sides and has sides that
are the same length.
A
B
Circle the shapes that have
3 sides or a consonant.
A
B
A
B
Circle the shapes that are
not triangles.
C
D
C
D
C
D
For 1–3, use the shapes at the right.
1
Draw the shapes that have exactly
4 sides and the number 1.
1
1
2.
Draw the shapes that are triangles
or have the number 2.
2
3.
1
2
1
2
2
Draw the shapes that do not
have exactly 4 sides.
Use the shapes with the numbers. Write a sentence of your own for each of
the words and, or, not. Draw the answer.
4.
5.
6.
CW162
Challenge
© Harcourt
1.
LESSON 30.4
Name
Name Mix-Up
Read the clues given. They describe
the probabilities of pulling specific
students’ names from a bag. The six
names at right were not put into
either bag. Use the information to
decide into which bag each name
should go. Write the correct names
on the cards below.
Gina
ile
err
e
M
Mia
Mrs. Kipp’s Class Bag
The probability of pulling a name
a.
ier
Errol
Otis
Ms. Simon’s Class Bag
J av
, or 1
.
beginning with a vowel is 3
9
3
.
ending in the letter l is 2
9
c. beginning with the letter J, K,
, or 2.
L, or M is 6
9
3
b.
The probability of pulling a name
.
ending in a vowel is 5
9
3
1
b. with 5 or more letters is , or .
9
3
0
c. beginning with the letter V is .
9
a.
Jamie
Kim
Elise
Chu
Stan
Ava
Miguel
Eddie
Candace
Pearl
Bob
© Harcourt
Laurence
Challenge
CW163