Saddleback Math Covers
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MATH COMPUTATION SKILLS & STRATEGIES Every book in the Math Computati...
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Saddleback Math Covers
10/22/06
6:24 PM
Page 5
MATH COMPUTATION SKILLS & STRATEGIES Every book in the Math Computation Skills and Strategies series contains over 100 reproducible pages.These highinterest activities combine computation practice with strategy instruction. Featuring a Scope and Sequence chart, the books allow educators to supplement their math lessons with the extra math practice all students need. In addition, periodic reviews allow for reinforcement and assessment of skills.
H I G H - I N T E R E S T M AT H C O M P U TAT I O N S K I L L S & S T R AT E G I E S
HIGH-INTEREST
• LEVEL 7
The books are grade specific, but they were created with students of all ages in mind. Each book features ready-to-use pages with instructional tips at the beginning of each lesson. Math Computation Skills and Strategies reproducible books are the perfect choice for educators.
HIGH-INTEREST
MATH COMPUTATION SKILLS & STRATEGIES Operations Fractions and Decimals Whole Numbers Perimeter and Area Regrouping
Three Watson • Irvine, CA 92618-2767 • 888-SDL-BACK • www.sdlback.com
S A D D L E B A C K E D U C AT I O N A L P U B L I S H I N G
Saddleback E-Book
Solving Word Problems Money Measurement
LEVEL
7
100 plus+ REPRODUCIBLE ACTIVITIES
MATH COMPUTATION SKILLS & STRATEGIES
LEVEL
7
ISBN 1-56254-970-7 Copyright © 2006 by Saddleback Educational Publishing. All rights reserved. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system without written permission of the publisher, with the following exception. Pages labeled Saddleback Educational Publishing ©2006 are intended for reproduction. Saddleback Educational Publishing grants to individual purchasers of this book the right to make sufficient copies of reproducible pages for use by all students of a single teacher.This permission is limited to an individual teacher and does not apply to entire schools or school systems. Printed in the United States of America
Table of Contents Page Lesson 5 . . . . . . . . . Introduction Unit 1 . . . 6 ......... 7 ......... 8 ......... 9 ......... 10 . . . . . . . . 11 . . . . . . . . 12 . . . . . . . . 13 . . . . . . . . 14 . . . . . . . . 15 . . . . . . . . 16 . . . . . . . . 17 . . . . . . . . 18 . . . . . . . . 19 . . . . . . . . 20 . . . . . . . . 21 . . . . . . . . 22 . . . . . . . . 23 . . . . . . . . 24 . . . . . . . . 25 . . . . . . . . 26 . . . . . . . . 27 . . . . . . . . 28 . . . . . . . . 29 . . . . . . . . 30 . . . . . . . . 31 . . . . . . . .
Numbers and Number Sense Understand Integers Add and Subtract Integers Find Absolute Values Read Coordinate Graphs Find Squares and Square Roots Express Powers of Ten Use Exponents Identify Equivalent Fractions Convert Decimals and Fractions Work with Non-terminating Decimals Compare Integers Order Integers Rounding Rounding and Estimating Find Percentages Find Percentages Convert Percents and Decimals Convert Fractions and Percents Understand Ratios Find Ratios Understand Irrational Numbers Solve Word Problems Solve Word Problems Solve Word Problems Review Numbers and Number Sense Review Numbers and Number Sense
Unit 2 . . . . 32 . . . . . . . . 33 . . . . . . . . 34 . . . . . . . . 35 . . . . . . . . 36 . . . . . . . . 37 . . . . . . . . 38 . . . . . . . . 39 . . . . . . . . 40 . . . . . . . . 41 . . . . . . . . 42 . . . . . . . . 43 . . . . . . . . 44 . . . . . . . . 45 . . . . . . . . 46 . . . . . . . . 47 . . . . . . . . 48 . . . . . . . . 49 . . . . . . . . 50 . . . . . . . .
Addition and Subtraction Use Addition Properties Add Two Digits Add Up to Four Digits Add Up to Seven Digits Add Decimals Practice Addition Practice Addition Subtract Two Digits Subtract Up to Four Digits Subtract Up to Seven Digits Subtract Decimals Practice Subtraction Practice Subtraction Add and Subtract Greater Integers Check Addition and Subtraction Solve Word Problems Solve Word Problems Review Addition and Subtraction Review Addition and Subtraction
Unit 3 . . . . 51 . . . . . . . . 52 . . . . . . . . 53 . . . . . . . . 54 . . . . . . . . 55 . . . . . . . . 56 . . . . . . . . 57 . . . . . . . . 58 . . . . . . . . 59 . . . . . . . . 60 . . . . . . . . 61 . . . . . . . . 62 . . . . . . . . 63 . . . . . . . . 64 . . . . . . . . 65 . . . . . . . . 66 . . . . . . . . 67 . . . . . . . . 68 . . . . . . . . 69 . . . . . . . . 70 . . . . . . . . 71 . . . . . . . . 72 . . . . . . . . 73 . . . . . . . . 74 . . . . . . . . 75 . . . . . . . .
Multiplication and Division Find Multiples List Factors Identify Prime and Composite Numbers Identify Prime and Composite Numbers Check Multiplication and Division Multiply 2 Digits by 1 Digit Multiply 4 Digits by 1 Digit Multiply 7 Digits by 1 Digit Multiply Decimals Multiply 2 Digits by 2 Digits Multiply 4 Digits by 2 Digits Multiply 7 Digits by 2 Digits Multiply Decimals Divide 2 Digits by 1 Digit Divide 4 Digits by 1 Digit Divide 7 Digits by 1 Digit Divide With Remainders Decimal Quotients Divide 2 Digits by 2 Digits Divide 4 Digits by 2 Digits Divide Decimals Solve Word Problems Solve Word Problems Review Multiplication and Division Review Multiplication and Division
Unit 4 . . . . 76 . . . . . . . . 77 . . . . . . . . 78 . . . . . . . . 79 . . . . . . . . 80 . . . . . . . . .......... 81 . . . . . . . . 82 . . . . . . . . 83 . . . . . . . . 84 . . . . . . . . 85 . . . . . . . . .......... 86 . . . . . . . . 87 . . . . . . . . 88 . . . . . . . . 89 . . . . . . . .
Fractions Add Fractions with Like Denominators Add Fractions with Unlike Denominators Subtract Fractions with Like Denominators Subtract Fractions with Unlike Denominators Add and Subtract Positive and Negative Fractions Understand Multiplying Fractions Multiply Mixed Numbers Divide Fractions Divide Mixed Numbers Multiply and Divide Positive and Negative Fractions Solve Word Problems Solve Word Problems Review Fractions Review Fractions
Table of Contents Unit 5 . . . . 90 . . . . . . . . 91 . . . . . . . . 92 . . . . . . . . 93 . . . . . . . . 94 . . . . . . . . 95 . . . . . . . . 96 . . . . . . . . 97 . . . . . . . . 98 . . . . . . . . 99 . . . . . . . . 100 . . . . . . . 101 . . . . . . . 102 . . . . . . .
Equations and Graphs Use Order of Operations Write Equations Solve Equations Solve Equations Understand Functions Graph Functions Graph Functions Graph Functions Graph Rates Graph Rates Review Equations and Inequalities Review Equations and Inequalities Review Graphing Functions
Unit 6 . . . . 103 . . . . . . . 104 . . . . . . . 105 . . . . . . . 106 . . . . . . . 107 . . . . . . . 108 . . . . . . . 109 . . . . . . . 110 . . . . . . . 111 . . . . . . . 112 . . . . . . . 113 . . . . . . . 114 . . . . . . . 115 . . . . . . .
Measurement Use Time Measurements Convert Temperatures Use Weight Measurements Identify Angles Find Angles Find and Convert Customary Lengths Find and Convert Metric Lengths Convert Customary to Metric Convert Metric to Customary Solve Word Problems Solve Word Problems Review Measurement Review Measurement
Unit 7 . . . . 116 . . . . . . . 117 . . . . . . . 118 . . . . . . . 119 . . . . . . . 120 . . . . . . . 121 . . . . . . . 122 . . . . . . . 123 . . . . . . . 124 . . . . . . . 125 . . . . . . . 126 . . . . . . . 127 . . . . . . . 128 . . . . . . .
Geometry Find Perimeters Use the Pythagorean Theorem Find Circumferences Find Area of Parallelograms Find Area of Triangles Find Area of Circles Find Area of Irregular Figures Find Surface Area Find Volume Solve Word Problems Solve Word Problems Review Geometry Review Geometry
Unit 8 . . . . 129 . . . . . . . 130 . . . . . . . 131 . . . . . . . 132 . . . . . . . 133 . . . . . . . 134 . . . . . . . 135 . . . . . . . 136 . . . . . . .
Probability Find Averages Figure Probability Understand Odds Identify Mean, Median & Mode Solve Word Problems Solve Word Problems Review Probability Review Probability
137 138 139 140 141 142 143 144
Scope and Sequence Answer Key Answer Key Answer Key Answer Key Answer Key Answer Key Answer Key
....... ....... ....... ....... ....... ....... ....... .......
About This Series This series was created by Saddleback Educational Publishing to provide extensive math practice as a supplement to in-class instruction. Math Computation Skills and Strategies can easily be integrated into math curricula to reinforce basic skills.The lessons focus on practice, with up to 70 items a page. In addition, the lessons are designed to challenge students as their skills grow stronger. As the students progress through the individual lessons, the degree of difficulty increases. Closely adhering to state standards, this series provides grade-level appropriate lessons that are approachable for students at a range of abilities. Review lessons are interspersed throughout the book to allow students to reinforce their skills. Furthermore, the Scope and Sequence chart at the back of the book will help you choose lessons that are applicable to your curriculum.This series covers a range of topics, allowing students to build skills in multiple areas. Additionally, the lessons provide a variety of approaches, including word problems that emulate real-life situations. Each book is designed to challenge students who are learning skills at the corresponding grade level. However, the lessons were created not just for younger children, but for students of all ages. Saddleback Educational Publishing believes in allowing students to strengthen their skills with fun and exciting practice lessons.We hope you enjoy using this series to supplement class instruction and help students gain skills for proficiency in math computation.
Understand Integers Integers can be positive, negative, or zero.
Directions: Circle the integers and cross out the non-integers. a
b
c
d
e
1 3
-709
f
1.
-35
0.5
1200
2.
3 4
18
9 10
-25,976
5.72
3.
97
-62
0.359
960,448
1
4.
573,068
3 10
-571
-6.003
28
0
-3960
40
2.54
-298
610
5.
2
4
17 19
-10.6
121
Directions: Complete the number line and then define the word integer.
-8
-6
-4
-2
0
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
2
4
6
8
Date 6
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add and Subtract Integers When you add or subtract integers, pay close attention to whether they are positive or negative. This will affect the sum or difference. Subtracting a negative integer is like adding its opposite. 3- -4 = 7 Adding a positive number and a negative number is like subtracting two positive numbers.The sum will be positive or negative, depending on which addend is greater. -5 + 9 = 4 -7 + 3 = -4 Directions: Solve. a
b
c
1. - 4 + - 8 =
-12 -13 =
-10 +15 =
2. 5 + - 9 =
5-9=
-7 - 8 =
3. 13 - - 8 =
-7 + 13 =
- 20 - - 40 =
4. - 6 - - 4 =
10 - 15 =
500 + - 600 =
a
b
c
d
e
5.
80 + 240
2200 + 1900
340 + 50
306 + 204
27 + 62
6.
130 + 450
600 + 700
950 + 951
532 + 472
130 + 900
7.
25 75
68
653
871
75
+ 32
+ 500
+ 13
+ 33
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 7
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Absolute Values The absolute value of a number tells how far it is from zero. |-5| = 5 |5| = 5
Directions: Solve. a
b
1.
|9|
|-57|
|-2.3|
2.
|-17|
-|57|
|5705|
3.
|-378|
|4.5|
|-3 1/3|
4.
|-1/5|
-|-4927|
-|- 489|
5.
|-94|
- |-3 + 2|
|0-14|
6.
|7 - 9|
-|32|
|13 - 7|
7.
-|13-5|
|-32|
-|35 ÷ 5|
8.
|-3 + 2|
(-|-3|)2
|9 - 15|
c
Directions: Write <,>, or = to complete the math sentence. a
9.
|-7|
10.
|3-4|
b
7 -|3-4|
c
-|5-2|
|-3|
-|-5|
|-5|
-|-25|
-52
|7-9|
(-|7-4|) +4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 8
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Read Coordinate Graphs Plotting points on a coordinate graph is easy. Just remember that the distance along the horizontal x-axis, is listed first.
Directions: Name each point.The first one is done for you. 1. A (2,7) B C
•A
D
•F •B
E F
•E •G
•C •D
G H
•
H
Directions: Plot the point at the correct place. 2. M (0, 3) N (7, 7) O (8, 5) P (9, 1) R (3, 8) S (5,7) T (1, 9) V (4, 6)
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 9
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Squares and Square Roots If you know your squares, it’s easy to find square roots. 9 = 3 32 = 9
Directions: Find the square or the square root. a
b
16
121
1.
52
2.
152
122
3.
225
152
4.
36
62
5.
c
72 64
252
4
92
6.
100
7.
400
8.
112
9.
302
10.
252
162 196
142 49
102 2500
22 25
12
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
d
132
625 202 81
502 900
42 256
202
289
402
324
Date 10
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Express Powers of Ten Using exponents can save time and space. For example 106 is the same as 1,000,000, or one million.
Directions: Write the number and its name.The first two are done for you.
a
b
1.
100 = 1, one
105 =
2.
101 = 10, ten
106 =
3.
102 =
107 =
4.
103 =
108 =
5.
104 =
109 =
Directions: Write the number using powers of ten. a
b
6.
100 =
1,000,000 =
7.
11 =
100,000,000 =
8.
11,000 =
10,000,000 =
9.
110 =
1,000,000,000 =
110,000 =
100,000 =
10.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 11
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use Exponents Exponents are handy when a number is multiplied by itself repeatedly.
5 x 5 x 5 = 53 =125 base exponent
5 to the power of 3
Directions: Write the equation and solve. a
b
c
1.
82 =
54 =
63 =
2.
26 =
23 =
110 =
3.
33 =
74 =
84 =
4.
61 =
45 =
38 =
5.
92 =
07 =
93 =
Directions: Write the exponent, then solve. a
b
6.
2x2x2=
6x6x6x6=
7.
4x4x4x4x4=
9x9
8.
7x7x7x7x7x7x7 =
3x3x3x3x3x3x3x3x3x3=
9.
8x8=
10 x 10 x 10 =
5x5x5=
1x1x1x1x1x1=
10.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 12
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Identify Equivalent Fractions Remember: Equivalent means equal.
Directions: Complete each number sentence with = or . a
b
c
7 3 ___ 8 4 2 1 ___ 6 3
12 6 ___ 16 8 2 1 ___ 12 4
4 2 ___ 5 3 4 2 ___ 16 8
3.
1 4 ___ 2 8
1 3 ___ 3 9
1 2 ___ 7 14
4.
2 10 ___ 3 12
3 1 ___ 12 3
5 9 ___ 6 12
1. 2.
Directions: Write equivalent fractions. a
5. 6. 7. 8. 9. 10. 11.
b
c
7 = 8 5 = 10 1 = 3
1 = 6 1 = 4 8 = 16
11 = 12 3 = 5 3 = 9
3 = 4 3 = 10 1 = 2 2 = 3
2 7 7 9 5 8 5 6
4 = 8 4 = 5 2 = 4 10 = 12
= = = =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 13
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Decimals and Fractions Fractions and decimals are different ways of writing the same amount.
4 = 0.8 = .8 5 Directions: Write the equivalent fraction or decimal. a
b
1 = 2 3 = 10
3 = 4 19 = 20
3.
0.75 =
0.1 =
0.60 =
4.
.4 =
1 = 2
2 = 5
5.
1 = 5
.25 =
.9 =
6.
0.125 =
3 = 5
1 = 100
7.
0.09 =
0.80 =
0.90 =
8.
59 = 100
.66 =
0.003 =
1. 2.
c
1 = 4 0.5 =
Directions: Complete the number sentence by writing <, >, or =.
9. 10. 11.
a
b
c
1 1 ___ 3 4 1 ___ 0.2 4
5 ___ 0.5 8 9 0.9 ___ 10 1 ___ 0.4 3
3 7 ___ 4 9 1 ___ 0.5 2 1 0.3 ___ 3
0.75 ___
75 100
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 14
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Work with Non-Terminating Decimals Some decimal numbers just never end! Here are some ways to deal with non-terminating decimals. Round to the nearest tenth.
7 = 2.6457513 = 2.6
Put a bar over the digits that repeat. 1 = 0.166666666 = 0.16 6 Use an established number. 3.1416
= 3.14159265358979323846264338 =
Directions: Find the decimal equivalent. If it is non-terminating, use a solution from above. a
b
2=
1.
6=
2.
1 = 8
13 =
3.
1 = 7
1 = 18
5.
1 = 9
3 = 7 11 = 12
5=
6. 7.
11 =
8=
4.
5 = 6
8.
7= 2 = 11
3=
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 15
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Compare Integers To compare integers, first look at the signs, then look at digits in the same place value. 38 < 41
- 256 > -276
Directions: Circle the number that is greater than the number in dark print. 1.
51
-52
55
49
-100
50
2.
478
469
379
380
480
-479
3.
-62
-60
-63
-65
-70
-100
4.
-300
-301
-298
-310
-350
-360
Directions: Complete the number sentence by writing < or >. a
b
178
c
8.13
8.14
-1
0
5.
175
6.
23
7.
643
633
7061
7062
1081
8.
-97
-96
4231
4321
354
9.
2576
10.
-5.3
-5.2
11.
809
12.
609
23.4
2476
-8
-0.3
-9
-0.31 1180 345
-50
2675
3675
0.51
0.5
4873
-4872
798
6498
6488
31,568
690
757
-52
758
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
-697
31,468 698
Date 16
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Order Integers The sign can make all the difference.
Directions: Write the numbers in order from least to greatest. 1.
52, -51, 357
2.
75, 68, -76
3.
0.8, 8, -8
4.
3157, 3298, 3536, 3300
5.
0.623, 0.236, 0.326
6.
51, 5.1, -51, -5.1, 5, -5
7.
40,579; 40,569; 41,559
8.
1, 0.001, 0.1, 0.01
Directions: Write the numbers in order from greatest to least. 9.
0.7, -7, 0.07
10.
5230, 5320, 5302
11.
-58, -59, 60
12.
2.5, 2.4, 2.45
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 17
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Rounding Sometimes you don't need to use exact numbers.You can round a number to the nearest ten or hundred, for example. To round a number, look at the digit in the place to the right of the place you are rounding to. Round up if it is 5 or greater. Round down if it is 4 or less. Directions: Look at the number in dark print. Circle the number next to it that is the same number rounded to the nearest ten. a
1.
14
2.
37
3.
50
10
b
14
15
20
88
80
85
90
100
30
35
40
50
96
80
90
95
100
40
50
55
60
121
100
110
120
130
Directions: Round the decimal to the nearest whole number. a
b
c
4.
0.3
3.09
72.25
5.
2.8
1.46
58.82
6.
4.04
9.5
416.707
Directions: Round the number to the nearest ten, hundred, and thousand. nearest ten 7.
737.5
8.
1,154
9.
2,608.06
10.
4,380.3
nearest hundred
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
nearest thousand
Date 18
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Rounding and Estimating Rounding and estimating can help you check your answers.
76 + 31 80 + 30 = 110 The symbol means “is approximately” or “is about equal to.” The exact answer is 107, which is close to 110. Directions: Round each addend and estimate the answer.Then find the exact answer. a
b
1.
89 + 19 =
56 + 2 =
2.
54 + 77 =
423 + 160 =
3.
452 + 36 =
807 + 998 =
4.
607 + 528 =
5,352 + 736 =
5.
3,121 + 4,094 =
62 + 80 =
6.
94 + 45 =
109 + 583 =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 19
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Percentages Percent means “out of each hundred.” Directions: Solve. a
b
1.
60% of 80 =
88% of 100 =
2.
50% of 90 =
75% of 150 =
3.
90% of 30 =
200% of 6 =
4.
70% of 200 =
35% of 50 =
5.
25% of 4000 =
10% of 30 =
6.
65% of 20 =
150% of 8 =
Directions: Find the percentage for each set of numbers. a
b
7.
20 out of 80 =
9 out of 9 =
8.
9 out of 15 =
3 out of 300 =
9.
6 out of 54 =
12 out of 8 =
10.
5 out of 75 =
6 out of 12 =
11.
11 out of 110 =
12 out of 6 =
12.
50 out of 200 =
5 out of 500 =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 20
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Percentages Working with percentages is like working with decimals.You may need to round percentages to the nearest whole number. 4 out of 12 = 33.333333...% round to 33%
Directions: Find the percentage for each set of numbers, rounding if needed. Show your work. a
b
1.
2 out of 7 =
10 out of 60 =
2.
400 out of 900 =
25 out of 20 =
3.
5 out of 6 =
1 out of 3 =
4.
1 out of 30 =
22 out of 24 =
5.
50 out of 30 =
17 out of 20 =
6.
0.5 out of 1 =
17 out of 19 =
7.
18 out of 24 =
400 out of 600 =
8.
60 out of 45 =
3 out of 4 =
9.
700 out of 800 =
28 out of 30 =
10.
30 out of 200 =
1 out of 12 =
11.
Tanner spent 50 minutes doing homework. Of that time, 40 minutes was on math. What percentage of his time did Tanner spend doing math homework?
12.
The next night,Tanner spent 80 minutes doing homework. Of that time, he spent about 45 minutes on math.What percentage of his time did Tanner spend doing math homework?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 21
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Percents and Decimals Percents and decimals are very similar to each other. Directions: Convert each decimal to a percent and each percent to a decimal. a
b
c
1.
85% =
200% =
1.5 =
2.
0.47 =
.34 =
10% =
3.
.72 =
98% =
40% =
4.
29% =
1.0 =
0.001 =
5.
50% =
15% =
0.8 =
6.
0.9 =
0.56 =
82% =
7.
0.06 =
99% =
132% =
8.
3% =
0.835 =
2.5 =
Directions: Write =, <, or > to compare the numbers. a
b
c
9.
0.4
0.39
10.
37%
0.4
0.7
75%
0.5
11.
0.9
90%
2.1
21%
200%
12.
0.05
50%
1.3
130%
0.61
62%
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
0.19
4%
20% 50% 0.2 0.4
Date 22
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Fractions and Percents Converting percents and fractions is tricky, but you can do it!
To convert a fraction to a percent: Divide the numerator by the denominator, multiply by 100, and add the percent sign. 3 = 3 ÷ 4 = 0.75 100 = 75% 4 To convert a percent to a fraction: Make the percent the numerator with a denominator of 100. Simplify. 80 4 80% = = 100 5 Directions: Convert each fraction to a percent and each percent to a fraction. a
1.
1 = 2
2. 40% = 3. 4.
b
c
7 = 8
1% =
30% =
1 = 20
9 = 10
2 = 3 5 = 9
99% =
1 = 4
110% =
Directions: Write =, <, or > to compare the numbers. a
5.
1 1 ___ 4 3
1 3 7. 85% ___ 17 20 8. 15% ___ 1 8 6.
35% ___
b
c
50% ___
3 5
3 ___ 31% 10 9 ___ 9% 100 5 110% ___ 4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
7 ___ 7% 1000 99 99% ___ 100 21 42% ___ 50 3 ___ 80% 4 Date
23
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Understand Ratios A ratio compares two amounts. A ratio can be expressed using a fraction, and can be simplified, or reduced to lowest terms. In the 2000 census, the U.S. Government counted 96 men for every 100 women in the country. The ratio of men to women was 96 out of 100, or 24 to 25.The ratio can also be expressed in these ways: 24 or 24:25. 25 Directions: Write a ratio for each. Garfield Middle School has an intramural sports program. The basketball team has 7 boys and 4 girls. The softball team has 5 boys and 7 girls. The volleyball team has 8 boys and 8 girls. 1.
girls in basketball to the basketball team
2.
boys in basketball to girls in basketball
3.
boys in basketball to boys in softball
4.
the basketball team to the boys in basketball
5.
boys in basketball to boys in the whole program
6.
girls to boys in volleyball
7.
girls in basketball to girls in volleyball
8.
girls in volleyball to students in the whole program
9.
boys in softball to boys in basketball and volleyball
10.
girls in volleyball to students in the program
11.
boys in the program to students in the program
12.
girls in the program to boys in the program
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 24
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Ratios Setting up a ratio can help you find a number.
The ratio of men to women is
24 . 25
If 2,000 women lived in a town, how many men (m) would there be?
24 m = 25 2000 25m= 24 2, 000 = 48, 000 m=1,920
Directions: Complete the ratio. a
b
c
1:4 = ?:44
2 6 = 9 ?
2. 5 to 9 = 10 to ?
15 to 18 = 5 to ?
4:5 = 16:?
3. 1:3 = 9:?
3 6 = 2 ?
18 to 27 = ? to 3
1.
3 ? = 4 16
4.
3 6 = 10 ?
7:10 = ?:40
15 ? = 3 1
5.
5 = ? to 35 7
24 to 26 = 12 to ?
80:1000 = 8:?
? 19 = 20 100
5 ? = 6 18
6. 1:6 = ? :18
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 25
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Understand Irrational Numbers An irrational number is a decimal that doesn't repeat or end and isn't a fraction. Other numbers are rational. is the ratio of the circumference of a circle to its diameter.This ratio is the same for all circles. = 3.1415926535897932384626433832795028841971... The points after the 1 at the right (... ) mean that the number continues on without repeating or terminating.
Directions: Write I if the number is irrational.Write R if it is rational. a
1.
2.
4.
3 = 0.75 4
2 = 1.4142135K 2 9
3.
b
= 0.222222K
9.3 = 3.04959K
11 = 0.9166K 12
2 = 0.6666K 3
3 = 1.732050K
6.5 = 2.5495K
5 = 0.625 8
5. e = 2.718281...
6.
3 = 0.42857K 7
7 = 2.64575K
7. 0.573
321.321321321...
8. 0.33333333...
2.673473
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 26
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Use what you know about numbers and number sense to solve these word problems. Directions: Solve. 1. Gabe ran seven laps around the track each day for seven days in a row. How many laps did he run in all? Express the total in standard form and using an exponent.
2. After his daily run, Gabe is only 50% done with his workout. Some days he lifts weights next. He met his friend Sabrina in the gym one day. She said that 2 she was done with her workout.Who was further along? 3 Show your conversion.
3. Sabrina has been weight training for years. Sabrina told Gabe that she can bench press 102 pounds. How many pounds is that?
4. Gabe lifted 125 pounds to build bulk, then subtracted 45 pounds and lifted that amount to build strength.What amount did he lift to build strength? Write the equation and the amount.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 27
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Use what you know about numbers and number sense to solve these word problems. Directions: Solve. 1. Julia scrapbooked her pictures. She bought special paper in squares to glue her photos onto.The area of the square was 49 square inches.What size was the paper?
2. The area of another square Julia bought was 64 square inches.What size was the paper?
3. Julia realized that two pictures were too big for her scrapbook. She wanted to scale them down by half. She wrote ratios to compare width and length. Complete the ratios. 8 4 6 ? = = 10 ? 10 5
4. The length of a square picture is 8 inches. Julia reduced it to 4 inches.What percentage of the area of the larger picture is the area of the smaller picture?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 28
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems You already have the skills — now practice applying them. Directions: Solve. 1. Scientists have measured extremely cold liquids.Which of the following readings is the coldest? -7°, -26°, 32°, 0°
2. Scientists have weighed seeds.Write these weights in order from lightest to heaviest, or least to greatest mass. 0.1273 g, 0.1327 g, 0.1237 g, 0.1372 g
3. When the scientists tried to grow their seeds, only 24 out of 32 grew. 24 Write three fractions equivalent to . 32
24 4. What is the decimal number equivalent to ? Is it a rational or irrational 32 number? How can you tell?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 29
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Numbers and Number Sense Now you have the chance to show what you know!
Directions: Look at the number.Write IN for integer, IR for irrational number, or R for ratio. a
1.
-27
2.
1,400
b
1 8
3.
c
0.5
3
2
-439
d
-2.7 60,571
11 12
0
Directions: Solve. Show all your work. a
4.
b
1.09
121 =
5.
6x6x6x6=
3:4 = 15:
6.
-40 + 70 =
108 =
7.
83 =
36 to 9 = 8 to
8.
-|-7| =
13 - -8 =
9.
95
10.
81 =
Callie did an experiment with plants.At the end of the experiment she measured the height of the plants to see which grew the tallest.Write the heights in order of least to greatest to help her. 3.6 in, 3.24 in, 3.42 in, 2.9 in, 3.5 in, 2.09 in
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 30
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Numbers and Number Sense Here’s another chance to show what you know.
Directions: Write <, >, or = to show how the numbers compare. a
1. 2.
b
8 4 ___ 10 5 1 0.1 ___ 9
3. 50% ___ 0.05 4.
1 ___ 0.125 8
5.
13% ___
1 7
6.
3 ___ 1.75
7.
17 ___ 85% 20
8. -15 ___ -16
c
5 ___ 0.85 6
200% ___ 2.0
-0.34 ___ -0.23
0.4 ___ 4%
2 ___ 45% 5
61 100 1 30%___ 3 0.6 ___
15% ___ 1.5
14 7 ___ 36 18 1 ___ 21% 5
2 ___ 1.5
9 ___ 9% 100 1 0.33 ___ 4
0.8 ___ .80
3 ___ 75% 4
10% ___0.2
Directions: Name where points A-E are located, then plot points F-J at the correct places. 9. A B C D E
F (8, 3) G (10, 7) H (6, 10) I (4, 3) J (3, 6)
•B •A
•D
•C • Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
E
Date 31
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use Addition Properties Learn the properties of addition below to help you add more quickly and easily. The Identity Property says that the sum of any number and zero is that number. The Commutative Property says that you can add two numbers in either order and get the same sum. The Associative Property says that you can group three or more numbers in any way and get the same sum.
Directions: Write C if the equations demonstrate the Commutative Property, A for Associative, and I for Identity. a
b
1.
6 + 7 = 13
7 + 6 = 13
2.
15 + 0 = 15
0+3=3
3.
(1 + 2) + 3 = 6
1 + (2 + 3) = 6
4.
95 + 5 = 100
5 + 95 = 100
5.
20 + (6 + 4) = 30
(20 + 6) + 4 = 30
6.
0 + 3700 = 3700
62 + 0 = 62
7.
48 + 4 = 52
4 + 48 = 52
Directions: Write two examples to demonstrate each property. 8.
Identity
9.
Commutative
10.
Associative
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 32
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Two Digits Always start by adding the ones column. Remember to regroup into the next greater place value, if needed. Directions: Add. a
b
c
35
68
76
89
75
+ 24
+ 71
+ 76
+9
+ 65
2.
16 + 43
49 + 38
38 + 25
52 + 37
49 + 47
3.
58 + 60
92 + 40
47 + 58
64 + 18
38 + 63
4.
84 + 54
53 + 47
22 + 67
40 + 46
72 + 28
5.
8 + 85
16 + 94
96 + 81
58 + 23
37 + 28
1.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
d
e
Date 33
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Up to Four Digits Try adding numbers in the thousands.
Directions: Add. a
1.
573 + 425
2.
962
b
284 + 76
c
d
e
697 + 328
837 + 629
508 + 757
537
5228
3041
653
+ 468
+ 829
+ 554
+ 748
+ 2346
3.
2512 + 4396
6683 + 741
7052 + 8353
7236 + 4543
2834 + 2834
4.
5485 + 3333
3691 + 6317
4493 + 1857
3958 + 4062
8751 + 6352
Directions: Rewrite in vertical form, then add. Remember to line up the digits in the ones place. a
b
5. 475 + 366 =
598 + 3702 =
6. 7086 + 3259 =
6113 + 987 =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 34
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Up to Seven Digits Adding numbers in the millions is the same as adding other numbers.You Tip may need to regroup more than once. Directions: Add. a
b
c
d
1.
7390 + 4386
52,174 + 2,583
84,528 + 3, 471
58, 496 + 785
2.
33,673 + 26,325
38, 209 + 43,352
62,630 + 584
95,332 + 22, 257
3.
461, 037 + 32,843
249, 426 + 75,185
326,124 + 173,859
608,892 + 372, 209
4.
876,958 + 98,167
735, 245 + 466,729
2, 093, 461 + 1,357, 477
6,738,745 + 3, 017, 283
Directions: Rewrite in vertical form, then add. Remember to line up the digits in the ones place. a
b
5. 93,158 + 46,873
698,543 + 56,781
6. 843,420 + 750,985
4,256,329 + 327,466
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
Date 35
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Decimals When adding decimals, line up the numbers on the decimal points. Regroup Tip as you would other numbers. Directions: Add. a
b
c
d
e
5.3
4.8
5.5
12.8
3.2
+ 6.4
+ 3.7
+ 7.9
+ 3.6
+6
2.
6.21 + 2.36
3.25 + 6.33
8.47 + 3.26
2.4 + 6.03
21.34 + 0.25
3.
0.336 + 0.283
1.803 + 0.089
0.521 + 0.359
2.1 + 0.683
0.685 + 2.37
4.
41.3 + 3.76
7.75 + 0.98
23 + 0.23
4.5 + 0.45
7.02 + 2.98
1.
Directions: Rewrite in vertical form, then add. Remember to line up the decimal points. a
b
5. 3.5 + 2.6
6.3 + 9
6. 10.22 + 3.79
3.04 + 0.974
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
Date 36
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Practice Addition See how quickly — and accurately — you can complete these addition equations. Directions: Add. a
b
c
597
3489
9.35
684
96
+ 23
+ 504
+ 7.19
+ 97
+ 345
2.
672 + 934
96.7 + 82.7
854 + 3986
81.76 + 57.79
7.39 + 68.71
3.
8143 + 5589
6235 + 4745
338 + 572
59 + 33
853 + 276
1.
a
b
d
e
c
d
4.
7,671 + 26, 286
21,680 + 74,532
852,873 + 464,566
407,325 + 3,598,633
5.
93,507 + 46,868
368,192 + 485
283,938 + 62,338
567, 433 + 3,557,942
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 37
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Practice Addition Always remember to line up the numbers on the ones or on the decimal points. Directions: Rewrite the equations vertically, then add. a
b
1. 47 + 58
3,672 + 362,759
2. 2398 + 4871
8.037 + 2.58
3. 2.5 + 3.7
76,521 + 8,797
4. 3673 + 5436
968 + 786
5. 52,370 + 36,389
25,300 + 30,435
6. 45.35 + 75.25
6,543,219 + 876,123
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 38
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Two Digits Start subtracting at the ones place. Regroup as needed.
Directions: Subtract. a
b
c
d
e
1. 86 - 35
13 - 8
39 - 18
44 - 21
71 - 59
2. 97 - 34
29 - 18
82 - 73
90 - 56
47 - 18
3. 56 - 38
64 - 34
78 - 39
32 - 4
64 - 37
4. 60 - 47
85 - 37
93 - 46
87 - 38
38 - 6
5. 83 - 43
51 - 40
33 - 27
62 - 35
94 - 35
6. 75 - 16
21 - 8
46 - 38
73 - 44
50 - 23
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 39
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Up to Four Digits You might have to borrow more than once. Remember to keep track each time. Directions: Subtract. a
b
c
d
e
1.
657 452
934 733
688 471
590 322
2.
684
805
427
4726
6738
277
74
359
624
514
3.
3986 1122
5139 3621
9455 7440
6107 328
8265 931
4.
2835 2826
6928 4717
7863 3598
9072 7203
4120 1517
365 49
Directions: Rewrite in vertical form, then subtract. Remember to line up on the ones place. b
a
5. 475 - 389 =
682 - 590 =
6. 6851 - 3632 =
9332 - 782 =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 40
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Up to Seven Digits Subtracting in the millions is just like subtracting other numbers.
Directions: Subtract. a
b
5,876
67,745
38,696
72, 457
4,766
53, 224
15, 473
69,342
2.
93, 067 72,749
85, 436 8,732
77,512 46,331
544,680 321,547
3.
476,375 259, 260
700,000 351, 289
517, 289 366,198
270,834 9,851
4.
2, 483,599 1,352,479
4,325,928 627,635
6,817,500 3,921,622
8,351,701 7,892,663
1.
c
d
Directions: Rewrite in vertical form, then subtract. Remember to line up on the ones place. a
b
5. 65,723 - 27,641
875,400 - 6,785
6. 380,452 - 276,368
5,423,167 - 3,246,897
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 41
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Decimals You can always add zeroes after a decimal point to hold a place.
Directions: Subtract.Write the answer in its shortest form. a
b
c
8.9
6.9
5.24
7.577
9.346
4.5
2.8
3.33
4.034
4.394
2.
3.57 2.2
12.5 3.4
4.6 0.75
8 0.5
10.63 3.07
3.
1 0.001
5.75 2.28
6.203 3.4
7.36 5.36
15 0.15
4.
14.43 8.702
3 1.75
7.1 2.68
8.9 0.89
2.48 1.09
1.
d
e
Directions: Rewrite in vertical form, then subtract. Remember to line up on the decimal point. a
b
5. 7.2 - 5.6
6 - 3.17
6. 5 - 2.25
2.1 - 0.308
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 42
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Practice Subtraction The biggest mistake people make is regrouping when it's not needed or forgetting to borrow when it is. Directions: Subtract.
1.
2.
3.
a
b
c
85
157
62
39
d
e
623
582
73
476
93
18
367
2361
285
487
4759 2892
5000 2541
a
5932
7184
85
89
377
62
6079 2184
9645 2763
4540 3636
b
c
d
4.
46,300 18,596
583, 256 34,164
920,157 6, 221
632,700 270, 070
5.
721,361 719,275
867, 073 668, 069
7,834,603 6,934,747
3,525, 400 1, 287,364
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 43
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Practice Subtraction Always remember to line up the numbers on the ones or on the decimal points. Directions: Rewrite the equations in vertical form, then subtract. a
b
1. 87 - 35
9216 - 4775
2. 7436 - 279
4.523 - 0.36
3. 5 - 3.75
76,921 - 6,877
4. 31,455 - 28,364
600 - 147
5. 570 - 248
5,432,198 - 1,234,567
6. 671,388 - 87,500
59,723 - 6,894
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 44
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add and Subtract Greater Integers Apply the same rules for adding and subtracting greater integers.You may wish to change the order of some problems for easier computation.
17 + 35 18
35 + 17 18
Directions: Rewrite the equations in vertical form, then solve. a
b
1. - 4385 + -5927
-23.6 + - 33.27
2. 508 - -926
-5281 + 6572
3. 67,293 + -36,198
-485 - 672
4. 7.6 + -1.9
-83,436 - 24,754
5. -2364 - -6374
75 - 6308
6. 1615 - 2739
1268 + - 3522
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 45
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Check Addition and Subtraction Because addition and subtraction are inverse operations, you can use one to check the other. Directions: Write and solve a subtraction problem to check each sum, and an addition problem to check each difference. Circle correct answers. a
b
c
1. 435 + 627 = 1162
9114 - 2477 = 7637
74,331 + 25,388 = 100,291
2. 3379 - 2859 = 620
8675 + 7863 = 16,538
971 - 795 = 166
3. 58,210 + 3,586 = 61,796
61,300 - 39,282 = 21,018
697,343 + 486,304 = 1,083,647
4. 4663 - 2738 = 1935
5768 + 5789 = 11,557
8405 - 2377 = 5028
5. Adrian once counted 77 steps from the street to his locker.Today he's already walked 29 steps, so he figures he has 58 more to go. Is he correct? Write the equation he used and the equation to check it.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 46
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Look for key words to help you decide which operation to use.
Addition word problems often involve putting sets of numbers together or gaining a certain amount. Clue words that may indicate addition include altogether, total, or in all. Subtraction word problems often involve comparing sets of numbers or losing a certain amount. Clue words that may indicate subtraction include difference, more, or borrow. Directions: Write the letter of the expression that matches each word problem.Then solve. A 475 + 104
B 475 - 104
C -475 + -104
D -475 + 104
1. Most of the year, the town of Sagebrush has a population of 475. During the hot summer, 104 people leave for cooler areas. How many people live there in the summer? 2. Stony Mountain path goes to where the mountain is 475 feet tall.The last 104 feet of the mountain is a sheer rock wall that no one can climb. How tall is the mountain altogether? 3. Little Canyon is 475 below sea level. If one climbs from the bottom to the first overlook, you will have climbed 104 feet. How far below sea level will you be now? 4. You can take a whitewater rafting trip starting in Little Canyon.The canyon is at 475 feet below sea level, but the river takes you 104 feet even lower. How much lower will you be at the end of the rafting trip? Directions: Write the equation and solve. 5. One night, the temperature on Stony Mountain got down to -20.The temperature rose by 47 degrees the next day. How warm did it get that day?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 47
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems If you're not sure of an answer, you can always use the inverse operation to check yourself. Directions: Write an equation, then solve. Show your work. Remember to line up the numbers in the equation correctly and to label your answers. 1. Luke was learning a new card game. His score the first hand was -243 and the second hand was 368.What was his total score after two hands?
2. Meg skiied down Bull Hill in 58.78 seconds.The next time she tried, she did it in 58.69 seconds. How much faster was she the second time?
3. Meg had only 207 pages left to read of her graphic novel.The next day, she only had 132 pages more to read. How many pages had she read?
4. Luke read 93 pages of a book one day and 118 the next. How many pages had he read in all?
5. At the football game, 34,264 people sat on one side of the stadium and 33,987 sat on the other. How many people were sitting in the stadium in all?
6. How many more people sat on one side than the other in the football stadium?
7. Luke lives in a city of 35,207 people.The city next to his has 27,655 people. Luke says that there are 8,652 more people where he lives. Is he correct? Write the subtraction equation he used and an addition equation to check his subtraction.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 48
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Addition and Subtraction Be careful to watch the signs!
Directions: Add or subtract. a
b
c
1.
682 + 739
836 556
4597 + 8384
2.
9056 + 8477
7039 4254
52.3 26.35
3.
42,963 35,956
d
5701 2342
846,213 + 352,749
92, 461
4.367 + 7.88
3567 2438
+ 356,878
Directions: Solve.Write the inverse equation to check yourself. a
b
c
4. 4183 + 2877
8500 - 3423
55,576 - 29,048
5. 9216 - 6636
76,309 + 8,931
6718 + 7894
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 49
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Addition and Subtraction You have all the information you need to solve them all!
Directions: Rewrite the equation in vertical form, then solve. a
b
1. 10 - 0.503 =
4.8 + 5.94 =
2. 68 + 735 =
941 - 736 =
3. 6829 - 3144 =
54,328 + 97,143 =
4. 72,038 + 57,358 =
9633 - 5727 =
5. 852,316 - 39,427 =
845,365 + 2,635,354 =
Directions: Write the equation and solve it. 6. Dylan bought a new shirt for $29 and new pants for $37. How much did his new clothes cost in all?
7. Erin looked at one cell phone that cost $127 and another that cost $65. What was the difference in cost?
8. Erin had a gift certificate for $50, but her phone cost $127. She said she spent $72 of her own money. Is that correct? Show her equation and the equation you can use to check it.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 50
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Multiples When you multiply any integer by 1, 2, 3, and so on, the product is a multiple of the first number: 6 x 1 = 6; 6 x 2 = 12; 6 x 3 = 18 4 x 5 = 20; 4 x 6 = 24; 4 x 7 = 28 6, 12, and 18 are multiples of 6. 20, 24, and 28 are multiples of 4. Directions: Fill in the blank with the correct number. a
b
.
4, 10, 14, and 18 are multiples of
.
1.
6, 9, and 12 are multiples of
2.
14, 21, and 49 are multiples of
.
28, 35, 42, and 56 are multiples of
3.
10, 25, and 40 are multiples of
.
12, 18, and 24 are multiples of both
4.
27, 36, and 81 are multiples of
.
16, 24, and 32 are multiples of
,
. and , and
. .
Directions: Circle the number that is a multiple of the first number. a
b
5.
5
22
16
20
11
21
22
23
6.
9
54
19
39
4
34
43
64
7.
3
23
31
21
7
70
27
17
8.
6
58
42
16
14
34
42
45
9.
8
18
42
24
19
119
91
114
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 51
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
List Factors Numbers that you multiply together to get a product are called the factors of that number. 1 x 12 = 12 12 x 1 = 12 3 x 4 = 12 4 x 3 = 12
2 x 6 = 12
6 x 2 = 12
1, 2, 3, 4, 6, and 12 are the factors of 12. Directions: Circle the one or more numbers that are factors of the first number. a
b
1.
16
32
2
8
6
14
1
2
4
7
2.
20
5
2
10
9
18
4
8
12
18
3.
9
3
4
5
6
48
2
6
8
24
4.
30
5
6
3
10
90
6
11
15
45
5.
5
25
15
5
1
55
25
20
11
6
Directions: List all the factors of each number. a
b
6.
8
56
7.
15
22
8.
16
35
9.
19
4
10.
24
28
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 52
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Identify Prime and Composite Numbers All positive integers greater than 1 are either prime numbers or composite numbers. A prime number is a positive integer that has as factors only 1 and itself: A composite number has other factors as well as 1 and itself. 4 is composite because its factors are 1, 2, and 4. 6 is composite because its factors are 1, 6, 2, and 3. 7 is prime because its only factors are 1 and 7. Directions: Circle the number in each group that is a prime number. a
b
1.
6
11
9
21
12
31
2.
5
8
14
34
43
44
3.
16
18
19
16
13
25
4.
29
39
49
73
15
35
5.
17
170
54
51
72
37
Directions: Write the factors of each number. If the number is prime, write a P in the blank next to the number. 6.
47 Factors:
7.
38 Factors:
8.
42 Factors:
9.
19 Factors:
10.
51 Factors:
11.
65 Factors:
12.
77 Factors: Date
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
53
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Identify Prime and Composite Numbers Composite numbers are the products of factors other than 1 and the number itself. 6 is a composite number because 1 x 6 = 6 and 2 x 3 = 6. 15 is a composite number because 1 x 15 = 15 and 3 x 5 = 15. Directions: Write the factors of each number.Then, if the number is prime, write a P in the blank next to the number. If the number is composite, write a C in the blank next to the number. 1.
18 Factors:
2.
27 Factors:
3.
63 Factors:
4.
41 Factors:
5.
49 Factors:
6.
70 Factors:
7.
97 Factors:
8.
29 Factors:
9.
58 Factors:
10.
81 Factors:
11.
105 Factors:
12.
125 Factors:
Directions: Write the first ten prime numbers. 13.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 54
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Check Multiplication and Division Just as addition and subtraction are inverse operations, so are multiplication and division. Use one to check the other. 7 x 12 = 86? Check by dividing. 86 ÷ 7 = 12 remainder 2. No, 7 x 12 does not equal 86. Try again. 7 x 12 = 84? Check by dividing. 84 ÷ 7 = 12. Yes, you are correct. Directions: Write an inverse problem to check each equation, then solve it. a
b
1.
8 x 14 = 112
6 x 19 = 106
2.
67 x 3 = 204
76 ÷ 4 = 19
3.
34 ÷ 11 = 3
9 x 18 = 166
4.
234 ÷ 9 = 26
45 ÷ 3 = 15
5.
94 ÷ 6 = 16
6 x 71 = 426
6.
4 x 24 = 71
144 ÷ 18 = 6
7.
Kaylee scored 5 goals for her lacrosse team in one game. She hoped to do this in each of her team’s 16 games. If she did, she said that she would reach 84 goals and set the team record. Is her multiplication correct? Write Kaylee's equation.Then write a division equation to check it.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 55
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 2 Digits by 1 Digit You’ll solve problems like this in real life all the time. Remember to regroup as needed. 24 5 20
65 9 45
87 6 42
10 120
54 585
48 522
Directions: Multiply. a
b
c
d
e
1.
59 6
83 3
48 9
92 3
36 5
2.
42 3
14 8
97 5
84 6
58 2
3.
60 2
91 9
62 5
29 9
70 7
4.
37 7
52 8
51 9
17 4
39 9
5.
75 2
73 4
73 4
40 8
56 4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 56
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 4 Digits by 1 Digit Multiply numbers in the thousands just as you would other numbers. Remember to regroup as needed. Directions: Multiply. a
b
c
d
e
1.
9, 021 7
6, 490 6
3,964 6
6, 423 3
4,849 9
2.
5,386 2
4,371 4
5,803 2
5,510 8
9,321 2
3.
2,974 9
5,575 9
9,182 9
9,893 4
8, 456 8
4.
3, 002 5
9, 007 8
7,105 4
7,370 7
7,789 3
5.
8,853 6
7, 201 3
4, 484 7
2, 445 6
5, 413 7
6.
7,979
2,376
7, 290
5,509
6, 094
8
5
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
8
5
5
Date 57
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 7 Digits by 1 Digit Multiply numbers with seven digits (millions) just as you would other numbers. Remember to regroup as needed. Directions: Multiply. a
b
7,348,901
1.
4
c
1,722,300
8
d
9,947,983
2
2,556,998
5
2.
2,955,571 7
4, 412,939 6
5,736, 029 4
4,567,212 8
3.
5,711,904
8,809,942
8,637,782
7, 224,228
4.
3,600,518
3
2
6,948, 226 5
5
7
3
6,822, 245 9
6
7
4
2, 434,871
3,399,574
7
9
5, 014, 484 6
6,366,105 3
3,409,970 3
7,820,625
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
3,556,669
9,957,382
5.
6.
9
1,145,669
Date 58
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply Decimals If both factors have a decimal, count the places in both and move the decimal in the product from the right that amount. 6.92 0.8 5.536
Directions: Multiply. a
b
1.
2.6 5
59 0.9
4.57 0.3
71.19 8
2.
8.7
8.6
45.7
3.37
31
6
0.3
0.3
5
0.05
3.
57 0.3
0.38 0.8
4.57 3
0.392 0.6
9.63 0.6
4.
32 0.8
0.44 0.6
45.7 3
45.29 0.4
90.9 0.9
5.
7.3
4.76
457
4.6
c
7
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
d
3
e
715 0.6
66.5
23.7
8
0.004
Date 59
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 2 Digits by 2 Digits To multiply a number by a two-digit number, first multiply by the digit in the ones place.Then multiply by the digit in the tens place. 57 23 171 114 1311
Directions: Multiply. a
b
c
d
1.
62 93
76 32
35 75
27 54
2.
88 12
51 27
98 17
52 98
3.
37 33
93 62
44 68
31 41
4.
48 74
71 91
82 45
72 38
5.
29
42
64
58
56
69
70 23
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 60
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 4 Digits by 2 Digits Multiplying four-digit numbers is the same as multiplying two-digit numbers.
Directions: Multiply. a
4,959
1.
2.
25
b
7, 202
9,938
49
c
8, 498
16
5,832
d
49
5, 029
1,832
54
35
27
3,845
53
3.
1, 245 93
3, 445 78
4,771 61
9,541 88
4.
8, 285
2,948
2, 257
5,748
5.
37
6, 031 65
39
9,788 22
6, 003 70
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
14
17
7, 226 94
Date 61
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply 7 Digits by 2 Digits Multiplying with seven digits may look complicated—but it’s not.
Multiplying numbers in the millions is the same as multiplying other numbers. Start by multiplying the ones place. Directions: Multiply. a
b
5,938,964 72
3, 471,109 53
1, 201,905 49
4,586,873 52
2.
7,849,338 43
6, 048,722 35
7,527,394 23
2,770,638 64
3.
2, 255,830
9,339, 020
3, 449,723
8,311,194
1.
4,733,837
4.
5.
68
26
1,983,674 18
c
88
8, 203, 478
92
7,374,599 63
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
d
39
9,885,752
6, 299,715
74
5,639,826 13
39
83
3, 266,686
43
Date 62
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply Decimals Keep an eye on the decimal—and put it in its proper place!
Multiplying numbers with decimals is no different than with other numbers. Remember to put the decimal point in the correct place. Directions: Multiply. a
b
c
d
1.
37 0.6
57 0.32
0.638 28
5.675 0.81
2.
7.3 9
5.21 8.7
56.6 5.6
3.497 4.9
3.
4.2
17.4
37
6.6
8.3
7.7
37.92
5.6
7.7
0.44
95.7 8.9
3.82 4.3
3.892 7.6
4.
5.
63.03
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
9
34.97
4.9
349.7
4.9
3, 497
4.9
Date 63
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide 2 Digits by 1 Digit Don't let the numbers overwhelm you—take division one step at a time.
Directions: Divide. a
b
c
d
6 96
)
3 60
)
4 68
)
9 54
)
4 78
)
3 87
)
4 84
)
2 56
)
4 92
)
3 69
3 63
)
4 96
)
2 42
)
6 78
)
6 66
)
5 35
)
8 96
)
5 70
)
7 63
)
6 84
1.
)
2.
4 76
)
3.
9 45
)
4.
)
5. 7 84
)
6.
8 88
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
)
Date 64
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide 4 Digits by 1 Digit Practice dividing with some larger numbers.
Directions: Divide. a
b
c
d
1.
)
6 3,168
)
9 6,156
)
8 7,616
)
7 2,506
)
4 2,564
4 1, 908
)
5 9,735
)
7 4,564
)
2 4,822
)
6 2, 580
)
5 8,860
)
8 3,192
)
)
6 3, 282
)
8 6,104
)
3 6, 768
)
4 2,332
2.
5 4, 230
)
3.
8 2,936
)
4.
2 4, 428
)
5.
3 5,874
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
)
Date 65
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide 7 Digits by 1 Digit Is division getting easier for you? If you’ve been doing well, this page will be a breeze! Directions: Divide. 1.
6,504,279 ÷ 3 =
2.
2,310,232 ÷ 4 =
3.
6,663,000 ÷ 5 =
4.
6,502,210 ÷ 2 =
5.
4,251,312 ÷ 9 =
6.
6,508,012 ÷ 4 =
7.
5,621,937 ÷ 3 =
8.
4,598,100 ÷ 5 =
9.
3,150,270 ÷ 9 =
10.
7,770,120 ÷ 5 =
11.
6,536,470 ÷ 2 =
12.
8,231,073 ÷ 3 =
13.
6,508,308 ÷ 4 =
14.
2,707,860 ÷ 5 =
15.
4,241,970 ÷ 2 =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 66
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide With Remainders Sometimes a number does not divide another evenly.The letter R stands for remainder.
3R1 4 13
Directions: Divide. Remember to write the remainder if there is one. a
b
c
d
1.
8 42
5 326
6 2, 476
8 265
2.
7 87
4 1,380
3 1,557
6 1, 284
3.
9 245
7 7, 077
2 115
7 349
4.
5 8,304
2 3, 471
5 3, 297
4 1,618
5.
6 7,738
5 1,050
9 349
3 2,164
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 67
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Decimal Quotients When a number does not divide another evenly, you can continue dividing. The quotient will be expressed as a decimal. 3.25 4 13.00
)
Directions: Divide. a
b
c
d
1.
4 15
7 44
6 146
8 4,967
2.
5 26
3 20
3 101
6 5, 052
3.
7 24
8 32
2 355
3 2,333
4.
9 54
2 19
5 600
4 4,570
5.
6 41
5 63
9 532
7 6, 248
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 68
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide 2 Digits by 2 Digits To divide by two-digit numbers, use the same steps as dividing by one-digit numbers. Directions: Divide. a
b
c
d
1.
21 63
17 85
24 86
15 90
2.
12 88
35 95
45 90
23 86
3.
38 76
22 66
14 84
37 71
4.
40 90
11 74
19 95
26 98
5.
13 91
39 99
30 85
18 24
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 69
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide 4 Digits by 2 Digits Divide larger numbers using the usual strategy–do one step at a time.
Directions: Divide. a
b
c
1.
71 4, 402
57 4,617
63 3,848
2.
72 2,808
45 2, 020
72 4,680
3.
14 1, 442
36 5,112
90 1, 269
4.
66 6, 470
87 4,528
17 4,307
5.
43 3,526
29 1,824
74 6,808
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 70
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide Decimals To multiply or divide numbers with decimals, remember these rules.
To divide a decimal, first place a decimal point in the quotient above the decimal point in the dividend. Add a zero if needed to hold a place.
10.1 5 50.5
. 5 50.5
If there is no decimal point in the dividend, but there is one in the divisor, add a zero to the dividend for each place value after the decimal point in the divisor. 100 5.12 51200
)
5.12 512
Directions: Divide. Remember to write the remainder if there is one. a
b
c
d
6 14.5
8 32.8
1.
6 4.2
8 22.4
2.
3 8.7
9 0.58
0.04 92
0.5 510
3.
0.2 68
0.03 64
0.7 273
0.2 0.0037
4.
0.05 45
0.6 270
5 3.58
9 6.61
)
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 71
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Use your multiplication and division skills to solve these real-life problems.
Directions: Solve. Show your work. 1. Maria worked at a summer camp. Each week she earned $95. If she worked for 9 weeks, how much money did she make that summer?
2. If Maria worked 40 hours each week, how much did she make per hour?
1 3. The lifeguard at the camp earned 1 times as much for the summer as 2 Maria did. How much did she earn for the summer?
4. The lifeguard worked 25 hours per week. How much more per hour did she earn than Maria?
5. At each session of the camp, there are 96 campers.These campers live in 8 cabins. How many campers live in each cabin?
6. At one popular camp session, 120 campers signed up.The extra campers had to sleep in 4-person tents. How many tents did the camp need to set up?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 72
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems You have all the skills you need to solve these word problems.
Directions: Solve. Show your work. 1. Maria’s friend Andy works in the camp kitchen. He is serving fruit cocktail to 96 campers and 16 staff members. If each can of fruit cocktail contains 24 servings, how many cans will he need?
2. Andy is baking sheet cakes for dessert. Each sheet cake can be cut into 18 pieces. If he bakes 6 cakes, will there be enough pieces of cake for everyone?
3. The cook at the camp buys 76 pounds of flour for $30.40. How much is the flour per pound?
4. The high diving board at the camp lake is 10 feet high. If 1 foot is .33 of a yard, how many yards high is the diving board?
5. The lifeguard is organizing a swimming meet. 48 campers sign up to take part. How many teams of 8 swimmers can the lifeguard create?
6. At the last minute, 16 more campers sign up for the swimming meet. How many teams with the same numbers of campers can the lifeguard make now?
7. At the swimming meet, first place earns 6 points, second place 3 points, and third place 1 point. One team, the Dolphins, won 2 races.They finished second in 3 races and third in six races. How many total points did the Dolphins earn?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 73
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Multiplication and Division Use what you know about multiplication and division.
Directions: Solve. Show your work. a
1.
b
126 2
45 71
6, 203
2.
c
5
5,331
d
0.4 147.4
0.64 23
5 41
0.65 128
63
3.
4 84
7,942,735 24
3 90
1.47 3
4.
6 1, 068
78 13
72 936
5.2 4.65
5.
6 6,785, 442
8 7, 048
7 7, 070
0.15 737.9
6.
8,500, 213 9
13 78
4 3, 434
54.81 2.3
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 74
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Multiplication and Division Look at how much you've learned!
Directions: Solve. Show your work. a
b
c
d
1.
6,930,952 x 47 =
2,959 ÷ 62 =
3 x 6,093,951 =
4.8 ÷ 0.7 =
2.
8,944,478 ÷ 7 =
67 x 5,919 =
49 ÷ 6 =
7.72 x 4.2 =
3.
82 x 76 =
7,553 ÷ 6 =
34 x 8 =
73.68 ÷ 1.45 =
4.
97 ÷ 13 =
8 x 4,092 =
56 ÷ 8 =
91.66 x 0.55 =
Directions: Write the first 6 multiples of these numbers. a
5.
b
4
c
7
13
Directions: List all the factors of these numbers. a
6.
32
b
c
56
96
Directions: Circle the prime numbers in this list. 7.
11
46
50
29
21
19
2
33
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
18
5
9
41 Date
75
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Fractions with Like Denominators To add fractions with like denominators, simply add the numerators.To add mixed numbers, add fractions first, regroup if needed, then add the whole numbers. Directions: Add. Remember to reduce fractions to simplest terms. a
b
1.
1 1 + = 3 3
3 1 + = 8 8
2.
3 1 + = 4 4
7 7 + = 10 10
3.
3 4 + = 5 5 3 5 + = 9 9
1 4 +6= 5 9 7 +2 = 16 16
5.
1 2 1 + = 3 3
2 2 5 +1 = 3 3
6.
5 5 4 +1 = 6 6
1 1 9 + = 4 4
7.
1 3 3 +2 = 5 5
3 5 + = 7 7
8.
2 2 6 +3 = 3 3
2 5 + = 9 9
9.
3 7 6 +3 = 8 8
7 1 + = 11 11
10.
1 5 5 +3 = 9 9 1 7 + = 12 12
2 4 + = 9 9 1 2+2 = 4
1 2 3 +7 = 3 3
1 1 4 +4 = 3 3
4.
11. 12.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 76
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add Fractions with Unlike Denominators To add fractions with unlike denominators, convert them to like fractions using the least common multiple of the denominators. Directions: Add. Remember to reduce fractions to simplest terms, if needed. a
b
1.
2 1 + = 3 2
3 1 3 + = 10 2
2.
1 1 + = 4 6
2 1 +2 = 3 4
3.
5 5 + = 8 16 2 3 + = 3 7
1 7+6 = 4 4 1 1 +2 = 9 5
5.
5 4 + = 6 9
3 3 3 + = 4 5
6.
6 1 + = 7 6
1 2 2 +4 = 3 7
7.
1 2 + = 4 3
1 1 3 +4 = 2 3
8.
2 4 + = 5 7
1 3 +2 = 2 5
9.
1 5 + = 4 8
1 2 + = 5 4
1 5 + = 2 7 3 3 2 +2 = 4 5
5 1 1 + = 8 4 7 2 + = 9 3
4 1 1 +3 = 9 2
1 3 3 +1 = 5 4
4.
10. 11. 12.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 77
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Fractions with Like Denominators To subtract fractions with like denominators, simply subtract the numerators. To subtract mixed numbers, subtract fractions first, borrowing from the whole number if needed.Then subtract the whole numbers. Directions: Subtract. Remember to reduce fractions to simplest terms. a
b
c
1.
3 1 = 4 4
11 7 = 15 15
5 1 = 11 11
2.
4 1 = 5 5
3 1 = 7 7
7 5 = 8 8
3.
7 3 = 8 8
7 5 = 9 9
1 1 = 3 3
4.
3 5 1 2 5 6
6
5
1 2
3
1 2
5.
2 7 6 1 7
1 3 1 1 3
1 3 2 1 3
6.
6
5 8 3 2 8
1 5 4 3 5
4
1 3
2
6
5
8
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 78
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Subtract Fractions with Unlike Denominators To subtract fractions with unlike denominators, convert to like fractions using Tip the least common multiple of the denominators. Directions: Subtract. a
b
c
1.
5 3 = 7 5
7 2 = 8 3
7 1 = 10 7
2.
1 1 = 2 4
8 1 = 9 4
5 1 = 6 9
3.
4 2 = 5 3
2 1 = 3 2
15 2 = 16 3
1 2 1 1 4
1 3 1 2 2
5.
4 5 3 2 4
2 9 5 1 7
1 2 3 3 8
6.
7 9 2 2 3
1 4 2 3
2 3 3 1 5
4.
3
3
6
6
4
2
5
1
3
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
5 8
Date 79
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Add and Subtract Positive and Negative Fractions Tip are the rules for adding and subtracting positive and negative fractions. Here
The sum of two negative fractions is always negative.
3 1 5 1 + = = 1 4 2 4 4
Adding a negative fraction to a positive is like subtracting. 5 1 1 + = It will be positive or negative, depending on which addend 3 2 6 is greater. Subtracting a negative fraction is like adding. 1 1 = 7 2 5 10 Directions: Write P if the answer is positive or N if the answer is negative. a
b
1.
5 1 = 8 2
4 1 = 5 4
2.
3 1 + = 8 2
3 1 + = 5 4
3.
2 1 + = 3 5
4 1 = 5 7
Directions: Add or subtract. a
b
c
4.
5 1 = 8 2
2 1 = 3 5
3 5 = 8 8
5.
5 1 + = 8 2
3 3 + = 5 8
1 5 + = 2 7
6.
3 1 + = 4 3
3 1 = 5 8
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
3 4 + = 10 5 Date
80
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Understand Multiplying Fractions When you multiply fractions, multiply the numerators and then the denominators. A shortcut when multiplying fractions is to cancel out compatible numbers when they occur. 1
3 51 1 = 5 5 15 1 65
Directions: Multiply. Remember to reduce or express products in simplest form. a
b
c
1.
3 2 = 4 3
2 1 = 3 2
5 2 = 8 3
2.
3 4 = 5 9
3 3 = 10 5
4
3.
4 1 = 7 2 1 1 = 3 4
1 = 3 2 9 = 3 10
1 7 = 10 9 3 9 = 4
4.
10
5 = 16
5.
5 1 = 8 4
3 1 = 5 3
1 5 = 3 7
6.
3 5 = 5 8
7 1 = 8 4
2 4 = 5 5
7.
1 4 = 3
18
5 = 6
1 12 = 4
8.
3 3= 5
1 10 = 5 11
2 3 = 3 4
9.
5 7= 7
1 2 = 2 7
3 14 = 7
2 = 3
3 7 = 5 10
1 1 = 2 2
10.
3
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 81
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply Mixed Numbers When multiplying mixed numbers, convert them to improper fractions first. Remember to cancel out compatible numbers when you can. Directions: Multiply. a
b
c
9 2 = 10 3
1 3 2 = 10 5
1.
2 1 2 = 3 2
4
2.
3 1 1 = 4 4
4 7 2= 5
3 2 2 = 7 7
3.
1 5 8= 8
7 2 3 = 9 5
1 3 2 = 3
2 = 3
1 1 2 = 2 7
4 4 2 = 5 9
2 5 3 = 3 8
1 33 = 3
4.
5.
12
12 2
3 = 4
6.
1 7 2 = 3 8
1 3 3 3 = 3 5
3 1 6= 4
7.
1 1 3 = 4 4
1 2 2 = 2 3
1 1 3 3 = 6 3
8.
1 1 3 3 = 3 4
3 53 = 4
4 6 7 2 = 5 7
9.
1 6 3= 5
24
10.
2 3 3 = 3 4
2 1 1 = 3 5
1 = 2
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
7 2 5= 10 1 64 = 3
Date 82
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide Fractions Dividing by a fraction is the same as multiplying by the divisor's reciprocal.
1 1 1 4 4 2 ÷ = = = =2 2 4 2 1 2 1
Directions: Rewrite each division problem as a multiplication problem using the divisor's reciprocal.Then solve. a
b
1 = 3
1 3 ÷ = 5 10
1.
12 ÷
2.
1 1 ÷ = 3 3
3.
7÷
4.
9÷2=
5.
8÷
1 = 4
1 1 ÷ = 4 4
6.
1 ÷8= 4
1 2 ÷ = 2 3
7.
3 1 ÷ = 7 2
3 4 ÷ = 4 5
8.
10 ÷
1 = 9
5 2 ÷ = 9 3
9.
3 1 ÷ = 4 4
5 1 ÷ = 6 3
10.
3 3 ÷ = 4 8
4 6 ÷ = 5 7
7 1 ÷ = 9 3
1 = 2
7 1 ÷ = 10 2 3 1 ÷ = 4 3
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 83
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Divide Mixed Numbers When dividing mixed numbers, convert them to improper fractions first.
Directions: Divide. a
b
1.
1 3 ÷3= 2
1 3 ÷6= 6
2.
1 4÷2 = 3
1 1 8 ÷ = 5 5
3.
3 7 7 ÷ = 5 10
1 9÷4 = 3
4.
2 1 3 ÷1 = 3 10
7 2 3 ÷ = 8 7
5.
4 1 ÷1 = 7 7
3 3 ÷3= 4
6.
7.
18 ÷ 4 4
2 = 3
7 1 ÷3 = 6 16
1 1 ÷ = 4 2
4÷4
1 = 12
8.
5 2 ÷ = 7 3
3 2 3 ÷2 = 5 5
9.
1 1 1 ÷ = 5 2
1 1 2 ÷6 = 2 5
10.
1 6÷4 = 3
1 3 6 ÷2 = 3 4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 84
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Multiply and Divide Positive and Negative Fractions Here are the rules for multiplying and dividing positive and negative fractions.
When you multiply or divide two positive fractions, the answer is always positive. When you multiply or divide two negative fractions, the answer is always positive. When you multiply or divide a negative by a positive or a positive by a negative, the answer is always negative.
Directions: Write P if the answer is positive or N if the answer is negative. a
b
c
1.
3 1 = 5 4
1 1 = 3 4
1 1 = 6 4
2.
3 ÷ 6 = 10
1 9 ÷ = 3
1 2 ÷ = 3 5
3.
1 2 = 4 3
2 1 = 3 5
1 1 = 6 2
Directions: Multiply or divide. a
b
4.
7 ÷ 4 = 10
6 ÷
5.
5 2 ÷ = 6 3
6.
8÷
2 = 7
2 = 3
3 2 ÷ = 4 3
5 3 = 7 8
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
c
1 2 ÷ = 9 3 8
4 = 5
1 1 ÷ = 3 3 Date
85
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Multiplication word problems often involve putting together sets of equal numbers. Division word problems often involve splitting up a group into equal parts. Directions: Solve. 1 1. Jessie was studying for a big math test. One day she studied for 2 2 hours. 2 For of that time, Jessie studied fractions. How many hours did she work 3 on fractions?
2 1 hours studying. of that time was 5 3 spent on math. How many hours did Jessie spend on subjects other
2. Jessie told a friend that she spent 8 than math?
1 3. Jessie decided she needed to study history for 6 hours. If she 3 1 divided her history studying over 4 days, how long would she 2 spend studying history each day? 1 4. Jessie’s friend Rex spent 5 hours working on his project for history class. 5 3 Jessie spent 3 hours on hers. How many hours did they spend together on 4 their projects?
5. How much more time did Rex spend on his history project than Jessie did on hers?
3 6. Rex thinks Jessie spends too much time studying. He suggests she spend 1 hours per night, 5 nights a week, to leave more time for skateboarding. 4 If Jessie follows Rex’s advice, how many hours will she study per week?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 86
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Now for some real-world fraction problems.
Directions: Write the letter of the equation that matches each word problem.Then solve. Remember to label your answers. A. 1 1 4 4 5 B.
3 4 1 ÷ 4 5
C. 13 1 ÷ 3 2 4 4 D. 96 11
E. 13 1 3 2 4
1 1. Li and Genna are painting Li’s bedroom.The longest wall is 13 feet long.The 2 3 roller they are using is foot wide. How many passes with the roller will 4 they need to paint the entire wall? 4 of the wall. If the area of 11 the wall they need to paint is 96 square feet, how much of the wall is taken
2. There’s a window on one of the walls. It takes up
up by the window?
4 1 gallons of wall paint. But the girls used only of what 5 4 Li mixed. How much paint was used?
3. Li mixed up 1
3 1 hours to paint the entire room. If they finished of 4 2 the job on a Saturday, how many hours did they work?
4. It took the girls 13
4 of a foot wide. How many brush strokes would it 5 3 take to make a brush mark 1 feet wide? 4
5. A big brush they used is
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 87
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Fractions Make sure to watch the signs so that you perform the correct operation!
Directions: Solve. a
b
c
1.
1 1 + = 3 3
1 4 1 = 5 5
1 1 = 2 5
2.
4 3 + = 5 5
4 1 = 7 2
3 3 2 = 4 5
3.
5 7 +1 = 8 8
2 4 + = 7 5
5 2 ÷ = 8 3
4.
3 1 + = 5 3
3 1 = 4 3
3 1 ÷ = 4 2
5.
8 5 = 9 9
2 1 = 5 4
2 1 2 ÷ = 3 6
6.
3 4 = 4 7
1 2 ÷5= 4
2 5 = 3 8
7.
1 5 3 +4 5
1 4 1 +5 3
2 3 4 +1 5
8.
4
4 7 6 2 7
2 5 3 6 8
4
1
1 4
1
3
6
8
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 88
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Fractions Now you can solve fraction problems in half the time.
Directions: Solve. a
b
c
1.
3 1 + = 4 4
1 5 ÷ = 4 7
5 ÷5= 8
2.
2 1 + = 3 3
3 3 = 4 4
2 6 1 = 3
3.
1 1 = 6 4
4 1 + = 7 3
1 3 + = 3 5
4.
3 1 + = 7 3
4 1 = 9 5
7 7 = 8 8
5.
4 5 2 1 = 5 8
3 23 = 10
7 3 ÷1 = 10 10
Directions:Write the letter of the matching equation, then solve. Remember to label your answers and show all your work. C. 11 ÷ 3 = 2 2 3 6. Li used of a small can of paint. It took of what she used to paint a 3 4 stool for her room. How much of the paint did it take to paint the stool?
A. 1 ÷ 1 = 3 2
B. 3 2 = 4 3
7. Genna wants to mix up some wallpaper paste to use for Li’s room. She 1 1 only has enough paste mix to make of a bucket, the amount she 3 2 wants to make. How much wallpaper paste does she want to make?
1 quarts of varnish. If she wants to finish 3 end tables for her 2 room, how much varnish can she use on each table?
8. Li has 1 Name
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 89
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use Order of Operations To solve any equation, always perform the operations in the order given below. 3 (4 + 6) + 2 – 3 = ? operations in parenthesis multiplication, then division from left to right addition or subtraction from left to right
3 (10) + 2 – 3 = ? 30 + 2 – 3 = ? 32 – 3 = 29
Directions: Follow the order of operations to solve each equation. Show your work. a
b
c
1. 2 x 4 + (6 + 1) – 4 =
64 ÷ (8 + 6 + 1 + 8) =
(4 x 15 + 3) x 15 =
2. (7 + 9) + 3 x 4 =
64 ÷ 8 + (6 + 1 + 8) =
4x8–4x3=
3. 8 – 4 ÷ 3 – 2 =
(5 x 30) + 40 =
4 x (8 – 4) x 3 =
4. 5 + 2 x 5 + 2 =
5 x (30 + 40) =
4 x (8 – 4 x 3) =
5. (5 + 4) x (3 + 1) =
5 x 30 + 40 =
(5 + 1) x 3 + 7 =
6. (2 + 3) x 5 + 2 =
4 x 15 + 3 x 15 =
5 + (1 x 3) + 7 =
7. 72 ÷ 9 + 6 + 2 + 5 =
4 x (15 + 3) x 15 =
5 + 1 x (3 + 7) =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 90
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Write Equations An equation is a math sentence with equal amounts on both sides of an equals sign. A variable often stands for an unknown amount.
1 Francis has a radio-controlled (R/C) monster truck that is 24 the size of a real truck. If the headlights on the actual car are 3 inches tall, how tall are they on the R/C car? 1 h stands for the height of the headlight 3 24 = h 3 =h 24 The headlights on the R/C car are 1 =h 1 inch tall. 8 8
Directions: Solve. Use a variable that makes sense to you. 1. Francis has a R/C speedboat with a rudder on the back that is 2 inches long. If the full-size speedboat is 26 times larger than the R/C speedboat, how large is its rudder? 2. To run his R/C cars and boats, Francis charges his batteries for 30 minutes to get 20 minutes of running time. About how much charging time does it take to make a minute of running time? 3. Francis added up the value of the R/C cars and boats he owned. He owned 4 R/C cars that cost around $30. He owned 3 R/C trucks that cost around $40. He owned 1 R/C speedboat that cost $120. How much were all his R/C vehicles worth together? 4. For his birthday Francis's parents gave him $25. His grandmother gave him 4 $20. Francis used of his birthday money to buy parts for his R/C vehicles. 9 How much did he spend on parts?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 91
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Equations To solve equations, first perform all calculations. Then isolate the variable using inverse operations. Whatever you do to one side of the equation, you must do to the other side. 5x – 1 = 29 5x –1 + 1 = 29 + 1 5x = 30 5x ÷ 5 = 30 ÷ 5 x=6 Directions: Use inverse operations to solve the equations. Show your work. a
b
c
1. 4n = 24
j + j + 3 = 15
h – 9 = 14
2. x – 3 = 4
5 + n = 18
70 ÷ p = 5
y =5 3
6f – 2 = 5f
f
4. 4 + z = 0
11 = 2t + 3
3q – q = 12
5. 3k = 24
y÷8=9
c2 – 3 = 46
6. m + 4 = 17
4=9–k
5t – 2t = 21
3.
7. 2x + 2 = 16
8.
n +2=5 5
1 z= 9 z 2 72 ÷ r = 24
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
1 =7 2
13 – m = m + 7
2x = x + 3 Date
92
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Equations Tip more practice in solving equations. Here’s
Directions: Use inverse operations to solve the equations. Show your work. a
b
c
1. x + x – 5 = 27
4n = 8
h – 9 = 22
2. y – 2 = 9
5 + n = 11
75 ÷ p = 15
3. 3f + 2 = 4f
y = 30 3
z
4. 4 + z = 1
19 = 2t + 3
5q – q = 12
5. 3k = 15
y÷4=9
c2 – 3 = 33
6. 56 ÷ r = 8
14 = 9 + k
7x – 2x = 30
7. 2x – 2 = 16
1 z = z 30 2
16 – n = n + 10
m + 4 = 10
3x = x + 16
8.
n +2=5 6
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
1 =8 2
Date 93
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Understand Functions Tipfunction is a special kind of equation with two variables. A
In a function, there is only one value of x for each value of y, and vice versa. x=y+3 x=y–5 x = 3y y x= 4
When x is 4, y can only be 1. When x is 7, y can only be 2. When x is 6, y can only be 2. When x is 2, y can only be 8.
Directions: Answer each question. 1.
In the function x = y + 2, if x is 3, then y is
.
2.
In the function x = y – 4, if x is 6, then y is
.
3.
In the function x = 4y, if x is 8, then y is
4.
In the function x = 6y, if x is 18, then y is
.
5.
In the function x = 6y, if x is 12, then y is
.
6.
In the function x = y/4, if x is 8, then y is
.
7.
In the function x = y/4, if x is 12, then y is
8.
In the function x = 4y – 2, if x is 10, then y is
.
9.
In the function x = 2y + 6, if x is 12, then y is
.
10.
In the function x = 3y + 2 , if x is 14, then y is
.
11.
In the function x = y/4 – 2, if y is 12, then x is
.
12.
In the function x = y/4 – 2, if y is 16, then x is
.
13.
In the function x = 3y + 1, if x is 7, then y is
.
14.
In the function x = 3y + 1, if x is 4, then y is
.
15.
In the function x = 3y + 1, if y is 4, then y is
.
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
.
.
Date 94
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Functions It’s easy to graph a function.
To graph a function, plot two pairs of points on the x (horizontal) and y (vertical) axis.Then draw a straight line through both points. Put an arrowhead at the end of the line to show that it continues off the graph. To graph the function x = y + 1, find and plot any two pairs of values of x and y. x=y+1 x y 2 1 3 2 4 3 5 4 6 5
Directions: Complete the tables and graph each function. a
1.
b
x=y+2 y x 2 3 4 5 6
x = y -1 y x 0 1 2 3 4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 95
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Functions Here’s more practice in graphing functions.
Directions: Complete the tables and graph each function. a
1. x = 2y x y 2 4 6
y x= 3 x y 1 2 3
x = 2y + 1 x y 3 5 7
x = 2y – 1 x y 3 5 7
b
2.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 96
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Functions Here’s more practice in graphing functions.
Directions: Complete the tables and graph each function. 1.
y x= 2 x y 2 4 6
2.
x 1= x
a
x =y 3 x y 1 2 3
y 3 y 3 6 8
x = 2y – 1 x y 1 2 3
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
b
Date 97
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Rates A rate is a special kind of function or ratio.
A rate compares different units. For example, a car gets 25 miles to a gallon of gas.The rate is 25 miles to 1 gallon, or 25 miles:1 gallon, or 25 miles /1 gallon. You can graph rates the same way you graph a function.With a rate, however, the axes are labeled differently.
Directions: Read the description. Label the axes and mark the scale. Then graph each rate. 1. A 5-pound bag of flour costs 3 dollars.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 98
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Rates Now try these.
Directions: Read the description. Label the axes and mark the scale.Then graph each rate. 1. For each half-hour Martin exercises, he burns 300 calories.
2. Jerome has two plants. For each inch his jade plant grows, the snake plant grows 2 inches.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 99
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Graph Equations and Inequalities Graphs can be used to display inequalities.
All points in the shaded area are solutions to the inequality. x y–2 y x 0 2 1 3 2 4 3 5
Directions: Match the inequality with its graph. 1.
3.
A. x < y + 3 B. y > 2x C. x < 3y - 2 D. y < 2x + 2
2.
4.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 100
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Equations and Inequalities Use what you know about equations to solve these.
Directions: Solve. Show your work. a
b
c
1. x + x – 1 = 15
4n = 12
4x = x + 27
2. 2 – -y = 4
6 + n = 17
h–8=0
3. 3a + 3 = 4a
y =15 3
60 ÷ p = 15
4. 3 + z = 11
15 = 2t + 3
z
5. 4k = 20
y÷3=9
5q – q = 16
6. 45 ÷ r = 5
27 = 9 + k
b2 – 22 = 42
7. 5x – 3 = 12
1 z = z 10 2
7x – 2x = 35
m + 4 = 16
12 – n = n + n
8.
n +2=6 4
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
1 =9 2
Date 101
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Graphing Functions Here’s a chance to use what you learned about functions, rates, inequalities, and graphs. Directions: Graph each function. 1.
2.
x y1= 2 y x
x y+1 y x
3. Thomas is raising cavies (guinea pigs) for the county fair. He finds that for each 100 grams of food he feeds his cavies, they gain 50 grams in weight.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 102
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use Time Measurements You can multiply, divide, and convert using units of time.
Directions: Fill in the blank. Show your work. a
b
1.
A quarter of a day is
2.
A quarter hour is
3.
A half day is
4.
A half hour is
5.
4 hours =
6.
3 days =
7.
4
8.
6 days =
hours. minutes.
hours.
days = 52 hours
2 hour = 3 1 5 days = 2
minutes
190 min =
hours
days minutes hours hours
1 min = 5 hours 2
minutes hours
7 days =
hours = 325 minutes
9.
minutes
166 hours =
minutes.
1 hours = 2
1 3 hours = 4
hours
minutes = 164 hours
Directions: Write the equation, then add or subtract. 10.
A group’s hike lasted five hours, forty minutes from start to finish.They rested for fifteen minutes once and ten minutes another time. How long were they actually walking?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 103
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Temperatures The Metric System measures temperatures using the Celsius scale. On this scale, water freezes at 0° and boils at 100°.
5 (F 32) = C 9 9 To convert Celsius to Fahrenheit, use this formula: C + 32 = F 5 9 Hint:To multiply a number by , you can multiply using the fraction, you 5 can multiply by the decimal (1.8), or you can multiply by 9 then divide by 5. To convert Fahrenheit to Celsius, use this formula:
Directions: Convert the temperature to the nearest degree. a
b
c
1.
92°F =
°C
60°F =
°C
19°F =
°C
2.
21°C =
°F
–2°C =
°F
4°C =
°F
3.
80°F =
°C
8°F =
°C
–15°F =
4.
–15°C =
0°C =
°F
40°F =
5.
4°C =
°F °F
°F
92°C =
°C °C °F
–78°C =
Directions: Write <, >, or = to show how the temperatures compare. a
b
c
6.
100°F
100°C
22°C
57°F
85°C
185°F
7.
32°C
32°F
–15°F
–15°C
212°F
100°C
8.
12°F
12°C
25°C
77°F
–95°C
-–175°F
9.
6°C
48°F
–100°C
10.
32°F
0°C
125°F
45°C
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
–30°F
–16°C
0°F
60°F
15°C Date
104
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use Weight Measurements In the Customary System, weight is measured in ounces, pounds, and tons.To find part of a unit of weight, divide.To find multiples of a unit of weight, multiply. oz = ounce lb = pound T = ton 16 oz = 1 lb 2000 lbs = 1 T
Directions: Solve. a
b
1.
1 lb = 2
oz
2.
32 oz =
lb T = 1000 lb
3. 4.
5 lb =
5.
52 oz =
oz lb
3T =
c
lb =
1 T 4
lb
2 oz =
1 lb = 2
lb oz = 3 lb
oz
4.5 lb =
1
1 2 T= 2
lb
oz
1 5 T= 4
lb
12 oz =
lb
1 oz = 2
lb
Directions: Write <, >, or = to show how the weights compare. a
1 lb 2
6.
2
7.
6000 lb
8.
6 oz
b
36 oz
2 3 lb 4
1 T 2
6T
12,000 lb
1
3 lb 4
8 oz
2 lb 3
9000 oz
1 T 2
800 lb
64 oz
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
c
25 oz
1 T 4 3 lb
Date 105
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Identify Angles Angles are the measure of turning where two lines meet.
Directions: Answer the questions. A.
B.
C.
D.
1. Which two shapes have right angles?
2.
Which two shapes have acute angles?
3. Which shape has obtuse angles?
4. Draw a shape to show each type of angle. Label each angle with its angle name.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 106
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Angles Two angles whose sum is 90° are called complementary.Two angles whose sum is 180° are called supplementary. Directions: Answer the questions.
1.
Name 2 sets of complementary angles.
2.
Name 2 sets of supplementary angles.
3.
What type of angle is angle D?
4.
What is the measure of angle D?
5.
What type of angle is angle K?
6.
What is the measure of angle K?
7.
What type of angle is angle L?
8.
What is the measure of angle L?
9.
What is the measure of angle M?
10.
What is the measure of angle B?
11.
Draw a set of supplementary angles and a set of complementary angles below and label each.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 107
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find and Convert Customary Lengths The U.S. Customary System measures length using inches, feet, yards, and miles. inch = in foot = ft yard =yd mile = mi
12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi
Directions: Solve. a
b
1.
1 mi =
yd
2.
36 in =
ft
1 mi = 3
3.
36 in =
yd
9240 ft =
4.
8
5.
1 mi = 4
1 ft = 2
in
c
2 ft 3
in =
ft mi yd
11 ft =
ft
3 mi 5
ft =
20 ft =
yd
32 in =
ft yd
5280 ft = yd
2 mi =
1 mi = 2
yd
Directions: Write <, >, or = to show how the lengths compare. a
b
3
1 ft 2
20 yd
6.
36 in
7.
9 ft
8.
3 mi
9.
1 1 yd 3
5 ft
16 in
10.
75 in
2 yd
27 in
3 yd 15,000 ft
c
2
1 mi 2
21 in
1
13,000 ft
10 yd
3 ft 4 1 yd 3 1 2 ft 3
_1
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
1 mi 2
20 ft
2200 yd
7000 ft 30 ft
1
1 mi 2
6 mi
30,000 ft
9 in
3 ft 4 Date
108
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find and Convert Metric Lengths In many places, people measure length with the Metric System instead of the Customary System. A centimeter is shorter than an inch and a kilometer is shorter than a mile. A meter is a little longer than a yard. centimeter = cm meter = m kilometer = km
100 cm = 1 m 1000 m = 1 km
Directions: Fill in the blank with the units you would use to measure the length. a
b
1.
a pencil
a paper clip
2.
a woman
a flagpole
3.
a mouse
the distance to the moon
4.
a car trip
a basketball player
Directions: Solve. a
b
c
10 cm =
m
6.
10 m =
cm
3000 m =
7.
10 m =
km
500 m =
km
m
80 cm =
m
8. 9.
1 km = 2 1 m= 2
cm = 2 m
cm
1 m= 2 3 km = 4 1 1 km = 3
m
50 cm =
km
4 km = 5
cm
7
5.
km
km = 15,000 m
cm
m
Directions: Write <, >, or = to show how the lengths compare. a
10.
1m
b
100 cm
10 cm
1m
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
c
1 m 2
500 cm
Date 109
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Customary to Metric Converting from Customary to Metric isn’t hard. Just use this table.
1 1 1 1
in = 2.54 cm ft = 0.3048 m yd = 0.9144 m mi = 1609 m
Directions: Solve.You may wish to round your answers. a
b
1. 4 in =
cm
200 yd =
2. 6 ft =
m
48 in =
cm
3. 10 in = 4. 2
1 mi = 2
m
c
km m m
7 ft =
km
18 mi =
18 in =
cm
20 in =
m
1 ft = 2 1 mi = 3
m km
Directions: Write <, >, or = to show how the lengths compare. a
b
5. 40 in
40 cm
1m
6. 30 in
3m
1 804 m 3
7. 3 mi
3000 m
6 cm
8. 2 yd
2m
3m=
9. 1 mi
2 km
70 cm
40 in
1 mi 2 2 in
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
c
8m
8 ft
4 yd
4m
10 km
5 mi
90 in
15 in
15 cm
7 in
10 m
11 yd
Date 110
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Convert Metric to Customary Here’s a table you can use to convert Metric to Customary.
1 cm = 0.3937 in 1 m = 39.37 in 1 km = 0.621 mi
Directions: Solve.You may wish to round your answers. a
b
1. 4 cm =
in
1200 m =
2. 2 km =
mi
12 cm =
3. 50 cm =
ft
2m=
mi
100 km =
4.
1 km = 2
c
ft in in
3 m= 4 200 m =
mi
mi
4000 m =
1 km =
in yd yd
Directions: Write <, >, or = to show how the lengths compare. a
5. 22 km 6. 2 m
b
18 mi 6 ft
1 km
621 ft
39 m
3937 in
7. 1 km
3270 ft
6m
8. 621 m
1 mi
1 cm
9. 2 m
72 in
3 yd
1 m 10 1 km 2
9 3 in 10 5280 ft
161 km
100 mi
2.54 in
50 cm
1 y yd 2
1 mi
50 cm
17 in
1609 m
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
c
Date 111
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Look back in the book to find conversion tables, if you need help.
Directions: Write the equation, then solve. Remember to label your answers and show all your work. 1. The movie Shauna is watching is 130 minutes long. How many hours and minutes is that?
2. It took Shauna one and three-fourths hours to do her homework. It took her younger sister, Darcie, thirty minutes to do hers. How much longer did it take Shauna to complete her homework?
3. The temperature outside dropped to freezing.Then it went down another eight degrees Fahrenheit.What was the temperature?
4. Shauna helped Darcie heat a pot of water until it boiled. On the Fahrenheit scale, how hot was the water?
5. How hot is boiling water using the Celsius scale? Freezing water?
6. Darcie compared her braid with her friend's. Darcie's braid is one-and-onefourth foot long. Her friend's is fourteen inches long.Whose is longer?
1 7. Shauna bought 1 pounds of apples at the store. How many ounces is that? 3 3 8. One bag of grapes was 1 pounds, another was 20 ounces.Which bag 4 was heavier?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 112
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Sarah wrote her pen pal Mia in Sweden.When Mia replied, Sarah had to convert the measurements to understand how they compared. Directions: Read the letters.Then answer the questions by converting the measurements in the letters. Hi Mia,
1
We're fine here in Ohio.Today it was 89°F at 9:00 in the morning.Yow! I had to walk 1 mile 3 to the pool.You wouldn’t believe how hot I was by the time I got there! Last month I went to the county fair. I saw a gourd that grew to be 150 pounds! Do you have gourds in Sweden? I think about what you are doing when I am writing.You’re six hours ahead of us. So, when I’m eating dinner, you’re already asleep. Talk 2 yu later, Sarah
Hello, Sarah, I am glad you are well. It is 23°C here.That’s about as hot as it usually gets here. How hot and cold does it get where you live? The lake where we swim is two km away. Sometimes I walk there, and sometimes my mother drops me off on her way to work. Yes, we have gourds. But the biggest one I’ve ever seen weighed about 60 kg.We also have vegetables like carrots, tomatoes, onions, and peppers—and, of course, potatoes. Hej då (it means "bye") Mia
1. Which place is warmer in the summer, Sweden or Ohio? How hot was it in Sweden in F? How hot was it in Ohio in C? 2. Who lives closer to a place to swim, Mia or Sarah? 3. How heavy was the gourd Sarah saw (in kilograms)? Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 113
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Measurement Let’s review what you’ve learned in this unit.
Directions: Use what you have learned to answer the questions. a
1. 2
2 hours = 5
2.
b
minutes
days = 78 hours days
3. 144 hours =
7 hour = 12 1 5. 3 hours = 3
°C
28°C =
°F
82°F =
°C
–36°C =
°F
minutes
115°F =
°C
days = 156 hours
37°C =
°F
days
380°F =
°C
–2°C =
°F
7. 120 hours = 8.
65°F =
minutes
4.
6.
c
2 hour = 3
days
6T =
lb lb =
3 T 4
2.2 lb =
oz lb
4 oz =
3 lb = 4 1 3 T= 10
oz lb
oz = 4 lb
15
1 T= 4
lb
9. Draw three shape to show a right, an acute, and an obtuse angle. Label each angle with its angle name.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 114
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Measurement Did you know you’ve learned so much?
Directions: Use what you have learned to answer the questions. a
1.
in =
2.
1 mi = 8
3.
13,200 ft =
4.
14 ft =
3 ft 4 ft
5000 m =
mi
40 ft =
yd
7.
28 in =
ft
8.
10560 ft =
9.
2 in =
1 1 yd = 12
800 m =
km
km = 750 m
m
75 cm =
2 mi 5
6.
10.
c
cm = 3 m
yd
ft =
5.
b
mi = 100 km
cm
ft
2 km = 3
m
500 cm =
in
cm =
m = 21 in
1 1/2 m =
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
m=
2 mi = 3
km
1 km 5
cm
21 in =
5 m = 8 km yd 1
km
22 mi =
km = 11,000 m
7 1/2 m=
ft
in
1 ft 4 km
in = 16 cm
36 m =
ft
Date 115
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Perimeters Perimeter is the distance around a shape. Find perimeter by adding the length of each side.
4 + 6 + 6 + 2 = 18 ft
Directions: Find the perimeter for each figure. Label your answer. a
b
4 x 4 in
5 + 5 + 3 ft
1.
2.
6+6+6+6+6m
8 + 8 + 3 + 3 mi
3.
top 4, bottom is 2 + 1 + 2, right is 6, left is 7 in.
all cutouts are 1 yard, top and bottom are 4, sides are 3
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 116
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Use the Pythagorean Theorem The Pythagorean Theorem helps you find the lengths of the sides of a right triangle. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25
Directions: Find the length of the unlabeled side. a
b
1. 15 in 9 in
15 in x
2. 10 in x 8 in
3.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 117
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Circumferences Circumference is the distance around a circle.
Pi ( ) is often used when measuring circles. Use the number 3.14 for . To find circumference use the formula: C = d
Directions: Find the circumference. a
b
1.
2.
3.
4.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 118
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Area of Parallelograms Tip is the space inside a figure. Area
If the four-sided figure has all right angles, simply multiply the length times width to find area. If the figure’s angles aren’t 90°, multiply the length times the height. You might have to use the formula for right triangles to find the height.
Directions: Find the perimeter and the area for each figure. a
b
1.
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
2.
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
Date 119
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Area of Triangles To find the area of any triangle, multiply length by height and then divide in Tip half.
Directions: Find the area for each triangle. a
b
1.
2.
3.
4.
Name Math Computation Skills and Strategies, Level 7 Saddleback Publishing, EducationalInc. Publishing ©2006 ©2006
Date 120
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Area of Circles r2
To find the area of a circle, use the formula: A =
The radius (r) is a line from any point on a circle to its center. The radius is half the length of its diameter.
Directions: Find the radius and the area for each circle. Use 3.14 for a
.
b
1.
2.
3.
4.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 121
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Area of Irregular Figures Wondering how to find the area of irregular figures?
To find the area of an irregular figure, divide it up into regular figures, such as squares, triangles, rectangles, parallelograms, and circles.Then find the areas of the regular figures and add them together. For this figure, find the area of part A, a square with sides 2 in.Then find the area of part B, a rectangle 1 in by 2 in. Part A = 2 in x 2 in = 4 in
Part B = 1 in x 2 in = 2 in
4 in + 2 in = 6 in
Directions: Find the area. a
b
1.
2.
3.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 122
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Surface Area Surface area is all the outside area of a three-dimensional figure.To find surface area, find the area of each face, then add to get the total. Remember that some faces may be hidden from view! Directions: Find the surface area for each figure. Show all your work. 1.
front: top: bottom: back: left side: right side: Total surface area:
2.
front: top: bottom: back: left: right: Total surface area:
3.
front: left side: right side: back: bottom : Total surface area:
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 123
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Volumes Volume is how much space is inside a three-dimensional figure. Find volume by multiplying the area of the base times height. Directions: Find the volume for each figure.
a
b
1.
Volume:
Volume:
Volume:
Volume:
Volume:
Volume:
2.
3.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 124
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Real people use real geometry.
Directions: Solve the word problems. 1. Robert is wrapping a gift. Find the circumference to find the length of ribbon he should use to wrap around the gift, find the surface area to find how much wrapping paper he needs, and find the volume to find the amount of Styrofoam peanuts he needs for inside the gift. (Hint: to find the area of the long part of the cylinder, use the circumference of the circle as two sides and the height the other two.)
7 in height Ribbon length:
Amount of wrapping paper:
Amount of styrofoam: 2. Cassie is helping her mom form a concrete patio. Find the missing dimensions from the perimeter given. Find the surface area to know how much paint they'll need and find the volume to know how much concrete they'll need. (Hint: they won't paint the bottom of the patio.Also, you'll need to convert the feet to inches, then back again when working with volume and surface area.)
Height: 2 in Perimeter: 44 ft
Missing side length:
Area to be painted:
Amount of concrete:
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 125
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Here are some more real-world word problems to solve using geometry.
Directions: Solve the word problems. 1. Drake and his friends are building a skateboard ramp. It will look like the drawing below and be made of plywood. Plywood comes in sheets that are four feet by eight feet. How many sheets of plywood will they need to buy to make sure they have enough to build the ramp? (Hint:The ramp has no bottom.) 4 ft
5 ft 3 ft 5 ft
2. An oil storage tank is a cylinder fifty-five feet tall.The radius of the top and bottom is twenty-eight feet. An engineer wants to find out how much oil can be pumped into the tank to fill it to 90 percent of its capacity. Help her find the answer by drawing a picture of the tank, labeling its dimensions, and solving for the answer to her question.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 126
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Geometry You may have to work backwards to find an answer.
Directions: Find the missing dimension on each figure.
1.
Missing side: Perimeter: 30 ft Area: 56 sq ft
2.
Missing side: Area: 72 sq cm
3.
Diameter: Circumference: 153.9 in
4.
Width: Volume: 140 cu yd
5.
Total Surface Area:
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 127
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Geometry Here are some more review problems.
Directions: Find the perimeter and area for each figure. 1.
2.
Directions: Find the circumference and area for each circle. 3.
4.
Directions: Find the volume and surface area for each figure. 5.
6.
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 128
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Find Averages When most people think of an average, they think of a mean.To find the mean, add to find the total, then divide by the number of addends. Directions: Find the average for each set of numbers. Show all your work. 1. 12, 18, 22 2. 54, 47, 80, 59, 38 3. 5, 10, 10, 5, 10, 5, 10, 5, 5, 5, 10 4. 200, 250, 100, 100, 400 5. 1.3, 0.4, 2.1, 0.9, 1.2, 1.8, 1.8 6. 4, 20, 5, 16, 7, 12, 13 7. A group of nine friends took a survey of how many people lived in their homes (including themselves). Find the average number of people in a home. 4, 5, 7, 3, 4, 2, 5, 2, 3
8. Eight students formed a study group. After a test, they compared their scores. What was their average score on the test? 88, 90, 92, 87, 82, 98, 91, 88
9. Ten movie reviewers saw the latest thriller.They all rated the movie on a scale of 1 to 10, 10 being the best. Find the average score of the reviewers. 7, 7, 9, 5, 3, 6, 7, 9, 10, 6
10. Marlie kept track of her math quiz scores for four weeks. Help her find her average for that time. 86%, 90 %, 79%, 82%, 88%, 86%, 91%, 91%, 96%, 89%
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 129
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Figure Probability Probability is the chance of an event occurring.There is a 1 in 6 or 1/6 chance of spinning 1 on the spinner.
1 outcome of a 1 6 possible outcomes
Directions: Figure the probability for each situation. Simplify fractions, if needed. 1. What is the probability of spinning an odd number? 2. What is the probability of spinning a 6? 3. What is the probability for spinning an even number sometime in two spins? 4. What is the probability for spinning four times and getting a 5 more than once? 5. What is the probability for spinning an even or an odd number? 6. What is the probability for spinning a 3 or a 4, then spinning again and getting a 3 or a 4?
You have a bag of 10 buttons: 1 is red, 3 are blue, and 6 are green. 7. What is the probability of pulling out a red button? 8. What is the probability of pulling out a blue button? 9. What is the probability for pulling out a blue button, keeping it out and pulling out another one? 10. What is the probability for pulling out a green button, keeping it out and pulling out a blue one? 11. What is the probability for pulling out a blue button, putting it back and pulling out a red button again? 12. What is the probability for pulling out three blue buttons in a row, keeping each of them out?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 130
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Understand Odds Odds compare the possibility of an event happening to the event not happening. Just as in fractions, you can simplify odds.The odds against spinning an even number on this spinner are 2 to 2 or 1 to 1. Odds of spinning a 3 number of ways to spin a 3 1 1
number of ways to spin anything else to :
3 3
Directions: Write the odds for each situation. Simplify, if needed. 1. What are the odds for spinning an odd number? 2. What are the odds for spinning a five? 3. What are the odds for spinning an even or an odd number? 4. What are the odds for spinning a 1 or a 4, then spinning again and getting a 1 or a 4? 5. What are the odds against spinning a 2,3, or 4? 6. What are the odds for spinning a number greater than 3? 7. What the odds against spinning a number greater than 3? You have a bag of 10 buttons: 5 are red, 3 are blue, and 2 are green. 8. What are the odds for pulling out a red button? 9. What are the odds for pulling out a blue button? 10. What are the odds against pulling out a green button? 11. What are the odds for pulling out a red button, keeping it, then pulling another red button? 12. What are the odds against pulling out a red button, putting it back, and pulling a red button?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 131
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Identify Mean, Median, and Mode You found the mean earlier. Here’s how to find two other types of averages.
The median is the “middle value” of a set of numbers. Half the numbers are greater, half are smaller. The mode is the number that appears most often in a set. If the numbers in a data set aren’t in order from least to greatest, put the numbers in order before you start working with the data set. Directions: Find the mean, median, and mode for each set of numbers. Show your work. 1. A group of friends wrote down the number of telephones each of their families had at home. 3, 4, 2, 3, 5, 4, 2, 1, 3, 4, 3
Mean:
Median:
Mode:
2. Here are Alicia’s math scores for the last month: 85, 89, 94, 91, 87, 88, 87, 93, 90
Mean:
Median:
Mode:
3. Ms. Fernandez decided to remodel her kitchen. She got these estimates of the cost from several builders: $22,500 $20,100 $19,999
$20,100 $17,800 $21,850
$18,000 $22,100 $24, 575
Mean:
Median:
Mode:
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 132
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems You know how to solve these now.
Directions: Solve. Use the space below the problems to work out the answers. 1. Jason made a spinner for his little sister’s board game. It is a circle divided into eight equal parts. Four of them are red, four are yellow.What is the probability his little sister will spin a yellow on her first try?
2. If you had four blue t-shirts, three red t-shirts, and five white t-shirts in a drawer, what are the odds that you would pull out a blue shirt without looking?
3. Imagine you pulled a blue shirt out of your drawer. Now what is the probability that you will pull out a red one? A white one?
4. The probability that you will pull a clear marble out of a marble bag is 1 to 8. The probability that you will pull a green marble out of the same bag is 1 to 6. Are there more clear marbles or green marbles in the bag?
5. There are four kids named Sarah in your math class. If your odds of being paired with a Sarah for a partner project are 1 to 6. How many kids are in your math class?
6. There are 850 tickets for the door prize at a 4-H party.You and your brother each have two tickets.What are the odds of you or your brother winning the door prize?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 133
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Solve Word Problems Now try these.
Directions: Solve. Use the space below the problems to work out the answers. 1. Five friends decided to pool all the money they had in their pockets to buy some pizza. Here’s what they pooled: $2.35, $1.70, $.90, $1.25, and $1.55. Find the mean amount the five friends had.Then find the median.
2. Here are the number of CDs a group of friends has: 23, 26, 18, 19, 31, 17, 22, 19, and 29. Is the mode 22, 19, or 23? Is the median 23, 26, or 19? What is the mean?
3. Rachel has a paper route. Here are the number of papers she delivered one week: 52, 56, 56, 59, 57, 52, and 64. She gets a bonus if she has a mean average of more than 56 papers a week. Did she earn a bonus this week? By how much did she earn or miss her bonus?
4. Donnell hopes to get a 90, or B+, quiz average for this grading period in math. Here are his scores on quizzes so far, with one quiz to go: 88, 90, 91, 87, 89, 84, 95. what grade does he need to get on the last quiz to end up with a 90 mean average?
5. Brandy plays basketball. In her last five games, she scored 15, 8, 12, 14, and 21 points. Her best friend Carly scored 16, 11, 38, 10, and 7.Which friend has the higher mean scoring average?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 134
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Probability This review will help you remember how to find and write odds.
Directions: Look at the spinner and write the odds for each situation. Simplify, if needed.
1. What are the odds for spinning an even number? 2. What are the odds against spinning an even number? 3. What are the odds for spinning a six? 4. What are the odds against spinning a 3 or 4? 5. What are the odds for spinning a number greater than 3? 6. What are the odds against spinning a number greater than 3? 7. Are the odds greater for spinning an even number or a number above 6? 8. What are the odds for spinning a number greater than 3 or an odd number?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 135
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Review Probability You’ll be surprised how much you’ve learned about probability!
Directions: Look at the spinner.Then answer the questions.
1. What is the probability of spinning an even number? 2. What is the probability of spinning an odd number? 3. What is the probability of spinning a six? 4. What is the probability of spinning an eight? 5. What is the probability of spinning a number greater than 4? 6. What is the probability of spinning a number less than 4? 7. Is the probability greater of spinning an even number or a number above 5? 8. Is the probability greater of spinning a number higher than 4 or an even number?
Name Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
Date 136
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Scope and Sequence
Students
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
137
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Answer Key PAGE
6
PAGE
1. I NI I NI I NI 2. NI I NI I NI NI 3. I I NI I NI I 4. I NI I NI I I 5. NI I I NI I I An integer can be a positive whole number, its opposite, or zero. PAGE
7
1. -12 -25 2. -4 -4 3. 21 6 4. -2 -5 5. -320 300 6. 320 -1300 7. -50 36 PAGE
5 -15 20 -100 290 -1 -153
-510 35 60 -770 -884 -42
1. 9 57 2.3 2. 17 -57 5,705 3. 378 4.5 3 1/3 4. 1/5 -4,927 -489 5. 94 -1 14 6. 2 -9 6 7. -8 9 -7 8. 1 9 6 9. = < < 10. > > > PAGE
9
1. B (3,6) C (2,4) D (4,3) E (6,6)
•T •R •N
•V •O
PAGE
•M •P
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
10
2.5 225 15 6 81 10 20 121 900 625
11 144 9 36 2 196 7 4 5 1
4 49 8 625 256 14 100 50 400 1,600
PAGE
626 8 2,401 1,024 0 1,296 81 59,049 1,000 1
216 1 4,096 6,561 729
13
1. = 2. = = 3. = = = 4. Answers for items 5-11 may vary. Sample answers are listed. 5. 14/16 2/12 22/24 6. 1/2 2/8 6/10 7. 2/6 1/2 1/3 8. 9/12 4/14 1/2 9. 6/20 14/18 8/10 10. 4/8 10/16 1/2 11. 4/6 25/30 5/6
2.
PAGE
12
64 64 27 6 81 9 1,024 77 64 125
PAGE
F (8,7) G (8,4) H (9,0)
•S
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
8
11
1. 1 or one 100,000 or one hundred thousand 2. 10 or ten 1,000,000 or one million 3. 100 or one hundred 10,000,000 or ten million 4. 1,000 or one thousand 100,000,000 or one hundred million 5. 10,000 or ten thousand 1,000,000,000 or one billion 6. 102 106 7. 101 + 100 108 8. 104 + 103 107 9. 102 + 101 109 10. 105 + 104 105
169 25 225 9 2,500 30 16 16 17 18
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
14
0.5 0.33 3/4 2/5 0.20 1/8 9/100 0.59 < > > > = = = < =
0.75 0.95 1/10 0.5 1/4 0.6 4/5 2/3
138
0.25 1/2 3/5 0.4 9/10 0.01 9/10 3/1,000
15
1. 1.4 2. 0.125 3. 0.142857 0.05 4. 2.8 5. 0.11 6. 2.2 7. 0.833 8. 1.7 PAGE
1. 2. 3. 4. 5. 6.
17
18
10 40 50 0 3 4 740 1,150 2,610 4,380
PAGE
1. 2. 3. 4. 5. 6.
16
-51 -76 -8 3,157 0.236 -51 40,569 0.001 0.7 5,320 60 2.5
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
3.3 0.4 0.916 2.6 0.18
55 480 -60 -298 < < < < > >
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
2.4 3.6
19
7. 8. 9. 10. 11. 12.
> < > < > <
< < < > > <
< > < > > <
52 68 0.8 3,298 0.326 -5.1 40,579 0.01 0.07 5,302 -58 2.45
357 75 8 3,300 3,536 0.633 -5 5 5.1 51 41,559 0.1 1 -7 5,230 -59 2.4
90 100 120 3 1 10 700 1,200 2,600 4.400
72 59 417 1000 1,000 3,000 4,000
110, 108 130, 131 490, 488 1,140, 1135 7,220, 7,215 140, 139
60, 58 580, 583 1,810, 1,805 6,090, 6,088 140, 142 690, 692
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
PAGE
1. 2. 3. 4. 5. 6.
PAGE
1. 2. 3. 4. 5. 6.
17% 125% 33% 33% 92% 89%
23
25
27
PAGE
PAGE
1. 2. 3. 4. 9.
30
IN R IR IR IN IR IN IN R IN R IR 11 1.1 1,296 20 30 100,000,000 512 2 -7 21 100 9 2.09 in., 2.9 in., 3.24 in., 3.42 in., 3.5 in., 3.6 in.
PAGE
5. 6. 7. 8.
> > = >
< < = <
31
= < = < < > > < < = < < A(1,5) B(2,9) C(2,2)
5. 6. 7. 8. D(6,6) E(7,10)
< < = >
= < = <
3. 6,908 7,424 15,405 11,779 5,668 4. 8,818 9,908 6,350 8,020 15,103 5. 841 4,300 6. 10,345 7,100 PAGE
1. 2. 3. 4.
1. 2. 3. 4. 5. 6. < = > =
1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 6.
•G •J
•D
•A 7. 8. 9. 10. 11. 12. 27 20 2
4/8 8 to 34 5:15 8/39 20 to 39 20:19
4. 20 5. 25 6. 3
28 13 95
5 100 15
5. 6. 7. 8.
I R R R R I I R
3. 100 4. 80
28
7x7 8x8 8/10 = 4/5, 6/10 = 3/5 25%
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
•I • PAGE
1. 2. 3. 4.
E
32
C C 5. A A I I 6. I I A A 7. C C C C Answers for items 8-10 may vary. Sample answers are listed. 8. 100 + 0 = 0 + 100 5 + 0 = 0 + 5 9. 1 + 2 = 3 2 + 1 = 3 10. 5 + (7 + 3) = 15 7 + (5 + 3) = 15 PAGE
1. 2. 3. 4. 5.
33
59 59 118 138 93
PAGE
139 87 132 100 110
152 63 105 89 177
34
98 89 82 86 81
139
51 63 18 13 40 59
PAGE
1. 2. 3. 4. 5. 6. 1. 2. 3. 4.
1,265 2,999
13.4 11.75 0.880 23.23
16.4 8.43 2.783 4.95
9.2 21.59 3.055 10.00
37
38
105 7,269 6.2 9,109 88,759 120.6
39
366,431 10.617 85,318 1,754 283,435 7,419,342
5 11 30 48 11 13
40
205 407 2,864 9 86 3,219
PAGE
140 96 101 100 65
1. 998 350 1,025 1,466 2. 1,430 1,366 5,782 3,789
1. 2. 3. 4. 5. 6.
8.5 4.58 1.892 8.73 15.3 4.014
520 3,993 16.54 781 441 1,606 179.4 3,840 139.55 76.00 13,632 10,980 910 92 1,129 33,957 106,212 1,317,439 4,005,958 140,365 368,677 346,266 4,115,375
PAGE
•F
•C
36
11.7 8.57 0.619 44.06 6.1 14.01
PAGE
•B
35
11,796 54,757 87,999 59,281 59,998 81,561 63,214 117,789 493,870 324,611 499,973 981,101 975,125 1,201,974 3,450,938 9,756,028 5. 140,031 755,324 6. 1,594,405 458,795 PAGE
•H
< = = <
26
1. 49, 72 2. 1/2 1. 2. 3. 4.
0.01 0.05 99/100 25%
24
I R R R R R I R
PAGE
67% 75% 93% 8%
29
-26˚ 0.1237 0.1273 0.1327 0.1372 12/16 6/8 3/4 Rational. It is nonrepeating.
PAGE
87.5 3/10 90% 1.10%
1. 12 11 2. 18 6 3. 27 4 PAGE
75% 133% 88% 15% 80% 56%
1. 2. 3. 4. 1. 2. 3. 4. 5. 6. 7. 8 9. 10.
150% 0.1 0.4 0.1% 80% 0.82 1.32 250% 11. = > > 12. < < <
4 to 11 7:4 7/5 11 to 7 7:39 8 to 8
PAGE
1. 2. 3. 4.
7. 8. 9. 10. 11. 12.
100% 1% 150% 50% 200% 1%
22
50% 2/5 61% 56%
PAGE
1. 2. 3. 4. 5. 6.
21
0.85 2.00 47% 34% 72% 0.98 0.29 100% 0.5 0.15 90% 56% 6% 0.99 0.03 83.5% > = < > < =
PAGE
1. 2. 3. 4.
PAGE
88 7. 25% 112.5 8. 60% 12 9. 11% 17.5 10. 6.66% 3 11. 10% 12 12. 25%
29% 44% 83% 3% 166% 50%
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
20
48 45 27 140 1,000 13
21 9 39 47 6 8
201 731 1,518 2,211 92 8,550
23 34 28 49 27 29
217 68 2,015 4,265
12 29 27 32 59 27 268 4,102 5,779 1,869
316 6,224 7,334 2,603
41
1,110 14,521 23,223 3,115 20,318 76,704 31,181 223,133 217,115 348,711 151,091 260,983 1,113,120 3,698,293 2,895,8878 459,038 5. 38,082 868,615 6. 104.084 2,176,270
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
Answer Key PAGE
1. 2. 3. 4. 5. 6.
PAGE
1. 2. 3. 4. 5.
42
4.4 1.37 0.999 5.728 1.6 2.75
PAGE
4.1 1.91 9.1 3.85 3.47 2.803 1.25 442 2.83 1.792
43
44
1. 52 4,441 2. 7,157 4.163 3. 1.25 70,044 PAGE
4. 3,091 453 5. 322 4,197,631 6. 583,888 52,829
45
1. -10312 -56.87 2. 1,434 1,291 3. 31,095 -1157 PAGE
47
PAGE
5. 27˚
48
49
1,421 17,533 7,007 7,060 2,580
PAGE
1. 2. 3. 4. 5. 6.
3. D 371 4. C 579
125 0.09 seconds 75 pages 211 pages 68,251 people 277 people No, there are 7,552 more people where he lives.
PAGE
50
9.494 803 3,685 129,396 812,889 $66
1. 2. 3. 4. 5. 6. 7. 8. 9.
3 7 5 9 20 54 21 42 24
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
280 2,765 12.247 5,077 85,240
12,981 3,359 25.95 1,198,962 449,339 1,129 26,528 14,612
10.74 205 151,471 3,906 3,480,719 7. $62
1. 2. 3. 4. 5. 6.
8. $77
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
1,2,7 18 2,6,8,24 6,15,45 11 1,2,4,7,8,14,28,56 1,2,11,22 1,5,7,35 1,2,4 1,2,4,7,14,28
54
55
56
354 126 120 259 140
114 correct 162 correct correct 8
249 112 819 416 292
432 485 310 459 511
140
276 504 261 68 320
180 116 490 351 224
57
63,147 10,772 18,766 15,010 53,118 63,832
PAGE
53
correct 201 33 correct 96 9.6 80
PAGE
1. 2. 3. 4. 5.
52
1. 2. 3. 4. 5. 6.
C 1,2,3,6,9,18 C 1,3,9,27 C 1,3,7,9,21,63 P 1,41 C 1,7,49 C 1,2,5,6,10,14,35,70 P 1,97 P 1,29 C 1,2,29,58 C 1,3,9,81 C 1,3,5,7,15,21,35,105 C 1,5,25,125 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
PAGE
1. 2. 3. 4. 5. 6. 7.
PAGE
2 7 3 and 6 2,4, and 8 22 64 70 42 114
11 31 7. 1,2,19,38 5 43 8. 1,2,3,6,7,14,21,42 19 13 9. (prime) 1,19 29 73 10. 1,3,17 17 37 11. 1,5,13,65 (prime) 1,47 12. 1,7,11,77
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
51
2, 8 5,2,10 3 5,6,3,10 5,1 1,2,4,8 1,3,5,15 1,2,4,8,16 1,19 1,2,3,4,6,8,12,24
PAGE
46
1. B 371 2. A 579 feet
1. 2. 3. 4. 5.
4. 5.7 108,190 5. 4,010 -6,233 6. -1,124 -2,254
1,062 6,637 99,719 520 correct 176 correct 22,018 1,183,647 1,925 correct 6,028 No, he has 48 to go.
PAGE
1. 2. 3. 4. 5. 6. 7.
4.952 7.56 14.85 1.39
23 118 247 489 55 82 1,874 5,843 6,807 23 1,867 2,459 3,895 6,882 904 27,704 549,092 913,936 362,630 2,086 199,004 899,856 2,238,036
PAGE
1. 2. 3. 4. 5.
3.543 7.5 2 8.01
38,940 17,484 50,175 72,056 21,603 10,880
58
1. 29,395,604 19,895,966 2. 20,688,997 22,944,116 3. 51,407,136 51,826,692 4. 10,801,554 23,797,018 5. 19,914,764 10,311,021 6. 34,741,130 19,098,315 PAGE
1. 2. 3. 4. 5.
PAGE
1. 2. 3. 4. 5.
60
5,766 1,056 1,221 3,552 1,682
PAGE
1. 2. 3. 4. 5.
59
13 52.2 17.1 25.6 33.58
61
1.371 13.71 13.71 137.1 1.371
2,432 1,377 5,766 6,461 2,352
2,625 1,666 2,292 3,690 4,416
115,232 314,928 268,710 114,972 215,336
62
1. 427,605,408 58,893,345 2. 337,521,534 173,130,062 3. 153,396,440 134,539,197 4. 123,079,762 466,178,910 5. 35,706,132 73,317,738 PAGE
1. 2. 3. 4. 5.
19,269 44,080 39,572 51,590 12,670 27,545
43,661 18,642 67,648 23,367 37,891 30,450
13,378,400 12,784,990 26,477,634 36,537,696 44,049,710 28,896,912 24,896,683 17,044,097 23,461,875 30,086,904 21,400,205 10,229,910
53.1 2.58 .304 .264 33.32
123,975 486,962 115,785 306,545 392,015
PAGE
23,784 11,626 82,638 28,420 31,388 58,320
569.52 16.85 .2352 18.116 532
429 1.55 5.778 81.81 .0948
1,458 5,096 1,271 2,736 1,610
416,102 64,120 291,031 31,598 420,210
135,783 203,785 839,608 97,716 679,244
183,968,777 238,517,396 211,705,270 177,320,832 821,833,760 324,136,566 754,719,976 820,517,416 464,599,737 140,467,498
63
22.2 65.7 155.4 46.48 851.73
18.24 45.327 114.84 59.29 16.426
17.864 316.96 567.27 16.6848 29.5792
4.59675 17.1353 171.353 1713.53 17,135.3
3 Watson, Irvine, CA 92618 Phone (888) SDL-BACK www.sdlback.com
PAGE
1. 2. 3. 4. 5. 6.
PAGE
1. 2. 3. 4. 5.
1. 2. 3. 4. 5. 1. 2. 3. 4.
9. 10. 11. 12. 13. 14. 15.
350,030 154,024 3,268,235 2,743,691 1,627,077 541,572 2,120,985
65 R1 345 1,011 1,735 R1 210
412 R4 519 57 R1 659 R2 38 R7
33 R1 7,704 49 R6 404 R2 721 R1
68 6.29 6.667 4 9.5 12.6
24.33 33.667 177.5 120 59.11
620.875 842 777.667 1,142.5 892.57
5 2.714 3 6.72 2.54
3.58 2 6 5 2.838
6 3.74 1.92 3.77 1.33
70 81 44.88 142 52.05 62.90
61.08 65 14.1 253.35 92
71 2.8 0.064 2,133.33 450
2.42 2,300 390 0.716
4.1 1,020 0.0185 0.734
72
1. $855 2. $2.38 3. $1,282.50
PAGE
4. $3.32 5. 12 campers per cabin 6. 6 tents
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
74
252 31,015 21 178 1,130,907 76,501,917
4. 5. 6. 7.
3,195 335,853 190,625,640 1,014 881 6
3.39 yards 6 teams 8 teams 27 points 368.5 8.2 30 13 1,010 858.5
14.72 196.9 4.41 0.89 4,919.33 126.063
75
1. 325,754,744 47.73 18,281,853 6.86 2. 1,277,782.57 396,573 8.1667 32.424 3. 6,232 45,318 272 50.81 4. 7.46 32,736 7 50.413 5. 4,8,12,16,20,24 7,14,21,28,35,42 13,26,39,52,65,78 6. 1,2,4,8,16,32 1,2,4,7,8,14,28,56 1,2,3,4,6,8,12,16,24,32,48,96 7. 11,29,19,2,5,41 PAGE
1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6.
78
1/2 3/5 1/2 4 2/5 2 3/7 5 2/3
PAGE
1. 2. 3. 4. 5. 6.
77
1 1/6 5/12 15/16 1 2/21 1 5/18 1 1/42
PAGE
1. 2. 3. 4. 5. 6.
76
2/3 1 1 2/5 8/9 2 5 5/6
PAGE
69
0.7 2.9 340 900
PAGE
652 547 763 2,256 583
1. 2. 3. 4. 5. 6.
PAGE
62 39 103 98.03 82
PAGE
1,947 2,411 430 1,772 399
67
3 7.33 2 2.25 7
PAGE
PAGE
66
3.75 5.2 3.43 6 6.83
PAGE
1. 2. 3. 4. 5.
528 684 952 358 641
73
1. 5 2. No, there will be 4 too few. 3. 2.5 yards
6 21 23 13 12 14
65
5 R2 12 R3 27 R2 1,660 R4 1,289 R4
PAGE
1. 2. 3. 4. 5.
17 29 23 21 7 9
2,168,093 577,558 1,332,600 3,251,105 472,368 1,627,003 1,873,979 919,620
PAGE
1. 2. 3. 4. 5.
PAGE
20 19.5 28 24 11 14
477 846 367 1,107 1,958
PAGE
1. 2. 3. 4. 5. 6. 7. 8.
64
16 19 5 21 12 11
1/2 1 2/5 10 1/5 3 7 1/3 9 1/2
7. 8. 9. 10. 11. 12.
5 4/5 10 1/3 10 1/4 8 2/3 2/3 11
3 4/5 7. 11/12 2 11/12 8. 34/35 13 1/4 9. 7/8 3 29/45 10. 1 3/14 4 1/2 11. 5 7/20 6 13/21 12. 4 17/18
7 5/6 3 1/10 7/10 1 7/8 1 4/9 4 19/20
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
4/11 1/4 0 4 1/2 4 2/3 4 2/5
5/24 23/36 1/6 1 5/11 32/63 7/12
39/70 13/18 13/48 5 3/8 2 1/4 2 1/15
141
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
83
36 1 14 4 1/2 32 1/32 6/7 90 3 2
84
1 1/6 1 5/7 10 6/9 3 1/3 1/2 3 6/7 8 1/2 1 1/14 2 2/5 1 5/13
PAGE
1/4 3/14 -1 1/10
1/3 9/50 3 1/3 3/5 1/5 7/32 15 2/11 1/7 21/50
5/12 1 1/4 7/90 6 3/4 5/21 8/25 3 1/2 6 1/4
3 4/15 15 3/5 1 23/45 5/14 2 7/24 12 1 2/3 18 3/4 9 1/3
1 13/50 34/49 7 1 11/45 10 10 1/2 10 5/9 22 2/7 13 1/2 26
82
1 1/3 15/16 41 8 33 2 1/24 13/16 10 5/6 18 3/5 4 1/8
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
81
1/2 4/15 2/7 1/12 5/32 3/8 1 1/3 1 4/5 5 2
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
80
P P N N N P 1/8 13/15 -1 1/8 -39/40 -5/12 19/40
PAGE
4/15 2/7 2/9 3 1/2 1 3 2/8
79
4/35 1/4 2/15 2 1/4 1 3/5 4 1/9
1 1/7 7/9 8/11 2/3 4 1/4 8 2/3
1. 2. 3. 4. 5. 6.
85
1. N P P 2. N N P 3. N P P
2/3 2 1/3 1 2/5 2 1/4 1 3/4 15/16 5/6 2 1/2 14/15 19/36 41 2 1/13 13 9/16 1 1/4 8/165 48/49 1 1/2 25/62 2 10/33 4. -7/40 5. 1 1/4 6. -28
-9 -1 1/8 -15/56
1/6 10 -1
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Answer Key PAGE
86
PAGE
1. 1 2/3 hours 2. 5 hours 3. 1 11/27 PAGE
1. 2. 3. 4. 5.
C D A E B
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8.
18 34 10/11 1 gallon 10 1/8 2 3/16
88
89
-1/2 -1/3 5/12 -16/21 3 7/40 B 1/2 A 2/3 C 1/2
PAGE
1. 2. 3. 4. 5. 6. 7.
87
2/3 1 2/5 2 1/2 14/15 1/3 3/7 8 4/5 2 3/4
PAGE
90
11 28 4.667 17 36 27 21
PAGE
1. 2. 3. 4.
6 7 15 4
PAGE
1. 2. 3. 4.
11 11 2 -3
92
6 13 2 4
93
2 6 90 8
94
2. 6. 7. 8. 9. 10.
32 48 3 3 4
11. 12. 13. 14. 15.
•
1 2 2 1 13
9
1/10 1 13/20 15/16 1 1/2 16 5/12 5 7/15 2 1/40
PAGE
2.78 23 190 350 190 105 1,080
PAGE
•
6 5
•
4 3
95
•
2 1
0 1 2 3 4 5 6 7 8 9 jade plant growth in inches
96
PAGE
1. a. Plot these points: (2,1) (4,2) (6,3) 1. b. Plot these points: (1,3) (2,6) (3,9) 2. a. Plot these points: (3,1) (5,2) (7,3) 2. b. Plot these points: (3,2) (5,3) (7,4)
-1/8 -10 4/15 49/64 -91/100
•
8 7
1. a. Plot these points: (2,0) (3,1) (4,2) (5,3) (6,4) 1. b. Plot these points: (0,1) (1,2) (2,3) (3,4) (4,5)
7/20 -9/16 -5/21 -29/45 -1 3/10
91
1 10 2 3 2
PAGE
2/5 1/14 1 3/35 5/12 1/10 9/20 6 7/12 3 5/7
1. 52 inches 2. 1.5 minutes PAGE
1. 2. 3. 4. 5.
4. 8:57 5. 1 9/20 6. 8 3/4
100
1. D PAGE
1. 2. 3. 4.
8 2 3 8
PAGE
2. B
101 3 11 45 6
PAGE
1.
9 8 4 18
5. 6. 7. 8.
4. C
5 9 3 16
36 18 20 12
4 8 7 4
102
1. x: 2,4,6,8,10 y: 2,3,4,5,6
97
1. a. Plot these points: (1,2) (2,4) (3,6) 1. b. Plot these points: (3,1) (6,2) (9,3) 2. a. Plot these points: (2,3) (3,6) (4,8) 2. b. Plot these points: (0,1) (3,2) (5,3)
945 20 48 -16 25 15 50
3. A
• • • • •
98 2. x: 1,2,3,4,5 y: 0,1,2,3,4 •
27
•
24 21
• •
18 15
• •
12 9
3. $360 4. $20
6 3
23 14 14 6
5. 6. 7. 8.
8 13 7 15
72 5 6 3
7 7 3 3
31 5 16 2
5. 6. 7. 8.
5 7 7 18
36 5 60 14
6 6 3 8
•
•
•
•
•
•
• •
5 10 15 20 25 30 35 40 45 pounds
PAGE
1.
99
3. •
900
400
800 700
300
•
600 500 400 300
•
•
200
• •
•
100
•
200 100 0
1
2
3
4
100
200
300
400
food in grams
hours of exercise
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
142
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PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
104
6,000 500 72 1/8 24
1. 2. 3. 4. 5. 11.
106
1. 2. 3. 4. 9.
5,000 48 10,500 3/4 1/32
3. C 4. Answers will vary.
108
109
8 1,760 1.75 3.67 3,168
cm cm m m 0.1 200 1,000 3 0.01 0.5
6.67 6. 2.67 7. 1,760 8. 3,520 9. 880 10.
< = > < >
> > = > <
3. cm km 4. km m 750 750 1,333
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
> = < > =
0.00005 8,000
0.18288 1.22 2.1336 28.96
PAGE
45.72 0.508 0.1524 0.536
249 29.53 218.72 1,093
5. 6. 7. 8.
< > > <
112
1. 2. 3. 4. 5. 6. 7. 8. 9.
144 3.25 6 35 200 6.5 5 .0277 Answers
PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
115
9 660 2.5 4.67 2,112 13.33 2.33 3,520 0.167 39
PAGE
12,000 1,500 35.2 0.25 12 6.200 64 30,500
300 5 0.75 0.75 11 750 625 1,666.67 0.005 20,000
2,624.67 62.14 35.41 53.34 0.533 59.1 0.076 1.07 6.3 118.11
119
1. 28 yd, 49 sq yd 2. 44 in, 112 sq in PAGE
120
9 ft2 113.5 cm2 48 in2 6 m2
121
3.14 in2 63.6 yd2 16 in2 0.13 in2
PAGE
18.33 82.4 27.7 -32.8 46.1 98.6 193.3 28.4 will vary.
143
= < = >
1. 2. 3. 4.
1. Ohio is warmer. 73.4˚F 89˚F 2. Mia 3. 68 kilograms
114
> < > <
20 inches 28 inches 24 inches 25.13 feet 56.55 meters 78.54 centimenters 50.27 centimeters 10 ft, 6sq ft 36 cm, 81 sq cm 600 in2 151.8 yd2 144 ft2 170 in2 201.06 ft2 346.4 m2 113.1 cm2 572.56 cm2
122
1. 25.94 in2 2. 26 in2 3. 15 in2 PAGE
75 feet 24 miles 22 yards
118
6.28 inches 12.6 yards 11 inches 0.94 inches
PAGE
113
117
1. 12 inches 2. 6 inches 3. 45 inches
1. 2. 3. 4.
2 hours 10 minutes 1 hour 15 minutes 24˚F 212˚F 100˚F 0˚F Darcie’s; by 1 inch 21.33 ounces 1.25 pounds
PAGE
PAGE
1. 2. 3. 4.
111
116
1. 16 inches 2. 30 meters 3. 22 inches
PAGE
1.57 3,937 1.24 4.72 1.64 78.74 0.31 62.14 > = >
PAGE
1. 2. 3. 4. 5. 6. 7. 8.
110
10.16 1.8288 25.4 4,023.36 > > > < < < > > > < > > < > <
PAGE
107
1,760 3 1 102 1,320
PAGE
1. 2. 5. 6. 7.
-7.2 39.2 -26.1 4.44 -108.4
CD, MN 6. 120o AB, JK 7. Right angle Acute 8. 90o 45o 9. 45o Obtuse 10. 60o Answers will vary for item 11.
PAGE
1. 2. 3. 4. 5.
1. 2. 3. 4. 5. 6. 7. 8. 9.
PAGE
1. A, D 2. B, D PAGE
PAGE
105
8 2 1/2 80 3 1/4 > = > > < > < > >
PAGE
8. 500 0.8 9. 50 15 10. = < <
195 2 1/6 6 11/12 40 132 3 1/6 330 168 9,840 15 minutes
33.33 15.5 69.8 28.4 26.67 -13.3 5 32 39.2 197.6 < > = > < = < = > < < < = > <
PAGE
1. 2. 3. 4. 5. 6. 7. 8.
103
6 15 12 30 240 72 270 144 5.42 5 hours
28 in2 13.57 in2 13.43 in2
123
1. 36,36,36,36,36,36,216 m2 2. 98,98,98,98,28,28,448 in2 3. 80,80,80,80,100,420 yd PAGE
124
1. 216 yd3 2. 424.12 ft3 3. 432 cm3 PAGE
125
1. 43.98 2. 10 in PAGE
1,280 in3 192 m3 25,735 yd3
13,541 in2 123.6674 ft
153 in3 20.004 ft3
126
1. 3 sheets of plywood 2. 121,918.93 ft3 PAGE
127
1. 8 ft 4. 5 yd
2. 12 cm 3. 14 in 5. 184 in2
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Answer Key PAGE
128
1. 26 m 2. 18 ft 3. 15.708 in 4. 37.7 in 5. 1485 cu ft 6. 1024 cu in PAGE
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
130
131
1:1 0:4 1:0 1:1
PAGE
PAGE
5. 6. 7. 8.
6/6 1/9 1/10 3/10
9. 10. 11. 12.
1/15 1/5 3/100 1/120
5. 6. 7. 8.
1:3 1:3 3:1 1:1
9. 10. 11. 12.
3:7 4:1 4:5 1:1
3 3 89 87 20,100 20,100
133
134
1.55 1.55 19 22 23 Yes. By .57 96% Carly
PAGE
1. 2. 3. 4.
3:7 3:7 even even
1/2 1/3 3/11 5/11 green marbles 24 kids 2/425
PAGE
1. 2. 3. 4. 5.
5. 6. 7. 8.
132
1. 3.09 2. 89.3 3. 20,780.4 1. 2. 3. 4. 5. 6.
136
3:7 4:7 1:7 0
129
1/2 1/6 1/2 1/1296
PAGE
1. 2. 3. 4.
1. 2. 3. 4.
17.3 55.6 7.27 210 1.36 11 3.8 72.25 6.9 87.8%
PAGE
1. 2. 3. 4.
PAGE
24 sq m 14 sq ft 19.64 sq in 113.1 sq in 798 sq ft 640 sq in
135
1:1 1:1 1:8 3:4
5. 6. 7. 8.
5:3 2:5 even 3:2
Math Computation Skills and Strategies, Level 7 Saddleback Educational Publishing ©2006
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MATH COMPUTATION SKILLS & STRATEGIES Every book in the Math Computation Skills and Strategies series contains over 100 reproducible pages.These highinterest activities combine computation practice with strategy instruction. Featuring a Scope and Sequence chart, the books allow educators to supplement their math lessons with the extra math practice all students need. In addition, periodic reviews allow for reinforcement and assessment of skills.
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The books are grade specific, but they were created with students of all ages in mind. Each book features ready-to-use pages with instructional tips at the beginning of each lesson. Math Computation Skills and Strategies reproducible books are the perfect choice for educators.
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MATH COMPUTATION SKILLS & STRATEGIES Operations Fractions and Decimals Whole Numbers Perimeter and Area Regrouping
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Solving Word Problems Money Measurement
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100 plus+ REPRODUCIBLE ACTIVITIES
