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MILLIKEN PUBLISHING COMPMILLIKEN PUBLISHING COMPANY ANY STST. LOUIS, MISSOURI. LOUIS, MISSOURI
MP3443
Bonus
Assessment
Pages!
Reproducibles66 –– 88
SUPPLEMENTS�THE NCTM�
STANDARDS
Reproducibles
MP3443 Algebra IAuthor: Sara FreemanEditor: Fran LesserCover Design and Illustration: Cathy TranInterior Illustrations: Yoshi MiyakeInterior Design: Sara FreemanProduction: Linda Price, Sasha GovorovaProject Director: Linda C. Wood
ISBN: 0-7877-0508-XCopyright © 2002 Milliken Publishing Company11643 Lilburn Park DriveSt. Louis, MO 63146www.millikenpub.comPrinted in the USA.All rights reserved.
Developed for Milliken by The Woods Publishing Group, Inc.
The purchase of this book entitles the individual purchaser to reproduce copies by duplicating master or by any photocopyprocess for single classroom use.The reproduction of any part of this book for commercial resale or for use by an entireschool or school system is strictly prohibited. Storage of any part of this book in any type of electronic retrieval system isprohibited unless purchaser receives written authorization from the publisher.
Milliken Publishing Company St. Louis, Missouri
Table of Contents
Math Symbols . . . . . . . . . . . . . . . . . . . . . . 3
Number Properties . . . . . . . . . . . . . . . . . . . 4
Order of Operations I (MDAS) . . . . . . . . . . 5
Exponents . . . . . . . . . . . . . . . . . . . . . . . . . 6
Order of Operations II (PEMDAS) . . . . . . . 7
Evaluating Expressions . . . . . . . . . . . . . . . 8
Writing Equations . . . . . . . . . . . . . . . . . . . . 9
Solving Equations . . . . . . . . . . . . . . . . . . 10
Two-Step Equations . . . . . . . . . . . . . . . . . 11
Equation Word Problems . . . . . . . . . . . . . 12
Graphing Inequalities . . . . . . . . . . . . . . . . 13
Solving Inequalities . . . . . . . . . . . . . . . . . 14
Divisibility Tests . . . . . . . . . . . . . . . . . . . . 15
Greatest Common Factor . . . . . . . . . . . . . 16
Square Roots . . . . . . . . . . . . . . . . . . . . . . 17
Scientific Notation . . . . . . . . . . . . . . . . . . 18
Fractions, Decimals, Percents . . . . . . . . . 19
Percent Problems . . . . . . . . . . . . . . . . . . . 20
Adding & Subtracting Fractions . . . . . . . . 21
Multiplying Fractions . . . . . . . . . . . . . . . . 22
Dividing Fractions . . . . . . . . . . . . . . . . . . . 23
Equations With Fractions . . . . . . . . . . . . . 24
Absolute Value . . . . . . . . . . . . . . . . . . . . . 25
Adding Integers . . . . . . . . . . . . . . . . . . . . 26
Subtracting Integers . . . . . . . . . . . . . . . . . 27
Integer Magic Squares . . . . . . . . . . . . . . . 28
Multiplying Integers . . . . . . . . . . . . . . . . . 29
Dividing Integers . . . . . . . . . . . . . . . . . . . 30
Integer Expressions . . . . . . . . . . . . . . . . . 31
Equations With Integers . . . . . . . . . . . . . . 32
Graphing Vocabulary . . . . . . . . . . . . . . . . 33
Ordered Pairs . . . . . . . . . . . . . . . . . . . . . . 34
Graphing Points . . . . . . . . . . . . . . . . . . . . 35
Scatterplots . . . . . . . . . . . . . . . . . . . . . . . 36
Table of Values . . . . . . . . . . . . . . . . . . . . 37
Graphing Linear Equations . . . . . . . . . . . 38
Slope-Intercept Form . . . . . . . . . . . . . . . . 39
Slope-Intercept Graphs . . . . . . . . . . . . . . 40
Assessment A—Whole Numbers . . . . . . . 41
Assessment B—
Fractions, Decimals, Percents . . . . . . 42
Assessment C—Integers . . . . . . . . . . . . . 43
Assessment D—Graphing . . . . . . . . . . . . 44
Answers . . . . . . . . . . . . . . . . . . . . . . . 45–48
Find and circle the name of each symbol in the puzzle. (The words go across and down.)Then write the names by filling in the blanks.
© Milliken Publishing Company 3 MP3443
Name _________________________________ Math Symbols
= __ __ __ __ __ __
< __ __ __ __ __ __ __ __
> __ __ __ __ __ __ __ __ __ __ __
+ __ __ __ __ or __ __ __ __ __ __ __ __
– __ __ __ __ __ or __ __ __ __ __ __ __ __
x or · __ __ __ __ __
÷ or ) ___
__ __ __ __ __ __ __ __ __
__ __ __ __ __ __ __ __ __ __
% __ __ __ __ __ __ __
: __ __ __ __ (ratio)
| |__ __ __ __ __ __ __ __ __ __ __ __ __
p __ __
^ __ __ __ __ __ __ __ __ __ __ __ __ __
| | __ __ __ __ __ __ __ __
– __ __ __ __ __
__ __ __ __ __ __ __ __ __ __
\ __ __ __ __ __ __ __ __ __
el tg tp pm n
td b
s rpi ta vpppar at
g r e a t e r t h a n
i s t o g e t h e s e
a p a r a l l e l q g
e s b e i s s r l u a
p o s i t i v e m a t
e r o l m u n f o r i
r l l t i a u o t e v
p l u s n n r r l r e
e r t e u g p e m o s
n f e e s l y f h o m
d i v i d e d b y t p
i n a n t a t e e h e
c s l e s s t h a n r
u o u s n t i m e s c
l n e q u a l s e d e
a t t e p i m a t h n
r i g h t a n g l e t
Play these tic-tac-toe games witha partner. To earn an X or O fora box, write a sample problemthat supports the statement orexplains the property.
© Milliken Publishing Company 4 MP3443
Name _________________________________ Number Properties
The AssociativeProperty ofMultiplication
(a • b) • c =a • (b • c)
The DistributiveProperty
a • (b + c) =(a • b) + (a • c)
Subtractionis notcommutative. For mostnumbers, a – b ≠ b – a.
The IdentityElement forAddition is 0.
a + 0 = a0 + a = a
The sum of anumber and itsopposite(additiveinverse) is 0.
a + –a = 0
Division is notcommutative. For mostnumbers, a ÷ b ≠ b ÷ a.
The AssociativeProperty ofAddition
(a + b) + c =
a + (b + c)
The product ofa number andits reciprocal(multiplicativeinverse) is 1. a • = 1
Zero is not anidentityelement forsubtraction.
a – 0 = a, but0 – a ≠ a.
TheCommutativeProperty ofAddition
a + b = b + a
The IdentityElement forMultiplicationis 1.
a • 1 = a1 • a = a
Subtraction isnot associative. For mostnumbers, (a – b) – c ≠a – (b – c).
One is not anidentity elementfor division.
a ÷ 1 = a, but1 ÷ a ≠ a.
The DistributiveProperty
a • (b – c) = (a • b) – (a • c)
Division is notassociative. For mostnumbers, (a ÷ b) ÷ c ≠a ÷ (b ÷ c).
TheCommutativeProperty ofMultiplication
a • b = b • a
The ZeroProperty ofMultiplication
a • 0 = 00 • a = 0
Division by zerois undefined.
a ÷ 0 is undefined
1a
Tip! To remember the CommutativeProperty, think of a commuter train.It takes people back and forth.
Tip! To remember the AssociativeProperty, think of friends. You associatewith different groups of friends.
This problem proves divisionis not associative:
(100 ÷ 10) ÷ 2 ≠ 100 ÷ (10 ÷ 2)For the left-side problem,you get 10 ÷ 2 = 5. But forthe right-side problem, you
get 100 ÷ 5 = 20. 5 ≠ 20
Complete these number puzzles. Fill in the boxes with the correct operation symbols,choosing from x, ÷, +, and –. Each equation should have two different operations. Followthe correct order of operations to check each horizontal problem and vertical problem.
© Milliken Publishing Company 5 MP3443
Name _________________________________ Order of Operations I
18 4 2 = 10
18 – 4 x 2 = 10
14 x 2 = 1028 ≠ 10
Wrong!
Right!
Tip
Use the phrase, My Dear Aunt Sally, to remember the order of operations—Multiplication and Division, then Addition and Subtraction.
1. Multiply and divide in order from left to right or from top to bottom.
2. Add and subtract in order from left to right or from top to bottom.
18 4 2 = 10
18 – 4 x 2 = 10
18 – 8 = 1010 = 10
6 5 6 = 24
3 24 2 = 15
2 6 2 = 5
= = = =
12 1 10 = 21
5 4 2 = 18
3 9 24 = 3
3 3 3 = 12
= = = =
14 7 16 = 18
A.
B.
Solve the problems. Write the letter above each matching answer to finish the sentences.
© Milliken Publishing Company 6 MP3443
Name _________________________________ Exponents
Remember
1. In the expression 24, 2 is the base and 4 is the exponent.
An exponent tells how many times the base is used as a factor.
2. A number with an exponent of 1 is the number itself. 21
= 2
24
= 2 x 4 = 8
A. 62
= ______
B. 122
= _______
C. 53
= _______
D. 103
= ________
E. 101
= ______
F. 25
= ______
G. 42
= ______
H. 72
= ______
I. 202
= _______
J. 102
= ______
K. 51
= ______
L. 22
= ______
M. 111
= ______
N. 32
= ______
O. 03
= ______
P. 63
= ______
Q. 35
= _______
R. 23
= ______
S. 71
= ______
T. 43
= ______
U. 17
= ______
V. 92
= ______
W. 33
= ______
X. 52
= ______
Y. 112
= ______
Z. 31
= ______
24
= 2 x 2 x 2 x 2 = 16
Wrong!
Right!
___ ___ ___ ___ ___ ___ ___7 243 1 36 8 10 1000
___ ___ ___ ___32 400 81 10
___ ___ ___ ___ ___125 1 144 10 1000
___ ___ ___ ___32 0 1 8
___ ___ ___64 49 10
___ ___64 0
READ 52
AS “
POWER.” READ 43
AS “
OR “FOUR TO THE POWER.” READ 24
AS “
” OR “FIVE TO THE
”
.”
___ ___ ___ ___ ___ ___7 10 125 0 9 1000
___ ___ ___ ___ ___ ___32 0 1 8 64 49
___ ___ ___ ___ ___64 49 400 8 1000
___ ___ ___ ___ ___216 0 27 10 8
___ ___ ___64 27 0
© Milliken Publishing Company 7 MP3443
Name _________________________________ Order of Operations II
Use the order of operations to solve these problems.Follow the correct answers through the maze.
[36 – (22
x 3)] ÷ 3 =
[32 x 3 ] ÷ 3 =
96 ÷ 3 =
= 32
Tip
1. Do the operations within parentheses or other grouping symbols first. If there ismore than one set, begin with the inner group.
2. Use PEMDAS or the phrase Please Excuse My Dear Aunt Sally to rememberthe order of operations: Parentheses, Exponents, Multiplication and Division (inorder from left to right), then Addition and Subtraction (in order from left to right).
[36 – (22
x 3)] ÷ 3 =
[36 – 12 ] ÷ 3 =
24 ÷ 3 =
= 8
1. 12 – (3 + 5) = _____
2. 32
+ 8 ÷ 2 = _____
3. 36 ÷ (6 + 6) = _____
4. (4 + 5) x (10 – 2) = _____
5. 102
– 5 x 12 = _____
6. (52
+ 15) ÷ 5 = _____
7. 7 + 5 x 8 = _____
8. 3 x (12
+ 42) = _____
9. (11 x 6) ÷ (2 + 1) = _____
10. [16 + (11 – 3)] ÷ 4 = _____
11. 48 – [(22
+ 3) x 5)] = _____
12. 48 – [22
+ (3 x 5)] = _____
13. 4 + 5 x 10 – 2 = _____
14. 11 x 6 ÷ 2 + 1 = _____
15. 23
+ 7 x 6 = _____
16. 62
÷ [(4 – 1) x ( 3 + 9)] = _____
Wrong!
Right!
59
51205
90
29
18
613
9
284714
4
12
13 3
72
40
1,140
90
8
19
88 22
152
34 50
172
Evaluate each expression given that a = 3, b = 5, and c = 2.
© Milliken Publishing Company 8 MP3443
Name _______________________________ Evaluating Expressions
1. a + b = _____
2. 14 = _____
3. 4b + c = _____
4. b – 2c = _____
5. 5b = _____
6. 10a = _____
7. 2b – 2a = _____
8. 7ac = _____
9. ab + c = _____
10. a 2 = _____
11. 3a 2 = _____
12. (3a)2 = _____
13. (a + b)(b + c) = _____
14. 2(a + c) = _____
15. b(c 2 + a) = _____
16. 6bc = ______
17. (2a – c)2 + b = ______
18. a2c 2 + 2(b + c) = _____
c
b
b
a + c
b
Remember
1. Follow the order of operations (PEMDAS) when evaluating expressions.
2. A fraction bar is a grouping symbol. It indicates division.
3. When a number or letter is written next to a letter, it indicates multiplication.
9b + c 2
a + c 2= (9b + c 2) ÷ (a + c 2)
Given a = 3, b = 5, and c = 2,evaluate the expression.
=
=
= 15
Given a = 3, b = 5, and c = 2,evaluate the expression.
=
=
= 7
9b + c 2
a + c 2
9(5) + 43 + 4
453
9b + c 2
a + c 2
[9(5) + 4](3 + 4)
497
9b = 9(b) or 9 • b or 9 x b
Use the answer code to find the name of an importantArabic math scholar and the place where he studiedin Baghdad in the 800s. The word algebra comesfrom the title of his math work.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ; ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 8 17 81 42 6 21 8 56 4 10 9 4 25 27 35 2 22 27 1 12 4 2 7 27 9
a
d
e
f
H
h –
i
K
l
m
o
r
s
u
W
w
z
8
a a
Wrong!
Right!
Draw straight lines to match up the sentences and equations. Then write the missingequation in each set. The uncrossed letters will spell out a message.
© Milliken Publishing Company 9 MP3443
Name _________________________________ Writing Equations
Twelve is three more than x.
Twelve is half of x.
X decreased by two is twelve.
One more than twice x is twelve.
Eighteen is nine less than x.
The product of nine and x is eighteen.
X divided five is eighteen.
The sum of five and x is eighteen.
Twice x is thirty.
The difference of x squared and thirty is five.
X is five more than thirty.
X is thirty squared.
One number is seven times another number.
One number is seven less than another number.
One number squared is seven more than another number.
Seven times one number is half of another number.
Six times a number is ten more than the number.
Double a number plus ten is six times the number.
Sixty-three is three times a number.
Sixty-three increased by a number is ten times the number.
12 = x
2x + 1 = 12
12 = x + 3
______________
5 + x = 18
18 = x – 9
x = 18
______________
x = 302
x = 30 + 5
2x = 30
______________
x 2 = y + 7
x = y – 7
x = 7y
______________
63 + x = 10x
63 = 3x
2x + 10 = 6x
______________
1.
2.
3.
4.
5.
••••
••••
••••
••••
••••
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••••
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2
5
F
T
Y
S
N
A
I
C!
W
W
T
O
A
R
N
G
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E!
Solve each equation. Then connect your answers in the order of the problem numbers.
© Milliken Publishing Company 10 MP3443
Name _________________________________ Solving Equations
Remember
1. To solve an equation, first isolate the variable—get it alone on one side of theequation.
2. Undo the operation involving the variable by doing the opposite operation. Youmust do the same thing to both sides.
Addition Subtraction Multiplication Division
1. x – 5 = 10 x = _____
2. 3x = 6 x = _____
3. x = 4 x = _____
4. x + 4 = 9 x = _____
5. 5x = 80 x = _____
6. x – 7 = 13 x = _____
7. 7x = 7 x = _____
8. x = 7 x = _____
9. x + 15 = 23 x = _____
10. x – 5 = 5 x = _____
11. x = 5 x = _____
12. 4x = 52 x = _____
13. x – 6 = 16 x = _____
14. x + 3 = 3 x = _____
15. x = 15 x = _____
16. x – 7 = 93 x = _____
17. x = 5 x = _____
18. 25x = 150 x = _____
= 12
x =
x = 4
x3
123
= 12
= 12 · 3
x = 36
x33 ·
x3
10
7
9
6
15
Wrong!
Right!
15 20 45100
40
49
226
16109021
13
75
5
80
Begin and endat the star.
© Milliken Publishing Company 11 MP3443
Name _________________________________ Two-Step Equations
Solve each equation. Use mental math to check your workby substituting your answer for x in the original equation.Follow the correct answers through the maze.
Tip
When solving two-step equations, undo the addition or subtraction before undoingthe multiplication or division.
1. 12x – 8 = 64
2. 5x + 4 = 29
3. x + 1 = 9
4. 2x – 3 = 5
5. x – 7 = 4
6. x + 9 = 19
7. 3x + 6 = 51
8. x + 2 = 14
9. 4x – 1 = 99
10. x – 5 = 1
11. 10x – 500 = 100
12. 9x + 7 = 70
3x – 6 = 24
3x – 6 = 24
x – 6 = 8
x – 6 + 6 = 8 + 6
x = 14
3 3
10
4
2
8
3
3x – 6 = 24
3x – 6 + 6 = 24 + 6
3x = 30
3x = 30
x = 103 3
Wrong!
Right!
68
10
22
11
9
13
5020
5
16
4
64
3 2
39
1
88
10015
48
2518
60
4
7
135
7 1 4 2 0 8 3 1 3 2 0 4 4 1 8 1 5 2 0 6 1 8
Write an equation to match each problem, then solve the problem. When you are finished,find and circle the numeric part of your answer in the box at the bottom of the page.
© Milliken Publishing Company 12 MP3443
Name _____________________________ Equation Word Problems
1. Max’s age is 2 more than his father’s age divided by 4. Max is 13 years old. How old is his dad?
2. Tanya is 1 year less than three times the age of her sister Jessica. Jessica is five years old. How old is Tanya?
3. The Zigzag River is 114 miles longer than twice the Petite River. If the Petite River is 46 miles long, how long is the Zigzag River?
4. A used CD is a dollar more than one-third the price of a new CD. If a new CD costs $18, how much is a used CD?
5. Sixth graders have an average of 60 minutes of homework, four days a week. Seventh graders have 20 minutes more per day than sixth graders. How many minutes per week of homework does a seventh grader have?
6. An Internet bookseller charges $6 per paperback book plus a$3 shipping and handling fee per order. If Mr. Montoya spent$111 on books for his class, how many books did he buy?
7. The number of adults at the middle school dance is equal to the number of studentsdivided by 8. If there are 26 adults at the dance, how many students are there?
8. The basketball team finished its season with 12 wins. It won twiceas many games as it lost. How many games did it play in all?
9. The rec center has two payment choices. Plan A is $35 per month for unlimited visits.Plan B is $15 per month plus $2 per visit. If Nicole will go to the rec center 8 times amonth, which is the cheaper plan for her? How much will it cost?
Example The sum of four times a number and 12 is 72. What is the number?
4n + 12 = 72 4n + 12 – 12 = 72 – 12 4n = 60 4n = 60 n = 15___4
___4
Draw straight lines to match the descriptions and inequalities. Then graph the inequalityon the corresponding number line. The uncrossed letters will spell out a message.
© Milliken Publishing Company 13 MP3443
Name _________________________________ Graphing Inequalities
Remember
1. The arrowhead always points tothe smaller value.
2. When graphing a linear inequalityon a number line, use . . .
an open dot for < or >.a solid dot for ≤ or ≥.
0 1 2 3 4 5 6
0 1 2 3 4 5 6
0 1 2 3 4 5 6
6 – 4 < 55 > 6 – 4
n > 1
n ≤ 4
�
�
1. Six is greater than three.
2. Three is less than five.
3. Six is less than ten.
4. Ten is less thanthree times five.
5. Ten is greater thanfive minus five.
6. Twenty is greater than fifteen.
7. A number is less than orequal to five.
8. A number is greater than three.
9. A number is greater than orequal to eight plus two.
10. A number is less than theproduct of five and two.
11. A number is less than or equalto the sum of three and five.
12. A number is greater thanfive times two.
6 < 10
10 < 3 · 5
6 > 3
20 > 15
3 < 5
10 > 5 – 5
n ≥ 8 + 2
n > 3
n ≤ 3 + 5
n ≤ 5
n > 5 · 2
n < 5 · 2
•
•
•
•
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•
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G
T
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A
J
U
B
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!
0 2 4 6 8 10 12
0 5 10 15 20 25
0 1 2 3 4 5 6
0 1 2 3 4 5 6
0 1 2 3 4 5 6
0 2 4 6 8 10 12
0 1 2 3 4 5 6
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
© Milliken Publishing Company 14 MP3443
Name _________________________________ Solving Inequalities
Solve each inequality. Draw lines to connect your answer to the matching graph.
Remember
Isolate the variable. Undo the operation involving the variable by doing the opposite operation to both sides of the inequality.
1. x – 9 < 3 x < _____
2. 6x > 54 x > _____
3. x > 2 x > _____
4. x + 16 ≤ 25 x ≤ _____
5. 45x < 90 x < _____
6. x – 8 ≥ 8 x ≥ _____
7. x + 18 > 20 x > _____
8. x ≤ 3 x ≤ _____
9. x + 11 < 21 x < _____
10. x – 10 ≤ 5 x ≤ _____
11. 9x > 72 x > _____
12. x < 4 x < _____
7x < 14
x < 14(7)
x < 98
5
6
4
0 3 6 9 12 15 18
0 3 6 9 12 15 18
0 3 6 9 12 15 18
0 4 8 12 16 20 24
0 4 8 12 16 20 24
0 5 10 15 20 25
0 5 10 15 20 25
0 5 10 15 20 25
0 1 2 3 4 5 6
0 1 2 3 4 5 6
7x < 14
<
x < 2
7x7
147
0 20 40 60 80 100 0 1 2 3 4 5
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•
•
•
•
•
•
•
•
•
•
•
•
•
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•
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0 4 8 12 16 20 24
0 3 6 9 12 15 18
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Wrong!
Right!
© Milliken Publishing Company 15 MP3443
Name _________________________________ Divisibility TestsTip
A number is divisible by . . . Examples
2 if the ones place is 0, 2, 4, 6, or 8. 56
3 if the sum of its digits is divisible by 3. 249 2 + 4 + 9 = 15 15 ÷ 3 = 5
4 if the number formed by the last two digits is divisible by 4. 728 28 ÷ 4 = 7
5 if the ones place is 0 or 5. 6,185
6 if it is divisible by 2 and by 3. 390 3 + 9 + 0 = 12 12 ÷ 3 = 4
9 if the sum of its digits is divisible by 9. 97,812 9 + 7 + 8 + 1 + 2 = 27 27 ÷ 9 = 3
10 if the ones place is 0. 425,130
Brain Blaster! Complete this divisibility rule: A number is divisible by 25 if . . .
A. Check if the numbers in the design are divisible by 10, 5, 2, or 3. Follow this coloringcode:
Green—divisible by 10 Blue—only divisible by 5 Yellow—only divisible by 2
Purple—divisible by 3 White—all other numbers
B. Check if the numbers inthe design are divisible by 4, 6, or 9. Follow thiscoloring code:
Red—divisible by 4
Orange—divisible by 6
Yellow—divisible by 9
White—all other numbers
157
189
149
152
141
92
102
549164
1,050
117
196
222
152
138
176
174
99
9,246
153
726
462
148906
9,189
114
232
150
3,210
189
66
44
29
17
80
97
103
409
211
4
88
40
28
8
53
56
78
140
4,002
1,035
113
188
139
111
176
181 123 118 121
159
163
142
183
197
134
177
137
194117
101
153
106
185 140
110 155
115 200
130 175
205 160
190 145
125 100
170 215
Find the GCF of each set of numbers. Connect the answers in the order of the problemnumbers to illustrate the name of the diagram showing prime factorization.
© Milliken Publishing Company 16 MP3443
Greatest Common Factor
Remember
1. The greatest common factor (GCF) is the greatest number that is a common factorof two or more numbers.
2. Find the prime factorization of each number. Then multiply the prime factors thatthe numbers have in common to find the GCF.
Name _____________________________
24 36
4 6 4 9
2 2 2 3 2 2 3 3
GCF = 2 • 2 • 3 = 12
24 36
4 6 4 9
GCF = 4
1. 12 and 18 ______
2. 20 and 30 ______
3. 45 and 60 ______
4. 54 and 81 ______
5. 36 and 52 ______
6. 70 and 72 ______
7. 48 and 80 ______
8. 50 and 100 ______
9. 85 and 100 ______
10. 12, 15, 18 ______
11. 45, 75, 90 ______
12. 36, 54, 99 ______
13. 125 and 175 ______
14. 405 and 486 ______
15. 300 and 312 ______
Wrong!
Right!
6
10
15
27
50
3
4
165
15
9
81 25
12
2
3
2
30
22
1631
23
38
1
0
8
17
35
8
19
47
4
11
55
0
9
13923
31
2
74
46
2
14
5
97
1012
13
11
1520
18
2581
9
10
1230
3624
© Milliken Publishing Company 17 MP3443
Name _________________________________ Square Roots
Solve each problem. Follow the answers through the maze.
Tip
Use prime factor trees and divisibility rules to help find square roots of large numbers.
=
+ 6 =
5 + 6 = 11
1. = ______
2. = ______
3. = ______
4. = ______
5. = ______
6. = ______
7. = ______
8. = ______
9. = ______
10. = ______
11. = ______
12. = ______
13. = ______
14. = ______
15. = ______
=
=
x =
2 x 8 = 16
Wrong!
Right!
256256
4 64
4 64¥25
9
25
81
49
100
144
169
121
225
400
324
625
900
1 296,
576
Fill in the missing equivalent amounts in each row.
0.00003
0.0009
0.00006
0.075
0.00028
0.000633
3 x
9 x
1 x
2.8 x
4.75 x
© Milliken Publishing Company 18 MP3443
Name _________________________________ Scientific NotationRemember
1. A negative exponent means the reciprocalof the base.
2. For powers of 10, the exponent tells thenumber of zeros.
10–1
=
105
= 100,000 (five zeros)
110
1
32
19
3–2
= =
1
105
1
104
8100
1
106
1
104
1
103
Scientific Notation Positive Exponent Fraction Decimal
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
3100,000
31,000
7.5100
5.4100,000
4.751,000
3 x 10–5
8 x 10–2
2 x 10–3
7.5 x 10–2
9.3 x 10–3
6.33 x 10–4
© Milliken Publishing Company 19 MP3443
Cut apart the puzzle squares. Rearrange them to make a new 4 x 4 square with equivalent fractions, decimals, and percents nextto each other. For example, 50% could be next to 0.5 or or 1.When you finish, the letters in the puzzle should spell out a four-word message. Clue! Match up the easy decimals and percentsfirst. Then change fractions to decimals.
Name ________________________ Fractions, Decimals, Percents0.5
2 1.0– 1 0
= 0.5
50% = = 50100
12
12
0.50 = 50%
50% = 0.5
50100
38
23
12
111
35
49
13
18
112
120
310
80100
99100
50100
51100
1100
34
14
37
78
56
25
67
0.9375 5% 8.3%
0.09
0.416
60%70%
0.002
0.125
0.625 50%
0.7
55%
0.0625
62.5% 6.25%
80% 83.3%
72%
87.5%18%
2% 0.3
0.3 95%0.4
15%
0.375 100% 16.7% 75% 0% 0.95
0.25
0.15 0.16
0.2 0.6
0.4
1.0 8%A B E E
H G I O
R R R T
U V Y Y
)____
Tip
Change the question to an equation: replace is with =, of with · (times), and whatwith a variable, x. Write a given percent as a decimal. Then solve the equation.
a. What is 5% of 80? x = 0.05 · 80 x = 4
b. 9 is what percent of 12? 9 = x · 12 9 = x 75% = x
c. 150 is 30% of what? 150 = 0.3 · x 150 = x 500 = x
Change each question to an equation. Then solve it. Shade in your answers to reveal a mathematical symbol.
© Milliken Publishing Company 20 MP3443
Name _______________________________ Percent Problems
12
0.3
0.7512 9.0
– 8 460
– 60
500.00.3. 1500.0
– 15
4 is what percent of 5?
4 · 5 = 20%
4 is what percent of 5?
4 = x · 5
= x
80% = x
0.85 4.0
– 4 0
45
1. What is 85% of 20? ______
2. 6 is what percent of 24? ________
3. 42 is 75% of what? ______
4. 36 is what percent of 40? ________
5. What is 70% of 250? _______
6. 91 is 100% of what? ______
7. What is 8% of 50? ______
8. 27 is what percent of 90? ________
9. 48 is 60% of what? ______
10. What is 50% of 1,200? ________
11. 300 is 12% of what? _________
12. 1 is what percent of 10? ________
) _____
) _____
) ___________
Wrong!
Right!
170
175
10%
90%
25%
100%
36%
8%
17%2,500
25
400
91
1
7
%
600
10
80
30%
9
2
6
4
17
3%
56
31.5%
14
Add or subtract. Reduce the answers to lowest terms. Draw lines to matcheach addition problem to the subtraction problem with the same answer.
© Milliken Publishing Company 21 MP3443
Name _________________________________ Adding & SubtractingFractions
– =
Remember
1. Fractions must have common denominators before you can add or subtract them.
2. Add or subtract the numerator. Leave the common denominator the same.
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
+ = _______
34
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
– = _______
– = _______
– = _______
– = _______
– = _______
– = _______
– = _______
– = _______
– = _______
– = _______
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
59
16
43
– =59
16
– =1018
3 18
59
x 2 = 10x 2 = 18
x 3 = x 3 =
16
718
3 18
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
12
14
25
16
14
19
618
310
25
14
27
23
512
12
13
112
38
13
35
910
14
79
13
2728
37
2 68
23
28
58
16
74
46
78
740
4745
19
1718
19
Wrong!
Right!
Multiply the fractions. Write the answers in lowest terms. Shade the answers to find thename of a famous mathematician and scientist.
© Milliken Publishing Company 22 MP3443
Name _________________________________ Multiplying Fractions
Remember
1. A whole number has 1 as its denominator.
2. Multiply straight across—numerator times numerator and denominator times denominator.
3. Reduce fractions before multiplying or at the end.
3 x =47
1221
3 x =47
x =
=
47
127
31
3 31
x = =59
3045
23
65
x =59
23
65
2
1
1
3
x = _____
x = _____
x = _____
x = _____
x = _____
x = _____
x = _____
x = _____
x = _____
x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
x x = _____
35
14
5
37
910
914
23
1011
6
13
12
89
25
79
215
47
512
45
713
52
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
910
35
13
26
23
58
4
78
19
2210
23
1532
2728
95
23
411
4
910
32
211
14
83
49
203
23
2
34
89
1718
110
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Wrong!
Right!
108
2
7
12
4
90
5
3
1
6 11
710
320
210
29
25100
12
325
52
125 42
13
141
7348
11
518
627 10
15112
17108
511
15
107
310
56 8
27
4927 1
31849
19
74
152
364
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
÷ = _____
1 16
© Milliken Publishing Company 23 MP3443
Name _________________________________ Dividing Fractions
Divide the fractions. Write the answers in lowest terms. Use the code to complete arhyme your parents may have heard when they learned how to divide fractions.
“OURS IS NOT TO QUESTION WHY,
Remember
To divide by a fraction, multiply by its reciprocal.
47
5
136
910
1114
23
78
13
83
56
523
26
47
4
45
1011
1532
89
53
53
3
25
63
57
58
23
18
1013
112
1415
5
÷ = x =34 6
1.
2.
3.
4.
5.
6.
7.
8.
316
9.
10.
11.
12.
13.
14.
15.
16.
÷ =120
25
x =120
150
25
10
1
÷ =
= 8
120
25
x =201
81
25
1
4
554
34
16
3532
25
1411
2710
314
43
36 25
18
6 554
136
16
3532
118
136
37
.”
J
R
M
D
E
P
T
I
V
S
T
U
L
A
Y
N
34
16
18
1
2
Wrong!
Right!
1. x = 16 x = _____
2. x – = x = _____
3. = x = _____
4. x + = x = _____
5. 3x = x = _____
6. x – = x = _____
7. x = x = _____
8. x + = 4 x = _____
9. x – = x = _____
10. 10x = 5 x = _____
11. = x = _____
12. x + = x = _____
x = 4
· x = ·
x = 10
© Milliken Publishing Company 24 MP3443
Name _____________________________ Equations With Fractions
Solve each equation. Express improper fractions as mixed numbers. Follow your answersin order of the problems through the maze.
Remember
1. To solve an equation, you need to isolate the variable.
2. Undo the operation involving the variable by doing the opposite operation. Youmust do the same thing to both sides.
Addition Subtraction Multiplication Division
3. Dividing by a number is the same as multiplying by its reciprocal.
x = 4
x = ·
x =
25
x10
41
85
25
41
25
52
52
25
13
23
47
35
27
13
56
57
421
34
78
23
89
59
16
35
x2
13
12
12
2
1
Wrong!
Right!
2119
1110 18
13
1716
2011
81
51
91
619
8
21
31
32
92
32
6
38
14
2
8 11 2
30
22
7
61
1
151
4
181
173
5START
FINISH
1. –7 L | –7 | = _____
2. –5 T | –5 | = _____
3. 8 E | 8 | = _____
4. 0 L | 0 | = _____
5. –11 B | –11 | = ______
6. 4 I | 4 | = _____
7. 13.5 ! | 13.5 | = ______
8. –4 E | –4 | = _____
9. –10.5 S | –10.5 | = ______
10. 6 S | 6 | = _____
11. 11 S | 11 | = _____
12. 1.25 U | 1.25 | = ______
13. –1 A | –1 | = _____
14. –1 V | –1 | = _____
15. 2 E | 2 | = _____
16. –6 U | –6 | = _____
17. –8 O | –8 | = _____
18. 12.3 Y | 12.3 | = ______
19. –13 A | –13 | = _____
20. 10 A | 10 | = _____
Graph each number on the number line and write the correspondingletter above it. Then write the absolute value of the number. The letters on the number line will spell out a message.
© Milliken Publishing Company 25 MP3443
Name _________________________________ Absolute Value
| –13 | = –13
Remember
The absolute value is the distance of a number from zeroon a number line. An absolute value is always positive.
| –13 | = 13
| –5 | = 5| 5 | = 5
0 5 10–5–10
13
12
12
12
23
23
23
23
23
23
12
12
12
13
13
–7
7
L
13
Wrong!
Right!
© Milliken Publishing Company 26 MP3443
Name _________________________________
Use the decoder to write the value of each letter. Find a subtotal for thepositive numbers and the negative numbers within each word. Then findthe total value of the word. Draw a line to the star with the matching answer.
Brain Blaster! Set a target amount, such as –10 or 7. Find a word whoseletters add up to that value.
Adding Integers
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
6
5
4
3
2
1
0–1–2–3–4–5–6–6–5–4–3–2–1
0
1
2
3
4
5
6
___ ___ ___ ___ ___ ___ ___A L G E B R A
= _____ + _____
= M A T H
–6 6 0 –1 6 + –7 = –1
Remember
1. If the signs are the same, add the numbers and keep the same sign in the sum.
2. If the signs are different, subtract the numbers and keep the sign of the numberwith the larger absolute value.
1.
___ ___ ___ ___ ___ ___ ___ ___I N T E G E R S
= _____ + _____2.
___ ___ ___ ___ ___ ___ ___ ___P O S I T I V E
= _____ + _____3.
___ ___ ___ ___ ___ ___ ___ ___N E G A T I V E
= _____ + _____4.
___ ___ ___ ___ ___ ___ ___ ___A D D I T I O N
= _____ + _____5.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___S U B T R A C T I O N
= _____ + _____6.
–10
–7
–3
0
4
12
= M A T H
–6 6 0 –1 –13Wrong!
Right!
1. –16 – 5 = ______
2. 4 – 8 = ______
3. 5 – –2 = ______
4. 9 – 6 = ______
5. –6 – 17 = ______
6. –11 – –12 = ______
7. –2 – 3 = ______
8. 4 – –5 = ______
9. 8 – 10 = ______
10. –12 – 7 = ______
11. 15 – –1 = ______
12. 7 – 3 = ______
13. –10 – 16 = ______
14. –2 – –8 = ______
15. 0 – –11 = ______
16. –20 – –7 = ______
17. –13 – 9 = ______
18. –3 – –31 = ______
19. 18 – 24 = ______
20. 4 – –4 = ______
Subtract. Shade your answers to reveal the answer to the question below.
© Milliken Publishing Company 27 MP3443
Name _________________________________ Subtracting Integers
12 – 20 =
–12 + –20 = –32
12 – 20 =
12 + –20 = –8
Remember
To subtract integers, add the opposite of the integer being subtracted.
8 – 5 = 8 + –5 = 3 8 – –5 = 8 + +5 = 13 –8 – 5 = –8 + –5 = –13 –8 – –5 = –8 + +5 = –3
Which integer is neither positive nor negative?
Wrong!
Right!
–4
–10
–6–34
–13
–7
–23
–5
–3
–19–1
–8
–9
–2
–22 –21
–11
–26–18
8 24
0 10 277
42
31
12
3
25
28
11133
616
18
9
5 14
15
100
In a magic square, the sum of the numbers in eachrow, column, and diagonal is equal. You can use thisformula involving a, b, and c to create three-by-threemagic squares with integers.
© Milliken Publishing Company 28 MP3443
Name _________________________________ Integer Magic Squares
a + c
a + b – c
a – b
a – b – c
a
a + b + c
a + b
a – b + c
a – c
1. Substitute these values for a, b, and c. a = –5 b = 1 c = –3
Write the integer for each square. (A samplehas been done for you.) Add the threeintegers in each row, column, and diagonalto find the magic sum.
The magic sum for this square is _______.
2. Choose new values for a, b, and c. Make a and b negative integers and make c a positive integer.
a = ______ b = ______ c = ______
Substitute the values in the formula to findthe integer for each square. Add the threeintegers in each row, column, and diagonalto find the magic sum.
The magic sum for this square is _______.
3. Create your own integer magicsquare puzzle. Trade and solvepuzzles with a partner.
–5 + –3 = –8
–8
1.
2.
–2
1
Example:Fill in these missing integers, –5, –3, –1,0, 2, 3, and 5, so that each row,column, and diagonal adds up to 0.
A. In this ring, each circle shouldcontain a different integerbetween –12 and 12. Thespace where two circlesoverlap should contain theproduct of the two integers.Fill in the missing factors and products.
B. Choose your own integersbetween –20 and 20 to write ineach circle. Make each onedifferent and include bothnegative and positive integers.In each space where two circlesoverlap, write the product of thetwo integers.
© Milliken Publishing Company 29 MP3443
Name _________________________________ Multiplying Integers
Remember
1. If two integers have the same sign, either both positiveor both negative, the product will be positive.
2. If two integers have different signs, one positive and onenegative, the product will be negative.
–7 x –4 = –28 –7 x –4 = 28
3 x 12 = 36–3 x –12 = 36–3 x 12 = –363 x –12 = –36
A.
B.
12
44
–6
–11
–4
8 –7
–2–24
–30
–3
9
35
Wrong!
Right!
© Milliken Publishing Company 30 MP3443
Name _________________________________ Dividing Integers
Remember
1. If two integers have the same sign, either both positiveor both negative, their quotient will be positive.
2. If two integers have different signs, one positive and oneother negative, their quotient will be negative.
–32 ÷ –4 = –8 –32 ÷ –4 = 8
54 ÷ 6 = 9–54 ÷ –6 = 9–54 ÷ 6 = –954 ÷ –6 = –9
1. –30 ÷ 6 = ______
2. –48 ÷ –12 = ______
3. 22 ÷ –2 = ______
4. 28 ÷ 4 = ______
5. –6 ÷ 6 = ______
6. –18 ÷ –3 = ______
7. 36 ÷ –2 = ______
8. 100 ÷ –5 = ______
9. 108 ÷ 9 = ______
10. –49 ÷ 7 = ______
11. 14 ÷ –1 = ______
12. 75 ÷ 5 = ______
13. –72 ÷ 18 = ______
14. –64 ÷ –8 = ______
15. 51 ÷ –3 = ______
16. –27 ÷ –9 = ______
17. –52 ÷ 4 = ______
18. –100 ÷ –10 = ______
19. 35 ÷ 7 = ______
20. 144 ÷ –2 = ______
21. –42 ÷ 7 = ______
22. –12 ÷ –12 = ______
23. –96 ÷ 12 = ______
24. 99 ÷ 11 = ______
25. 39 ÷ –3 = ______
26. –28 ÷ –14 = ______
27. –45 ÷ 5 = ______
28. –76 ÷ –4 = ______
29. 100 ÷ 4 = ______
30. 90 ÷ –6 = ______
31. –75 ÷ 3 = ______
32. –77 ÷ –7 = ______
33. –64 ÷ 4 = ______
Subtract. Spell a word by connecting your answers in order.
Wrong!
Right!
4 15
–13–8
1 –13
3–72
–18 –712
6 8–20
7
–11–14
–4 225
11
–6
10
5
–5
–17
9 19
–15–9 –25 –16
–1
1. x + y = _____
2. x – y = _____
3. 7z = _____
4. xy = _____
5. = _____
6. –z – 2y = _____
7. 8x + z = _____
8. 9(x + z) = _____
9. –y2
= _____
10. = _____
11. (3z )2
– 10 = _____
12. = _____
13. (y + z )(x – z) = _____
14. = _____
15. 5(y – x) + z = _____
16. = _____
z2
x – 7
© Milliken Publishing Company 31 MP3443
Name _____________________________ Integer Expressions
Given x = –2, y = 4, and z = –3,evaluate the expression.
=
=
4(–3) = –12
–xyz – x
––24(–3) – –2
Given x = –2, y = 4, and z = –3,evaluate the expression.
=
=
=
= –
–xyz – x
(–1 · –2)(4 · –3) – –2
2–12 + +2
2–10
15
–5yx
Evaluate each expression given that x = –2, y = 4, and z = –3. Shade in your answers.
Remember
1. Follow the order of operations (PEMDAS) when evaluating expressions.
2. A fraction bar is a grouping symbol. It indicates division.
3. A negative variable is the same as –1 times the variable.
–xyz – x
= (–x) ÷ (yz – x)
–x = (–1)(x) or –1 · x
–3y2
x + 1
25xy–1 – 2z
4(10 – y )
x3
–5 –40
–45–1
–21
–3
–6
–10
–48–16 –8
–19
01
8
7127
212
7
10
5
48
9
–11
Wrong!
Right!
1. x + 3 = –1 x = ______
2. 5x = –25 x = ______
3. x = –3 x = ______
4. x – 6 = –2 x = ______
5. –2x = 6 x = ______
6. x + 9 = 1 x = ______
7. x = –5 x = ______
8. 6x – 4 = –40 x = ______
9. x + 4 = 0 x = ______
10. –x + 7 = –7 x = ______
11. x + 5 = –1 x = ______
12. –5x + 20 = –60 x = ______
13. x + 10 = 9 x = ______
14. 2x – 3 = –2 x = ______
Solve for x. Use mental math to check your work, substituting your answer for x in theoriginal equation.
Followyouranswersin orderof theproblemnumbers.
© Milliken Publishing Company 32 MP3443
Name ______________________________ Equations With Integers
–3x = 18
x = 18(–3)
x = –54
Remember
Undo the equation by doing the opposite operation(s). You must do the same thing toboth sides. For two-step equations, undo the addition or subtraction first.
–3x = 18
–3x = 18
x = –6
–3 –3
4
3
7
5
2
Wrong!
Right!
–5–4
–18 120
–12
–7
–3 –9
–15
3
1416
8
5
36 4
–10
–8
75
–20
25
11 –6
12
–�
© Milliken Publishing Company 33 MP3443
Name _________________________________ Graphing Vocabulary
Across
1. The point at which a graph intersectsthe x-axis.
4. The vertical axis in a coordinate plane.7. The second number in an ordered pair. 10. The x-axis and the y-axis divide a
coordinate plane into four ____.12. In Quadrant I, both the x- and y-
coordinates are ____.13. The ____ of a line, also called rise-
over-run, measures the steepness. 15. The point at which a graph intersects
the y-axis.16. A ____ equation is one whose graph
on the coordinate plane is a line.
Word Boxcoordinate planefunctiongraphlinear negativeordered pairoriginpositivequadrantsslopex -axisx -coordinatex -intercepty-axisy-coordinatey-intercept
Down
2. The plane formed by two number linesthat intersect at right angles.
3. A pair of numbers, such as (3, –6), thattells the location of a point.
5. The first number in an ordered pair. 6. The horizontal axis in a coordinate plane.8. A pictorial representation of a
mathematical relationship.9. A relation in which every x-value has a
unique y-value.11. In Quadrant II, the x-coordinates are
____ and the y-coordinates are positive.14. The point where the x- and y-axes
intersect; its coordinates are (0, 0).
1 2
3
4 5 6
7
8
9
10
11
12
13 14
15
16
1. Write the letter from the graph that corresponds to each ordered pair to decode the punch line to this knock-knock joke.
2. Write a favorite riddle or knock-knock joke here. Encode the punch line by writing thematching ordered pair in place of each letter. Trade and solve riddles with a partner.
© Milliken Publishing Company 34 MP3443
Name _________________________________ Ordered Pairs
Remember
The first number in an orderedpair is the x-coordinate. It tells where a point is locatedalong the horizontal axis.
The second number in anordered pair is the y-coordinate. It tells where a point is located along thevertical axis.
Examples:
D (–2, 4) J (5, 3)
Q (–3, –4) W (2, –2)
Knock-knock. Who’s there? Cantaloupe. Cantaloupe who?
(–5, 3) (1, –4) (6, 2) (3, –1) (3, 2) (4, –3) (–4, –2) (4, 5) (3, 2)
(3, –1) (–4,–2) (6, 2) (–1,–4) (4, –6) (2, 4) (3, –1) (–1,–4) (–6, 1) (–2,–3) (1, 1) (–4, 5) (–5,–5)
–1
–2
–3
–4
–5
–6
6
5
4
3
2
1
0
x
y
C•X•
M•
F•
W•
S•D•
E• N•U•
H•K•
P•
J•
L•Q•
V•
Y•
I•
O•B•
G•
A•
T•
Z•
R•
’
’ !’
1 2 3 4 5 6 –6 –5 –4 –3 –2 –1
(–2, 4)
(–3, –4)
(2, –2)
(5, 3)
Follow the steps to draw and color the state flag of Texas.
1. To make a rectangle, plot and connect these points in order. Color it red.(–3, 0) (3, 0) (9, 0) (9, –6) (3, –6) (–3, –6) (–3, 0)
2. Plot and connect these points to make another rectangle. Leave it white.(–3, 0) (–3, 6) (3, 6) (9, 6) (9, 0) (3, 0) (–3, 0)
3. Plot and connect these points to make a star. Leave it white.(–8, 1) (–6.5, 1) (–6, 2.5) (–5.5, 1) (–4, 1) (–5, 0) (–4.5, –1.5) (–6, –0.5) (–7.5, –1.5) (–7, 0) (–8, 1)
4. Plot and connect these points to make a rectangle surrounding the star. Color its background dark blue.(–9, 0) (–9, 6) (–3, 6) (–3, 0) (–3, –6) (–9, –6) (–9, 0)
© Milliken Publishing Company 35 MP3443
Name _________________________________ Graphing PointsRemember
The first number in an ordered pair is the x-coordinate. It tells how far to move acrossfrom the origin. A positive number means go right. A negative number means go left.
The second number in an ordered pair is the y-coordinate. It tells how far to move upor down. A positive number means go up. A negative number means go down.
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1–1
–2
–3
–4
–5
–6
–7
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 100
–6.5 ishalfwaybetween–6 and –7
x
y
A. Plot the data from the table below thatlists the amount of time students studiedand the scores they earned on a test. A sample point has been done for you.Look for a pattern among the points onthe graph. Draw the trend line.
B. Label each statement as True or False. If a statement is false, cross out the letter nextto the answer blank. Find the missing word below by writing the uncrossed letters in order.
G _____________ 1. In general, the more time studied the better the test score.
R _____________ 2. One student scored high even though he or she didn’t study much.
E _____________ 3. Several students who studied for three hours scored low.
A _____________ 4. The scatterplot in problem A shows a positive trend.
T _____________ 5. The scatterplot in problem A shows a negative trend.
M _____________ 6. The trend line does not pass through every point.
A SCATTERPLOT IS ALSO CALLED A “SCATTER ____ ____ ____ ____.”
© Milliken Publishing Company 36 MP3443
Name _________________________________ ScatterplotsQuick Review
1. If the points in a scatterplot form a pattern, you can draw astraight line that approximates their position. The line is calleda trend line or line of best fit.
2. A positive trend line goes up. A negative trend line goes down.If the points do not form a pattern, there is no trend.
•
•
•
•
•
•
•
•
•
•
•
•
•
Negative Trend
0 30 60 90 120 150 180Minutes Studied
100
90
80
70
60
50
Test
Sco
re
Does studying affect your test score?
Minutes Studied 60 30 180 90 60 0 120 180 60 150 30 120 75 90
Test Score 65 60 95 70 72 50 84 100 68 96 100 90 70 80
•
Draw straight lines to match each equation to its correspondingtable. Complete the missing values in each table. The uncrossedwords are another name for a function table, or table of values.
© Milliken Publishing Company 37 MP3443
Name _________________________________ Table of Values
y = x y = –x y = x + 1 y = x – 3 y = –x + 2
x y
–3 3
–2 2
–1
0
1
2
•
x y
–3 –6
–2 –5
–1
0
1
2
•
x y
–4 –4
–3 –3
–2
–1
0
1
x y
–1 3
0 2
1
2
3
4
•
x y
–3 –2
–2 –1
–1
0
1
2
•
• • • •
1. 2. 3. 4. 5.
y = 4x y = –2x y = 2x + 1 y = 3x – 4 y = –2x + 5
x y
–3 6
–2
–1
0
1
2
•
x y
–3 –12
–2
–1
0
1
2
•
x y
–4 13
–3
–2
–1
0
1
•
x y
–3 –13
–2
–1
0
1
2
•
x y
–4 –7
–3
–2
–1
0
1
•
• • • • •
6. 7. 8. 9. 10.
disastrous
input- algebraican
mathematical
turbo-poweredintergalactic quadratic expression
graphingmy
outputchair
table
–2
•
•
Complete the table of values for each equation and plot thematching points on the graph. Then draw a line connectingthem. Each line will cross through a set of letters. Write thecrossed sets of letters in order of the problems on the blanksin the box below.
© Milliken Publishing Company 38 MP3443
Name ___________________________ Graphing Linear Equations
The coordinate plane is sometimes called the Cartesian coordinate plane.
It is named after the French mathematician _________ ______________________.1 2 3 4
5–5
5
x
y
x y
–3
–1
0
3
1. y = x + 2
5–5
5
x
y
x y
–4
0
2
4
3. y = – x + 1
5–5
5
x
y
x y
–2
0
1
2
2. y = –2x
5–5
5
x
y
x y
–1
0
1
2
4. y = 3x – 112
René
Jean
Luc LaMath
Des
car
tes
pla
ine
son
hus
–5 –5
–5 –5
Solve for y to rewrite each equation in slope-intercept form. Shade in your answers below to reveal a message.
© Milliken Publishing Company 39 MP3443
Name _________________________________ Slope-Intercept Form
Remember
Putting an equation in slope-intercept form makes it easier to understand and graph.In the equation y = mx + b, m is the slope of the line and b is the y-intercept.
Wrong!
Right!
2x + 4y = 8
2x – 2x + 4y = –2x + 8
4y = –2x + 8
4y =–2x +
y = – x + 2
2x + 4y = 8
4y = 2x + 8
4y = 2x + 8
y = 2x + 24 4 8
412
44
1. 4x + 2y = 10 y = __________
2. 5y – 25x = 10 y = __________
3. x – y = 1 y = __________
4. 3y – 12x = 6 y = __________
5. 4y + 4x = –4 y = __________
6. 9x – 3y = 18 y = __________
7. 7y – 14x = –28 y = __________
8. 3y – x = 12 y = __________
9. –5x – y = –1 y = __________
10. x + 4y = 36 y = __________
11. 3y – 2x = –9 y = __________
12. 2y + 8x = 6 y = __________
4x + 2
–x – 2
x +
3x – 6
5x– 9
4x+ 6
–3x– 6
x– 9
34
x + 413
– x + 914
12
x– 6
–2x + 5
2x+
5
–x + 1
3x+ 12
–x – 1
–4x + 3 x – 1
2x+
4
2x – 4
5x– 5
x+ 3
5x + 2
5x+
10
–5x+
1
4 – x13
x – 115
x – 323
x – 112
23
© Milliken Publishing Company 40 MP3443
Name _______________________________ Slope-Intercept Graphs
Graph each equation using the slope and y-intercept. Each line will cross one letter.Write that letter on the matching numbered line to spell out a message.
4–4
4
–4
x
y
4–4
4
–4
x
y
4–4
4
–4
x
y1. y = x + 1 2. y = –x + 1 3. y = –2x – 1
4–4
4
–4
x
y
4–4
4
–4
x
y
4–4
4
–4
x
y4. y = x 5. y = x – 1 6. y = 2x – 2
4–4
4
–4
x
y
4–4
4
–4
x
y
4–4
4
–4
x
y7. y = –3x – 3 8. y = – x + 2 9. y = 3x + 1
1 2 3 4 5 6 7 8 9
B
A
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© Milliken Publishing Company 41 MP3443
1. Which equation shows thecommutative property of addition?
A 72 + 0 = 72
B 72 + 28 = 28 + 72
C 72 + –72 = 0
D (72 + 28) + 5 = 72 + (28 + 5)
2. What is the value of 43 ?
A 12 B 16
C 32 D 64
3. What is ?
A 14
B 15
C 25
D None of these answers.
4. Find the value of 9 + 12 ÷ 3 – 1.
A 12 B 10
C 6 D 15
5. Which expression has a value of 21?
A 3 · 22
+ 12 ÷ 4
B (3 · 2)2
+ 12 ÷ 4
C 3 · (22
+ 12 ÷ 4)
D 3 · (22
+ 12) ÷ 4
6. Given x = 5, y = 2, and z = 4, evaluatethe expression:
A 12 B 14
C 18 D 22
7. Which equation matches “one more thantwice a number is seven”?
A 1 + (n + 2) = 7
B 2n + 1 = 7n
C 1 + 2 = 7
D 2n + 1 = 7
8. Solve for x. 5x = 15
A x = 75 B x = 10
C x = 3 D x = 20
9. Solve for x. 2x + 3 = 21
A x = 12 B x = 18
C x = 9 D x =
10. Which inequality matches the graph?
A x > 3 B x < 3
C x ≥ 3 D x = 3
Shade in the circle of the correct answer.
Name ______________________________
Date ________________ Score ______ %Assessment A
Whole Numbers
4x + zy
232
0 1 2 3 4 5 6
�
12
225
1. Which decimal is equivalent to 3 x 10–2
?
A 0.03
B 0.003
C –300.0
D –0.006
2. Which percent is equivalent to thedecimal 0.2?
A 0.2% B 2%
C 20% D 200%
3. Which fraction is equivalent to 85%?
A
B
C
D None of these answers.
4. Solve:
15 is 60% of what number?
A 9 B 21
C 25 D 90
5. Add 4 + 3 .
A 7 B 8
C 7 D
6. Which expression is equal to ?
A –
B –
C –
D –
7. Which expression is equal to ?
A ·
B 2 ·
C ·
D · 5
8. Divide ÷ .
A B
C D
9. Solve for x. 5x =
A x = B x =
C x = D x =
10. Solve for x. x + =
A x = B x =
C x = D x = 3
© Milliken Publishing Company 42 MP3443
Name ______________________________
Date ________________ Score ______ %Assessment B
Fractions, Decimals, Percents
1011
211
4511
5011
5511
23
34
78
12
69
314
314
314
57
1724
1830
16
23
16
56
38
625
512
512
104
518
58
13
89
34
119
59
76
89
310
35
15
35
13
23
34
18
Shade in the circle of the correct answer.
© Milliken Publishing Company 43 MP3443
Name ______________________________
Date ________________ Score ______ %Assessment C
Integers
1. Which number is equal to | –4 | ?
A –4 B 4
C –16 D
2. What is –29 + –7 ?
A –22 B 22
C –36 D 36
3. What is 12 – 30 ?
A –42
B 18
C 42
D None of these answers.
4. Which expression is equal to –81 ?
A 92
B 3(–27)
C –3 · –3 · –3 · –3 D –9(–9)
5. What is –56 ÷ –8 ?
A 7 B –7
C 8 D –8
6. Follow the order of operations tofind the value of 3 + –15 ÷ 3 .
A –2 B –4
C –6 D –8
7. Given x = –6, y = 9, and z = –2, evaluatethe expression x
2+ z .
A –38 B 38
C –14 D 34
8. Given x = –6, y = 9, and z = –2, evaluatethe expression.
A –3 B 3
C D –
9. Solve for x. x + 20 = –25
A x = –5 B x = –45
C x = 5 D x = 45
10. Solve for x. = –12
A x = –2 B x = 2
C x = –72 D x = 72
11. Solve for x. –8x – 4 = –20
A x = 2 B x = 3
C x = –2 D x = –3
12. Solve for x. + 10 = 0
A x = 0 B x = –10
C x = –2 D x = –50
14
–5y – xy – 2z
435
515
x6
x5
Shade in the circle of the correct answer.
© Milliken Publishing Company 44 MP3443
Name ______________________________
Date ________________ Score ______ %Assessment D
Graphing
1. What is the name of the point (0, 0),where the x- and y-axes intersect?
A double goose egg
B slope
C origin
D center-intercept
2. Which ordered pair represents a pointon the x-axis?
A (0, 5) B (5, 0)
C (5, 5) D (–5, –5)
3. Which letter is at the point (3, –1)?
A Q
B K
C L
D T
4. Which is theordered pairfor point R?
A (2, –1) B (–2, 1)
C (1, –2) D (–2, –1)
5. Which equation matches the table?
A y = x + 1
B y = x – 1
C y = 2x
D y = –2x
6. This scatterplot shows a
A positive trend.
B negative trend.
C function.
D no trend.
7. Which term refers to the steepness of aline?
A quadrant B intercept
C linear D slope
8. At what point will the line of this equationcross the y-axis? y = 3x – 2
A (0, –2) B (3, –2)
C (3, 0) D (–2, 0)
9. Solve for y to write this equation in slope-intercept form: 4y – 20x = 8
A y = 4x + 2 B y = –5x + 2
C y = 5x + 2 D y = –4x + 4
10. Whichequationmatchesthe graph?
A y = x + 1
B y = –x + 1
C y = x – 1
D y = –2x + 1
S•K•
T•
M•
N•
Q•
R•
P•
L•
4–4
4
–4
x
y
x y–1 –2
0 0
1 2
2 4
•
•
•
•
•
•
•
•
••
••
•
•
4–4
4
–4
x
y
�
�
Shade in the circle of the correct answer.
© Milliken Publishing Company 45 MP3443
AnswersPage 3
Page 5Possible answers. Order may vary.
A. 6 x 5 – 6 = 24+ – x –3 + 24 ÷ 2 = 15x ÷ – ÷2 + 6 ÷ 2 = 5= = = =12 – 1 + 10 = 21
B. 5 x 4 – 2 = 18+ + x ÷3 x 9 – 24 = 3x ÷ ÷ +3 x 3 + 3 = 12= = = =14 ÷ 7 + 16 = 18
Page 6A. 36 J. 100 S. 7B. 144 K. 5 T. 64C. 125 L. 4 U. 1D. 1000 M. 11 V. 81E. 10 N. 9 W. 27
F. 32 O. 0 X. 25G. 16 P. 216 Y. 121H. 49 Q. 243 Z. 3I. 400 R. 8
READ 52 AS “FIVE SQUARED” OR“FIVE TO THE SECOND POWER.”READ 43 AS “FOUR CUBED” OR“FOUR TO THE THIRD POWER.”READ 24 AS “TWO TO THE FOURTHPOWER.”
Page 71. 4 9. 222. 13 10. 63. 3 11. 134. 72 12. 295. 40 13. 526. 8 14. 347. 47 15. 508. 51 16. 1
Page 81. 8 7. 4 13. 562. 7 8. 42 14. 23. 22 9. 17 15. 354. 1 10. 9 16. 125. 25 11. 27 17. 216. 6 12. 81 18. 10
al-Khwarizmi; House of Wisdom
Page 9FANTASTIC!
Page 101. 15 13. 222. 2 14. 03. 40 15. 904. 5 16. 1005. 16 17. 756. 20 18. 67. 18. 499. 8
10. 1011. 4512. 13
Page 111. 6 5. 88 9. 252. 5 6. 100 10. 183. 16 7. 15 11. 604. 4 8. 48 12. 7
Page 121. 44 years old2. 14 years old3. 206 miles4. $75. 320 minutes6. 18 books7. 208 students8. 18 games9. Plan B is cheaper; $31
Page 13 GREAT JOB!
1. 6 < 10
2. 10 < 3 · 5
3. 6 > 3
4. 20 > 15
5. 3 < 5
6. 10 > 5 – 5
7. n ≥ 8 + 2
8. n > 3
9. n ≤ 3 + 5
10. n ≤ 5
11. n > 5 · 2
12. n < 5 · 2
g r e a t e r t h a ni s t o g e t h e s ea p a r a l l e l q ge s b e i s s r l u ap o s i t i v e m a te r o l m u n f o r ir l l t i a u o t e vp l u s n n r r l r ee r t e u g p e m o sn f e e s l y f h o md i v i d e d b y t pi n a n t a t e e h ec s l e s s t h a n ru o u s n t i m e s cl n e q u a l s e d ea t t e p i m a t h nr i g h t a n g l e t
equalsless thangreater thanplus positiveminus negativetimesdivided bysquare rootpercent
is toabsolute valuepiperpendicularparallelangleright angletherefore
12 =2x + 1 = 1212 = x + 3___________
5 + x = 1818 = x – 9
= 18___________
x = 302
x = 30 + 52x = 30___________
x 2 = y + 7x = y – 7x = 7y
___________
63 + x = 10x63 = 3x2x + 10 = 6x___________
x – 2 = 12
6x = x + 10
x2 – 30 = 5
9x = 18
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© Milliken Publishing Company 46 MP3443
Page 14 1. x < 122. x > 93. x > 104. x ≤ 95. x < 26. x ≥ 167. x > 28. x ≤ 189. x < 10
10. x ≤ 1511. x > 812. x < 16
Page 15
Page 161. 6 9. 52. 10 10. 33. 15 11. 154. 27 12. 95. 4 13. 256. 2 14. 817. 16 15. 128. 50
Page 171. 3 9. 152. 5 10. 203. 9 11. 184. 7 12. 255. 10 13. 306. 12 14. 367. 13 15. 248. 11
Page 18
Page 19Assembled puzzle:
Page 201. 17 7. 42. 25% 8. 30%3. 56 9. 804. 90% 10. 6005. 175 11. 2,5006. 91 12. 10%
Page 211.
2.
3.
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Page 221. 11.
2. 12.
3. 2 13.
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5. 15.
6. 16.
7. 17. 12
8. 18.
9. 19.
10. 20.
NEWTON
Page 231. 9.
2. 10.
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4. 12.
5. 13.
6. 14. 36
7. 15.
8. 16.
JUST INVERT AND MULTIPLY
Page 241. 32 7.
2. 8. 4
3. 6 9. 1
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5. 11.
6. 12.
••••••••••••
••••••••••••
Y O U A
R E V E
R Y B R
I G H T
54
1. 8 x 10–2 8 x 0.08
2. 9 x 10–4 9 x 0.0009
3. 2 x 10–3 2 x 0.002
4. 6 x 10–5 6 x 0.00006
5. 1 x 10–6 1 x 0.000001
6. 3 x 10–3 3 x 0.003
7. 7.5 x 10–2 7.5 x 0.075
8. 2.8 x 10–4 2.8 x 0.00028
9. 9.3 x 10–3 9.3 x 0.0093
10. 5.4 x 10–5 5.4 x 0.000054
11. 4.75 x 10–3 4.75 x 0.00475
12. 6.33 x 10–4 6.33 x 0.000633
1102
1104
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11,000,000
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© Milliken Publishing Company 47 MP3443
Page 25ABSOLUTE VALUE IS EASY!
1. 7 11. 11
2. 5 12. 1.25
3. 8 13. 1
4. 0 14. 1
5. 11 15. 2
6. 4 16. 6
7. 13.5 17. 8
8. 4 18. 12.3
9. 10.5 19. 13
10. 6 20. 10
Page 26 1. 6 –5 0 2 5 –2 6 =
19 + –7 = 122. –2 –6 0 2 0 2 –2 –1 =
4 + –11 = –73. –4 –5 –1 –2 0 –2 2 2 =
4 + –14 = –104. –6 2 0 6 0 –2 2 2 =
12 + –8 = 45. 6 3 3 –2 0 –2 –5 –6 =
12 + –15 = –3 6. –1 1 5 0 –2 6 4 0 –2 –5
–6 = 16 + –16 = 0
Page 271. –21 11. 162. –4 12. 43. 7 13. –264. 3 14. 65. –23 15. 116. 1 16. –137. –5 17. –228. 9 18. 289. –2 19. –6
10. –19 20. 8zero
Page 281.
2. & 3. Answers will vary.
Page 29A.
B. Answers will vary.
Page 301. –5 12. 15 23. –82. 4 13. –4 24. 93. –11 14. 8 25. –134. 7 15. –17 26. 25. –1 16. 3 27. –96. 6 17. –13 28. 197. –18 18. 10 29. 258. –20 19. 5 30. –159. 12 20. –72 31. –25
10. –7 21. –6 32. 1111. –14 22. 1 33. –16
Integers
Page 311. 2 9. –162. –6 10. –13. –21 11. 714. –8 12. 485. 10 13. 16. –5 14. –407. –19 15. 278. –45 16. –3
Page 321. –4 8. –62. –5 9. –203. –12 10. 144. 4 11. –185. –3 12. 166. –8 13. –77. –10 14.
Page 33
Page 341. CAN’T ELOPE TONIGHT,
I’M BUSY!2. Answers will vary.
Page 35
Page 36
1. True2. True3. False4. True5. False6. True
A SCATTERPLOT IS ALSO CALLEDA “SCATTER GRAM.”
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The magicsum for thissquare is –15.
© Milliken Publishing Company 48 MP3443
Page 37an input-output table1. 2. 3. 4. 5.y = x y = –x y = x + 1 y = x – 3 y = –x + 2
6. 7. 8. 9. 10.y = 4x y = –2x y = 2x + 1 y = 3x – 4 y = –2x + 5
Page 381. 2.
3. 4.
René Descartes
Page 391. y = –2x + 5 7. y = 2x – 4
2. y = 5x + 2 8. y = x + 4
3. y = x – 1 9. y = –5x + 1
4. y = 4x + 2 10. y = – x + 9
5. y = –x – 1 11. y = x – 3
6. y = 3x – 6 12. y = –4x + 3
Page 401. 2. 3.
4. 5. 6.
7. 8. 9.
BRILLIANT!
Page 411. B 6. A2. D 7. D3. B 8. C4. A 9. C5. C 10. B
Page 421. A 6. D2. C 7. B3. D 8. C4. C 9. A5. B 10. B
Page 431. B 7. D2. C 8. A3. D 9. B4. B 10. C5. A 11. A6. A 12. D
Page 441. C 6. A2. B 7. D3. D 8. A4. B 9. C5. C 10. B
x y–3 3–2 2–1 10 01 –12 –2
x y–3 –6–2 –5–1 –40 –31 –22 –1
x y–4 –4–3 –3–2 –2–1 –10 01 1
x y–1 30 21 12 03 –14 –2
x y–3 –2–2 –1–1 00 11 22 3
• • • • •
• • • • •
x y–3 6–2 4–1 20 01 –22 –4
x y–3 –1–1 10 23 5
x y–2 40 01 –22 –4
x y–4 30 12 04 –1
x y–1 –40 –11 22 5
x y–3 –12–2 –8–1 –40 01 42 8
x y–4 13–3 11–2 9–1 70 51 3
x y–3 –13–2 –10–1 –70 –41 –12 2
x y–4 –7–3 –5–2 –3–1 –10 11 3
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