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MILLIKEN PUBLISHING COMPMILLIKEN PUBLISHING COMPANY ANY STST. LOUIS, MISSOURI. LOUIS, MISSOURI

MP3443

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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.


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.


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.


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


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.


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.


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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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.


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.


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.


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.


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

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

G

T

H

E

R

A

J

U

B

T

O

M

A

R

L

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S

!

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


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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0 4 8 12 16 20 24

0 3 6 9 12 15 18

�

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Wrong!

Right!


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.


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


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


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


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.


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? ______


5. What is 70% of 250? _______

6. 91 is 100% of what? ______

7. What is 8% of 50? ______


9. 48 is 60% of what? ______

10. What is 50% of 1,200? ________

11. 300 is 12% of what? _________


) _____

) _____

) ___________

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.


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.


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


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


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.


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!


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.


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.


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.


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!


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


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.


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

–�


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.


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

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6

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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)


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 ____ ____ ____ ____.”


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.


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.

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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.


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

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–5 –5

–5 –5

Solve for y to rewrite each equation in slope-intercept form. Shade in your answers below to reveal a message.


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


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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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


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


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



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


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



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

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M•

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x

y

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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

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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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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.

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Page 241. 32 7.

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••••••••••••

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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

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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.”

12

23

13

12

23

23

12

–8 –3 –4

–1 –5 –9

–6 –7 –2

12–60

–2

8

–3

9

–7

–5

–30–4

35

–24

–32

44

–7010

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–54–27

–6

–11

1

–11

–6

12

0

x

y

–1

–2

–3

–4

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–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0

The magicsum for thissquare is –15.


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

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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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