1

Name

______________

Period ______

2

3

Multiplying Exponential Expressions

Expand and Count

Fill in each line of the table. Look for patterns.

Multiplication

Problem Expanded Notation

Simplified

Exponential

Form

Standard

Form

Look at the Problem and Simplified Exponential Form columns. Explain any

patterns that you see.

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

4

Dividing Exponential Expressions

Expand, Find 1’s and Count Fill in each line of the table. Look for patterns.

Division

Problem Expanded Notation

Simplified

Exponential

Form

Standard

Form

Look at the Problem and Simplified Exponential Form columns. Explain any

patterns that you see.

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

5

Exponential

Form

Standard

Form

23

22

21

Exponential

Form

Standard

Form

33

32

31

Exponential

Form

Standard

Form

43

42

41

Exponential

Form

Standard

Form

53

52

51

Exponential

Form

Standard

Form

63

62

61

Exponential

Form

Standard

Form

73

72

71

Exponential

Form

Standard

Form

83

82

81

Exponential

Form

Standard

Form

93

92

91

Exponential

Form

Standard

Form

103

102

101

6

Marisol had a carton with a dozen eggs in it. She weighed the carton with different numbers

of eggs and got the weights shown in the table below.

Number of eggs (X) 0 3 6 9 12 30 X

Weight (Y) 16 25 34 43

a) Make a graph showing the weight of the eggs vs. the number of eggs in the carton.

Ounces

Number of eggs 20 2 4 6 8 10 12 14 16 18

0

5

15

25

35

45

0 3 7 11 15 19

10

30

50

5 13

50

40

9

20

17 1

Eggs in a Carton Table, Graph and Equation

Name __________________

Date: __________ Per.: ____

7

b) Looking at your graph, find the rate at which the weight increases as the number of eggs

increases.

c) What is the change in number of eggs from one x-value to the next?

d) What is the change in weight from one y-value to the next?

e) Write the rate of change as the weight over eggs.

f) What part of the equation shows the rate of change?

g) Where does the line cross the y-axis?

h) The point where the line crosses the Y-axis has a special meaning in this problem.

What does it represent?

8

More Exponent Patterns Name _____________________________

Exponential

Form

Standard

Form

33

32

31

Exponential

Form

Standard

Form

53

52

51

Exponential

Form

Standard

Form

83

82

81

Show each expression below in expanded

and standard form.

Exponential

Form Expanded Form

Standard

Form

43

25

61

40

71

104

103

92

42

70

63

90

9

Simplifying Expressions with Variables III

Draw pictures and use the values x = -5 and y = 8 to evaluate these expressions.

Basic Problems

1.

2x 8 2.

3y 3.

2y 3x

Challenging Problems

4.

xy 6y 5.

3 2x 3y 6.

x2 y2

Answers to problems 1-6, but not in order: -37, -2, 1, 8, 24, 89

Extra Challenging Problems: Use the following numbers to make expressions that each

equal the target number of 24.

7. 2, 2, 4, 6 8. 1, 2, 6, 7 9. 2, 2, 2, 4 10. 1, 2, 5, 8

128 (5 3)8

This whole thing is called an _________________

These grouping symbols are called _________________

DO THESE FIRST!

x y x 2

This expression has three parts called _________.

These parts are separated by ______ and _______

symbols.

Letters

in an expression

are called

_________.

10

A New Family of Graphs Name _____________________________

In (x) 0 1 2 3 4 5 10 100 -1 -3 -5 x

Out

(y)

0 2 8

In (x) 0 1 2 3 4 5 10 100 -1 -3 -5 x

Out

(y)

2x - 2

In (x) 0 1 2 3 4 5 6 10 100 -5 -3 x

Out

(y)

3x - 2

Complete each table above and graph the points.

What is the same about the patterns in each

of the tables above? Answer in complete

sentences.

What is the same about the three graphs

made from the tables above? Answer in

complete sentences.

y

x 7 -6 -4 -2 1 3 5 7

17

-11

-9

-7

-5

-3

-1

2

4

6

8

10

12

14

16

-7 -5 -1 4

-12

-10

-6

-2

3

7

11

15

-7 2

-12

-4

5

13

-3

-8

9

6

17

1

11

Multiplying Exponential Expressions

Expand and Count

Fill in each line of the table. Look for patterns.

Multiplication

Problem Expanded Notation

Simplified

Exponential

Form

Standard

Form

32 35

3 3 3 3 3 3 3

37 2187

53 52

5 5 5 5 5

55 3125

2 2 2 2 2 2 2 2 2

102 104

62 62

7 7 7

23 24

52 52

36

105 103

54

Look at the Problem and Simplified Exponential Form columns. Explain any

patterns that you see.

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

12

Dividing Exponential Expressions

Expand, Find 1’s and Count Fill in each line of the table. Look for patterns.

Division

Problem Expanded Notation

Simplified

Exponential

Form

Standard

Form

65

62

63 216

28

26

36

35

56

53

22

28

42

Look at the Problem and Simplified Exponential Form columns. Explain any

patterns that you see.

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

6 6 6 6 6

6 6 Note: 6 ÷ 6

equals 1.

2 2 2 2 2 2 2 2

2 2 2 2 2 2

10 10 10 10 10 10

10 10

13

Squares and Square Roots

It is often useful in mathematics to find the area of a square when the side is known. At other

times it is necessary to find the side when the area of a square is known. There are symbols

for each of these situations which are shown below, along with examples and a general case.

side2 area Read as "The side squared equals the area."

area side Read as "The square root of the area equals the side."

Give six more pairs of square and square root equations.

32 9 Read as “3 squared equals 9”

9 3 Read as “The square root of 9 is 3”

202 400 Read as “20 squared equals 400”

400 20 Read as “The square root of 400 is

20”

side Area

9 3 20 400

14

Squares and Square Roots II

DIRECTIONS: Give a drawing below to show the squared numbers, then write the answer.

12

=

22

=

32

=

42

=

52

=

62

=

72

=

82

=

92

=

102

=

112

=

122

=

15

Squares and Square Roots III DIRECTIONS: Give the answer to each problem along with an explanation.

EXAMPLE: 10010000 because 100 x 100 equals 10000

4

49

64

144

100

9

25

1

121

16

169

225

36

81

16

Squares and Square Roots Tree

DIRECTIONS: On this tree, make a rough draft of your Square Root Tree project. In the tree,

draw your “square fruit”. You should have at least 8 square fruits connected to their square

roots, and each square fruit/square root pair needs to be a unique color. When your rough

draft has been approved, draw a nice copy of your tree on a separate piece of paper.

17

Scientific Notation

Standard Form Conversion Work Scientific Notation

18

Multiple Mini-Problems in Multiplying Monomials

Here are three mini-problems. Simplify each.

4 5

a3 a4

b2 b4

Here is one problem that includes all three of the mini-problems above.

4a3b2 5a4b4

Use the strategy of “Expand, Rearrange, and Simplify.”

2x2y2 3x3y3

8m4n8 6m4n3

10a6 3a3

9a5b7 5a3b4

Use complete sentences to explain the strategy of “Expand, Rearrange, and Simplify.”

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

19

Multiple Mini-Problems in Dividing Monomials Here are three mini-problems. Simplify each.

10

5

a6

a2

b4

b

Here is one problem that includes all three of the mini-problems above.

10a6b4

5a2b

Use the strategy of “Expand, Rearrange, Find Ones, and Simplify.”

12x 3y 6

4x 9y 3

8m5n2

2mn4

15a6

5a6

12a4b4

8a3b5

Use complete sentences to explain “Expand, Rearrange, Find Ones, and Simplify.”

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

20

Pairs of Graphs Name _________________________

In (x) 3 1 2 7 4 0 -2 -1 -5 5 100 x

Out (y)

7 9 3

In (x) 3 1 2 7 4 0 -2 -1 -5 5 100 x

Out

(y)

2 -1 95

Complete each table above and graph the points.

Compare and contrast the two equations above and

their graphs. What is the same? What is different.

Compare and contrast the two equations below and

their graphs. What is the same? What is different.

In (x) -4 -3 -2 -1 0 1 2 3 4 10 20 x

Out

(y)

9 0 1 16

x 2

In (x) -4 -3 -2 -1 0 1 2 3 4 10 20 x

Out

(y)

1 10 101

x2 1

y

x 7 -6 -4 -2 1 3 5 7

17

-11

-9

-7

-5

-3

-1

2

4

6

8

10

12

14

16

-7 -5 -1 4

-12

-10

-6

-2

3

7

11

15

-7 2

-12

-4

5

13

-3

-8

9

6

17

1

21

Exponents Review Name _________________________________

Write each in standard form.

1.

34= 5.

53=

2.

53= 6.

2 3

=

3.

42= 7.

20=

4.

2

3

3

= 8.

3

4

4

=

Write each in expanded form and then simplified exponential form.

9.

35 34 =

10.

52 53 =

11.

26 24 =

12.

102 103 =

13.

56

52 =

14.

612

64 =

15.

85

85 =

16.

4 3

4 9 =

22

23

Topic ________________

Topic Sentence

Concrete Detail

Concrete Detail

Concrete Detail

Commentary

Concluding Sentence

24

Zero and Negative Exponents

1) Complete the following patterns. Express any decimals as fractions.

2) What does any number elevated to the 0 power equal?

3) Do negative exponents with a positive base yield a negative number?

4) Show

52 in expanded form and standard form.

5) Give three more examples, using different bases, of negative exponents. Show the

expanded and standard forms for each.

25 = 32 35 = 243

24 = 16 34 = 81

23 = 8 33 =

22 = 4 32 =

21 = 31 =

20 = 30 =

2 -1 = 3 -1 =

2 -2 = 3 -2 =

2 -3 = 3 -3 =

2 -4 = 3 -4 =

2 -5 = 3 -5 =

25

Exponents Quiz Name __________________________________

An _________ is a small

number that shows how many

times the base should be

multiplied.

One strange idea about

exponents is that anything to

the power of zero equals

____.

__________ exponents mean

you will have a fraction.

Instead of repeated

multiplication they mean

repeated ____________.

Using the _______________

form of an exponential

expression can help you

simplify it

Write each in Standard Form

1.

24=

2.

52=

3.

4

5

2

=

4.

3 3

=

5.

50=

Write each in Expanded and Simplified

Exponential Form.

6.

63 62 =

7.

56

52 =

8.

24 22=

9.

6a5b

8a3b2 =

10.

2x3 3x2=

26

Practice Multiplication Table

X 0 1 2 3 4 5 6 7 8 9 10 11 12

0

1

2

3

4

5

6

7

8

9

10

11

12

Accuracy: number of mistakes = _____________

Speed: time = _____________

Dear Parent,

Your child is building speed and accuracy by practicing the completion of this

chart. Please sign to verify this practice session.

My child filled in the above chart at home. ___________________ Parent

Signature.

27

Practice Multiplication Table with Negative Numbers

X -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

Accuracy: number of mistakes = _____________

Speed: time = _____________

Dear Parent,

Your child is building speed and accuracy by practicing the completion of this

chart. Please sign to verify this practice session.

My child filled in the above chart at home. ___________________

Parent

Signature.

28

Exponents Quiz 2 Name _________________________________

An _________ is a small

number that shows how many

times the base should be

multiplied.

One strange idea about

exponents is that anything to

the power of ______ equals

one.

Negative exponents mean

you will have a _________.

Instead of repeated

multiplication they mean

repeated ____________.

Using the _______________

form of an exponential

expression can help you

simplify it

Write each in Standard Form

1.

53=

2.

72=

3.

2

3

3

=

4.

60=

5.

2 4

=

Write each in Expanded and Simplified

Exponential Form.

6.

42 44 =

7.

38

32 =

8.

55 53=

9.

10p3q2

6pq4 =

10.

5x2 4x2=