Download Document

Name
______________
Period ______
1
2
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.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
3
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.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
4
Exponential
Form
23
22
21



Exponential
Form
Standard
Form
53
52
51
Exponential
Form
Standard
Form
33
32
31
Exponential
Form
Standard
Form
63
62
61
Standard
Form
43
42
41
Standard
Form



Exponential
Form
Standard
Form
93
92
91



Exponential
Form
Exponential
Form
83
82
81









Standard
Form



Exponential
Form
Standard
Form
73
72
71
Exponential
Form
10 3
10 2
101






5
Standard
Form
Eggs in a Carton
Name __________________
Date: __________ Per.: ____
Table, Graph and Equation
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
Weight (Y)
3
6
9
12
16
25
34
43
30
X
a) Make a graph showing the weight of the eggs vs. the number of eggs in the carton.
Ounces
50
45
40
35
30
25
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
10
11
6
12
13
14
15
16
17
18
19
20
Number of eggs
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?
7
More Exponent Patterns
Exponential
Form
Standard
Form
Show each expression below in expanded
and standard form.
33
32
31
Exponential
Form
43



25
Exponential
Form
Standard
Form
53
52
51






Name _____________________________
Exponential
Form
83
82
81
Standard
Form

61

40

71

104

103

92

4 2

70

63

90


8
Expanded Form
Standard
Form
Simplifying Expressions with Variables III
This whole thing is called an _________________
This expression has three parts called _________.
12  8  (5  3)  8
Letters
in an expression
are called
_________.
These grouping symbols are called _________________
DO THESE FIRST!

x  y  x 2
These parts are separated by ______ and _______
symbols.

Draw pictures and use the values x = -5 and y = 8 to evaluate these expressions.
Basic Problems
3y
2y  3x
2x  8
1.
2.
3.



Challenging Problems
xy  6y
4.

5.
3 2x  3y
2
2
6. x  y


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.
9
2, 2, 2, 4
10.
1, 2, 5, 8
A New Family of Graphs
In (x)
Out
(y)
0
In (x)
Out
(y)
0
In (x)
Out
(y)
0
1
2
Name _____________________________
3
0
1
2
4
5
10
2
3
4
100
-1
-3
-5
x
100
-1
-3
-5
x
8
5
10
2x - 2
1
2
3
4
5
6
10
100
-5
-3
x
3x - 2
y
Complete each table above and graph the points.
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
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.
x
-7 -6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
10
1
2
3
4
5
6
7







Multiplying Exponential Expressions
Expand and Count
Fill in each line of the table. Look for patterns.
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
Multiplication
Problem

10 104

2
2
6 6

2
2 2 2 2 2 2  2 2 2


7  7 7
23  24
52  52

36
105 103

54
Look at the Problem and Simplified Exponential Form columns. Explain any
patterns that you see.

_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
11
Dividing Exponential Expressions
Expand, Find 1’s and Count
Fill in each line of the table. Look for patterns.
Division
Problem
65
62



Expanded Notation
Simplified
Exponential
Form
Standard
Form
6 6 6 6 6
6 6
63
216
Note: 6 ÷ 6
equals 1.
28
26
2 2 2 2 2 2 2 2

2 2 2 2 2 2
36 
35

10 10 10 10 10 10
10 10
56
53

22

28
42

Look at the Problem and Simplified Exponential Form columns. Explain any
patterns that you see.

_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
12
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.
3
32  9
93
9
20
202  400
Read as “3 squared equals 9”
400  20
Read as “The square root of 9 is 3”




side
2
side  area
area  side
400
Read as “20 squared equals 400”
Read as “The square root of 400 is
20”
Area
Read as "The side squared equals the area."
Read as "The square root of the area equals the side."
Give six more pairs of square and square root equations.
13
Squares and Square Roots II
DIRECTIONS: Give a drawing below to show the squared numbers, then write the answer.
2
1 =
7 =
2
2
2
2 =
8 =
2
2
3 =
9 =
2
2
4 =
10 =
2
2
5 =
11 =
2
2
6 =
12 =
14
Squares and Square Roots III
DIRECTIONS: Give the answer to each problem along with an explanation.
EXAMPLE:
10000  100 because 100 x 100 equals 10000
4
1
49 
121 
64 
16 
144 
169 
100 
225 
9
36 
25 
15
81 
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.
16
Scientific Notation
Standard Form
Conversion Work
17
Scientific Notation
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.”
8m4 n 8  6m4 n 3
2x 2 y 2  3x 3 y 3

3
10a  3a
6


9a5b7  5a3b4

Use complete sentences to explain the strategy of “Expand, Rearrange, and Simplify.”
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
18
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.

10a 6b 4
5a 2b

Use the strategy of “Expand, Rearrange, Find Ones, and Simplify.”
8m 5 n 2
2mn 4
12x 3 y 6
4 x9y3

15a 6
5a 6

12a 4 b 4
8a 3b 5


Use complete sentences to explain “Expand, Rearrange, Find Ones, and Simplify.”
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
19
Pairs of Graphs
In (x)
3
1
2
7
7
Out (y)
In (x)
Out
(y)
Name _________________________
3
1
2
4
0
-2
9
7
4
2
-1
-1
-5
5
100
x
3
0
-2
-1
-5
5
100
x
95
y
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
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.
x
-7 -6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
In (x)
Out
(y)
-4
In (x)
Out
(y)
-4
-3
-2
-1
9
-3
-2
-1
0
1
0
1
0
1
2
3
4
1
2
3
10
4
20
1
3
10
4
6
7
x
x2
16
2
5
10
101

20

20
x
x 2 1
Exponents Review
Name _________________________________
Write each in standard form.




1.
34 =
5.
53 =
2.
53=
6.
2 =
3.
4 2 =

7.
20=

 3 4
 
8. 
 4  =
3
2 

4. 
3  =

3
Write each in expanded form and then simplified exponential form.
9.
35  34 =

10. 5  5 =
2
3

11. 2  2

12. 10 10

56
13.
52 =




4
6
2
=
3
=
612
14.
64 =
85
15.
85 =
43
16.
49 =
21

22
Topic ________________
Topic Sentence
Concrete Detail
Concrete Detail
Concrete Detail
Commentary
Concluding Sentence
23
Zero and Negative Exponents
1) Complete the following patterns. Express any decimals as fractions.
2 5 = 32
3 5 = 243
2 4 = 16
3 4 = 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 =
2) What does any number elevated to the 0 power equal?
3) Do negative exponents with a positive base yield a negative number?
2
4) Show 5
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.
24
Exponents Quiz
Name __________________________________
An _________ is a small
Write each in Standard Form
number that shows how many
times the base should be
multiplied.

One strange idea about
exponents is that anything
to
1.
24 =
2.
52 =
4 2

3. 
5  =
the power of zero equals
____.
Instead of repeated
5.
50=

__________ exponents mean
you will have a fraction.
4.
3 =


multiplication they mean
3
Write each in Expanded and Simplified
Exponential Form.
6.
63  62 =
7.
56
52 =
8.
24  22 =
9.
6a 5b
8a 3b 2 =
repeated ____________.

Using the _______________
form of an exponential
expression can help you
simplify it


10. 2x  3x =
3


25
2
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. ___________________
26
Parent
Signature.
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. ___________________
27
Parent
Signature.
Exponents Quiz 2
Name _________________________________
Write each in Standard Form
An _________ is a small
number that shows how many
1.
53=
2.
72 =
times the base should be
multiplied.

One strange idea about
exponents is that anything
to
the power of ______ equals
one.
4.
60=
5.
2 =

Negative exponents mean
you will have a _________.
Instead of repeated
2 3

3. 
3  =

multiplication they mean
4
Write each in Expanded and Simplified
Exponential Form.
6.
42  44 =
7.
38
32 =
8.
55  53 =
repeated ____________.

Using the _______________
form of an exponential
expression can help you
simplify it


10 p 3q 2
9.
6 pq 4 =
10. 5x  4x =
2


28
2