1-3 - My CCSD
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Transcript 1-3 - My CCSD
1-3
1-3 Exponents
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-3 Exponents
Warm Up
Multiply.
1. 3 3 3
27
2. 4 4 4
64
3. 2 2 2 2
16
4. 5 5 5 5
625
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1-3 Exponents
Problem of the Day
Replace the letters a, b, and c with the
numbers 3, 4, and 5 to make a true
statement.
2a + 2a = bc
25+ 25 = 43
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1-3 Exponents
Learn to represent numbers by using
exponents.
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1-3 Exponents
Vocabulary
exponent
base
exponential form
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1-3 Exponents
An exponent tells how many times
a number called the base is used
as a factor.
A number is in exponential form
when it is written with a base and
an exponent.
Exponent
Base
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3
=
7
7
7=
343
7
1-3 Exponents
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Exponential Form
101
Read
Multiply
“10 to the 1st power”
Value
10
10
1-3 Exponents
Exponential Form
Multiply
“10 squared” or
“10 to the 2nd power”
10 10
Value
100
Read
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102
1-3 Exponents
Exponential Form
Multiply
“10 cubed” or
“10 to the 3rd power”
10 10 10
Value
1,000
Read
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103
1-3 Exponents
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Exponential Form
104
Read
Multiply
“10 to the 4th power”
10 10 10 10
Value
10,000
1-3 Exponents
Additional Example 1: Writing Numbers in
Exponential Form
Write each expression in exponential form.
A. 5 5 5 5
54
5 is a factor 4 times.
B. 3 3 3 3 3
35
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3 is a factor 5 times.
1-3 Exponents
Check It Out: Example 1
Write each expression in exponential form.
A. 7 7 7
73
7 is a factor 3 times.
B. 6 6 6 6 6 6
66
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6 is a factor 6 times.
1-3 Exponents
Additional Example 2: Finding the Value of
Numbers in Exponential Form
Find each value.
A. 26
26 = 2 2 2 2 2 2
= 64
B. 45
45 = 4 4 4 4 4
= 1,024
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1-3 Exponents
Check It Out: Example 2
Find each value.
A. 34
34 = 3 3 3 3
= 81
B. 25
25 = 2 2 2 2 2
= 32
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1-3 Exponents
Additional Example 3: Problem Solving Application
A phone tree is used to contact families at
Paul’s school. The secretary calls 4 families.
Then each family calls 4 other families, and so
on. How many families will be notified during
the fourth round of calls?
1
Understand the Problem
The answer will be the number of families
called in the 4th round.
List the important information:
• The secretary calls 4 families.
• Each family calls 4 families.
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1-3 Exponents
2
Make a Plan
You can draw a diagram to see how many
calls are in each round.
Secretary
1st round – 4 calls
2nd round–16 calls
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1-3 Exponents
3
Solve
Notice that in each round, the number of calls
is a power of 4.
1st round: 4 calls = 4 = 41
2nd round: 16 calls = 4 4 = 42
So during the 4th round, there will be 44 calls.
44 = 4 4 4 4 = 256
During the 4th round of calls, 256 families will
have been notified.
4
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Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
1-3 Exponents
Check It Out: Example 3
A phone tree is used to contact families at
Paul’s school. The secretary calls 3 families.
Then each family calls 3 other families, and
so on. How many families will be notified
during the fourth round of calls?
1
Understand the Problem
The answer will be the number of families
called in the 4th round.
List the important information:
• The secretary calls 3 families.
• Each family calls 3 families.
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1-3 Exponents
2
Make a Plan
You can draw a diagram to see how many
calls are in each round.
Secretary
1st round – 3 calls
2nd round–9 calls
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1-3 Exponents
3
Solve
Notice that in each round, the number of calls
is a power of 3.
1st round: 3 calls = 3 = 31
2nd round: 9 calls = 3 x 3 = 32
So during the 4th round, there will be 34 calls.
34 = 3 3 3 3 = 81
During the 4th round of calls, 81 families will
have been notified.
4
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Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
1-3 Exponents
Lesson Quiz
Write each expression in exponential form.
1. 12 12 12
123
2. 9 9 9 9 9 9 9
97
Find each value.
3. 202 400
4. 64
1,296
5. In a phone tree, each of three people will call
three people, and then each of those will call
three more. If there are five levels of the tree,
how many people will be called? 243
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1-3
1-4 Exponents
Order of Operations
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-3 Exponents
Warm Up
Perform the operations in order from
left to right.
1.
2.
3.
4.
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8+4–2
93+1
7–3+5
20 ÷ 4 + 6
10
28
9
11
1-3 Exponents
Problem of the Day
0123456789=1
Put the appropriate plus or minus signs
between the numbers so that the total
equals 1.
0 + 1 – 23 + 45 + 67 – 89 = 1
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1-3 Exponents
Learn to use the order of operations.
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1-3 Exponents
Vocabulary
numerical expressions
evaluate
order of operations
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1-3 Exponents
A numerical expression is a mathematical
phrase that includes only numbers and operation
symbols.
Numerical
4+8÷2
Expressions
6 371 – 203 + 2 5,006 19
When you evaluate a numerical expression, you
find its value.
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1-3 Exponents
When an expression has more than one
operation, you must know which operation to do
first. To make sure that everyone gets the same
answer, we use the order of operations.
ORDER OF OPERATIONS
1. Perform operations in parentheses.
2. Find the values of numbers with exponents.
3. Multiply or divide from left to right as
ordered in the problem.
4. Add or subtract from left to right as ordered
in the problem.
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1-3 Exponents
Helpful Hint
The first letters of these words
can help you remember the
order of operations.
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Please
Parentheses
Excuse
Exponents
My
Multiply
Dear
Divide
Aunt
Add
Sally
Subtract
1-3 Exponents
Additional Example 1A: Using the Order of
Operations
Evaluate the expression.
15 – 10 ÷ 2
15 – 10 ÷ 2
There are no parentheses or
exponents.
15 –
Divide.
5
10
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Subtract.
1-3 Exponents
Additional Example 1B: Using the Order of
Operations
Evaluate the expression.
9 + (21 ÷ 7) 5
9 + (21 ÷ 7) 5
9+
9+
24
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3
5
15
Perform operations within
parentheses.
Multiply.
Add.
1-3 Exponents
Check It Out: Example 1A
Evaluate the expression.
12 – 6 ÷ 2
12 – 6 ÷ 2
There are no parentheses or
exponents.
12 –
Divide.
9
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3
Subtract.
1-3 Exponents
Check It Out: Example 1B
Evaluate the expression.
7 + (24 ÷ 6) 3
7 + (24 ÷ 6) 3
7+43
Perform operations within
parentheses.
7 + 12
Multiply.
19
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Add.
1-3 Exponents
Additional Example 2A: Using the Order of
Operations with Exponents
Evaluate the expression.
24 + 6 4
2 +64
There are no parentheses.
16 + 6 4
Find the value of the number
with the exponent.
16 + 24
Multiply.
4
40
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Add.
1-3 Exponents
Additional Example 2B: Using the Order of
Operations with Exponents
Evaluate the expression.
24 ÷ (9 – 6) 32 – 10
24 ÷ (9 – 6) 32 – 10
Perform operations within
24 ÷ 3 32 – 10
parentheses.
Find the value of the
24 ÷ 3 9 – 10
number with the exponent.
8 9 – 10
Divide.
72 – 10
62
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Multiply.
Subtract.
1-3 Exponents
Check It Out: Example 2A
Evaluate the expression.
42 + 3 7
42 + 3 7
There are no parentheses.
16 + 3 7
Find the value of the number
with the exponent.
16 + 21
Multiply.
37
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Add.
1-3 Exponents
Check It Out: Example 2B
Evaluate the expression.
32 ÷ (8 – 4) 22 – 12
32 ÷ (8 – 4) 22 – 12
32 ÷ 4
22
– 12
32 ÷ 4 4 – 12
8
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4 – 12
Perform operations within
parentheses.
Find the value of the
number with the exponent.
Divide.
32 – 12
Multiply.
20
Subtract.
1-3 Exponents
Additional Example 3: Consumer Application
Mr. Kellett bought 6 used CDs for $4 each and
5 used CDs for $3 each. Evaluate the
following expression to find the amount Mr.
Kellett spent on CDs.
64+53
24
+
15
39
Mr. Kellett spent $39 on CDs.
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1-3 Exponents
Check It Out: Example 3
Ms. Nivia bought 4 new CDs for $8 each and 6
used CDs for $4 each. Evaluate the following
expression to find the amount Ms. Nivia spent
on CDs.
48+64
32 +
24
56
Ms. Nivia spent $56 on CDs.
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1-3 Exponents
Lesson Quiz
Evaluate each expression.
1. 15 + 4 2
23
2. (12 – 5)2 – 10
39
3. 3 + 9 2 – 5
16
4. 43 – 30 ÷ 2
49
5. Chaz bought 4 football cards for $2 each and 8
baseball cards for $3 each. Evaluate the
expression to find the amount Chaz spent on
cards: 4 2 + 8 3. $32
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