Algebra StAIR Lesson:
The Order of Operations
Mrs. Lewis
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Lesson Objectives
This lesson will teach you everything you need
to know about the Order of Operations. By
the end of this lesson you will be able to…
1.
2.
3.
4.
Understand and explain why we need an established
Order of Operations
State the correct Order of Operations
Use the Order of Operations to simplify numerical
expressions
Use the Order of Operations to simplify algebraic
expressions
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Instructions
• Complete this lesson on your own and at your own
pace.
• Use the navigational buttons along the bottom to
move throughout the lesson.
• Take notes as you go. The objectives (on the previous
page) will be assessed by a quiz at the end of this
lesson and on our Chapter Test.
• After linking to a website, simply close your
browser window to return to this lesson.
• Have a pencil, paper, and a calculator handy.
• Have fun!
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Let’s warm up!
1. Simplify
2
4
a.
8
b.
2
c.
16
d.
1/2
Click here if you
need a quick
refresher on powers.
Let’s warm up!
1. Simplify
2
4
Exponent
Base
Hint:
The exponent tells you how
many times to multiply the
base! Go back and try again!
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Let’s warm up!
1. Simplify
Great!
2
4
2
4
 4 4
 16
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Let’s warm up!
2. Simplify
5  16
a.
11
b.
-11
c.
21
d.
-21
Click here if you
need a quick
refresher on
absolute value.
Let’s warm up!
2. Simplify
5  16
Absolute
Value Bars
Hint:
The absolute value of a number
is its distance from zero on a
number line. (always positive)
Go back and try again!
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Let’s warm up!
2. Simplify
Great!
5  16
5  16
  11
 11
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Let’s warm up!
3
3. Simplify
(2)
a.
-6
b.
-5
c.
8
d.
-8
Click here if you
need a quick
refresher on powers.
Let’s warm up!
3. Simplify
3
(2)
Exponent
Base
Hint:
The exponent tells you how
many times to multiply the
base! Go back and try again!
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Let’s warm up!
3. Simplify
Great!
3
(2)
( 2)
3
 ( 2)( 2)( 2)
 ( 4)( 2)
 8
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Now that’s all fine and dandy…
…but what happens when we have to simplify
an expression with more than one operation?!
How do you know which operation to do first?
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For example…
15  2  3  1
Take a moment to think about how you
would solve this problem. When you have
an answer in your head, click next.
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Without an Order of Operations…
Sally might do this…
15  2  3  1
 13  3  1
 39  1
40
Einstein might do this…
15  2  3  1
Mrs. Lewis might do this…
15  2  3  1
 15  6  1
 9 1
10
Billy might do this…
15  2  3  1
 13  3  1
 15  6  1
 13  4
 15  7
52
8
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Question of the day…
Who is right?
The truth is…if there were no established Order of Operations,
everyone would be right. But that doesn’t get us anywhere!
Maybe someone should decide on a standard order for doing
mathematical operations so that we can all get the same
answer every time!
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The ORDER OF OPERATIONS
Parentheses
Exponents
Multiplication/Division (Left to Right)
Addition/Subtraction (Left to Right)
PEMDAS
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How am I supposed to remember that?
Please Excuse My Dear Aunt Sally
Watch a music video here!
(Video will play after a short advertisement)
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So who was right?
Mrs. Lewis! Who did you think?!
Let’s take a look at the problem again…
15  2  3  1
 15  6  1
 9 1
 10
Parentheses? No.
Exponents? No.
Multiply/Divide? Yes! L to R
Add/Subtract? Yes! L to R
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Click play
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Let’s look at some examples…
1. Simplify  4  24  3  2
2
 16  24  3  2
 16  8  2
 16  16
Parentheses? No.
Exponents? Yes!
Multiply/Divide? Yes! L to R
Add/Subtract? Yes! L to R
0
See another example
Challenge me
Let’s look at some examples…
2. Simplify 12  3  10  2
2
 12  9  10  2
 12  9  5
 3 5
8
Parentheses? No.
Exponents? Yes!
Multiply/Divide? Yes! L to R
Add/Subtract? Yes! L to R
Review more
Move on
Challenge!
Simplify
Brackets are just
like parentheses
425 ( 5  2)
2

a.
81
Parentheses? Yes! 2 sets.
Work from the inside out.
b.
96
Exponents? Yes!
c.
0
Multiply/Divide? Yes! L to R
d.
64
Add/Subtract? Yes! L to R
Challenge!
Simplify
 425  3

 425  9
 4 16
 64
2
Brackets are just
like parentheses
425 ( 5  2)
2

Parentheses? Yes! 2 sets.
Work from the inside out.
Exponents? Yes!
Multiply/Divide? Yes! L to R
Add/Subtract? Yes! L to R
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Let’s look at some examples…
3. Evaluate 21  x  2  5 for x  7
 21  7  2  5
 21  7  10
 14 10
 24
See another example
Substitute 7 for x.
Parentheses? No.
Exponents? No.
Multiply/Divide? Yes! L to R
Add/Subtract? Yes! L to R
Challenge me
Let’s look at some examples…
4. Evaluate 5 (30  x ) for x  24
2
 5 (30  24)
2
 5 6
2
 25  6
 150
Review more
Substitute 24 for x.
Parentheses? Yes!
Exponents? Yes!
Multiply/Divide? Yes! L to R
Move on
Challenge!
Evaluate ( x  2 ) (2  6) for x  6
2
a.
18
b.
78
c.
3
d.
152
Substitute 6 for x.
Parentheses? Yes! 2 sets.
Exponents? Yes!
Multiply/Divide? Yes! L to R
Challenge!
Evaluate ( x  2 ) (2  6) for x  6
2
 (6  2 ) (2  6)
Substitute 6 for x.
 (6  4)  8
Exponents? Yes!
2
 24 8
Parentheses? Yes! 2 sets.
Multiply/Divide? Yes! L to R
3
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Let’s change things up…
Choose the operation that makes the statement
true.
12 6  9

Choose the operation that makes the statement
true.
17 ( 12  7)  12

Choose the operation that makes the statement
true.
108 ( 7  2)  12

Now it’s your turn…
1. Simplify 5( 1  2) (3  2)
a.
-6
b.
-2
c.
4
d.
2.5
“That was absolutely dreadful.”
Go back and try again!
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Now it’s your turn…
2. Simplify (6  2  3) ( 9  7)
2
a.
-6
b.
6
c.
3
d.
-3
“You’re fired!”
Go back and try again!
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Now it’s your turn…
3. Evaluate 3( x  12  2) for x  8
a.
48
b.
72
c.
-32
d.
-48
“Bring me your torch. The tribe has
spoken.”
Go back and try again!
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Time for a game…
• You will now play a game of Order of
Operations Millionaire!
• After choosing a player and typing in your
name, you will answer 10 questions.
• Please print your certificate and turn in to
Mrs. Lewis when you are finished.
• Click here to play!
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Review
What is the correct Order of Operations?
a. Always go straight from left to right.
b. Do the easy parts first and then everything else.
c. You get the same answer no matter what order.
d. parentheses, exponents, multiply/divide, add/subtract
You are nearing the end…
Choose an option from the list below.
I am completely lost!
I need to go through the examples again.
Can I see one more video explanation?
I’m ready for the quiz!
QUIZ
Please record all work and your answers on a
piece of paper and turn it in to Mrs. Lewis
when you are finished.
I’m ready
QUIZ
1. Why do we need an established Order of
Operations?
2. What is the correct Order of Operations? Be
specific.
2
3. Simplify 5  8  4  16 2
4. Evaluate x  y( y  2) for x  3, y  2
done
Great job!
You have completed this lesson!
Turn in:
Quiz
Math Millionaire Certificate