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. Understand and explain why we need an established Order of Operations

2. State the correct Order of Operations3. Use the Order of Operations to simplify numerical

expressions4. Use the Order of Operations to simplify algebraic

expressionsback next

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. Simplify24

a. 8

b. 2

c. 16

d. 1/2

Click here if you need a quick refresher on powers.

Let’s warm up!

1. Simplify24

Hint:

The exponent tells you how many times to multiply the base! Go back and try again!

Base

Exponent

back

Let’s warm up!

1. Simplify24

Great!

16

44

42

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Let’s warm up!

2. Simplify 165 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 165 Hint:

The absolute value of a number is its distance from zero on a number line. (always positive) Go back and try again!

Absolute Value Bars

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Let’s warm up!

2. Simplify 165 Great!

11

11

165

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Let’s warm up!

3. Simplify 3)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(

back

Hint:

The exponent tells you how many times to multiply the base! Go back and try again!

Base

Exponent

Let’s warm up!

3. Simplify 3)2(Great!

8

)2()4(

)2()2()2(

)2( 3

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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…

13215 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…

40

139

1313

13215

Sally might do this…

Billy might do this…

Einstein might do this…

Mrs. Lewis might do this…

10

19

1615

13215

52

413

1313

13215

8

715

1615

13215

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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

ParenthesesExponentsMultiplication/Division (Left to

Right)Addition/Subtraction (Left to

Right) PEMDASnext

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…

13215 Parentheses? No.

Exponents? No.

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R

191615

10next

Click play

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Let’s look at some examples…

232442

232416 2816

1616

Parentheses? No.

Exponents? Yes!

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R0

1. Simplify

Challenge me

See another example

Let’s look at some examples…

210312 2

210912 5912

53

Parentheses? No.

Exponents? Yes!

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R8

2. Simplify

Move onReview more

Challenge!

2)25(254

Parentheses? Yes! 2 sets. Work from the inside out.

Exponents? Yes!

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R

a. 81

b. 96

c. 0

d. 64

Brackets are just like parentheses

Simplify

Parentheses? Yes! 2 sets. Work from the inside out.

Exponents? Yes!

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R

Challenge!

2)25(254

64 164

Simplify

23254

9254

Brackets are just like parentheses

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Let’s look at some examples…

52721 10721

1014

Substitute 7 for x.

Parentheses? No.

Exponents? No.

Multiply/Divide? Yes! L to R

Add/Subtract? Yes! L to R

24

3. Evaluate for

Challenge me

See another example

5221 x 7x

Let’s look at some examples…

)2430(52

652 625

Substitute 24 for x.

Parentheses? Yes!

Exponents? Yes!

Multiply/Divide? Yes! L to R

150

4. Evaluate for)30(52 x 24x

Move onReview more

Challenge!

Substitute 6 for x.

Parentheses? Yes! 2 sets.

Exponents? Yes!

Multiply/Divide? Yes! L to R

a. 18

b. 78

c. 3

d. 152

Evaluate for

)62()2( 2 x 6x

Challenge!

3824

)62()26( 2

8)46(

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Evaluate for

)62()2( 2 x 6x

Substitute 6 for x.

Parentheses? Yes! 2 sets.

Exponents? Yes!

Multiply/Divide? Yes! L to R

Let’s change things up…

Choose the operation that makes the statement true.

9621

Choose the operation that makes the statement true.

12)712(17

Choose the operation that makes the statement true.

12)27(108

Now it’s your turn…

)23()21(5 1. Simplify

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)79()326( 2.

Simplifya. -6

b. 6

c. 3

d. -3

“You’re fired!”

Go back and try again!

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3. Evaluate for

Now it’s your turn…

)212(3 x

a. 48

b. 72

c. -32

d. -48

8x

“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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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

Review

What is the correct Order of Operations?

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.

3. Simplify4. Evaluate for

2216485

)2( yyx 2,3 yx

done

Great job!You have completed this

lesson!Turn in:

QuizMath Millionaire Certificate