Order of Operations

Algebra Standard

GLE 0506.3.1 Understand and Use Order of Operations

SPI 0506.3.2 Evaluate multi-step numerical expressions involving fractions using order of operations.

CCSS Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Order of Operations

Why use Order of Operations???

Do both sentences mean the same?

• The teacher said, “The student is wrong.”

• “The teacher,” said the student, “is wrong.”

• “In mathematical expressions, what would have

the same type of effect as punctuating a sentence?”

22 + (12 x 2) = 22 + 24 = 46 (22 + 12) x 2 = 34 x 2 = 68

How does a parenthesis change the evaluation of the expression?

•Evaluate: 5 + 4 x 2

Is the answer 18 or 13? The order of

operations become important.

• “What if there are no parentheses in an expression? How do we evaluate it?”

Order of Operations

Just as it is important for you to add your items when you are shopping first before adding sales tax, it is equally important to solve

expressions involving more than one operation in a certain order. When evaluating

expressions with more than one operation, you should use the order of operations.

We have an order to evaluating an expression

The order of operations is a set of rules used for evaluating an expression with more than one operation.

Order of Operations“Please Excuse My Dear Aunt Sally” (PEMDAS) is a way

to help remember how to perform the order of operations.

• 1st: Work within the parentheses • 2nd: Exponents 2¶= 2x2x2x2x2 = 32• 3rd: Multiplication & division from left to right• 4th: Addition & subtraction from left to right

•Order of OperationsExample 1

Evaluate this expression: 14 – 6 3Strategy: Use the order of operations.

Step 1: There are no grouping symbols or exponents, so multiply and divide from left to right.

14 – 6 3 14 2

Step 2: Add and subtract from left to right.14 2 12

Solution 14 6 3 12

Priority of Operations•Parenthesis•Exponents•Multiplication/Division•Addition/Subtraction

Group Activity•Distribute one card to each participant• Solve the expression• Circulate and find a partner with an equivalent expression• Explain to partner order used to evaluate the expression

Priority of Operations

( ) Please x2 Excusex, My Dear+, - Aunt Sally

Example : Evaluate 9 - 5 ÷ (8 - 3) x 2 + 6

• Step 1: 9 - 5 ÷ (8 - 3) x 2 + 6 = 9 - 5 ÷ 5 x 2 + 6 Parentheses

• Step 2: 9 - 5 ÷ 5 x 2 + 6 = 9 - 1 x 2 + 6 Division

• Step 3: 9 - 1 x 2 + 6 = 9 - 2 + 6 Multiplication

• Step 4: 9 - 2 + 6 = 7 + 6 Subtraction

• Step 5: 7 + 6 = 13 Addition

PEMDASColored-coded

(5 - 4) x 22 1 x 22

22

2 - 1 + (3 x 4) 2 - 1 + 12

1 + 12 13

Identify the steps in different colors. Second, complete each step in that color.

20 + 10 – 5 x 10 Â 2 20 + 10 – 50 Â 2

20 + 10 – 25 30 – 25

5

Dr. Xpression Operation!

Solve each expressionCut out the expression an glue under the

equivalent expression to match

To find lesson plans and activities

www.TN-5thGrade.wikispaces.com

• Your Turn!!!Solve these expressions using the order of operations.• 1) 18 - 6 x 2 • 2) 10 + 3(2 + 6) • 3) 50 - 10(4 - 2) + 6 • 4) 2 x 9 - 3(6 - 1) + 1 • 5) 8 + 24 ÷ 4 x 2

• 1) 6• 2) 34• 3) 36• 4) 4• 5) 20

Check Your Answers