3 4 Order of Operations X When you

3 4 Order of Operations () + - X

When you get dressed, do you put on your shoes or socks first? Why? Explain your thinking.

When you make cereal, do you fill the bowl with milk or cereal first? Why? Explain your thinking.

In our lives and in math, we need to do things in a certain order to make sure they turn out right. Try to come up with three or more examples from your life.

In your notebook, make a list… What do you know about Order of Operations? List as many things as you can!

Compare your list with your partner’s list. Can you add anything to your list?

The Order of Operations tells us how to do a math problem with more than one operation, in the correct order.

Order of Operations A standard way to simplify mathematical expressions and equations.

In most languages, the meaning of words depend on the order: Ex. Sign the check Is not the same as Check the sign

Mathematics is a type of language and it also has a specific order. Ex. 3 + 5 X 2 Oh no! What do we do first? Add or multiply? If we add first: 3+5 X 2 8 X 2 16 If we multiply first: 3+5 X 2 3 + 10 Help ! 13 Uh Oh! Which one is the correct answer?

What is PEMDAS? In order to make sure every person gets the same answer to a math problem, mathematicians came up with a rule called the order of operations Parenthesis ( ) [ ] Exponents 23 Whichever comes first Multiplication X from left to right! Division ÷ Addition + Whichever comes first Subtraction from left to right!

Purpose u. Avoids Confusion u. Gives Consistency For example: 8 + 3 * 4 = 11 * 4 = 44 Or does it equal 8 + 3 * 4 = 8 + 12 = 20

The Rules 1. Simplify within Grouping Symbols ( ), { }, [ ], | | 2. Simplify Exponents Raise to Powers 3. 4. Complete Multiplication and Division from Left to Right Complete Addition and Subtraction from Left to Right

How am I supposed to remember that! e s a e l P e s u c Ex My Dear Aunt Sally

Please Excuse My Dear Aunt Sally This will help to you to remember the order of operations.

Please Excuse My Dear Aunt Sally P E M D A S Parentheses ( Exponents Multiply Divide Add + Subtract - x ) 3 4

Please Excuse My Dear Aunt Sally Parentheses ( Always do parentheses 1 st. )

Please Excuse My Dear Aunt Sally Exponents 3 4 Always do Exponents 2 nd.

Please Excuse My Dear Aunt Sally Multiply Divide x Do multiplication and division 3 rd, from left to right.

Please Excuse My Dear Aunt Sally Add + Subtract Do addition and subtraction 4 th, from left to right.

Z-Book o Cut out the z-book. o Fold the book as you would a fan. Be sure to fold so the first page remains on top of the z-book. o Write your name on the back.

Pocket Assembly o Cut out the pocket. o Fold the three flaps backward and tape or glue. o Tape or glue into your math journal.

Let’s Try Some Problems!

Example 1: 2 x 3 - (4 -2) + 32 Parenthesis Multiplication Subtraction Exponents Addition

2 x 3 - (4 -2) + 32 Parenthesis 2 x 3 Exponents - 2 + 32 2 x 3 -2+9 Multiply Add or 6 -2+9 Subtract – Left to Right 4+9 13

PEMDAS 3 3+2 - (9+1) 3 3+2 - 10 3+8 -10 11 -10 1

PEMDAS 3 (9+1) + 2 3(10)+6 2 6 3(10)+36 30+36 66

PEMDAS 4+5 x (6 -2) 4+5 x 4 4+20 24

PEMDAS 64 (9 x 3 -19) 64 (27 – 19) 64 8 8

Part 2 Using grouping Symbols Grouping symbols such as parenthesis ( ) and brackets [ ] come first in the order of operations. A fraction bar is also a grouping symbol since: 4 + 2 = (4 + 2) ÷ 3 3 Always work inside grouping symbols first!

Order of Operations 1) Work inside grouping symbols. 2) Multiply and divide from left to right. 3) Add and subtract in order from left to right.

Example 3 Simplify 10 ÷ [9 – (2. 2)]. PEMDAS. 10 ÷ [9 – (2 2)] Multiply in parenthesis. 10 ÷ [9 – 4 ] Subtract in brackets. 10 ÷ 5 Divide. 2

! y r T u Yo 9) 2[ (13 – 4) ÷ 3] 10) 1+ 10 - 2 4

Have fun doing the Order of Operations!

Practice Problems Try these on your own. 1. 3 + 5 x 7 2. (1 + 3) x (8 - 4) 3. 6 - 6 + (7 - 0) - 7 4. 4 - 3 + (5 - 1) - 3 5. 3 + 9 x 8 – 62 6. 2+3 x (4+(6 x 3 -8)) x 2

Answers 1. 2. 3. 4. 5. 6. 38 16 0 2 13 86

It’s in the Cards o You and a partner will complete the series of problems inserting the correct operations (+, -, x, ÷) making the sentence true.

EXIT SLIP On a separate piece of paper, complete the following problems. Please turn in your paper before you exit the room. 1. Insert grouping symbols to make the number sentence true: 7 X 8 – 6 + 3 = 17 2. How does the order in which you do the operations affect your answer? 3. Why do we need to agree on an order of operations?