Order of Order of OperationsOperations( ) +

X-

43

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

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.

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 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!

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?

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

Order of Operations Webquest• You will find your partner for the webquest by

matching scientific notation numbers.• EVERYONE will turn in a worksheet.• Go to

http://imet.csus.edu/imet10/portfolio/esquivel_w/284/webquest.html

• Your goal is to get to #7 today. You may work ahead.

• Raise your hand if you need help!

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

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

103 +

13

Uh Oh! Which one is the correct answer?

Help!

Oh no!

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 23Multiplication XDivision ÷Addition +Subtraction -

Whichever comes first from

left to right!

Whichever comes first from

left to right!

Purpose

Avoids ConfusionGives 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. Complete Multiplication and Division from Left to Right

4. Complete Addition and Subtraction from Left to Right

How am I supposed to

remember that!

Please

Excuse

My

Dear

Aunt

Sally

Please Excuse My Dear

Aunt Sally

This will help to you to remember the order of operations.

Add +

Subtract -

Multiply x

Divide

Please Excuse My Dear Aunt Sally

PEMDAS

Parentheses ( ) Exponents 43

Please Excuse My Dear Aunt Sally

Parentheses ( )

Always do parentheses

1st.

Please Excuse My Dear Aunt Sally

Exponents 43

Always do Exponents

2nd.

Multiply x

Divide

Please Excuse My Dear Aunt Sally

Do multiplication

and division 3rd, from left to

right.

Add +

Subtract -

Please Excuse My Dear Aunt Sally

Do addition and subtraction 4th,

from left to right.

Let’s Try Let’s Try Some Some Problems!Problems!

Example 1:Example 1:2 x 3 - (4-2) + 322 x 3 - (4-2) + 32

MultiplicationParenthesis

Subtraction Addition

Exponents

2 x 3 - (4-2) + 322 x 3 - (4-2) + 32

2 x 3 - 2 + 32

Parenthesis

Exponents

6 - 2 + 9

Multiply

2 x 3 - 2 + 9

Add

or

Subtract

– Left to Right

4 + 913

PEMDAS3+23- (9+1)3+23-

103+8-1011-101

PEMDAS3 (9+1) + 623(10)+62

3(10)+3630+3

6 66

PEMDAS4+5 x (6-2)4+5 x 4

4+2024

PEMDAS

64 (9 x 3-19)64(27 –19)

64 8

8

Worksheet

Do problems 1-10

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)]..

10 ÷ [9 – (2 2)].

10 ÷ [9 – ]

10 ÷

4

5

2

Multiply in parenthesis.

Subtract in brackets.

Divide.

PEMDAS

You Try!

9) 2[ (13 – 4) ÷ 3]

10) 1 10 - 24

+

Have fun Have fun doing the doing the Order of Order of Operations! 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)) x2

Answers

1. 382. 163. 04. 25. 136. 86

Worksheet

Finish problems 11-20

EXIT SLIPOn a separate piece of paper, complete the following problems.

Please turn in your paper before you exit the room.

EXIT SLIPOn 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?

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?

WorksheetWorksheet

• River Rapids side• Worksheet 1-2 problems 1-12

• River Rapids side• Worksheet 1-2 problems 1-12

SubstitutionSubstitution

• Plug the numbers in for the letters and solve using order of operations.

• If there is no space between numbers and letters it means MULTIPLY!

• Plug the numbers in for the letters and solve using order of operations.

• If there is no space between numbers and letters it means MULTIPLY!

ExampleExample

• Solvea=4 b=-2 5a+2b

• Solvea=4 b=-2 5a+2b

Try oneTry one

Solvex=4 y=-1 z=7

z+y-7x

Solvex=4 y=-1 z=7

z+y-7x

Number Cube ActivityNumber Cube Activity

• Work with a partner but each one will turn in a worksheet.

• Roll your number cube to see what each letter stands for.

• Work with a partner but each one will turn in a worksheet.

• Roll your number cube to see what each letter stands for.

Worksheet 1-2Worksheet 1-2

• Work on problems 13-26• Work on problems 13-26