43 Order of Operations  ( ) + - X

When you get dressed, do you put on your shoes or socks first. Why When you get dressed, do you put on your shoes or socks first? Why? Explain your thinking. This PowerPoint was created for 7th grade students, but could be used in other grade levels as well. The students in my classes range from FBB to Advanced. I have students who speak English as their second language and students with learning disabilities. This presentation is intended to introduce the concept of Order of Operations. Students will watch videos of how to perform the Operations before they explore some problems of their own on the internet. The goals of this presentation are to have students solve problems by applying the Order of Operations, evaluate why these rules are important and must be agreed upon, and demonstrate their knowledge of the Order of Operations by inserting grouping symbols to make an equation true.

When you make cereal, do you fill the bowl with milk or cereal first 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 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.

A standard way to simplify mathematical expressions and equations. 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. Oh no! Ex. 3 + 5 X 2 What do we do first? Add or multiply? If we add first: If we multiply first: 3 + 5 X 2 3 + 5 X 2 8 X 2 3 + 10 Help! 16 13 Uh Oh! Which one is the correct answer?

Have no fear! PEMDAS is here!

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 from left to right! Multiplication X Division ÷ Addition + Whichever comes first from left to right! Subtraction -

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

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

Please Excuse My Dear Aunt Sally Parentheses ( ) E Exponents 43 M D Multiply x Divide  A S Add + Subtract -

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

Please Excuse My Dear Aunt Sally Exponents 43 Always do Exponents 2nd.

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

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

Let’s Try Some  Problems!

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

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

PEMDAS 3+23- (9+1) 3+23- 10 3+8-10 11-10 1

PEMDAS 3 (9+1) + 62 3(10)+62 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

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

You Try! 9) 2[ (13 – 4) ÷ 3] 10 - 2 + 10) 1 4

Have fun doing the Order of  Operations!

Practice Problems Try these on your own. 1. 3 + 5 x 7 (1 + 3) x (8 - 4) 6 - 6 + (7 - 0) - 7 4 - 3 + (5 - 1) - 3 3 + 9 x 8 – 62 6. 2+3 x (4+(6 x 3-8)) x2

Answers 38 16 2 13 86

Worksheet Finish problems 11-20

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?

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

Substitution 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!

Example Solve a=4 b=-2 5a+2b

Try one Solve x=4 y=-1 z=7 z+y-7x

Number 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.

Worksheet 1-2 Work on problems 13-26