Transcript Order of Operations Nolan

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?
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/esquiv
el_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+5X2
8 X2
16
Oh
no!
If we multiply first:
3+5X2
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
Avoids
Confusion
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!
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 x
Divide 
Add +
Subtract -
3
4
Please Excuse My Dear Aunt Sally
Parentheses (
Always do
parentheses
1st.
)
Please Excuse My Dear Aunt Sally
Exponents
Always do
Exponents
2nd.
3
4
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
Multiplication
Parenthesis
Subtraction
Exponents
Addition
2 x 3 - (4-2) + 32
Parenthesis
2 x 3Exponents
- 2 + 32
2x3-2+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
2
6
3 (9+1) +
2
3(10)+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
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
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)) x2
Answers
1.
2.
3.
4.
5.
6.
38
16
0
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