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**Order of Operations aka: PEMDAS**

Beth Rickerts th Grade NW Guilford Middle School

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What kind of operation?

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**I want to see what you already know…**

Write the steps for the Order of Operations. You can make a list or write in sentences. You have 4 minutes.

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**Students come to sixth grade thinking they know PEMDAS**

Students come to sixth grade thinking they know PEMDAS. But do they know WHY they excuse Aunt Sally?

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**Of course! For looking too rough!**

Poor Aunt Sally.

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FOR LOOKING TOO ROUGH? From Left To Right

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**But what does PEMDAS FLTR really mean**

But what does PEMDAS FLTR really mean? It means that mathematicians have all agreed that to solve for a non-algebraic equation or expression, we ALL follow the same steps. We follow an order and we then we work from left to right, just as when we are reading.

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**BUT WHY AUNT SALLY? Why not ….**

Penguins??? Penguins Eat Delicious Minnows Swimming Around

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**Would this work???? PEDMSA??? Parenthesis Exponents**

Division and Multiplication From Left to Right Subtraction and Addition From Left to Right Would this work????

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**I mean who decided it was Aunt Sally and not PENGUINS**

I mean who decided it was Aunt Sally and not PENGUINS???? Regardless of your preference, all mathematicians follow the same rule and that is Parenthesis FIRST. Exponents SECOND. And then…it’s up to you to pick out the operators.

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Order of Op Hop….. Just like in hopscotch, the first two squares must stand alone. Parenthesis Exponents Then you get to pick which square to hop in…multiplication or division….addition or subtraction.. One at a time, from left to right, Multiplication or Division One at a time, from left to right, Addition or Subtraction

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Order of Op Hop- Scotch ( ) NE X ÷ + - ( ) NE ÷ X - +

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**Order of Operations 32(12 – 4)- 8 ÷ 2 + 6**

Besides the order, it is important to remember these two mantras: ◈Work it out ONE STEP AT A TIME and ◈ Focus on the operators 74

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**It should look like a slice of pizza when you are finished**

It should look like a slice of pizza when you are finished! ONE STEP AT A TIME 32(12 – 4)- 8 ÷ 2 + 6 32(8) - 8 ÷ 2 + 6 9(8)- 8 ÷ 2 + 6 72 – 8 ÷ 2+ 6 72 – 4 + 6 68 + 6 74

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**Did you follow the correct steps?**

Step Parenthesis (12-4) Step Exponent 32 Step Multiplication and/or Division from left to right 9 x 8 and 8 ÷ 2 Step Addition and/or Subtraction from left to right 72 – 4 and finally add for 74.

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**81 ÷ 9(2) – 24 + (5-3) ONE OPERATION AT A TIME Focus on the operators.**

One Step at a Time 81 ÷ 9(2) – 24 + (5-3) ONE OPERATION AT A TIME Focus on the operators. 81 ÷ 9(2) – 24 + (5-3) 81 ÷ 9(2) – 81 ÷ 9(2) – 9 (2) – 2 + 2 4

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Your Turn 12 (5) – (6 ∙ 22 ÷ 3) (5) – (6 ∙ 4 ÷ 3) (5) – (24÷ 3) (5) – (8) (5) – (5) – – 12 (5) – (6 ∙ 22 ÷ 3) Do NOT be tempted to work more than ONE operator at a time. You are going for a nice triangular shape and if you do two operators at a time you could be setting yourself up for a careless error! Did you get 23?

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**Double Parenthesis and Brackets**

Sometimes you might come across 2 parenthesis or brackets. Work from inside out… 7 +[7 x ( ) 2 ] [7 x (10) 2 ] [ 7 x 100]

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Fractional Parts If you see a problem that is over a whole number then you will need to solve for all of the numerator first before dividing by the denominator. 4 (2+3)( x 3)+ 120 – 32 6 Or it could be just a fraction in your problem which would simply be a division problem. Pay attention! 22

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Practice PEMDAS 1. ( 8 ÷ 4 ) 2 + (( ) + 32 ) 2. ( ) +(12 ÷ 2 ) ( ( 1+ 2 ) 3 ÷ 9 ) (16/4) - (24 ÷ 8 ) x ( 5 +4 ) – 13 5

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