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Order of Operations
Engage


      Solve the following
• 4( 11 - 3² ) ÷ 2 - 2 ∙ 6

• Once you have your
  answer find it around the
  room and stand by your
  answer
What happened?
This is why the Order of Operations had to
                   be created.
 It is a set of rules that has been agreed
                      upon.
        It is not “mathematical fact”.
It is just an agreed upon math procedure in
   order to ensure consistency in answers.
Let’s Talk
• What order do we solve problems in?

• Does this order matter?

• Are there problems that you could do a
  different order and still get the right
  answer? Will it always work?
Explore


            Let’s Practice
• Take your worksheet to another student
  and agree on a problem to work
• Trade worksheets and work the problem
  on THEIR worksheet
• Sign the problem when you finish and
  agree on the answer
• Continue until all questions are answered
• Return to your seat when finished
Explain


  Let’s Forget Poor Aunt Sally!
and try a new way of thinking of order of
  operations
                       2nd




                     Pitchers
           3rd        Mound       1st




                      HOME
                      BASE
Let’s think of Order of Ops more
                  like baseball
                                  Multiplication/Division on
                                            second
                         2nd       “first come first serve”

Addition/Subtraction
         third
  “first come, first                                  Exponents are on
        serve”                                           first base



               3rd     Equation                 1st




                        HOME            We always have Grouping
                                      Symbols starting on home plate
                         Plate
Order of Operations
1. Parentheses (Grouping Symbols)
    ( )    [ ]   { }
2. Exponents
    43 = 4  4  4 = 64
3. Multiplication or Division (from left to
   right) “First Come, First Serve”


4. Addition or Subtraction (from left to right)
         “First Come, First Serve”
•Parentheses             Example
•Exponents
•Multiply/Divide
•Add/Subtract
                   9÷3 + (4²+2) + 3 × 5

                   9÷3 + (16+2) + 3 × 5
                    9÷3 + (18) + 3 × 5
                     3 + (18) + 3 × 5
                       3 + (18) + 15
                          21 + 15
                            =36
Grammar of mathematics
• The drama club sponsor will provide 320
  chairs and the choir director will provide
  280 chairs. The audience will be divided
  into 4 sections. Write an expression to
  calculate how many chairs will be placed
  into each section.
• (320 +280) ÷ 4
• 320 +280 ÷ 4 are these the same???
• No way!! Why?

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Order of Operations

  • 2. Engage Solve the following • 4( 11 - 3² ) ÷ 2 - 2 ∙ 6 • Once you have your answer find it around the room and stand by your answer
  • 3. What happened? This is why the Order of Operations had to be created. It is a set of rules that has been agreed upon. It is not “mathematical fact”. It is just an agreed upon math procedure in order to ensure consistency in answers.
  • 4. Let’s Talk • What order do we solve problems in? • Does this order matter? • Are there problems that you could do a different order and still get the right answer? Will it always work?
  • 5. Explore Let’s Practice • Take your worksheet to another student and agree on a problem to work • Trade worksheets and work the problem on THEIR worksheet • Sign the problem when you finish and agree on the answer • Continue until all questions are answered • Return to your seat when finished
  • 6. Explain Let’s Forget Poor Aunt Sally! and try a new way of thinking of order of operations 2nd Pitchers 3rd Mound 1st HOME BASE
  • 7. Let’s think of Order of Ops more like baseball Multiplication/Division on second 2nd “first come first serve” Addition/Subtraction third “first come, first Exponents are on serve” first base 3rd Equation 1st HOME We always have Grouping Symbols starting on home plate Plate
  • 8. Order of Operations 1. Parentheses (Grouping Symbols) ( ) [ ] { } 2. Exponents 43 = 4  4  4 = 64 3. Multiplication or Division (from left to right) “First Come, First Serve” 4. Addition or Subtraction (from left to right) “First Come, First Serve”
  • 9. •Parentheses Example •Exponents •Multiply/Divide •Add/Subtract 9÷3 + (4²+2) + 3 × 5 9÷3 + (16+2) + 3 × 5 9÷3 + (18) + 3 × 5 3 + (18) + 3 × 5 3 + (18) + 15 21 + 15 =36
  • 10. Grammar of mathematics • The drama club sponsor will provide 320 chairs and the choir director will provide 280 chairs. The audience will be divided into 4 sections. Write an expression to calculate how many chairs will be placed into each section. • (320 +280) ÷ 4 • 320 +280 ÷ 4 are these the same??? • No way!! Why?