1. ORDER OF OPERATIONS

2. Did you get one of these numbers as an answer? 18? 12? SOLVE THIS PROBLEM

3. TRY THIS PROBLEM Did you get one of these numbers as an answer? 320? 128? 80? 20?

4.  Why do we need order of operations?  Order of Operations gives us a common set of rules that everyone can follow to solve a problem.  What are the order of operations? WHY? (1.) Parentheses or Grouping (2.) Exponents (3.) Multiplication or Division (4.) Addition or Subtraction

5.  Why did mathematicians decide on this order? Why not just work from left to right?  I can hold 4 boxes with 4 apples in each box plus two apples in my pockets. How many apples can I hold?  4 x 4 + 2  I can hold two apples in my pockets plus 4 boxes with 4 apples in each box. How many apples can I hold?  2 + 4 x 4 WHY THIS ORDER?

6.  Multiplication is just another way to add fast. For this reason, multiplying is more important than addition. This is why we multiply before adding.  Exponents are a fast way of multiplying. For this reason, exponents are more important than multiplication. This is why we do exponents before multiplications.  Exponents are similar to saying “I have four friends that can hold four boxes with four apples in each box.” WHY THIS ORDER?

7.  What are groupings?  Groupings are often expressions that don’t contain parentheses but are connected by an operation. Here’s an example:  Notice that even though there are no parentheses. We should still add 4 + 4 before we divide by 4. PEMDAS OR GEMDAS (1.) Parentheses or Grouping (2.) Exponents (3.) Multiplication or Division (4.) Addition or Subtraction

8.  Back to our order of operations  Notice that multiplication and division share the same step. That’s because they have the same level of importance. Try this problem from left to right and right to left.  In both cases the answer is 4. PEMDAS OR GEMDAS (1.) Parentheses or Grouping (2.) Exponents (3.) Multiplication or Division (4.) Addition or Subtraction 4 x 4 ÷ 4

9.  Back to our order of operations  Notice that addition and subtraction share the same step. That’s because they have the same level of importance. Try this problem from left to right and right to left.  In both cases the answer is 4. PEMDAS OR GEMDAS (1.) Parentheses or Grouping (2.) Exponents (3.) Multiplication or Division (4.) Addition or Subtraction 4 + 4 - 4

10. Using our order of operations let’s find our answer. 1.) We should first do anything with parentheses. Since there are no parentheses we move on. 2.) We should do anything with exponents. Since there are no exponents we move on. 3.) Let’s do our multiplication. 3 x 3 = 9 and then rewrite our problem. 4.) Now we’re only left with addition and subtraction. So let’s work from left to right. REMEMBER THIS PROBLEM 3 + 3 x 3 – 3 + 3 = ? 3 + 9 – 3 + 3 = ? 12 – 3 + 3 = ? 9 + 3 = ? 9 + 3 = 12 Our answer is 12

11. TRY THIS PROBLEM Using our order of operations let’s find our answer. 1.) We should first do anything with parentheses. Since there are no parentheses we move on. 2.) We should do anything with exponents. Since there are no exponents we move on. 3.) Let’s do our multiplication. 4 x 4 = 16 and then rewrite our problem. 4.) Now we’re only left with addition and subtraction. So let’s work from left to right. 4 x 4 + 4 x 4 + 4 – 4 x 4 = ? 16 + 16 + 4 – 16 = ? 32 + 4 – 16 = ? 36 – 16 = ? 36 – 16 = 20 Our answer is 20

12. 1.) 3 + (3 x 3) – 4 x (2 + 1) 0 LET’S TRY SOME DIFFICULT PROBLEMS 3.) 3 x (3 - 3) + 4 – (2 + 1) 1 2.) 3 x (3 + 3) – 4 + (2 – 1) 15 4.) 3 x (3 + 3) – 4 x (2 + 1) 6 Complete 2 of the 4 problems. Show all work! Still too easy?

13. 1.) ((16 - 2 x 4 ) + 8) – 13 3 TRY TO SOLVE THESE PROBLEMS 3.) ( 7 + (16 ÷ 8 + 4 )) + 4 17 2.) ( 3 + (24 ÷ 4 + 5 )) – 8 6 4.) (( 9 - 4 x 2 ) + 8) - 3 6 Complete 2 of the 4 problems. Show all work! Still too easy?

14. 1.) (4 ² + (12 ÷ 2 + 5 ² )) - 4 ² 31 TRY TO SOLVE THESE PROBLEMS 3.) (6 ² + (20 ÷10 + 3 ² )) - 2 ² 43 2.) 4 +(9 x (9 - 6) ² ) + 3 88 4.) (12 ÷ 4) ² + ((13 - 3) + 4 ² ) 35 Complete 2 of the 4 problems. Show all work!

15.  Using ALEKS, send me a message with the subject “Order of Operations Exit Ticket”  In the body write down and explain your answer for solving this problem. ((3 +4) ² + 2) - 11 + 7 ² The quiz for this lesson is available in ALEKS under WHOLE NUMBERS – ORDER OF OPERATIONS. EXIT TICKET