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Order of Operations

4 3. 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.

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Order of Operations

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  1. 43 Order of Operations  ( ) + - X

  2. When you get dressed, do you put on your shoes or socks first? Why? Explain your thinking.

  3. When you make cereal, do you fill the bowl with milk or cereal first? Why? Explain your thinking.

  4. 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.

  5. In your notebook, make a list… What do you know about Order of Operations? List as many things as you can!

  6. Compare your list with your partner’s list. Can you add anything to your list?

  7. 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!

  8. The Order of Operations tells us how to do a math problem with more than one operation, in the correct order.

  9. Order of Operations A standard way to simplify mathematical expressions and equations.

  10. In most languages, the meaning of words depend on the order: Ex. Sign the check Is not the same as Check the sign

  11. 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?

  12. Have no fear! PEMDAS is here!

  13. 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 -

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

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

  16. How am I supposed to remember that! Please Excuse My Dear Aunt Sally

  17. Please Excuse My Dear Aunt Sally This will help to you to remember the order of operations.

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

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

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

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

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

  23. Let’s Try Some  Problems!

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

  25. 2 x 3 - (4-2) + 32 Parenthesis 2 x 3 - 2 + 32 Exponents 2 x 3 - 2 + 9 Multiply 6 - 2 + 9 AddorSubtract– Left to Right 4 + 9 13

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

  27. PEMDAS 3 (9+1) + 62 3(10)+62 3(10)+36 30+36 66

  28. PEMDAS 4+5 x (6-2) 4+5 x 4 4+20 24

  29. PEMDAS 64  (9 x 3-19) 64(27 –19) 64 8 8

  30. Worksheet • Do problems 1-10

  31. 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!

  32. 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.

  33. 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

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

  35. Have fun doing the Order of  Operations!

  36. 1. 3 + 5 x 7 Practice Problems Try these on your own. • (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

  37. Answers • 38 • 16 • 0 • 2 • 13 • 86

  38. Worksheet • Finish problems 11-20

  39. EXIT SLIPOn 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?

  40. Worksheet • River Rapids side • Worksheet 1-2 problems 1-12

  41. 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!

  42. Example • Solve a=4 b=-2 5a+2b

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

  44. 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.

  45. Worksheet 1-2 • Work on problems 13-26

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