2. Welcome to Class #5 3/12/14 Please turn in HW #4: Extra practice booklet –Topic #1 “Arithmetic Operations with Numbers” #1 – 32 ONLY Textbook: P. 6 #4, P. 16 #21, 22, 23, 25 P. 17 #30

3. Warm-up: Sample Test #2: Do #1 – 9, 10 – 24, 32 – 34 only Work on this on your own or in pairs. This is practice for Test #2 next week.

4. Tonight’s positive quote 3 Often people attempt to live their lives backwards; they try to have more things, or more money, in order to do more of what they want, so they will be happier. The way it actually works is the reverse. You must first be who you really are, then do what you need to do, in order to have what you want. ~Margaret Young

5. 1.Warm-up (turn in HW#4) 2.Prime factored form 3.More practice with integers 4.Go over HW & Quiz #1 5.Exponents 6.Order of Operations 7.Absolute value of a number 8.OOP chains fun! Agenda 10/1/14

6. How to write a number in prime factored form

7. Factors, Prime Numbers & Composite Numbers

8. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product

9. Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

10. Definition Factor – a number that divides evenly into another number. 56 ÷ 8 = 7 Factors

11. More practice with integers

12. Example: 7 is prime because the only numbers that will divide into it evenly are 1 and 7. Definition Prime Number – a number that has only two factors, itself and 1.

13. Examples of Prime Numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…

14. Example: The number 8. The factors of 8 are 1, 2, 4, 8. Definition Composite number – a number that has more than two factors.

15. Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, …

16. One is special because... One is not prime. (because it does not have exactly two different factors). One is not Composite. (because it does not have more than 2 factors).

17. Definition Prime Factorization – A way to write a composite number as the product of its prime factors. 2 x 2 x 3 = 12 or 22 22 x 3 = 12

18. How to do a Prime Factorization 48 Step 1 – Write down any composite number. - - Factor Tree Method - - Step 2 – Start dividing by the prime #s (start with 2). If the composite number is divisible by 2, write it down and find the next factor. If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc. 2 x 24

19. How to do a Prime Factorization 48 Step 3 – Check the factors. If they are prime, you are done. If they are not, proceed to Step 4. - - Factor Tree Method - - Step 4 – Continue dividing. If one of the factors is divisible by 2, write it down and find the next factor. If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc. 2 x 24 2 x 2 x 12

20. How to do a Prime Factorization 48 Step 5 – Check the factors. If they are prime, proceed to Step 6. If they are not, repeat Step 4. - - Factor Tree Method - - 2 x 24 2 x 2 x 12 2 x 2 x 2 x 6

21. How to do a Prime Factorization 48 Step 5 – Check the factors. If they are prime, proceed to Step 6. If they are not, repeat Step 4. - - Factor Tree Method - - Step 6 – Write the Prime Factorization in Exponential Form. 2 x 24 2 x 2 x 12 2 x 2 x 2 x 6 2 x 2 x 2 x 2 x 3 2 4 x 3 = 48

22. Find the Prime Factorization 27 3 x 9 3 3 = 27 3 x 3 x 3 Prime Factorization in Exponential Form

23. Find the Prime Factorization 18 2 x 9 2 x 3 2 = 18 2 x 3 x 3 Prime Factorization in Exponential Form

24. Rules for Multiplication & Division If the signs are the same, the product or quotient will be positive If the signs are the different, the product or quotient will be negative.

25. Simplify. 1) 2) 3) 4) 5) 6) 7) 8)

26. Simplify the following. Be careful! 1) -6(7) = 2) 6(-7) = 3) 6 - 7 = 4) (-6) - 7 = 5) (-9) - 5 = 6) -9(-5) = 7) (9) - 5 = 8) 9(-5) = -42 -13 -14 45 4 -45

27. Exponents or Powers

28. Objective - To simplify expressions involving exponents. 3 4 = 3 3 3 3= 81 Exponent or power Base Read, “Three to the fourth power.” Rewrite each power as repeated multiplication and evaluate (find the value). 1) 2) 3) 4)

29. PowerVerbal PhraseMeaning “Seven to the 2nd power” “Seven squared” “Five to the 3rd power” “Five cubed” “Nine to the 4th power” “Two to the 5th power”

30. PowerMeaning

31. Simplify the following. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) -81 81 -64 16 25 3 54 -36 12

32. ORDER OF OPERATIONS

33. Order of Operations P arentheses (inside to outside) E xponents M ultiply & D ivide from left to right A dd & S ubtract from left to right PEMDAS

34. Order of Operations Parenthesis Exponents 6 + 5(6) 6 + 30 = 36 2 + 3 25 2 + 75 = 77 Multiply / Divide LEFT TO RIGHT 8 4 = 32 Add / Subtract LEFT TO RIGHT 10 - 3 + 8 7 + 8 = 15 1) 6 + 5(8 - 2) 2) 3) 4)

35. Simplify the following. 1) 2) 3) 4) (4 + 18)2 - 10 (22)2 - 10 44 - 10 = 34 24 - 2[18 6] 24 - 2[3] 24 - 6 = 18 8 - 9 + 5 -1 + 5 4 8 + 20 4 28 4 =7

36. The order of operations (Text p. 49)

37. | ABSOLUTE VALUE |

38. What do you know about the absolute value of a number? Talk to your shoulder partner!

39. Problem 9-45 Absolute Value Operation a.Study the relationship between the # entered in parentheses and the results shown. Write a statement describing this operation. b.Why would you ever need an absolute value?

40. Absolute value (p. 389)- A numbers distance from zero on the number line. It is represented by two vertical bars -5 -4 -3 -2 -1 0 1 2 3 4 5 3 5 10 12 -7 -23 0 5.4 -16

41. 10 4

42. Order of Operation Chains OOP Chains!

43. Work in pairs for this activity. Each person needs this worksheet and one envelope.

44. OOP Chains Worksheet Each problem has 3 correct pieces to get from the original problem to the simplified form. However, each problem also has a whammy (one incorrect piece) that is there to throw you off course! You need to correctly find the OOP Chains and correctly identify all the whammies!

45. Solution:

46. HW #5 Extra practice booklet topic # 3 “Order of Operations” # 1 – 15 (show all work) Worksheet p. 24 “Why did the ant run across the cracker box?” Worksheet p. 62 “Can you build this?”