1. Math 2/2/15

2. Monday- Test Day No Bell Work

3. Tuesday: Bell Work *show work Use notebook paper and create the bell work grid DateWorkAnswer 2/3 2/4 2/5 2/6 Problem of the day 1) A triangle has side lengths of 28 inches, 32 inches, and 36 inches. Which list shows the side lengths of a similar triangle? F 6 inches, 8 inches, 9 inches G 14 inches, 16 inches, 18 inches H 21 inches, 26 inches, 27 inches J 54 inches, 64 inches, 72 inches

4. Agenda 1- bell work 2- Agenda- *Quiz on Tuesday 2/10 over Direct and Inverse Variation *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28 3- Vocabulary 4- Objective 5- lesson *Direct Variation 6- exit ticket

5. 21. Slope What does this word mean to you? This word actually means….. measure of the steepness of a line on a graph (rise / run). Examples… Explain how you would use this word in math.

6. Objective SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

7. What is it? A set of inputs and outputs with a constant ratio called K Variable key: X is the input Y is the output K is the constant

8. Equation A direct variation equation follows this format y = kx Output = constant x input

9. What are other ways you could write this equation….. Y= kx

10. What are other ways you could write this equation….. Y= kx So we can rework it using inverse operations y/k = xor y/x = k

11. Examples Examples of DV equations: *notice they are 1 step!! y = 1/5x where k=1/5 y = -2x where k = -2

12. Non-Examples Non-Examples of DV equations: *notice they can’t be 2 step!! y = 7x + 5 y = 1/2x – 18

13. How do you test? Table:  Step 1: Check the direction – both up or both down  Step 2: Divide every y by its x to see if it matches *if they all have the same answer then that is the constant!!!

14. TABLES X Y X Y X Y 2 7 2 7 3 8 4 5 4 11 6 16 8 4 6 15 9 24 12 2 8 19 12 32 10 23 15 40

15. GRAPHS Direct variation lines have 2 requirements! Linear Through the origin

16. Graph Examples

18. Graph Non- Examples

19. Sum it up Line when graphed will be straight and go through the origin!

20. Lines on Graph can be classified as the following Linear Non linear Direct variation Inverse variation…. To come later

21. Review You can test for direct variation with equations, tables or graphs. Equations- 1 step and follows format y=kx Tables- check for 1) directions of columns *must be same direction 2) find constant--divide y by x Graphs- linear through the origin (0, 0)

22. Exit Ticket Partner Discussion Name two additional names for direct variation. Why is it important to know the different names?

23. Wednesday: Bell Work *show work

24. Agenda 1- bell work 2- Agenda- *Quiz on Tuesday 2/10 over Direct and Inverse Variation *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28 3- Vocabulary 4- Objective 5- lesson *Direct Variation 6- exit ticket

25. 22. Reciprocal What does this word mean to you? This word actually means….. one of two numbers whose product is one: aka as the multiplicative inverse. Examples… Explain how you would use this word in math.

26. Objective SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

27.  Proportional  Direct Variation

28.  Take each y value and divide it by its x value.  If the ratio of y divided by x comes out to the same value for EVERY pair of x and y, the function is proportional.

29. 1)X YProportional? 5 10 6 11 7 12Common ratio? 8 13 2)X YProportional? 5 10 6 12 7 14Common ratio? 8 16

30.  Direct Variation is very similar to proportional functions.  For direct variation, first check that X and Y both change in the same direction (both up or both down)  Then check to make sure the ratio of y divided by x matches for all pairs of x and y.

31. 1)XY 15 26 37 48 2)XY 12 24 36 48 3)XY 110 29 38 47 4)XY 110 29.9 39.8 49.7 31

32. 1)XY 150 2100 3150 4200 2)XY 100500 200400 300 400200 3)XY 663 555 442 331 4)XY 1.51 33 4.54 66 32

33. 1)XY 105 206 307 408 2)XY 102 2010 3016 4028 3)XY 10010 909 808 707 4)XY 110 29 38 47 33

34. 1)XY 105 2010 30 40 2)XY 604 503.3333 40 30 3)XY 1001 90.9 80 70 4)XY 18 216 3 4

35. Problem: If y = 10 and x = -5, find y when x = 13. Formula y/x 10/-5= -2 Multiply x by the quotient 13( -2) = -26 y = -26

36. Exit Ticket Partner Discussion What skills were needed for the N2K?

37. Thursday: Bell Work *show work 3) The graph shows five points of a relation. Which equation best represents this relation? F y = 3x + 6 G y = 3x - 6 H y = 2x - 3 J

38. Agenda 1- bell work 2- Agenda-* *Quiz on Tuesday 2/10 over Direct and Inverse Variation *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28 3- Vocabulary 4- Objective 5- lesson – N2K and Inverse Variation 6- exit ticket

39. 23. Inverse What does this word mean to you? This word actually means….. operations that undo each other: (addition/subtraction or multiplication/division). Examples… Explain how you would use this word in math.

40. Objective SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

41. Inverse Variation AKA: Inversely Proportional Or just plain Not-Proportional

42. Need 2 Know 3-5 Critical Thinking:  Answer the question  Justify in words and work your answer Constructed Response:  Make a function table then graph the answers  **label your axis correctly

43. What is it? A set of inputs and outputs with a constant product called K Variable key: X is the input Y is the output K is the constant *k cannot be 0

44. Equation A inverse variation equation follows this format y = k/x Output = constant divided input

45. What are other ways you could write this equation….. Y= k/x

46. What are other ways you could write this equation….. Y= k/x So we can rework it using inverse operations k/y = xor yx = k

47. Examples Examples of IV equations: *notice they are 1 step!! y = 5/x where k=5 y = -4/x where k = -4

48. Non-Examples Non-Examples of IV equations: *notice they can’t be 2 step and that it must be k/x!! y = x/6 y = x/-3

49. Tables Input (x) Output (y)

50. How do you test? Table:  Step 1: Check the direction – going in opposite directions *1 least to greatest and 1 greatest to least  Step 2: Multiply every y by its x to see if it matches (yx = k) *if they all have the same answer then that is the constant!!!

51. TABLES X Y X Y X Y 2 7 2 7 4 30 4 5 4 11 6 20 8 4 6 15 8 15 12 2 8 19 10 12 10 23 12 10

52. GRAPHS Inverse variation lines have 2 requirements! Non-Linear *curved lines!!! It is actually 2 curved lines in 2 opposite quadrants

53. Graph Examples

55. Graph Non- Examples

56. Sum it up Line when graphed will be 2 curved lines in opposite quadrants! Be careful because some graphs are only in the 1 st quadrant and when graphed you don’t see the 2 nd line.

57. Review You can test for inverse variation with equations, tables or graphs. Equations- 1 step and follows format y=k/x Tables- check for 1) directions of columns *must be opposite direction 2) find constant--multiply y by x Graphs- 2 non linear lines in opposite quadrants

58. Lines on Graph can be classified as the following Linear Non linear Direct variation Inverse variation

59. Exit Ticket Partner Discussion What are two distinguishing features of a direct variation line?

60. Friday: Bell Work *show work Reminder – bell work is due today!! Complete it quickly! 1) A recipe for making 12 cups of soup requires 5 cups of water. At this rate, how many cups of water are required to make 6 cups of soup? A 2 1/2 cups B 10 cups C 7 cups D 1 cup 2) A recipe for making 14 cups of soup requires 4 cups of water. At this rate, how many cups of water are required to make 7 cups of soup? A 3 cups B 1 1/2 cups C 10 cups D 2 cups

61. Agenda 1- bell work 2- Agenda- *Quiz on Tuesday 2/10 over Direct and Inverse Variation *retake for test on Monday on Friday during Falcon Time *ticket p. 325-326 #’s 14-28 3- Vocabulary 4- Objective 5- lesson *Inverse Variation 6- exit ticket

62. 24. Equation What does this word mean to you? This word actually means….. math sentence that shows two equivalent expressions. Examples… Explain how you would use this word in math.

63. Objective SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

64. Finish Thursday’s notes

65. Exit Ticket Partner Discussion What is the difference between a direct and inverse variation equations?