2. Inductive Reasoning  Reasoning that allows you to reach a conclusion based on a pattern of specific examples or past events

3. Continue the pattern for the next three terms: #1 3, 7, 11, 15,,,

4. Continue the pattern for the next three terms: #1 3, 7, 11, 15,,, +4 +4 +4 Since the pattern matches, we don’t have to add another level

5. Continue the pattern for the next three terms: #1 3, 7, 11, 15,,, +4 +4 +4 The pattern will continue

6. Continue the pattern for the next three terms: #1 3, 7, 11, 15, 19, 23, 27 +4 +4 +4

7. Continue the pattern for the next three terms: #2 11, 6, 1, -4,,,

8. Continue the pattern for the next three terms: #2 11, 6, 1, -4,,, -5 -5 -5

9. Continue the pattern for the next three terms: #2 11, 6, 1, -4,,, -5 -5 -5

10. Continue the pattern for the next three terms: #2 11, 6, 1, -4, -9, -14, -19 -5 -5 -5

11. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,,

12. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,, +8 +11 +14 +17

13. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,, +8 +11 +14 +17 Since the numbers don’t match, we must complete the process again

14. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,, +8 +11 +14 +17 +3 +3 +3 We don’t need to go to the next level, because now the numbers match

15. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,, +8 +11 +14 +17 +3 +3 +3

16. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50,,, +8 +11 +14 +17 +20 +23 +26 +3 +3 +3

17. Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50, 70, 93, 119 +8 +11 +14 +17 +20 +23 +26 +3 +3 +3

18. Continue the pattern for the next three terms: #4 3, 9, 27, 81,,,

19. Continue the pattern for the next three terms: #4 3, 9, 27, 81,,, x3 x3 x3

20. Continue the pattern for the next three terms: #4 3, 9, 27, 81,,, x3 x3 x3

21. Continue the pattern for the next three terms: #4 3, 9, 27, 81, 243, 729, 2187 x3 x3 x3

22. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41

23. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5

24. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5

25. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #5 What pattern do you observe:

26. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #5 What pattern do you observe: Each day 1 less student is absent

27. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #6 Using inductive reasoning, predict the number of absences for Friday:

28. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #6 Using inductive reasoning, predict the number of absences for Friday: 35

29. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #7 Can the pattern continue indefinitely? Explain:

30. The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday 53 50 46 41 -3 -4 -5 #7 Can the pattern continue indefinitely? Explain: No. The week starts over

31. #9. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points On your own, complete the 6 th circle Place six points on the circle and connect the segments

32. #10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points Record the number of segments in each circle

33. #10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points 1 3 6 10 Now find your pattern

34. #10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points 1 3 6 10 +2 +3 +4

35. #10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points 1 3 6 10 +2 +3 +4 +1 +1 # of Points 2345678910 # of Segments

36. #10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points 1 3 6 10 +2 +3 +4 +1 +1 # of Points 2345678910 # of Segments 13691215182124

37. n = 1,2,3 You need to find the sum (add) the negative of n all the way to the positive of n. If n=1, then you start with –n which is -1. -1 + 0 + 1 = _____

38. Conjecture is: The sum of the integers from –n to n is always zero.

39. Fibonacci Sequence Any ideas??? You add the previous numbers to get the next one!

40. Five football players throw a pass to each other. How many passes occur?

41. P1 P2 P3 P4 P5 Who does P1 have to pass to?

42. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5

43. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5 P3 P4 P5

44. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5 P3 P4 P5 P4 P5

45. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5 P3 P4 P5 P4 P5

46. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5 P3 P4 P5 P4 P5

47. Five football players throw a pass to each other. How many passes occur? P1 P2 P3 P4 P5 P2 P3 P4 P5 P3 P4 P5 P4 P5 10 Passes