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

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Presentation transcript:

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

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

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

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

Continue the pattern for the next three terms: #1 3, 7, 11, 15, 19, 23,

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

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

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

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

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

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

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

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

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

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

Continue the pattern for the next three terms: #3 0, 8, 19, 33, 50, 70, 93,

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

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

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

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

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday #5 What pattern do you observe:

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

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday #6 Using inductive reasoning, predict the number of absences for Friday:

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday #6 Using inductive reasoning, predict the number of absences for Friday: 35

The number of students absent on each of four consecutive days at the Great Avenue School was as follows: Monday Tuesday Wednesday Thursday #7 Can the pattern continue indefinitely? Explain:

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

#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

#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

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

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

#10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points # of Points # of Segments

#10. Complete the pattern with six points on the circle and tell how many segments can be drawn connecting a pair of points # of Points # of Segments

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 = _____

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

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

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

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

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

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

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

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

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

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