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INDUCTIVE REASONING
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, , ,
+4 +4 +4 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, , ,
+4 +4 +4 +4 +4 +4 The pattern will continue
Continue the pattern for the next three terms: #1
3, 7, 11, 15, 19, 23, 27
+4 +4 +4 +4 +4 +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, , ,
-5 -5 -5
Continue the pattern for the next three terms: #2
11, 6, 1, -4, , ,
-5 -5 -5 -5 -5 -5
Continue the pattern for the next three terms: #2
11, 6, 1, -4, -9, -14, -19
-5 -5 -5 -5 -5 -5
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, , ,
+8 +11 +14 +17
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
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
Continue the pattern for the next three terms: #3
0, 8, 19, 33, 50, , ,
+8 +11 +14 +17
+3 +3 +3 +3 +3 +3
Continue the pattern for the next three terms: #3
0, 8, 19, 33, 50, , ,
+8 +11 +14 +17 +20 +23 +26
+3 +3 +3 +3 +3 +3
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 +3 +3 +3
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 x3 x3 x3
Continue the pattern for the next three terms: #4
3, 9, 27, 81, 243, 729, 2187
x3 x3 x3 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 53 50 46 41
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
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
-1 -1
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
-1 -1#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 53 50 46 41
-3 -4 -5
-1 -1#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 53 50 46 41
-3 -4 -5
-1 -1#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 53 50 46 41
-3 -4 -5
-1 -1#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 53 50 46 41
-3 -4 -5
-1 -1#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 53 50 46 41
-3 -4 -5
-1 -1#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 6th circlePlace 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
1 3 6 10
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
1 3 6 10
+2 +3 +4
#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
2 3 4 5 6 7 8 9 10
# 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
1 3 6 10
+2 +3 +4
+1 +1# of Points
2 3 4 5 6 7 8 9 10
# of Segments
1 3 6 9 12 15 18 21 24
n = 1,2,3You 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 = _____
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?
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
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
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
P5
10 Passes
