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INDUCTIVE REASONING
We reason inductively when we reach a conclusion based on the
observation of some pattern
16 feet
Rapunzel lives in a tower.
Her window is 16 feet abovethe ground.
Rapunzel, Rapunzellet down thy hair!
It took exactly one second for the rabbit
to land
The next night,the prince tries again.
Rapunzel, Rapunzellet down thy hair!
It took exactly one second for the rabbit
to land
The next night,the prince tries again.
Rapunzel, Rapunzellet down thy hair!
It took exactly one second for the rabbit
to land
The same thing happens every night for two weeks… finally...
Rapunzel, Rapunzellet down thy hair!
Yet again, it took exactly one second for the rabbit
to fall the 16 feet fromRapunzel’s window!
Using my amazing powers of INDUCTIVE REASONING I conclude that a rabbit under the influence of gravity falls 16 feet in one second.
Finally becoming weary of Rapunzel and her rabbits, the prince decides to seek bunnies
elsewhere
YE OLDE BUNNY INN
END OF TALE
Laws of science are derived using INDUCTIVE
REASONING - they are conclusions drawn from the
patterns we observe in natureConsider one more example of
inductive reasoning
431 9531
167531
2597531
19...531
The sum of the first ten odd counting numbers
?
431 9531
167531
2597531
19...531
The sum of the first ten odd counting numbers
Sum of the first 2 = 2x2
Sum of the first 3 = 3x3
Sum of the first 5 = 5x5
Sum of the first 4 = 4x4
431 9531
167531
2597531
19...531
The sum of the first ten odd counting numbers
Sum of the first 2 = 2x2
Sum of the first 3 = 3x3
Sum of the first 5 = 5x5
Sum of the first 4 = 4x4
If you observe the pattern, and conclude that thesum of the first 10 odd counting numbers is 10x10then you are using inductive reasoning!
Inductive reasoning does not always yield a true conclusion.
Based on observation and experience, some ancient peopleconcluded that the sun revolved about the earth.
Inductive Reasoning:
1. Observing Data
2. Recognizing Patterns
3. Making conclusions from your observations
Students in a science class are instructed to sprinkle salt into a Bunsen burner flame. Each time salt is sprinkled into the flame, the flame turns yellow.
What assumption should the class make from their observations?
The class decides that the salt always burns with a yellow flame.
An auto assembly plant can produce a maximum of 300 cars per day. A production line technician observes that during the first three hours of a production day the number of cars coming off the assembly line double each hour.
Hours 1 2 3 4 …Cars 10 20 40 ? …
Make a observation about the 4th hour.
What about the 10th hour?
Use inductive reasoning to find the next two terms in each sequence of numbers.
1, 5, 9, …
-12, -5, 2, …
Give a counter example to show that each statement is false.
If a number is divisible by 2, then it is divisible by 4.
If x + 1 > 0, then x is positive.
Homework
Inductive Reasoning WS
