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Published byFrederica Woods Modified over 8 years ago

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Inductive Reasoning

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Reasoning based on patterns that you observe Finding the next term in a sequence is a form of inductive reasoning

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A conclusion that you reach based on inductive reasoning

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Count the number of ways 2 people shake hands Count the number of ways 3 people shake hands Count the number of ways 4 people shake hands Count the number of ways 5 people shake hands Make a conjecture about the number of ways 6 people shake hands People Handshakes 23456 13610?

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Finish the statement: The sum of any two odd numbers is ____________. Begin by writing several examples: What do you notice about each sum? Answer: The sum of any 2 odd numbers is: 1+1=2 1+3=4 3+5 = 8 5+7=14 7+9= 16 11+13 = 24 even

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Complete the conjecture: The sum of the first 30 odd numbers is ____________________. 1 = 1 1+3 = 4 1+3+5 = 9 1+3+5+7 = 16 1+3+5+7+9 = 25 1+3+5+7+9+11 = 36 What do you notice about the pattern? Conjecture: The sum of the first 30 odd numbers is 30 2.

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Just because a statement is true for several examples does not mean that it is true for all cases If a conjecture is not always true, then it is considered false To prove that a conjecture is false, you need ONE counterexample Counterexample: an example that shows a conjecture is false.

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You can connect any three points to form a triangle. Counterexample: three points on the same line Any number and its absolute value are opposites

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1. If the product of two numbers is even, then the numbers must be even. 2. If it is Monday, then there is school.

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