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Sec 2-1 Concept: Use Inductive Reasoning Objectives: Given a pattern, describe it through inductive reasoning

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Example 1:

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Example 2:

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Example 3: Find the next number in the pattern 1. 17,15,12,8,…..____= 3 2. 7,7.5,8, 8.5,….____ = 9

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3 Stages of Inductive Reasoning in Geometry 1. Look for a pattern 2. Make a conjecture Ø A Conjecture is an unproven statement that is based on observations. 3. Verify the conjecture

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Example 4: Sketch the next figure in the pattern 1. 2.

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Example 5: Complete the conjecture based on the pattern you observe 1. The sum of any two odd numbers is ____ EVEN Try some examples to see a pattern: 9+3 11+5 -3+-1 -7+3

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Example 6: Write a function rule relating x and y.

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Example 7: Show the conjecture is false by finding a counterexample A counterexample is an example that shows a conjecture is false. 1. If the product of two numbers is positive, then the two numbers must both be positive False: a negative number multiplied by another negative number is a positive number

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2.1 Use inductive reasoning You will describe patterns and use inductive reasoning. Essential Question: How do you use inductive reasoning in mathematics?

2.1 Use inductive reasoning You will describe patterns and use inductive reasoning. Essential Question: How do you use inductive reasoning in mathematics?

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