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Patterns and Inductive Reasoning

Patterns and Inductive Reasoning. Geometry Mrs. King Unit 1, Lesson 1. Definition. Inductive Reasoning : reasoning based on patterns you observe. Example #1. Find the next two terms of the number sequence: 1 , 2, 3, 4, …. 5, 6. Describe the pattern you observed. Example #2.

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Patterns and Inductive Reasoning

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  1. Patterns and Inductive Reasoning Geometry Mrs. King Unit 1, Lesson 1

  2. Definition Inductive Reasoning: reasoning based on patterns you observe

  3. Example #1 Find the next two terms of the number sequence: 1, 2, 3, 4, … 5, 6 Describe the pattern you observed.

  4. Example #2 Find the next two terms of the number sequence: 9, 6, 3, … 0, -3 Describe the pattern you observed.

  5. Example #3 Find the next two terms of the number sequence: 2, 4, 8, 16, … 32, 64 Describe the pattern you observed.

  6. Example #4

  7. Example #5

  8. Definition Conjecture: a conclusion reached by inductive reasoning

  9. Write the data in a table. Find a pattern. 2000 2001 2002 $8.00 $9.50 $11.00 The price of overnight shipping was $8.00 in 2000, $9.50 in 2001, and $11.00 in 2002. Make a conjecture about the price in 2003. Each year the price increased by $1.50. A possible conjecture is that the price in 2003 will increase by $1.50. If so, the price in 2003 would be $12.50.

  10. Definition Counterexample: a example for which the conjecture is incorrect

  11. 1 1 1 2 1 is not greater than = 1. is not greater than 2. Find a counterexample for each conjecture. 1.A number is always greater than its reciprocal. Sample counterexamples: 2.If a number is divisible by 5, then it is divisible by 10. Sample counterexample: 25 is divisible by 5 but not by 10.

  12. Homework Patterns and Inductive Reasoning in Student Practice Packet (Page 2, #1-10)

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