Patterns and Inductive Reasoning Patterns and Inductive Reasoning

Patterns and Inductive Reasoning

Patterns and Inductive Reasoning Counting Numbers: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, …} 1. Make a list of the positive even numbers. 2. Make a list of positive odd numbers. 3. Make a list of the first 10 perfect square numbers. 4. Describe the square of odd numbers.

Using Inductive Reasoning Inductive reasoning is a reasoning that is based on patterns observed. If a pattern is observed in a sequence, inductive reasoning is used to identify the next terms in the sequence.

Patterns and Inductive Reasoning Write the next two terms in each sequence. a. b. c. d. e. 1, 2, 4, 7, 11, 16, 22, … Monday, Tuesday, Wednesday, … 2, 4, 12, 48, … 2, 3, 5, 7, 11, … 2, 4, 8, 16, …

Using Inductive Reasoning A conjecture is a conclusion reached using inductive reasoning.

http: //www. phschool. com/atscho ol/academy 123/english/academy 1 23_content/wl-book-demo/ph 346 s. html

Using Inductive Reasoning Check Understanding 2: Make a conjecture about the sum of the first 35 odd numbers.

Using Inductive Reasoning Not all conjectures will turn out to be true. To prove that a conjecture is false, find a counterexample. A counterexample to a conjecture is an example for which the conjecture is incorrect.

Using Inductive Reasoning 5 x 7 = 35 5 x 3 = 15 5 X 11 = 55 5 x 7 = 35 5 X 9 = 45 5 X 25 = 125 Check Understanding 3: Some products have 5 as a factor. Make two conjectures based on the products, one that you believe is true and one that you know is false.

http: //www. phschool. com/atscho ol/academy 123/english/academy 1 23_content/wl-book-demo/ph 347 s. html