1. Review Examples

7. 1.1 Patterns and Inductive Reasoning “Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily, express our character…” -Stephen R. Covey

8. Inductive Reasoning Inductive reasoning is reasoning based on patterns you observe. Examples: Find the pattern of the sequence and show the next two terms or symbols. 2, 4, 8, 16, … 1, 3, 7, 13, 21, …

9. Using Inductive Reasoning A conjecture is a conclusion you reach using inductive reasoning. Example 1: Sum of odd numbers. 1 1 + 3 1 + 3 + 5 1 + 3 + 5 + 7 = 1 = 4 = 9 = 16 = 1 2 = 2 2 = 3 2 = 4 2 What is the sum of the first 30 odd numbers? The first 35 odd numbers? Conjecture:

10. Using Inductive Reasoning A conjecture is a conclusion you reach using inductive reasoning. Example 2: Sum of even numbers. 2 2 + 4 2 + 4 + 6 2 + 4 + 6 + 8 = 2 = 6 = 12 = 20 = 1(2) = 2(3) = 3(4) = 4(5) What is the sum of the first 30 even numbers? The first 35 even numbers? Conjecture:

11. Using Inductive Reasoning A counterexample to a conjecture is an example where the conjecture does not work. Examples: Find a counterexample to the statements. 1) “If a number is divisible by 2, then it is also divisible by 6.” 2) “You can connect any three points to form a triangle.” 3) “The difference of two negative integers is negative.”

12. Review and 1.1 Patterns and Inductive Reasoning “Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily, express our character…” -Stephen R. Covey HW: 1-13 ODD, 19, 25-28, 30, 47, 50, 53 Terms: conjecture, counterexample, inductive reasoning