Inductive Reasoning and Conjecture Chapter 1.1 and 1.2

How can inductive reasoning help predict weather conditions? What are normal temperatures for the month of August? How do people benefit from the inductive reasoning techniques of meteorologists?

Conjecture A conjecture is an educated guess based on known information. Examining several specific situation to arrive a conjecture is called inductive reasoning.

Example Lets look at the first 5 triangular numbers. 1, 3, 6, 10, 15 Find a pattern Conjecture: The next number will increase by 6. 15 + 6 is 21 so 21 is the next triangular number.

Example Given points P, Q, and R. PQ = 9, QR = 15, and PR = 12 Conjecture: P,Q, and R are noncollinear Illustrate conjecture Q 15 9 P R 12

Pg 5 #s 2- 30 evens

Bellringer

Counterexample A conjecture based on several observations may be true in most circumstances, but false in others. It takes only one false example to show a conjecture is not true. The false example is called a counterexample.

Example Given points X, Y, and Z Conjecture: X, Y, and Z are noncollinear. Counterexample: X Y Z

Classwork/Homework Pg 11 #s 1-19