Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis

Inductive what??? Scientists and mathematicians look for patterns and try to draw conclusions from them. A conjecture is an unproven statement that is based on a pattern or observation. Looking for patterns and making conjectures is part of a process called inductive reasoning.

Example 1: Complete the conjecture. The sum of any two odd numbers is _______. 1 st – Try some examples 1+1 = ___5 + 7 = ___9 + 1 = ___ 3+5 = ___ = ___9 + 5 = ___ 2 nd – Do you see a pattern? 3 rd – Make a conjecture. 4 th – Test it!

Example 2: Complete the conjecture. The sum of two positive numbers is ________. 1 st – Try some examples = ___ = ___6 + 2 = ___ _____________________________ 2 nd – Look for a pattern. 3 rd – Make a conjecture. 4 th – Test it!

Counterexamples!!! Just because something is true for several examples does not mean that it is true in general. To prove that a conjecture is false, all you need to do is find one counterexample. A counterexample is an example that shows a conjecture is false.

Example 3: Show the conjecture is false by finding a counterexample. All shapes with 4 sides are squares. All multiples of 3 are odd numbers.

Assignment: Worksheet 1.2