1. Unit 01 – Lesson 08 – Inductive Reasoning Essential Question  How can you use reasoning to solve problems? Scholars will  Make conjectures based on inductive reasoning  Find counterexamples 1

2. What is inductive reasoning? 2 A conjecture is an unproven statement that is based on observations. You see inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general cause.

3. How would you describe the visual pattern? 3

4. How can you make and test a conjecture? 4 Numbers such as 3, 4, and 5 are called consecutive integers. Make and test a conjecture about the sum of any three consecutive integers.

5. What is a counterexample? 5 To show that a conjecture is true, you must show that it is true for all cases. You can show that a conjecture is false, however, by finding just one counterexample. A counterexample is a specific case for which the conjecture is false.

6. How do you find a counterexample? 6 A student makes the following conjecture about the sum of two numbers. Find a counter example to disprove the student’s conjecture. CONJECTURE – The sum of two numbers is always more than the greater number. To find a counterexample, you need to find a sum that is less that the greater number. -2 + (-3) = -5 -5 ≯ -2 Because a counterexample exists, the conjecture is false.

7. Practice 7 Find a counterexample to show that the conjecture is false.  The value of x 2 is always greater than the value of x.  The sum of two numbers is always greater than their difference.