Unit 01 Lesson 08 Inductive Reasoning 1 Essential

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

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.

How would you describe the visual pattern? 3

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.

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.

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.

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.