1. Megan FrantzOkemos High School Math Instructor

2.  Use inductive reasoning to identify patterns and make conjectures.  Determine if a conjecture is true or false.

3. What comes next?

5. How did you do? An inductive reasoning test measures abilities which are important in solving problems. These tests measure the ability to work flexibly with unfamiliar information and find solutions. People who perform well on these tests tend to have a greater capacity to think conceptually as well as analytically. Question 1: E Question 2: D Question 3: D Question 4: B

6. Inductive Reasoning When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. You may use inductive reasoning to draw a conclusion from a pattern. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true.

7. Using inductive reasoning

8. Making Conjectures Conjecture : A statement you believe to be true based on inductive reasoning

9. Be careful! Some patterns have more than one correct rule. For example, the pattern 1, 2, 4, … can be extended with 8 (by multiplying each term by 2) or 7 (by adding consecutive numbers to each term).

10. Counterexamples To show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample. A counterexample can be a drawing, a statement, or a number.

11. False conjectures

12.  Use inductive reasoning to identify patterns and make conjectures.  Determine if a conjecture is true or false.