1. Missy McCarthy Okemos High School Math Instructor G EOMETRY WITH M C C ARTHY

2. W HAT DO YA KNOW ? In each of the following examples, you will find a logical sequence of five boxes. Your task is to decide which of the boxes completes this sequence. To give your answer, select one of the boxes marked A to E. At the end, you will be told whether your answers are correct or not. Let’s try a little activity to get your brain warmed up!

3. W HAT COMES NEXT ?

7. H OW 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

8. I NDUCTIVE R EASONING 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.

9. U SING INDUCTIVE REASONING

10. M AKING C ONJECTURES Conjecture : A statement you believe to be true based on inductive reasoning

11. U SING INDUCTIVE REASONING …

12. B E 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).

13. C OUNTEREXAMPLES 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.

14. F ALSE CONJECTURES

15. C OUNTEREXAMPLES 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.