This document discusses inductive reasoning and the process of making conjectures based on patterns. It explains that inductive reasoning involves making observations about a pattern, forming a conjecture to describe the pattern, and writing a rule to explain the pattern. It provides examples of patterns and questions to help observe patterns and write the corresponding rules. The document also discusses using counter-examples to determine if a conjecture is correct or incorrect.

1. Chapter 1, Section 7 Inductive Reasoning Ms. Dewey-Hoffman, 2009

2. What is the next figure in the pattern? Inductive Reasoning ? How did you know? You used your INDUCTIVE REASONING. Observation: what you notice about the pattern. Conjecture: a conclusion you make using inductive reasoning. Rule: a written explanation of the pattern or observation. This is your Conjecture

3. What is next in this pattern? 1, 3, 4, 12, 13….. Starts at 1, then multiplied by 3, then add 1, then multiply by 3, then add 1. So, 13(3) = next number in pattern. 39 is the next number in the pattern. What is the next number after 39 if the pattern is followed? Questions to ask yourself to understand what you observe and write a rule : Where does the pattern start? Does the pattern change as the pattern continues? What would be the next figure or number in the pattern? The Rule

4. Questions to ask yourself to understand what you observe and write a rule : Where does the pattern start? Does the pattern change as the pattern continues? What would be the next figure or number in the pattern? Write a rule for these patterns, then give the next number in the pattern. 30, 25, 20, 15 …… 2, -2, 2, -2 …… 4, 9, 14, 19 ……

5. Make A Conjecture You toss a coin four times, and it comes up heads each time. Is the conjecture “ The coin will come up heads on every toss ” reasonable? Why?

6. Counter Examples A Conjecture about an Observation is not always correct. If the Conjecture isn’t correct, write a counterexample to say why it isn’t correct. State whether the conjecture is correct or incorrect. If the conjecture is incorrect, write a counterexample to prove that it is incorrect. All US States end with the letter A. All dogs have tails. The last digit of the product of 5 and a whole number is either 0 or 5. A number and it’s absolute value are always opposites.

7. #6 Pages 38-39: 10-26 all. Be sure to do all parts of the problems. Do work on a separate sheet of paper and follow the homework format.