1. Patterns and Inductive Reasoning

2. Inductive reasoning A type of reasoning that reaches conclusions based on a pattern of specific examples or past events. In other words, you take specific examples, look at them, then, make a general statement that applies to all of them Example:

3. What can you imply from these examples? They are all dogs! By observing patterns, we can come to logical conclusions. If we said, “Monday, Tuesday, Wednesday” What would be the most logical assumption of what we say next? Thursday, Friday, Saturday

4. If I look at a sequence 1 2 4 7 11 16 22 What would be the next two terms? 29 37 Looking at something symbolic, what would be the next pattern

5. Conjecture The conclusion you reach through inductive reasoning Not all conjectures are true It only takes one counterexample to prove that it doesn’t hold up Example: Points on a circle joined by line segments 2 points 1 line segment 2 regions

6. 3 points 3 lines 4 regions 4 points 6 lines 8 regions

7. 5 points 10 lines 16 regions Let’s recap PointsLinesRegions 212 334 468 51016

8. Conjecture: Number of regions doubles as another point is added Does this conjecture hold true? 6 points 15 lines 31 regions Does our conjecture hold true?

9. Looking at the table, what conjectures can you make? 5 * 7 = 355 * 13 = 65 5 * 3 = 155 * 9 = 45 5 * 11 = 555 * 25 = 125 1.Product of 5 and a odd number is odd 2.Product of 5 and any number ends in 5

10. A skateboard shop finds that over a period of five consecutive months, sales of small-wheeled skateboards decreased What conjecture can we make? That in June they only sell 42. What about July? Would we want to make a conjecture about December?

11. ASSIGNMENT PAGE 6-7 PROBLEMS 1 – 6, 17 -22, 23,24,29,31-36, 42-46