1. Mrs. McConaughyGeometry1 Patterns and Inductive Reasoning During this lesson, you will use inductive reasoning to make conjectures.

2. Mrs. McConaughyGeometry2 Standards/Assessment Anchors:

3. Daily Warm Up Mrs. McConaughyGeometry3 Inductive reasoning ___________ Conjecture __________________________ Give an example of when you have used inductive reasoning in the real world.

4. Mrs. McConaughyGeometry4 reasoning based upon patterns you observe. Vocabulary Vocabulary Inductive reasoning ________________ ______________________________ Conjecture ______________________ _______________________________ Counterexample ___________________ _______________________________ the conclusion you reach using inductive reasoning an example for which the conjecture is incorrect

5. Mrs. McConaughyGeometry5 Examples: Number and Letter Patterns Finding and Using a Pattern

6. Mrs. McConaughyGeometry6 Finding and Using a Pattern Use inductive reasoning to a. find a pattern for each sequence, then b. use the pattern to find the next term in each sequence below: 20, 18, 16, 14, __ A, C, F, J, O, __ 1, 3, 6, 10, 15, 21, ___a, 6, c, 12, e, 18, __ ½, 9, 2/3, 10, ¾, 11, __1, 3/2, 9/4, 27/8, __ 12 28 4/5 U g 81/16

7. Mrs. McConaughyGeometry7 Using Inductive Reasoning to Make Conjectures EXAMPLE 3 + 5 = 8 -3 + 5 = 2 -1 + 1 = 0 13 +27 = 40 51 + 85 = 136 Conjecture: The sum of two odd numbers is always ___________. EXAMPLE 3 * 4 = 12 12 * 5 = 60 11 * -4 = -44 -24 * -3 = 72 -7 * 8 = - 56 Conjecture: The product of ______________ _________________ _________________. an even integer a prime number and an even integer is always an even integer.

8. Mrs. McConaughyGeometry8 Examples: Picture Patterns Finding and Using a Pattern

9. Mrs. McConaughyGeometry9 EXAMPLE: Testing a Conjecture When points on a circle are joined by as many segments as possible, overlapping regions are formed inside the circle as shown above. Use inductive reasoning to make a conjecture about the number of regions formed when five points are connected.

10. Mrs. McConaughyGeometry10 Did you guess that the number of regions doubles at each stage? Now find a counterexample to show this conjecture is false. PointsRegions 22 34 48 516 6? 31

11. Mrs. McConaughyGeometry11 Testing a Conjecture counterexample Not all conjectures turn out to be true. You can prove that a conjecture is false by finding one counterexample.

12. Mrs. McConaughyGeometry12 Applying Conjectures to Business

13. Mrs. McConaughyGeometry13 1.Find the next term in the following sequence: 2.Use inductive reasoning to make a conjecture: 3.Counterexample: 4.Draw the next picture in the picture pattern below: Final Checks for Understanding

14. Mrs. McConaughyGeometry14 Homework Assignments: Day 1: Inductive Reasoning WS Day 2: Number Patterns WS Day 3: Picture Patterns WS