Drill 1, 3, 5, 7, 9, , 2, 5, 8, 11, 14, , -3, -6, -10, -15, , , , OBJ: SWBAT use inductive reasoning in order to identify.

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Drill 1, 3, 5, 7, 9, __, __ 2, 5, 8, 11, 14, __, __ -3, -6, -10, -15, __ , , , __ OBJ: SWBAT use inductive reasoning in order to identify patterns and make conjectures.

Unit C Inductive Reasoning Copy: C1 CN, (RS C1 is on back of notes), C1 CW, Practice A can be used for HW Mr. Calise Geometry

Motivation How quickly can you add the odd numbers from 1 – 20? = 12 = 22 = 32 = 42 = 52 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25

Notes Inductive Reasoning: Allows you to reach conclusions based on a pattern of specific examples. Ex: Each morning you see your friend eating Cheerio’s for breakfast. You see this everyday for 3 weeks. The next day what do you expect to see when you see your friend? *Does that mean it will definitely happen?

Conjecture: A conclusion reached using inductive reasoning. Example: Make a conjecture about the shapes.

Points Regions 2 3 4 5 6

4 3 12 11 13 14 10 15 27 28 16 9 5 8 1 26 17 29 2 18 31 25 30 19 24 20 21 22 23 6 7

True or False? All teachers are taller than students. Can anyone prove this? Counterexample: is something that disproves a conjecture. Prove it… A counterexample can be a drawing, a statement, or a number. -Only one counterexample is needed to disprove a statement.

Counter Example Song

Text Messages On average, how many text messages do you send in a month? Based on our data, high school students send at least ______ text messages a month. Is this a true statement? What could be a counterexample? Is this a true statement? Why or why not?

450 450 Two complementary angles cannot be congruent. Show that the conjecture is false by finding a counterexample. Two complementary angles cannot be congruent. 450 450

Lesson Quiz Find the next item in each pattern. 1. 0.7, 0.07, 0.007, … 2. 0.0007 Determine if each conjecture is true. If false, give a counterexample. 3. The quotient of two negative numbers is a positive number. 4. Every prime number is odd. 5. Two supplementary angles are not congruent. 6. The square of an odd integer is odd. true false; 2 false; 90° and 90° true

1. 0, 2, 4, 6, 8, _____, _____ 2. 1, 2, 4, 7, 11, _____, _____ Follow This Pattern 1. 0, 2, 4, 6, 8, _____, _____ 2. 1, 2, 4, 7, 11, _____, _____ 3. 16, 8, 4, 2, 1, _____, _____ 4. 1, 1, 2, 3, 5, 8, _____, _____ 5. 4, –4, 4, –4, 4, _____, _____ 6. 1, ½ , ¼ , ⅛, _____, _____ 7. 1, 10, 100, 1000, 10000, ____, ____ 8. 1, 8, 27, 64, 125, _____, _____ 9. 1, 3, 6, 10, _____, _____ 10. 27, 9, 3, 1, _____, _____

11. 49, 36, 25, 16, _____, _____ 12. a, c, e, g, i, _____, _____ Follow This Pattern 11. 49, 36, 25, 16, _____, _____ 12. a, c, e, g, i, _____, _____ 13. 3, 5, 7, 9, 11, _____, _____ 14. 11, _____, 5, 2, _____, –4, –7 15. 1, 3, 9, 27, 81, _____, _____ 16. J, F, M, A, _____, _____ 17. 3, –6, 12, –24, 48, _____, _____ 18. 8, 7, 5, 4, 2, _____, _____ 19. 1/2, 2/4, 3/6, 4/8, _____, _____ 20. 1, 6, 11, 16, 21, _____, _____