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Inductive Reasoning Geometry Week 1 of 9 Unit 1: Logic & Reasoning 8/31 & 9/1 Standards & Vocabulary Standard 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. Standard 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. Vocabulary Inductive Reasoning Conjecture Counterexample Inductive Reasoning – “Bottom Up” 4. Theory ALL shirts at this store are 20% off. 3. Tentative Hypothesis It seems like shirts are 20% off at this store. 2. Pattern Another shirt is on sale, from $30 to $24. That is also 20% off. 1. Observation A shirt is on sale. It was $20, but after 20% off, is only $16. What Comes Next? - Inductive Reasoning Description: In groups of 2 to 4, create your own patterns using action, rhythm, letters/words, numbers or pictures. The class has to guess what is to come next in the pattern. Example: (Hey, Ho, Hey, Ho, __) (5, 10, 15, 20, _ , _ , _) Purpose: This activity is used to determine that students already use inductive reasoning. Vocabulary Defined Inductive Reasoning – reasoning that is based on continuing patterns you observe [Induce – to determine, based on a number of particular facts] Conjecture – a conclusion you reach using inductive reasoning (seem likely, but unproven) Counterexample – an example for which the conjecture is incorrect. It only takes one counterexample to prove the conjecture incorrect. More Practice… Find a Pattern For Each Sequence. 3, 6, 12, 24,… 1, 2, 4, 7, 11, 16, 22,… AL, AK, AZ, AR,… Derek, Kobe, Ron,… Red, Orange, Yellow, Green,… Counterexamples X=X·X X=0 0= X=1 1= However… X=2 2≠ X=3 3≠ …and so on… 0·0 1·1 True True 2·2 3·3 False False More Counterexamples Find a counterexample for each conjecture: a) The square of any number is greater than the original number. b) You can connect any three points to form a triangle.