+ Vocabulary… Conjecture: an unproven statement that is based on observations. Example: a. 1 x 9 + 2 = 11 b. 12 x 9 + 3 = 111 c. 123 x 9 + 4 = 1111 d.

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Presentation transcript:

+ Vocabulary… Conjecture: an unproven statement that is based on observations. Example: a. 1 x = 11 b. 12 x = 111 c. 123 x = 1111 d. ____________________

+ Deductive Reasoning vs. Inductive Reasoning Reasoning in Geometry

+ Inductive vs. Deductive Inductive Reasoning: taking specific example and makes sweep general conclusion. (This does not always lead to a valid conclusion.) Deductive Reasoning: taking general cases and making specific examples (definitions, postulates, previous theorems, corollaries, and given information).

+ Example of Inductive Reasoning My math teacher is skinny My last math teacher was skinny Conclusion by inductive reasoning: All math teachers are skinny.

+ Examples of Deductive Reasoning If quadrilaterals have 4 sides Then a square is a quadrilateral.

+

+ Inductive or deductive? All even numbers are divisible by 2 28 is even Therefore, 28 is divisible by 2.

+ Inductive or deductive? 3, 6, 9, 12, 15, … The next term is going to be 18

+ Inductive or deductive? My daddy has curly hair My mommy has curly hair My brother has curly hair Therefore, everyone I am related to has curly hair.

+ Inductive or deductive? Jimmy got bitten by a dog. Jimmy is now scared of all dogs.

+ Inductive or deductive? An apple a day keeps the doctor away Joe ate an apple every day. Dr. Dre stayed away

+ Inductive or deductive? 1, 4, 9, 16, 25, 36, 49, 64,… The next term will be 81.

+ Inductive or deductive? My soda had a roach in it. All soda has roaches.

+ Inductive or deductive? All speeders will be slapped Jimmy sped Jimmy got slapped

+ Inductive or deductive? Two episodes of The Big Bang Theory made me laugh and LOL. Therefore, The Big Bang Theory is always funny.

+ Inductive or deductive? Decide on a reasoning, write an example of it Share it with your partner Partner will decide if your example is a deductive or inductive reasoning.