2-1: Inductive Reasoning

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2-1: Inductive Reasoning Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School 2015-2016

Inductive Reasoning Defined Inductive Reasoning – Using patterns you observe to make an educated guess about what will happen next. Example: The last four A-days your friend who sits next to you in 1st block has asked you to for a pencil but you always have only one. What might you do on the fifth day? Bring two pencils to class on A-Days, sit somewhere else, make a new friend… Example: Every year starting with your 6th birthday, you mark your height on a wall. The first 5 marks are 42”, 45”, 48”, 51”, and on your 10th birthday you are 54”. How tall do you guess you’ll be on your 13th birthday? 63”

Inductive Reasoning - Examples

What is a Conjecture? Conjecture: An unproven, but seemingly valid general statement based on specific observations. Must always be true. Ex: (-2) (-4) (-3) = Ex: (-1) (-9) (-7) = Conjecture: The product of 3 negative integers is___________________________________ -24 -63 A negative integer

Making Conjectures

Making Conjectures 20 12 24 16 Examples: The sum of two odd numbers is always an even number. The sum of two odd numbers is divisible by four?

Counterexamples Counterexample – one single case that disproves a conjecture. Example: Conjecture: The sum of two odd numbers is a multiple of 4. Counterexample: 1 + 5 = 6, and 6 is not a multiple of 4. Conjecture: Multiplying a number by 2 makes the number bigger. Counterexample: 2(-10) = -20, and -20 < -10

Counterexamples Provide a counterexample to the conjecture: The value of x2 is always greater than the value of x. Possible Counterexamples: 1, 0, ½, ¾ The math teachers at PHS all have a double letter in their last name. Possible Counterexamples: Mrs. Mauk, Dr. Yankey