2-1: Inductive Reasoning

Mr. Schaab’s Geometry ClassOur Lady of Providence Jr.-Sr. High School

2015-2016

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 Defined

Inductive Reasoning - Examples

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___________________________________

What is a Conjecture?

A negative integer

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Making Conjectures

Making Conjectures

Examples: The sum of two odd numbers is always an even number.The sum of two odd numbers is divisible by four?

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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

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

Counterexamples