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

2. 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”

3. Inductive Reasoning - Examples

4. 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

5. Making Conjectures

6. 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?

7. Counterexamples
Counterexample – one single case that disproves a conjecture.
Example:
Conjecture: The sum of two odd numbers is a multiple of 4.
Counterexample: = 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

8. 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