Download - Review Evaluate the expression for the given value of n: 3n – 2 ; n = 4 n 2 – 3n ; n=6 10 and 18
Review
Evaluate the expression for the given value of n:
3n – 2 ; n = 4 n2 – 3n ; n=6
10 and 18
Inductive Reasoning and Conjecture
GeometryUnit 9, Day 1Mr. Zampetti
Objective
To learn how to make conjectures based on inductive reasoning
To find counterexamples of conjectures
Definition
Conjecture: an educated guess based on known information.
Example Given: 2, 4, 6, 8 Conjecture: The next number will be 10
Definition
Inductive Reasoning: reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction
You use inductive reasoning to find conjectures
Make a conjecture
Given: 1, 3, 6, 10, 15 find the next number
Conjecture: The next number will be 21.
Counterexample
A counterexample is a false example to show a conjecture to be not true
Find a counterexample: Given: points W, X, Y, Z
Conjecture: W, X, Y, and Z are noncollinear
Counterexample:
WX
Y Z
Example
Is the following conjecture always, sometimes, or never true?
Given: Points D, E, and F are collinearConjecture: DE + EF = DF
Sometimes!!
With a partner:
Make a conjecture about the next item in the sequence: -8, -5, -2, 1, 4
Determine whether each conjecture is true or false. Give a counterexample for a false conjecture: Given: x is an integer. Conjecture: -x is negative.
With a partner (cont.):
Determine whether each conjecture is true or false. Give a counterexample for a false conjecture: Given: WXYZ is a rectangle Conjecture: WX = YZ and WZ = XY
With a partner (cont.):
Most homes in the northern United State have roofs made with steep angles. In the warmer areas of the southern states, homes often have flat roofs. Make a conjecture about why the roofs are different.
Homework
Work Packet: Inductive Reasoning and Conjecture