Reasoning based on patterns that you observe Finding the next term in a sequence is a form of inductive reasoning
A conclusion that you reach based on inductive reasoning
Count the number of ways 2 people shake hands Count the number of ways 3 people shake hands Count the number of ways 4 people shake hands Count the number of ways 5 people shake hands Make a conjecture about the number of ways 6 people shake hands People Handshakes 23456 13610?
Finish the statement: The sum of any two odd numbers is ____________. Begin by writing several examples: What do you notice about each sum? Answer: The sum of any 2 odd numbers is: 1+1=2 1+3=4 3+5 = 8 5+7=14 7+9= 16 11+13 = 24 even
Complete the conjecture: The sum of the first 30 odd numbers is ____________________. 1 = 1 1+3 = 4 1+3+5 = 9 1+3+5+7 = 16 1+3+5+7+9 = 25 1+3+5+7+9+11 = 36 What do you notice about the pattern? Conjecture: The sum of the first 30 odd numbers is 30 2.
Just because a statement is true for several examples does not mean that it is true for all cases If a conjecture is not always true, then it is considered false To prove that a conjecture is false, you need ONE counterexample Counterexample: an example that shows a conjecture is false.
You can connect any three points to form a triangle. Counterexample: three points on the same line Any number and its absolute value are opposites
1. If the product of two numbers is even, then the numbers must be even. 2. If it is Monday, then there is school.