1-1 Patterns and Inductive Reasoning LEQ: How do you use inductive reasoning to make conjectures?
What is inductive reasoning? Reasoning that is based on patterns you observe. U
Example: Finding and using a pattern. Use the pattern to show the next 2 terms in the sequence. 3, 6, 12, 24, … 48 96
1, 2, 4, 7, 11, 16, 22, … 29 37
Monday, Tuesday, Wednesday,… Thursday Friday
What is a conjecture? A conclusion you reach using inductive reasoning.
Example: Using Inductive Reasoning. Make a conjecture about the sum of the first 30 odd numbers. Find the first few sums. Notice that each sum is a perfect square. 1 = 1 = 1 + 3 = 4 = 1 +3 + 5 = 9 = Using inductive reasoning you can conclude that the sum of the first 30 odd numbers is 30 squared, or 900.
What is a counterexample? An example for which the conjecture is false. You can prove that a conjecture is false by finding one counterexample.
Example: Testing a conjecture and finding a counterexample. If it is cloudy, then it is raining. It is cloudy and it is not raining.
If the day of the week is Monday, I will be in a bad mood.
This Monday is Labor Day, which means that there is no school, which means that I will most definitely be in a good mood.
Writing Prompt: Explain how you would use inductive reasoning to create a conjecture.