1.+Patterns+and+Inductive+Reasoning

=Patterns and Inductive Reasoning= Objective: To use inductive reasoning to make conjectures.

Visit Standards page to identify numbers. NCTM Standards: 1, 6, 7 CT Mathematics Standards: 1.1, 4.2
 * Standards **

Do this interactive lesson as an introduction to //patterns//: []

//Inductive reasoning// is a reasoning that is based on patterns you observe. If you observe a pattern in a sequence, you can use inductive reasoning to tell what the next terms in the sequence will be.

Find a patter for this sequence: 3, 6, 12, 24 For this pattern, each term is twice the previous term. You can use the pattern to predict the next term - 24 x 2 = 48.

Place examples of inductive reasoning here.

A conclusion that you reach using inductive reasoning is called a //conjecture.// Not all conjectures turn out to be true. If you can find one //counterexample//, that is enough to prove the conjecture false.

Watch this presentation about poverty in Africa. media type="custom" key="7443351" In the //Discussion// area please answer these questions:
 * What is the conjecture made here?
 * What kind of counterexample could be tested based on that conjecture?

One of the most common sequences is called the Fibonacci sequence. [].

This video shows some kids doing activities based on the Fibonacci sequence. After watching it, come up with your own examples of the Fibonacci sequence in nature. You may present your findings in any way you choose on this wiki below the video. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">media type="custom" key="7443533" <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">([])