Mead Session     January 24, 2009
Catalan Numbers- What Are Those?

Participants organized exhaustive lists of nested parentheses, using 2, then 3, then 4 sets of parentheses.

Then they determined the number of paths from one point to another on various-sized grids given that they could only move to the right and/or down. The data from the two contexts yielded the Catalan numbers. Participants sought the formula to determine the nth Catalan number.

Some of the AIMS Standards addressed include:
3.1.1 Communicate a an iterative or recursive pattern, using symbols or numbers.
3.1.2 Find the nth term of an iterative or recursive pattern.
3.1.3 Evaluate problems using basic recursion formulas.
5.1.4 Select an algorithm that explains a particular mathematical process.
5.2.5 Identify a valid conjecture using inductive reasoning.

Participants worked to determine all possibilities.	Participants shared ideas to solve the patterns.