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Grade Vs Difficulty:

Part 1 is an exploration of some different ways of thinking about Fibonacci numbers and some Fibonacci number identities (based in part on James Tanton's "Fibonacci Surprises" notes.
Part 2 is an exploration of several problems whose solutions all involve the Catalan numbers.
This lesson was used in January 2012 at the San Diego Math Teachers Circle, and a modified version was used at the 2012 Bay Area Circle for Teachers summer workshop.