Number Theory and Algebra Working Group

Friday, July 13

"Regressing to the Binomial Expansion Theorem"

Today, our working group session began with Victoria presenting the procedures for finding regressions using the TI-89. After Victoria’s presentation, John brought forth the idea of perhaps creating a "Scavenger Hunt" as introduction to the Graphing Calculator (be it a TI-83 or a TI-89). The group seemed to like this idea so we decided to dedicate the last 10 minutes of our session to generate the hunt.

We then continued investigating Pascal’s triangle. Ryota showed us the relationship of Pascal’s triangle and combinatorics (nCr–"n choose r"). He then led the discussion to Binomial Expansion. Ryota concluded with a short (15 minute) proof, which he shortened into a 2-minute proof QED! J

The last 10 minutes was spent brainstorming items for the scavenger hunt.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.