Park City Mathematics Institute
Exploring Discrete Mathematics
Project Abstracts

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Pascal's Triangle through Plinko and Paths

Jocelyn Co, Tatyana Finkelstein, Alice Fisher, Mark Franzak, Brian Hopkins, Dawn Leach, Malvia McDonald, Lars Nordfelt, Kymberly Riggins, Sergio Zepeda. We also want to acknowledge the input of Gene Abrams and Eric Pandisico, our guests during the first week.

These two multi-day class projects with teacher guides, student worksheets, and solutions projects introduce students to Pascal's triangle using methods besides numeric patterns.

The project "Pascal's Triangle through Plinko" can stand alone or lead in to the second project. Students toss coins to simulate a ball falling through a Plinko board, and then use an applet [Quincunx] to simulate a much larger number of trials.

"Pascal's Triangle though Paths" begins with students walking out lattice paths to various points on a grid made of tape on the floor. On the second day, students extend their results, look for patterns, verify Pascal's Identity using lattice paths, and consider extensions as time allows. This project also can stand alone or follow the first project.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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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.