Park City Mathematics Institute
Exploring Discrete Mathematics
Project Abstract

Drafts of Project Files (password required)

Water Jug Math
Ashli Black*, Monica Foss, Jemal Graham, Brian Hopkins (Group Coordinator), Jesse Johnson, Jet Warr
Motivated by a puzzle popularized in the movie "Die Hard: With a Vengeance," this group developed a lesson plan around the classic water jug problems. Working from the format and philosophy of the PCMI morning course, four days of rich problems help students develop mathematics including number patterns, relatively prime, algorithms, and tri-linear coordinates related to the problem. At another level, the lesson builds problem solving skills, helps develop effective group work and collaboration, leads students to recognize different approaches to a problem, and encourages them to consider the organization of their work and their use of mathematical notation. In addition to student worksheets, an extensive teacher document offers solutions, tips for this method of instruction, extensive notes on how to deal with potential student problems, and various ways of using parts of the material for different grade levels and durations.
A Reservoir of Counting Problems, Redux
Debra Gamson*, Randall Creek
This pair of teachers worked on renovating the 2009 project "A Reservoir of Counting Problems" with a new organizational scheme, additional problems, and the PCMI format. The product is a rich selection of counting problems with solutions, categorized and well-indexed, with the goal of teacher usability.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. 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.