Park City Mathematics Institute
Exploring Discrete Mathematics
Project Abstract

Drafts of Project Files (password required)

A Look into the Mathematics of Mastermind
Trevor Boehne, Marcelle Good, Brian Hopkins (group coordinator), Mahen Malixi*, Todd Vawdrey
This series of problems and activities has been created to provide ideas and resources to help design and implement lessons involving the mathematics of the game Mastermind. It currently addresses counting techniques and probability, but leaves open the possibility of strategy, logic, and other extensions. The questioning methods used are inspired by George Pólya's "How to Solve It" and the Common Core Standards for Mathematical Practice. They seek to create productive struggle, foster perseverance, encourage exploration of analogous problems, and help students look for and make use of structure.
Objectives, scaffolding questions, extension questions, teacher notes, and solutions have been included with each of the larger questions to help further guide the possible design and implementation of lessons. Although the modules are designed so that they may be used in any way that suits the educator's needs, possible roadmaps through the modules have been included. Templates for printing Mastermind game boards, code pieces, feedback pieces, and scoring sheets have also been included as an alternative for those without access to the original game.
Seven Bridges of New York City
Olimpia Castro Mora, Daniel Coffin, Timon Holman, Brian Hopkins (group coordinator), and Gabriel Rosenberg*
This lesson is designed to give students an introduction to graph theory. Students will analyze the toll bridges of New York City to discover under which circumstances they can create Euler paths and Euler circuits. The explorations are structured to consider bridge closings and bridge additions so that students realize the circumstances under which these paths are possible. The lesson has been augmented with a task to find a tourist route through Lima, Peru.
This lesson is intended to have multiple points of entry and exit so that it can be used with students of various levels from middle school through high school. The materials here include the student worksheets, an annotated teacher's guide, and notes about implementing problem-solving tasks effectively.

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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.