Park City Mathematics Institute
Exploring Discrete Mathematics
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
- 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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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King
With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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.