Math 149. Capstone Mathematics for Teachers.
Final Project
Choose one of the following options. The final project must be typed in LaTeX.
Option I.
Propose a new game and some variations of it for the Math Field Day Game Tournament.
- Learn the current games. The list of current games is
here, some of their possible variations are
here.
- General Requirements for a Math Field Day Game:
- Materials must be easy to get and inexpensive. We need to run the tournament for up to 150 participants and our budget is limited to a few
hundred dollars. For example, counters, dice, boards printed on paper, etc. are OK, while something like full chess sets would be too expensive.
- The rules must be simple enough so that they can be explained in a few minutes. The list of current games will give you an idea.
Again, something like chess is way too complicated.
- Each round must take no more than 3 minutes.
- The game must allow different minor variations such as the initial sizes of piles, initial posititions of the counters, etc.
- Describe the rules for the main ("first") game.
- Find a winning strategy for one of the players for the "first" game. Be detailed.
- Propose at least three variations (check out the current games for ideas.)
Try to find a winning strategy for one of the players for at least one of the proposed variations. Partial ideas/strategies or partial lists
of good and bad moves are welcome too.
Option II.
Propose an idea for a high school science fair project.
- A couple of examples will be described in class.
- The project should be beyond the standard high school math curriculum.
Feel free to use concepts and ideas you learned in college. However, the topic should be accessible to a high school student.
Suggest some reading (at least 2 sources).
- Clearly state one or more questions that a high school student (or a small team of students) could investigate.
- Carry out the investigation to some extent or for some of the questions. Provide proofs.
- Comment on the mathematics involved. What would a student learn (or master) by doing this project?
This page was last revised on 21 April 2017.