### Introduction

A key question for math circles is about the relationship of the session's topic to the curriculum. In my view, a rule of thumb is that sessions for students should not have too much curricular content, while sessions for teachers need not stray too far from the curriculum.

For students, it would be a mistake to duplicate what is already going on in the classroom. The whole idea of a math club or Math Circle is to give the participants a taste of the variety of math content, and to get away from the status differences that flow from different levels of achievement in school mathematics.

On the other hand, for teachers, a possible goal of a Math Teachers' Circle session can be to gain a deeper, teacher-level understanding of the material they teach, and also to be introduced to activities they may be able to adapt for classroom use.

That said, there are some topics that can work (in different ways) for both audiences, and there are topics whose proximity to curriculum is not obvious. Thus, I will not try to create two separate lists.

### Links

- Abstract Algebra
- An entertaining introduction to finite groups
- Function Diagrams
- Yet another representation of functions!
- Geoboard
- Many puzzles and activities
- Geometric Puzzles
- Tangrams, polyominoes, pentominoes, supertangrams, rep-tiles...
- Handy Math
- Base 5 arithmetic, by Betta and Tom Fisher-York
- Knot Theory
- A bit of topology!
- Map Coloring
- ...leading to the 2-color theorem
- Number Puzzles
- Number Pyramids, Staircases, Egyptian Fractions, Slumber Theory...
- Pattern Blocks
- A secondary school take on a kindergarten manipulative
- Symmetry
- Many puzzles and activities
- Taxicab Geometry
- What happens if we change the definition of distance?
- Teachers' Mathematics
- Concept exploration, problem analysis, formal development
- Tiling
- A fun springboard for ideas in geometry – traditional and transformational