Math Circle Presentations

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Advice on presenting at the Madison Math Circle

This page is meant as a resource for presenters at the Madison Math Circle.

Who is the audience?

The audience currently consists primarily of middle school students, but there are some high school students and a few advanced elementary school students as well. The number of students has varied somewhat dramatically in recent semesters, but you should expect about 10-15 students.

Selecting a topic

Basically any topic with a mathematical or quantitative component could be an appropriate topic. We have seen excellent presentations on: logic puzzles, sorting algorithms, computer graphics, the mathematics of juggling, origami, sine and cosine functions, Catalan numbers, the mathematics of the game Set, and more. One key is crafting problems that the students can explore on their own which will give them a feel for the larger topic. If you want help in fleshing out an idea, contact the organizers!

The book Circle in a Box by Sam Vandervelde (which is available online or at our very own math library) has lots of nice ideas.

Sample Schedule

We encourage presenters to spend half of the time having students explore problems on their own. For instance, a common and successful format would like this:

  • 6:00-6:05: Begin the session with a brief introduction of the topic. Set-up the first round of problems.
  • 6:05-6:20: Students work on problems. (Note: if you're presenting on a rich topic, like cryptography or computer graphics, it may be the case the problems only give a taste of the kind of mathematics involved. This is okay!)
  • 6:20-6:35: Discuss solutions to some of the problems and how they relate to your topic. Set up new problems.
  • 6:35-6:45: Work on new problems.
  • 6:45-7:00: Concluding discussion of topic. Discuss some of the directions this type of thinking can lead, maybe including further problems. Pizza arrives around 6:50, so discussion can end at any point between 6:50 and 7:00 depending on how things are going.

AV Equipment

For computer slides, we encourage you to bring your own laptop (and adapter, if using a Mac). In addition, our experience has been that sometimes computer issues arise with individual laptops, and so to avoid these issues, we will ask that you email a copy of your slides (in PDF or Powerpoint format) to at least 24 hours in advance of your presentation.

If you would like to use AV equipment for a purpose other than just computer slides, please let us know in advance! We want to make your presentation as seamless as possible.


If you want to include special supplies in your presentation, please let us know as soon as possible. The Madison Math Circle owns some supplies (decks of Set, ???) which will happily lend out. We are also happy to print out worksheets or any other handouts. Finally, we have a limited budget for purchasing other supplies, and we will do our best to accommodate any request.


If you have any questions at all, you can write directly to any of the organizers (Caitlyn Booms, Daniel Erman, Colin Crowley, Connor Simpson, Hyun Jong Kim, and Xiao Shen) or you can email the organizers list: