Math Circle Activity Database

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Mathematical Practices
  • MP1 - Make sense of problems and persevere in solving them. (1)
  • MP3 - Construct viable arguments and critique others' reasoning. (1)

Bicycle Math


You are brought to a crime scene. You are told that a thief just made off with a bag full of diamonds, escaping on a bicycle. You come across a pair of bicycle tracks in the snow, no doubt made by the fleeing thief. But which way did the thief go? Just by looking at the shapes of the tracks, can you determine which way the thieving cyclist went: left to right or right to left?

Factor Game


A teacher challenges students to a game. The rules are explained as the game progresses. The player with the highest total wins! Students then play against each other. Afterwards, while analyzing the game, prime, composite, perfect, deficient, and abundant numbers are discovered and defined. Students again play the game using the strategies they determined.

In a professional development video, teachers focus on the topic of number systems and number theory using a game setting to investigate the properties of prime, composite, abundant, deficient, and perfect numbers. This video can be used in conjunction with The Factor Game lesson plan.

Folding Perfect Thirds


Imagine you’re packing for a trip, and you’re planning on bringing your favorite tie. It’s too long to fit in your suitcase, even after folding it in half. You would fold it into fourths, but you don’t want all of those creases ruining your tie. You’ve decided folding it into thirds will be the perfect length to fit in your suitcase without noticeable creases on your tie. However, you don’t have a ruler or any means of making sure your tie is folded into perfect thirds. Is there anything you can do about this?

Grid Power


“When I grew up in the Soviet Union, all we used for math was grid paper. Grid paper leads to discovery.” This is how Tatiana Shubin, San Jose State University, begins her lesson demonstrating the myriad of wonderful math questions arising from a simple sheet of grid paper. Attempting to count all squares of any size on a limited grid will require participants to persevere, organize their thinking and construct viable arguments.

Prejudiced Polygons


We adapt “Parable of the Polygons” (Vi Hart and Nicky Case), an online simulation on diversity and segregation, into an appropriate MTC session. The session is interactive, and offers multiple layers of content depending on the age and comfort level of students with conversations on social issues. These levels include: (1) an exercise in fractions, (2) an introduction to game theory, (3) an invitation for students to think about the benefits of diverse groups, and (4) a discussion of how individual biases, no matter how small, can lead to detrimental societal effects like segregation. Triangles and Squares live together in...