## 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?

## 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.

## Acting Out Mathematics

In teams, participants will create body movements related to geometry facts and will use their body to create a convincing argument as to why the statement is true. Please bring your fun-meter, your creativity, your body, and open physical space (for moving) to this session.

## 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?

## 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.

## Measuring Up: “Perfect” Rulers

Is it possible to measure all possible integer lengths on a ruler without marking every integer on that ruler? This is an engaging and challenging problem for all. Beautiful mathematics can be revealed while delving deeper into this seemingly easy question.

## Conway’s Rational Tangles

What do adding positive and negative fractions have to do with tying knots? In this entertaining lesson, students will use ropes to explore and identify mathematical operations that untangle knots and lead to new thinking. Simple operations of twists and rotations circle back to practicing the addition of positive and negative fractions.

## The Game of SET

SET is a fun game that can be enjoyed by kids as young as 6 and is challenging even for adults. It is rich in counting problems and is great for getting people to pose problems. It is also an example of a finite geometry and interesting to explore how well one’s geometric intuition works.

## 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 neighborhoods. However, the Polygons all believe two things: “I am unhappy if fewer than 1/3 of my immediate neighbors are like me.” and “I am unhappy if I have no immediate neighbors.”