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Balance Beans

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If you start with some beans on a seesaw and you’re given certain additional beans to place on the seesaw, can you do it so the seesaw balances?

In this activity, students start by trying to solve various challenges involving different arrangements of beans on the seesaw and then design their own challenges. Next, they try to predict which arrangements will make the seesaw balance and which ones won’t (and why!).

Can Voting Ever Really Be “Fair”?

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What is “fair” when voting? In this session, the participants apply and analyze several established methods for determining the “voice” of the majority. They will discover these methods through an inquiry-based experience in a deep problem, and join an ongoing discussion that has gone on for hundreds of years about what is considered “fair voting.”

This session is also suitable for a high school student math circle or classroom.

The Dollar Game

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A group of people, some that just met, have a dilemma. Some people owe money and some have money. Problem is that only people that know each other, connected by nodes, can give or lend a dollar. But they must give each person they know a dollar, even if that puts themselves in debt!! Find ways to give money in such a way so that everyone in the group has money or owes 0 dollars.

Bicycle Math

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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

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“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.

Folding Perfect Thirds

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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?