### Fold & Cut

What shapes can result from the following fold-and-cut process?

Take a piece of paper.

Fold it flat.

Make one complete straight cut.

Unfold the pieces.

Are all shapes possible?

Skip to content # Supporting Material: Photos & Videos

### Fold & Cut

### Cup Stacking

### Balance Beans

### Solving Linear Equations: An M&M Mystery

### Can Voting Ever Really Be “Fair”?

### The Dollar Game

### Bicycle Math

### Grid Power

### Acting Out Mathematics

### Folding Perfect Thirds

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What shapes can result from the following fold-and-cut process?

Take a piece of paper.

Fold it flat.

Make one complete straight cut.

Unfold the pieces.

Are all shapes possible?

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Begin with a row of cups and end with all of the cups in a single stack.

Rules:

1. Count the number of cups in a stack. That stack must jump that number of

spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2

spaces; 3 cups have to move 3 spaces…

2. A cup or stack of cups cannot move into an empty space. They have to land

on another cup or stack of cups.

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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!).

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Developed as part of the Math Circles of Inquiry project, this session is aimed at grades 7 or 8, but may be useful for high school algebra. It consists of worksheets and series of videos meant to get students to develop an understanding of solving linear equations, using the real world example of distributing M&Ms into jars.

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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.

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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.

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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?

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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.

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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.

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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?