### 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: Virtual Tools

### Fold & Cut

### Making Connections Between Forms of Quadratic Equations

### Pick’s Theorem

### Intergenerational Wealth

### Animated Activities

### The Dollar Game

### Wolves and Sheep

### Measuring Up: “Perfect” Rulers

### Bubbling Cauldrons

### Humans, Zombies, & Other Problems Crossing the River

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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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Developed as part of the Math Circles of Inquiry project, the goal of this module is to help students in Algebra II become fluent in the various forms of a parabola equation based on the information that they are given. Students sometimes fail to understand that there are multiple ways to find an equation of a parabola. This module incorporates multiple activities both in the learning packet and using Desmos activities online to encourage students to discover and practice writing equations of parabolas in their various forms. At the end of this activity students will work more efficiently with equations...

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Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter pegs, and the number of interior pegs.

This session is also suitable for student circles or the classroom.

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Students will gather data on median household incomes from three towns across Connecticut (including their own town) and will calculate potential future wealth using exponential modeling. Students will compare outcomes of these models and discover factors that impact a household’s ability to accumulate and transfer wealth. Students will understand the complexity and interconnectivity of social issues. Note that this lesson is closer to a 1-week mini-unit, but that teachers may choose certain sections to focus on for a smaller 1-2 day exploration.

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In this session, we introduce participants to the programming language, Scratch, by giving them a rich task. As they explore possible approaches to achieving the goals of the task, they naturally uncover the three fundamental structures of programming (conditionals, loops, and sequential statements). We explore multiple approaches to the task, highlighting the creativity involved in programming, and even allow participants to declare their own variables to simplify coding work.

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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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The rules are simple: you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep. Can you place all your wolves and sheep on an nxn grid so all the sheep are safe?

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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.

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Place our numbers into the cauldrons in ascending order – you can choose which cauldron each one goes in. However, if two numbers in one cauldron add up to a third number in that same cauldron, they bubble up and cause an explosion! This means that all the numbers, leave the cauldrons, and you must start all over again.

Our goal is to find the largest number we can place in our cauldrons without them exploding… do you think you’re up for this daunting task?

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A town faces an epidemic of zombies! Luckily, the virus has just started to spread and the infected are able to stave off their hunger for human brains… for now. In fact, they’re willing to work alongside the remaining humans to help them get across a river to safety. Can you get all the humans and zombies across safely?