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Liar’s Bingo

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From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in the game of Liar’s Bingo, order seems to arise magically from something we first assume to be random or chaotic. In this case, we use the game of Liar’s Bingo to engage participants’ desire to find patterns, and supercharge that desire by demonstrating a magic trick that captivates attention by...

Locked Out: A Breakout Box Session for Your Circle

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Escape Rooms and “Bomb Disposal” activities are growing in popularity as a form of team building and entertainment. This session blends the two ideas to create a cooperative math activity where the challenge is to solve math problems whose solutions generate combinations to open a locked box. The math problems can be selected to fit any audience, and the activity appeals to problem solvers of all ages.

Piece of Cake; Delectable Fractions and Decimals

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While exploring the relationship between fractions and decimals, participants will have the opportunity to practice operations with fractions, notice and explain patterns, review understandings of place value and number sense, and justify their reasoning.

You can get a taste of math research by repeating these two steps: Think about an interesting unsolved problem, and Do Something to try solving it. Now Think about what you notice, and Do Something to explore your results. Repeat.

Semiregular Tilings

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Can you find all possible semiregular tilings of the plane? A tiling of the plane covers the (infinite) plane, without gaps or overlaps, using congruent copies of one or more shapes. A semiregular tiling is a tiling of the plane with certain constraints: two or more regular polygons are used, polygons meet edge-to-edge, and the pattern of polygons around every vertex is the same. Questions about polygonal tilings of the plane can utilize a classical area of mathematics to highlight and connect middle and high school mathematics content standards, mathematical practices, and the nuanced nature of mathematical justification. This session...

The Futurama Theorem

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In the television show Futurama, Professor Farnsworth and Amy decide to try out their newly finished “Mind-Switcher” invention on themselves. When they try to switch back, they discover a key flaw in the machine’s design: it will not allow the same pair of bodies to be used in the machine more than once. Is there a way to restore their minds back to their original bodies?

The Futurama theorem is a real-life mathematical theorem invented by Futurama writer Ken Keeler (who holds a PhD in applied mathematics), purely for use in the Season 6 episode “The Prisoner of Benda”.

The Roommate Game: An Exploration of Stable Matchings

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College students need to be matched with a roommate. They each make a list of who they prefer to room with. Given the preference lists for each individual, can we find a matching that is stable? That is, would any pair ask to change rooms because they would rather room together than with their current roommates? Explorations lead to new questions or new avenues to investigate using various mathematical methods including, but not limited to, combinatorics, graph theory, or matrices.

Tiling With Pentagons

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A pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. The plane cannot be tiled with regular pentagons. However, are there any convex pentagons that can tile the plane? This session explores various pentagons and their tiling abilities. From 1918 to 1985, fourteen irregular pentagons that would tile the plane were discovered. On August 14, 2015, Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced that they discovered a fifteenth pentagon. Interestingly, in 2017, Michaël Rao proved that there were no more than these...