Topic: Problem Solving / General

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  • MP1 - Make sense of problems and persevere in solving them. (83)
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  • MP8 - Look for and express regularity in repeated reasoning. (61)

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!).

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.

Mathematical Games

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This session includes 15 games using manipulatives or paper and pencil. The goal is to decide which one of the two players has a winning strategy. To solve a game means to find a winning, or a non-losing, strategy for one of the players. An answer must include a detailed description of such strategy, and you have to explain what the winning player should do so that this player wins regardless of his opponent’s moves.

These games may be presented as a single circle session, or individually in a circle or classroom.

Mathematical Magic for Muggles

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Presented are several easy-to-perform feats that suggest supernatural powers such as telepathy, “seeing fingers,” predicting the future, photographic memory, etc. Each trick uses simple mathematical ideas that allow information to flow effortlessly and sneakily, among them simple, efficient “coding” parity and other invariants symmetry probability One can approach these activities in many ways. At first, you may want to figure out HOW to do a trick. Then, you want to know WHY it works. Finally, you should strive to understand REALLY WHY it works: is there a simple theme or principle behind your possibly complex explanation? Look for simple and...

Optimal Locations of Firehouses (Taxi-cab Metric)

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This session asks participants to expand their notion of “distance,” using a nontraditional taxicab metric instead of the usual Pythagorean notion. Participants are guided to construct the equivalent of “circles” with this new metric and to look at the intersections of multiple such circles. In particular, two firehouses in Gridtown are a certain distance apart and at specific addresses. What firehouse should serve a given house with a specified address? What areas of town should each firehouse serve? What if there were three firehouses? The focus of the session is on a deeper understanding of the coordinate system and notions...