Connecting Mathematicians of All Ages

# Audience: For Teachers

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Supporting Materials
• Facilitator Guides (20)
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Session Styles
Session Styles
• Try a Smaller Problem (9)
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• Kinesthetic Element (2)
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Mathematical Practices
Mathematical Practices
• MP1 - Make sense of problems and persevere in solving them. (20)
• MP2 - Reason abstractly and quantitatively. (10)
• MP3 - Construct viable arguments and critique others' reasoning. (12)
• MP4 - Model with mathematics. (11)
• MP5 - Use appropriate tools strategically. (7)
• MP6 - Attend to precision. (5)
• MP7 - Look for and make use of structure. (16)
• MP8 - Look for and express regularity in repeated reasoning. (12)

### Acting Out Mathematics

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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.

### 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?

### Flipping Pancakes

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The Pancake Problem, first posed in 1975, is a sorting problem with connections to computer science and DNA rearrangements, which leads to discussions of algorithms, sequences, and the usefulness of approximations and bounds.

The original problem was first posed by mathematician Jacob Goodman under the pen name “Harry Dweighter” (read it quickly) in 1975, and it has delighted math enthusiasts (including undergraduate Bill Gates) ever since!

### The Jug Band

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“Using just that 5 pint jug and that there 12 pint jug, measure me 1 pint of water!” Is this possible with just the two jugs? What about a 7 pint jug and 17 pint jug? Or p pint and q pint jugs?

### I Walk the Line

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Your regular commute begins at your house and ends at your office at the corner of 5th street and 6th avenue. You have been making this trip for years, but you are the restless (or adventurous) type, and you try to take a different route each day. At some point, you start to wonder how long it will take you to try all of the routes.

Oh, did I mention that you have to avoid the zombies?

### Winning the Lottery, An Expected Value Mystery

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In 2005, while researching the expected value for lottery tickets in various states, a group of MIT students won millions of dollars in the Massachusetts \$2 Cash Winfall drawing. Do you want to know how they did it? This teacher led activity starts with a lottery, explores expected value, and finally ties into finite projective geometries.

### Measuring Up: “Perfect” Rulers

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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.

### Practical Probability: Casino Odds and Sucker Bets

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Gambling casinos are there to make money, so in almost every instance, the games you can bet on will, in the long run, make money for the casino. However, to make people gamble, it is to the casino’s advantage to make the bets appear to be “fair bets,” or even advantageous to the gambler. Similarly, “sucker bets” are propositions that look advantageous to one person but are really biased in favor of the other. We’ll examine what is meant by a fair or biased bet and look in detail at some casino games and sucker bets. Various problems can be...

### Tic-Tac-Toe 2.0

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The game of Tic-Tac-Toe has roots going back centuries. Grid-style game boards have been found in Ancient Egypt, during the Roman Empire, and in our current age on restaurant placemats. Multiple avenues of exploration are possible with this simple children’s game. A related game called “Gobblet Gobblers” takes Tic-Tac-Toe to a whole new level!

### The Game of SET

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SET is a fun game that can be enjoyed by kids as young as 6 and is challenging even for adults. It is rich in counting problems and is great for getting people to pose problems. It is also an example of a finite geometry and interesting to explore how well one’s geometric intuition works.

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