### The Jug Band

“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?

Skip to content # Mathematical Practice: MP7

### The Jug Band

### Winning the Lottery, An Expected Value Mystery

### Supreme Court Handshakes

### Function, Function, What’s Your Model?

### Practical Probability: Casino Odds and Sucker Bets

### One-Player Games

### Tic-Tac-Toe 2.0: New Takes on an Old Classic

### Frogs and Toads

### The Game of SET

### Magic Squares

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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?

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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.

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Developed as part of the Math Circles of Inquiry project, this session is a good introduction to the 8th grade or Algebra Math curriculum using inquiry based instruction. Students are asked to use their problem solving skills in order to determine the relationship between the number of Supreme Court justices and handshakes that occur when each pair shakes hands exactly once. Students will begin exploring with simpler numbers and work up to creating an algebraic expression to represent the function. This lesson allows for multiple representations by using a table, list, circle diagram, matrix and manipulatives.

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Developed as part of the Math Circles of Inquiry project, this session is an introduction to functions. This module allows students to investigate the definition of a function, function notation, key features of a function including increasing, decreasing (in both interval and inequality notation), maximum and minimum, average rate of change and domain and range.

Materials include a full packet of worksheets pertaining to this unit (54 pages). This part of the unit (not including transforming functions) should take about six hours of class time.

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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. In this article, we’ll examine what is meant by a fair or biased bet, and we will look in detail at some casino games and sucker...

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Here is a collection of seven one player games, and one two player game. Your goal in each game is to find the winning strategy. As the rules change, can you still win? Various mathematical strategies can be employed, including working backwards, problem posing, invariants, and parity. Each game can be explored alone or in sets, providing material for several circle sessions or the classroom.

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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!

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Frogs can only move right, or down, and toads can only move left, or up. Can you exchange all the frogs and toads? Can you create a formula for the fewest number of moves? This deceptively simple puzzle starts with a row of frogs and toads, then advances to a grid. The game can be played with manipulatives, online, or even with people to provide an engaging, solitary or cooperative activity for all ages.

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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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Your goal is the place the numbers 1 – 9 in a 3 by 3 grid so each row, column, and diagonal add up to the same magic number. Can you find what this magic number is?