Object: To collect tokens and adjust the values of variables to end with the highest value.

Set-Up: The game board is a series of ramps with doors, each of which may be opened or closed. Each player's holding bin is shown, which initially contains three coins. At the bottom of the screen are two treasure chests, one representing the value of x, the other representing the value of y

Play: There is a cost to open or close each door on the game board. On each turn, you may open or close any of the doors using the coins in your holding bin, provided you can afford it. Once you've opened or closed the doors that you want to, press the Start button.

A ball will then be released onto the top ramp, and tokens will be collected as it rolls. The doors you've opened and closed will dictate when the ball drops to a lower level. When the ball reaches the pool below, your turn is over.

The collected tokens will be moved to your holding bin. Note that the space in your holding bin is limited, and if the ball rolls over too many tokens, not all of them will be collected.

Once your turn is complete, you may then combine coins. Drag coins with like terms to the Combination Area, and then enter their combined value. But be careful! If you make a mistake, those coins will become locked — you will not be able to combine them for the rest of the turn (though you may still use them to open and close doors).

If you've collected any power coins (the gold +/- coins), you may apply them to the treasure chests for x and y at the bottom of the screen. Although the exact value of x and y will remain unknown, the adjustment to be applied at the end of the game will be noted on the treasure chest. For instance, if a +2 shows on the chest for x, the value of x will be increased by 2 at the end of the game.

The game ends when both players have taken five turns.

Winning the Game: At the end of the game, the secret value of x and y will be revealed, and any adjustments based on the power coins will be applied. The values of the variables will then be applied, and the winner is the player whose expression has the higher value.

Math Concepts: Coefficients, Variables, Like Terms

What You Can Do: Students have likely been exposed to variables in familiar contexts, even if they have never given the concept a name. For instance, students know that if a widget costs $2, then two widgets will cost $4, three widgets will cost $6, and, in general, the total cost is equal to two times the number of widgets, or 2n.

Students may have also seen variables in common formulas, such as P = 2b + 2h. From these formulas, students know that variables can represent values. Students can use or create other formulas based on their daily experiences. For instance, they can determine the average speed on a car trip using the formula distance = rate × time (d = rt), or they might realize that there are 12 inches per foot, which leads to the formula inches = 12 × feet (i = 12ƒ).

A variable machine can be used to introduce kids to variables. The idea is to assign a value to each letter in the alphabet, for instance, A = 1, B = 2, C = 3, and so forth. (An alternate assignment of values could be to use the keypad on a phone, where A, B, C = 2; D, E, F = 3; G, H, I = 4; and so on.) Students can then use those values to find the value of their name or other words by adding the values of the individual letters. You can then challenge students with questions such as, “What three-letter word has the highest value? ”

Students can use the variable machine to learn about combining like terms. For instance, students can find the value of the word banana by first realizing that the word contains three a's, two n's, and a b. This leads to the equation 3a + 2n + b, and the value of the word can be found by substituting values for each of the three variables.

Math in the Game: Students are forced to practice combining like terms to free up space in their holding bin. Strategy comes into play as students apply power coins to the treasure chests to change the value of the variables. An understanding of coefficients and how they will affect the student's overall score is a key to winning the game.

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