There are times when you can tell your class is a little fried and they need some short-term gratification rather than the usual drawn-out discussions. Last period Friday, in particular, is a time when it is useful to have some math games ready to go. So on this Friday I’ll describe a game that I stole from the wonderful Public Television show Square One. (Remember that?)
As the “host”, I set up the digits of an arithmetic problem like _ _ _ + _ _. (Actually, I make each digit a box rather than a dash, but that’s much easier to do on a whiteboard.) Students copy this into their notebooks. Then I use a calculator to randomly generate digits ranging from 0-9, repeats allowed. As I read each digit, students place the number in one of the boxes, with the goal of making the largest sum possible. The catch is that they are not allowed to move a digit once they place it. The winner, at the end, is the student with the largest sum. (You could also ask for the smallest sum, of course.)
Of course, this game is too easy for high school. The strategy is clear to the students, and after that it’s all luck. So after we play with the initial setup, to get the idea of the game, I begin to vary the game board, tailoring it to the level of the class. _^_ + _ _ _ _ is an interesting one – is it best to use a nine, if it is chosen, as the base of the exponent, the exponent itself, or the first digit of the four-digit number? Using fractions reinforces the concept that the bigger the denominator, the smaller the value of the fraction. You can also involve “sin(_ _)” in your expression (specifying that you are using degrees), and students will need to think about what degree value will maximize the sine function. For students thinking about limits, you can compare ratios of different types of functions so that students need to think about the shapes of their graphs and their end behavior.
I like this game for several reasons. First of all, there’s an element of suspense when choosing the final few digits that always puts students on the edge of their seats. Almost all students like this game and find it engaging. Secondly, when the game is over (and they are allowed to talk about it), students want to argue about what the best possible result would be. Because of this, they make all the mathematical arguments appropriate to the game board without my having to prompt them. Third, it is extremely malleable to the needs of the class, and it can be anywhere from very easy to very hard.
One final note: I’ve been able to find only one web clip of this game, here. They play a simple version in which the object is to make the largest five-digit number possible. Watching it (if you can make it past the super-silly intro) might give you an idea of the principle of the game.