Games in Math Class

[velvetpage]

What are the best properties to buy on a Monopoly board?
Which card should you cut from a Cribbage hand with a five, a six, two sevens, and an eight, if you didn't deal?
Is it worth it to play a three-of-a-kind in Rummy, or should you hold out for the run in that suit?

These are just a few of the questions players ask themselves continuously while playing three common games. The questions require an understanding of each game itself, and also an understanding of probability, sorting of series and sets, patterning, addition and subtraction, and a host of other mathematical concepts. That's right: playing Monopoly, Cribbage, Rummy, or almost any other board or card game, requires players to think actively about mathematics.

The best part is: they don't even realize they're doing it.

Take Cribbage, for example. Points are accumulated several ways in Cribbage. Players get two points for every set of cards that add up to fifteen in their hand (so in the above example, each seven paired with the eight is worth two points, for a total of four.) Players also get points for pairs, and they get quadratic points for three- or four-of-a-kind; that is to say, you get two points with a pair, and you can make three pairs with three-of-a-kind, so you get six points for three-of-a-kind, and twelve points for four-of-a-kind. That's advanced patterning and multiplication. It's also a game where decisions are based on probability. When you have to discard one card of five, into someone else's hand, which card will keep the most points for you, while giving the fewest points to your opponent? How likely is it that other players will have discarded face cards, which, when put together with the five you discard, will create a sum of fifteen and therefore, two points for that other player? Is it worth the risk that they'll get more points from you discarding that card, than you will lose from keeping it? And is the eight any better a discard? (It would take very poor understanding of the game to discard either the six or one of the sevens, but that means knowing why those would be bad moves and eliminating them off the bat.)

Then there's Monopoly. If you know that the three most common rolls on two six-sided dice are six, seven, and eight - indeed, that those three rolls make up sixteen of thirty-six possible combinations - then it's not hard to figure out that the most likely combination of two rolls from the Go square are between twelve and sixteen squares away, making the magenta properties (St. Charles, States, and Virginia) the best bets for people who are starting from Go. But is Go really the most common spot on the board? In fact, it's not - Jail is just slightly more likely. The calculations from Jail, though, are a bit different, because a player can get out of Jail by rolling doubles, all of which are equally likely. From Jail, the most likely spots are the two sets of orange properties on either side of Free Parking.

My point is that a player's strategies for winning change dramatically when they are thinking mathematically, using their knowledge of basic computation, patterns, and probability. This is true of almost any game that requires decision-making and strategy. Even games of pure chance have their elements of mathematical knowledge, however. Candyland, the quintessential first board game, requires no reading whatsoever. But it does require counting, an understanding of patterns, and one-to-one correspondence, not to mention such social niceties as turn-taking. A child of four can learn several important skills even from such a simple game.

These facts have several important implications for the classroom. Playing games isn't just an indoor-recess activity; it's a legitimate way to hone skills at computation, problem-solving, patterning, and probability. When I teach my students to play Cribbage, I'm teaching them a pass-time that can entertain them for years, while also reinforcing the problem-solving skills that are an integral part of the mathematics curriculum, and the critical thinking skills that are valuable to any academic pursuit.

I use card games as a regular part of my mathematics program. I use board games and games with dice as the backbone of my probability unit. I do this because it works - and because it's fun.

So if your child comes home and talks about how they didn't do real math that day in school, but played games instead, just smile and nod. They certainly did do real math, even if they didn't realize it at the time. Their brains were exercised and their math skills honed. And that's the important part.