I came up with a new game today for elementary kids in order to exercise my inner mathematician. The game is simply called “Trading Game” and it takes a few minutes to explain.
My school has groups of sturdy professionally printed flashcards for different types of objects; some examples are food, animals, things, and actions. The cards have an illustration and an English word, and are blank on the back. Most decks have just 2 or 4 of each word, maybe with 8 words in a deck. But the foods category has 20 different words, and the deck contains 8 of each card, making it ideal for card games.
Here’s how the trading game works. First, I make a “deck” containing one of every word. Then I remove some of the words so that I don’t have too many cards. I pass out 4 cards to each student, and ideally have a few cards left over, say around ten. Make sure that no student has 3 or more of the same card. The object of the game is to score points by trading cards with other students. The cards have different values depending on how rare each one is; I use the leftover cards to decide which cards are worth what. If I have one of a certain card left over after passing out 4 to each student, it’s worth 2 points, if I have two left the card is worth 3 points, and so on. The rest are worth 1 point.
Obviously, you want to trade for the higher cards, but there’s a catch. If you have 3 of the same card, the value of your hand doubles. If you have 4 of a kind, the value quadruples. A pair adds no bonus (so there’s no point in having 2 pairs). So, for example, if I hold 4 different cards worth 3 points each, I have 12 points. But I can get the same score of 12 with a single 3 point card and three of the same 1 point card, and if I have 4 of the same card each worth only 1 point, my score is 16 points.
Students walk around the room, trying to trade cards with other players. For a trade to take place, both parties have to agree.  Students can trade as many cards as they want, but no player can have more or less than 4 cards when the trading is done. It’s important to tell the students when trading will end, and to give the point values before trading starts. (Enterprising CS students will recognize this as being similar to the “stable marriage” algorithm, with a few twists. I’ve found that students tend to not trade unless they both see an immediate benefit, and only the older students trade with card point values in mind; the rest just try to accumulate 4 of the same card. It would be interesting to find out what an optimal strategy is, given a certain number of trading iterations.)
I teach them the phrases “I want ~~” and the responses “OK” (if they agree) and “No, thanks” (if they don’t want to give up that card) and also ”I don’t have ~~” (if they want to trade but don’t have what the other player wants). When the game is over, everyone counts up their points.
For a variation, you can group the students into teams, and tally up the scores that way. Or you could try it with more cards, maybe 5 or 6, and adjust the multipliers accordingly, though you need to make sure that a student who gets all of the lowest denomination will beat a student who just gets one of each high card. The game doesn’t work with just 3 cards, as the system becomes stable after just 2 or 3 trades (in other words, the kids get the cards they want and stop trading) and also there’s a very high probability that many students will start with a pair, meaning they only have to have one successful trade to finish.
