A Maths Game with a Psychological Twist

Today I'm going to tell you about one of my favourite ways to kill a spare fifteen minutes in a maths lesson. It's great because it requires absolutely no preparation, no prior knowledge, and no differentiation. All you need is a class set of mini whiteboards and pens.

Tell students that you're going to ask them to write down a number. It must be a whole number (no decimals, fractions or surds) and it must be zero or greater. They have to write this secretly and not show anyone their number. Tell them you are going to count down from 5. At 2, everyone's pens need to be down. At 1, everyone needs to show their boards. The winner, and this is the important bit, is the person who has the smallest number that no one else has.

This should be simple enough to understand, and if a student doesn't quite get it, they can at least write down a number and participate until it clicks.

When students hold up their boards, first look for zeros. If there's just one, the zero wins. If there's more than one, tell all the zeros to put their boards down and then look for ones. Repeat until you have found a number that only one person has written. They are the winner. This doesn't take very long at all, even with 32 students like my year 7 class.

I have found that this game intrigues students immediately. They have to try to predict what everyone else is thinking. I have found that I can usually predict who in the class will write zero. Zero rarely wins, and I've never seen it win in the first round. I've found that the winning numbers vary massively from class to class. The results are also very different when I've played this with adults. I'm sure there's a lot that can be explored here in terms of psychology (and economics, actually) but I'll leave that for you to think about.

I like to try to encourage strategic thinking and annoying my students at the same time by saying things like "oh, so three won that time. That means you are probably thinking about choosing three this time. But if other people think that too, you won't win, so you'd better choose four instead. But now that I've said that, you can't choose four, it's too obvious, so..." The students usually interrupt me at this point and beg me to shut up because I'm ruining their strategy.

The beauty of this game is it can be done with year 7s, year 13s, and even the Maths faculty as a pre-meeting warm-up. I have never met a class (or group of adults even) that doesn't enjoy this game.

A more mathematical version of this game is to have the same rules but this time the winner is the student whose number is the closest to the mean of all of the numbers. This is too difficult to do as a whole class, so I do this in table groups. The four students each choose a number, they calculate the mean, then the winner is whoever's closest. They keep a tally of how many times each person wins so they can declare a winner at the end of the fifteen minutes.

What's really nice about this variation is that students will be calculating means with much more enthusiasm and motivation than if they were meaningless numbers on a worksheet. Also, by playing this game and trying out different strategies, students begin to appreciate the nature of the mean. There will always be a student who will write down a million, thinking it will skew the mean towards them. However, if the other three numbers are low they still won't win.

You can also play this game with the median instead of the mean. It doesn't quite work with mode! Actually, maybe one of my amazing readers could come up with a way of making a mode variation. Comment below!

Try one of these games out when you have ten minutes to spare. Let me know how it goes by commenting below.

Emma x x x