A Counting Game

Every so often I'll post about an activity I did or a technique I used that was good. I find I often forget these good things when I should be reusing them. Hopefully by recording them on the blog I'll remember them.

So, what I'm sharing with you this week is an activity I did with my year 7 class. I told them they were going to have a little competition (which was met with a few "YES!"s), and that it would be a competition against me. This excited them because they know I'm both extremely competitive and extremely clever. They would love the opportunity to take me down a peg or two (as would most people, probably).

The competition was this: I will play against one person at a time. We will start from zero, and we will take it inturns to add either 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10. The winner is the person who reaches 100. It's very similar to 21 dares, or those games where you have to avoid being the one who takes the last matchstick.

Now obviously, there is a trick that means you always win. Work this out for yourself, I don't want to spoil your fun! (Hint: whoever gets up to 89 has won, because whatever the other person says, you will be able to reach 100 on your next go. By extension, whoever gets to 78 has won, as they can get to 89, and so on). I took on about 7 students in total and beat all of them. As I did it, pupils started to notice things. This is what the pupils discovered, in order:

1) If Miss says 89, then she's won
2) Whoever goes first always wins (false!)
3) You need to stop her getting to 89
4) Get to 78, because then she can't go to 89!

I then extended them to realise that there were certain numbers that you should always try to aim for to make sure you win, and they spotted the pattern of these numbers. On the next go, a student beat me. And as much as it pains me to admit it, he beat me fair and square (I got my numbers mixed up). You can imagine how happy that made the class: "We beat Miss, and she got bare A*s!"

The class was then desperate to show off this newfound skill by challenging the head of maths to a competition. This hasn't been arranged yet but I think it's a really nice idea. I hope they beat him!

You can obviously extend the activity by considering a different target instead of 100, and different numbers that you're allowed to add.

I'm going to do the same activity with my other classes to see how it turns out. If you try out this activity, please let me know how it goes!

Emma x x x