It’s good to know that something you’ve done has stuck with someone; out of the blue I had a call from someone I hadn’t seen for ten years or more. “Hello Alan, can you remind me about the Polar Bears?”
So here’s the activity that Gaynor wanted to talk about.
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I roll five dice: 
“There are six polar bears round the ice-hole.”
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Again:
“There are two polar bears round the ice-hole.”
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Once more:
“There are no polar bears round the ice-hole.”
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It’s much the best fun to do this informally when you can test out all sorts of ideas, but I’ll have to tell you that the colours of the dice don’t matter, nor their size, nor their positions. (Generally speaking, I’ll use five dice, but we could use a different number.) We’re left with just one factor to consider, that it’s the numbers showing on the top faces of the dice.
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Here are a few more:
“There are four polar bears round the ice-hole.”
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“There are no polar bears round the ice-hole.”
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“There are eight polar bears round the ice-hole.”
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“There are ten polar bears round the ice-hole.”
Any ideas?
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It begins to look as if the odd numbers are more importantly related to the number of polar bears than even numbers. A bit of a surprise, perhaps, because you were probably tempted to think that six might be heavily involved – let’s check that out:
“There are no polar bears round the ice-hole.”
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You’ll probably want to test this out further:
“There are no polar bears round the ice-hole.”
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“There are twelve polar bears round the ice-hole.”
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Both these seem pretty helpful. It seems even numbers don’t contribute at all, but that it’s the odd numbers – particularly the higher ones – which build the score.
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It’s sensible to try:
“There are ten polar bears round the ice-hole.”
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And:
“There are twenty polar bears round the ice-hole.”
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Also:
“There are no polar bears round the ice-hole.”
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Well, you should be pretty well there now.
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It looks as if only the three and five dice are involved. Actually, it was a bit misleading to tell you it’s the numbers showing on the dice, because in fact it’s the patterns of the dots.
.It’s polar bears round the ice hole, remember? And only three dice patterns have a central dot to show the ice hole – the one, the three and the five. So on the three there’s a central hole with two bears around it, and the five has a hole with four bears round it (and though the one shows the ice hole, there are no bears around it!).
Now, all this is great fun with a group of children and adults as well, but that doesn’t mean it’s trivial. Think of all the work you have to do. You’ll be involved in hypothesising and testing, assessing your results, refining and improving your ideas. Games like this give you a quite excellent insight into the process of scientific thinking and exploration – and I warn you I’ve a whole hatful of them.
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