Handfuls

Let's play a game called handfuls. Handfuls is really powerful in helping students and young children understand the structure of numbers and to think about working out the answer to the question how many without having to count. So you just need to use something that you have at home. You could use pasta, blocks, anything that isn't too small but also not too big. So you, like the name of the game suggests, grab a handful.

And now that I have a handful I have to try to imagine in my mind about how many pasta shells do I think I have? I think I might have about 18. So now what I need to do is to determine how many I have, but to try not to use counting as my first strategy. So what I could do is think about what do I already know and think about how I can workout, how many I have here by looking and by thinking. So what I know are things like when I see something that looks like this. I straight away know that that's five. I don't have to count that because I've seen it lots of time on a dice pattern.

So I could keep making fives and see how many of those I have. Even though they are a bit wonky, I can still trust that it's five. And so there we go. I have 3 fives at the top and I also have 3, I might just put them down the bottom, left over and so what I can see here is that I've got 3 fives and three more, and that's one way of explaining what I can see, but I also know something more about that, and that is that when I have 2 fives that actually combines to make 10.

So I have 10 over here and then I have five and three more. And actually I could reform that so that I know that I have 8. And so now what I can see is 1 ten and eight more and I know that that's just called 18. But what I've used here is looking and thinking to help me solve it.

Now if I wasn't quite as confident yet in knowing things about numbers, I might have gotten to this point right now that this is 10 and I'm still not sure what to do with these and that's where you might use counting, so I know this is 10 and I can trust that and I go 10, 11, 12, 13, 14, 15, 16, 17, 18 and I can use counting to help me check.

Since I'm a mathematician, I would also think about recording how I saw 18 and so I had 18 and I would say 18 is the same as 5 and 5 and 8. Or originally I had 5 and 5 and 5 and 3. I also thought about how I could make my 2 fives into 10 and my 5 and my 3 into 8. And so I know that 10 and 8 which we just rename as 18.

Then what I might do is say to someone else, hey, what's another way that you could organise these 18 pasta shells so that you can see how many just by looking and thinking.

And that's handfuls. Over to you mathematicians.