YouCubed

Hello everybody. This is a task from YouCubed at Stanford University. And it's all about thinking and representing numbers in different ways.

So the first thing I'd like you to think about is, what do you notice when you see this?

Ok, I'm going to move this over a little bit here. Aha, and I'm going to record down some of the things that you can see.

Yes, so I can see that too. The numbers increase in size, they get bigger. Look 1 dot, 2 dots, 3 dots, 4 dots, 5 dots so, so, oh well, that's something that we could notice. The smallest is 1 and the largest quantity? How many are there that you see? Yeah, I see that too. In fact, what I see here are a 2nd four. Yeah, you can see it too, a 3rd four, a 4th four and a 5th four and so that's 20 dots. And so the largest quantity on this sheet, some of you are using a different one, the largest quantity here is 20. Yeah, and that's actually an important thing to notice. That 1 is one dot, but 20, so inside of 20 we can see 5 fours. Ah yes, I can see your thinking there too. That if I partitioned these more, now you wouldn't see, oops, you wouldn't see fours, but twos. Aha and there would be 10 twos, yeah.

Oh yeah and some of you are now saying that if I rethink this as four again as a collection of four, it looks like this four. Yeah, like four on a dice pattern. Aha yes and the five, look. It looks like this five. See that it's the same, yes, so how we are we going to say that? That inside of the bigger numbers we see the same spatial structures or patterns of the smaller numbers.

Yeah, and can we see that anywhere else? Anything else that has a five in it? Where can you see it? There's a five here and a five there, Ah up here look. Yeah, which is 15 'cause it's 5 threes. Aha so so what we're saying here is that when we have 5 of something it follows this structure like a hexagon. So 5 is represented like a, not a hexagon a pentagon. Thank you for correcting. Yes, look like five. And then therse's 5 threes. Whoops. 5 ones, 5 threes and 5 fours.

Ah, so that's interesting, isn't it? And the fours I think are always like squares, are they? 4 fours. 3 fours. 2 fours. Oh my gosh, look at that. Did you see that pattern? Look 1 four, 2 fours, 3 fours, 4 fours. Wow, it increases by the number of fours on the diagonal.

Ok mathematicians, it is over to you to have a look at what do you notice and how could you use colour to help you capture some of the ideas, things that you're seeing.

Ok over to you to have fun with these representations.