A short instructional YouTube video by Rob Langman in which presenter Ben teaches primary-school children about square and cube numbers. He defines a square as n×n and a cube as n×n×n, demonstrates both using interlocking cubes (concrete), shows 2×2 as a pictorial square and 2×2×2 as a pictorial cube, introduces exponent notation (² and ³), and poses a two-digit challenge (64) that is both a square and a cube. The clip follows a concrete→pictorial→abstract teaching progression and gives specific numeric examples (e.g., 2²=4, 3³=27, 2³=8).
Questions this video answers
2 × 2 = 4 (also noted: 8 × 8 = 64 as a square example).
Hi, my name is Ben and in this short video we're going to be having a little look at square and cube numbers. Now to recap, a square number is when you get a number and you multiply it by itself, 2 times 2 equals 4. 4 is the square number. And with a cube number it'll be 3 times 3 times 3, which is 27. 27 is the cube number. Here we are going to look at arrays, but we're also going to look at concrete. Now, whenever I start exploring cube and square numbers with children, I always start with concrete firsts. So these are brilliant interlocking cubes. And you can see here we've got two by two, which is four. I would then get the children to explore with three times three and four times four and so on and see if they can realize what's happening. And all the shapes that they make will be square square numbers. Now that's really helpful for when we move from the concrete to the pictorial. Here we have two by two, which is four. And again, we're dealing with those two dimensions and we're dealing with the square shape. Two times two is four. To move on from that, we will look at cube numbers. So here in our cube we have two by two by two, which is eight. And the children can explore and they can take it to pieces and they can see that 2 times 2 times 2 or 2 cubed is 8. That's really valuable for them to have that chance. Now here we've got a cube, which might be a little bit abstract when we look at it pictorially, but if they've played with it concrete first, that will really help them. And again, we're now dealing with three dimensions. So height times width times depth. And we would write it like this. So 2 times 2 times times 2 equals 2 times 2 is 4 times 2 is 8. We could also write that like this, 2 and a small 3, which is 2 times 2 times 2. From then on, I would get the children to explore with different cube numbers and different square numbers and see if they could write it down. So they'd got the concrete, they'd got the pictorial, and then they got the abstract. They've got the numbers. If they understood that and they were able to write it down with the notation three for cubed or two for squared, that would really help them. And finally, as a challenge for some of the children or for some of your more able children, to have a question like this would really unpick what they knew. So I'm a two digit cube number that is also a square. What am I? In this case, the answer is 64. Because 4 times 4 times 4 is 64. That's the cube. And 8 times 8 is also 64. That's the square number. And that's just the beginning to square in cubed numbers.
