Coordinates and shapes: To recognise nets of 3D shapes

Key Stage 2

Maths

Coordinates and shape

﻿Welcome to our seventh lesson in the coordinates and shapes topic. Today we'll be learning to recognise the nets of 3D shapes. All you will need is a pencil and a piece of paper. Pause the video and get your equipment together if you haven't done so already. So today we'll be looking at recognising the nets of three 3D shapes, starting with a knowledge quiz to test your learning from our previous lesson. Then we'll be looking at recognising nets, then building nets before you move on to some independent learning and then a final quiz. We're looking at recognising nets. I want you to think, first of all, what do you notice about the faces of a cube? What do you already know about the cube's faces? So you know that a cube is made up of six square faces. So we can use that to help think about identifying the net of a cube. We've got two possible nets here, and we are looking for a net that is made up of six square faces. So we can count on this one. It has one, two, three, four, five, six square faces. So we think it's probably this one. And we'll check on this one. Well, this has two square faces and four rectangular faces. So therefore this must be the net of our cube. Let's have a look at another one. Think about what you already know about the faces of a cuboid. So we know a cuboid is made up of two square faces and four rectangular faces and that it has six faces all together. So again, looking at the nets, we're looking for a net with two square and four rectangular faces. Therefore, we can deduce that this must be the net of the cuboid. That means that it folds up to make a cuboid shape. So using this knowledge of what you already know about the faces of 3D shapes, I'd like you to pause the video now and match the 3D shape to its net, explaining your reasoning as you go. So beginning with the cylinder, we know that a cylinder has got two circular faces, and they are flat. And then we've got this one face that wraps around the whole shape as a curved face. And that is actually one rectangular face. So we know that the face of the net of the cylinder must be this one because it has two circular and one rectangular. And the way to, if you don't believe me about this being a rectangular face, if you go back to your tin of beans, and you take the label off the tin of beans, you will see that the label is rectangular. So this is the net of our cylinder. Moving on to our next shape, here, we have a tetrahedron, which is a triangular-based pyramid. You know that a triangular-based pyramid is made up of four triangular faces. So you're looking for a shape that has got four triangular faces. And this is it. This makes up, this is the net of the tetrahedron. And you can imagine that these three outside faces here fold up, and they meet at the apex to make the triangular-based pyramid or the tetrahedron, tetrahedron. Okay, on to the next one. Here, we're looking at a shape with a pentagon face, and it's got two pentagonal faces. So we can write that down as our notes, two pentagonal. And then we can see that this one has got one, two, three, four, five rectangular faces. And don't forget that a pentagonal prism, as this shape is, can also have five square faces. But this one relates to this net, which has two pentagonal faces and five rectangular faces. So this here is our pentagonal prism. And then that leaves one more, but we'll still go through the process. So this is a square-based pyramid. So we know that it has one square face and the remaining four faces are triangular. And then that net looks similar to the tetrahedron net in that these four triangles fold up to meet at the apex to make the square-based pyramid, square-based pyramid. Okay, so now you're well practised at recognising the nets. We're going to look at buildings nets. So Zak joins the 2D faces to make a net of a triangular prism. So we'll just check that he's got a triangular prism. We know that a triangular prism is made up of two triangular faces and three rectangular faces. So he's got the correct shapes there. Now we need to think about does the order of the shapes matter? Can he join those shapes in any way? And as long as he has two triangles and three rectangles, he will have the net of a triangular prism. Is that true? So let's have a look at these two nets. We need to think about, will these two nets make the triangular prism? So if we look here, we've got the three rectangles next to each other, and the word for something being next to something is adjacent. We've also got the two triangles being adjacent. Now I'm looking at this, and I'm wondering how would this fold up to make a triangular prism? If I look back at my 3D shape, I can see that the triangular faces are not adjacent. They're not next to each other in the shape. Therefore in the net, they cannot be adjacent. So this will not work because the two triangular faces cannot be adjacent. They cannot be next to each other. This one, on the other hand, will work because you can see that we've got our two triangular faces. They are separated by a rectangular face, which means when they fold up, they will be opposite each other. Therefore, this net will work because those two faces become opposite when it's folded into a 3D shape. So I want you to use that logic and apply it to this shape. So Elizabete joins the 3D faces to make a net of a pentagonal prism. So which of these nets will work? Pause the video and make some notes now. So looking at the 3D shape, we can see that the pentagonal faces are opposite each other. So we need a net that allows those two faces to be opposite. So this one has got a pentagon here and a pentagon here with rectangle in between, meaning that when they fold up, these two faces will be opposite, and they're separated by the rectangle. So this one will work. Will this one work? Now we can see that we've got our two pentagonal faces. They are adjacent, which means that this one won't work because these faces, when folded back into a 3D shape, they need to end up opposite each other. So that won't work at all. So now you're going to use what we've learned about the nets to apply them to word problems around 3D shapes. Pause the video and complete the task and click restart once you're finished, and we'll go through the answers together. Okay, so for your first independent task, you had the net of a dice, and you know that a dice is a cube. Therefore, the net was made up of six square faces. Now on a dice, the opposite faces sum to seven. So whichever numbers are on opposite faces, they had to add up to seven. So you had to place spots on each face to create a net of a dice. Now remember, we're talking about opposite faces, and we learned from our previous work that opposite faces will have an empty space between them. Okay. So let's start systematically. This top and bottom face, they will fold, and they will become opposite each other. So always try to work systematically. I'll start with the top. So I'm going to start by putting one in the top. Then I think about my number bonds. I know that the opposite face has to sum seven, and I know one and six makes seven. So therefore these two opposite faces add up to seven. Now I'll look at my left-hand face where I've already been given the number two. I know that its bond is five. I need to think, where does the bond go? Well, it won't go here because that is adjacent. Equally, it won't go here because when the cube folds round, this face will be adjacent to this one. So it must be this one. And that works because remember we said we skip a space to find that opposite face. So that's filled in with its bond, five. And then finally, the two remaining faces, we compare three and four. You might have these in different combinations, although you will have two and five there for sure. But your ones here and here, you might have had these the other way around, or you might have had three and four or four and three. That's fine as long as those two are bonds. And then here and here, again, you may have had one and six or six and one or the other way around. As long as they are bonds to seven, then that is the correct answer. So looking on at nets to make cuboids, you were asked whether the nets will make cuboids. So we look at what we know about a cuboid. We know that it has two square faces, and that's the first thing to check anyway because I may have given you nets with the wrong number of faces. And it has four rectangular faces. So first one, two square faces, yes, four rectangular faces, yes. So potentially it will work. We know that in a square, the two square, not in a square, in a cuboid, the two square faces are opposite each other. Therefore, this one won't work because these two square faces are adjacent. So we definitely cannot make a cuboid out of this net. This one, the two square faces are separated by a rectangular face, which means that when they fold up, they will be opposite. So this one will work to make a cuboid. Now this is the sort of case of the sort of questions we'll be looking at tomorrow. So we want to know what would the net of this patterned cube look like? And we need to visualise unfolding the cube. So if I unfolded the cube, I know that this face here is adjacent to this face here. So they're going to fold out like this. But if this is adjacent, when it falls out, it will have this rectangle poking up here. And this one is adjacent to this one, and it will have a horizontal rectangle. So it's going to be this one. In this case, this bit of the net had to move over here into this face here. So that doesn't work. And it's all about visualising how it would unfold. Question four, this will have taken you a bit of time to reason about which two parts of the nets fitted together. Let's have a look at the question. So the net of a cube has been cut into two in the example. it could be put together in several different ways. Now we're looking at these examples here and seeing where they have been cut into two pieces, where can we find the pieces that fit together to make a shape? So let's start systematically. We're looking at A. We can see that A has got a trapezium as a face. Therefore, it is a trapezoid prism. You may not have known that name, but what you did know you were looking for was another shape with a trapezium for a face. You were also looking for a shape, knowing that it has to fold to be fully enclosed. It would need to have another triangular, rectangular face, in order to fold into a full trapezoid prism. Therefore, A matches up with H because you can see your trapezium face here, and then you've got your additional rectangular face. So you've got A and H go together. And we're working systematically. We go to B. Looking at this straight away, I already know that this is going to be the net of a square-based pyramid. It's got a square as a base. It's got two triangular faces. I'm looking for two more triangular faces. And I'm looking for ones, they don't necessarily have to be in the way that we saw earlier where the net goes out like this. It can be in a different orientation. So I'm looking for two more triangular faces, and I'm going to go with F, but you may have gone with L or M. So I'm going with F. B and F go together to make a square-based pyramid. So being systematic, I'm going to cross them off as I go along. And I'm going to C. I can look at C and think. I think this is going to be a cuboid. It's got two square faces. It's got two rectangular faces. Therefore, I need two more rectangular faces. And I can see two here, but they look a bit thicker than these two up here. So I'm looking elsewhere. I can see P is the right size to fit on. So C and P will go together to make a cuboid. Okay, so moving on to D, which is down here, D has a pentagonal face. So my immediate thought is pentagonal prism, but then I see that it has some triangular faces. So now I'm thinking actually, this is going to be a pentagonal pyramid. So in order to finish off my pyramid, I need three more triangular faces, and I'm looking around, and I'm seeing them up here. So D and N go together to make a pentagonal pyramid. E is three squares. I'm thinking that this is going to be a cube, and I need three more squares to make it into a cube net. And that's going to be K. So E and K are going together. I've already done F. On to G. G is two rectangles. So think where else could that go? And now I need to go find which other shape needs two rectangles. And if I go to Q, I can see that this is a triangular prism that has only one rectangle and needs two more. And these look to be the same size as this one. So I'm going to put G and Q together. Q. Okay, so let's be systematic. H is gone. There was no I, so I'm going to J. J is a pentagonal prism which is missing two rectangles. So I'm looking for two rectangles, and it's also missing another pentagon. Otherwise it won't be complete. So it needs two rectangles and a pentagon to make a whole pentagonal prism. So it was going to go with R. And then K is done. We'll go to L next. So I'm looking for a shape that is in need of two more triangles. I'll scan around and have a look at what I've got left here. So, I can see, actually, if I put L and M together, that gives me four triangles, which gives me a tetrahedron net. So L and M will go together, and then I'll cross them off. And I'm left with two, S and O. S is going to be a hexagonal pyramid, and O gives us the extra four triangles that we need. Great work for persevering with that question. Now it's time for your final quiz. So pause the video and complete the quiz to test everything you've learned today. Great work today. In our next lesson, we will be solving problems involving 3D shapes.

Coordinates and shapes: To recognise nets of 3D shapes

Coordinates and shapes: To recognise nets of 3D shapes

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UnitMaths / Coordinates and shape

Maths