Coordinates and shapes: To recognise 3-D shapes

Key Stage 2

Maths

Coordinates and shape

The diagram shows the vertices of an isosceles triangle. What are the coordinates of the unlabelled vertex?

There are two identical rectangles on the coordinate grid. What are the coordinates for point D?

There are three identical squares on the coordinate grid. What are the coordinates for point A?

There are two identical right angle triangles on the coordinate grid. What are the coordinates for point A?

The pink line has been drawn one third of the way along the x axis. The blue line has been drawn half way up the y axis. What are the coordinates of the point at which the lines intersect?

﻿Hi, Year 6. Welcome to our sixth lesson in the coordinates and shapes topic. Today we'll be learning to recognise 3d shapes. All you will need is a pencil and a piece of paper, so pause the video and grab your things if you haven't done so already. Here's our agenda for the day. We're going to be recognising 3D shapes. You'll start off with a quiz to test your knowledge from our previous lesson. Then you will look at recognising parts of 3D shapes, then naming 3D shapes, and finally, identifying 2D faces on the surface of 3D shapes. Then you'll do some independent work and a final quiz. So, time to pause the video and complete the knowledge quiz if you haven't done so already. Click restart once you're finished. Now, first of all, we're going to look at the parts of shapes. We'll start with 2D shapes. 2D shapes are called 2D because they are two-dimensional. They have two dimensions that can be measured. You can measure their length and their width, and you can see that on the square that's on the screen. So, you can measure the length of the shape and the width of the shape. They're the two dimensions. The parts of a two-dimensional shape are called the sides. So, you can see this on my trapezium, the face, that's the flat part of the shape, and 2D shapes are always flat. And the vertex, that is where two sides meet. And you may have heard this called a corner before. Mathematical word is vertex. So, there's one vertex, and if you're talking about more than one vertex, then you refer to it as vertices. Vertices is the plural of vertex. If we look at 3D shapes, they're so called because they have three dimensions. You can measure their length and width, but also their depth. And we've got this displayed here on the cube on the screen, and I'll also show you with a cube here. We can measure the length and the width of the shape. So, that's the front face, but we can also measure the depth, which is how far back the shape goes. And then we've got the names of the different parts of a 3D shape. Only one is different from the 2D shapes. We have a face, which is the flat or curved surface on a 3D shape. Then we have the edge, which is where two faces meet. And then we have the vertex, and multiple is vertices. So, the different word here is edge. On a 2D flat shape, it's called a side, and on a 3D shape, it's called an edge. I'll show you on my triangular-based pyramid, or tetrahedron. We have the faces, which are the flat parts. We have the edges, which is where two faces meet. So, I can see that the two faces join here on the edge. And then we have the vertex, one vertex, that's the singular, and multiple vertices. That is the plural. So, on a tetrahedron, or a triangular-based pyramid, we've got one, two, three, four flat faces. We've got one, two, three, four, five, six edges, which is where the faces meet. And we've got one, two, three, four vertices. We're going to work more on looking at these properties in a moment. So, now I want you to have a look at these two shapes on your screen and think about what is the same about them and what is different. Use the key vocabulary on the bottom of your screen to help you and pause your video while you make some notes. The first, most striking difference is the fact that one of the shapes is three-dimensional and one is two-dimensional. The three-dimensional shape is a cube and the two-dimensional shape is a square. So, then, if we're thinking about the dimensions, we can label them that the cube, you can show the width, length, and depth, and the square, you can only show the width and the length. And then you may have labelled it, so you know that they both have vertices. They both have faces, although the 2D shape has one face, but then the 3D shape has the edges whereas the 2D shape has the sides. And you may have then talked about the number of things. So, the square has one face whereas the cube has one, two, three, four, five, six faces. And then you may have looked at the vertices. The square has four vertices. The cube has one, two, three, four, five, six, seven, eight vertices. Now let's look at recognising some 3D shapes using the named parts that we've just learnt. I've got some 3D shapes on the screen here. I've also got them in front of me to help. So, we're going to think about looking at their properties and also naming them. We'll start off with this one, and I've got the shape in front of me. This shape is a cylinder, and I always find it helpful when I'm thinking about shapes is to think about what shape do they look like in real life? So, a cylinder, which I rarely hold as a 3D shape like this in real life, I often have a tin of beans, and that's the shape of a cylinder. So, if you try and relate things back to real life, then it helps you visualise things. And you can even, when you pause the video to do some work on this, go and get some shapes from around your house that resemble these 3D shapes. So, I'm starting off with my cylinder. It's like a tin of beans, and I'll think about, okay, first of all, how many faces does it have? Well, it's got one, two flat, circular faces, but it also has one curved face, so it's got three faces. Then I look at the edges, and that's got one, two curved edges. But a cylinder does not have any vertices. So, that's one worth noting. That's an unusual 3d shape. We'll look at one more together. We will look at this shape, here. Okay, and I've got it in front of me as well. So, first of all, I'm thinking, I'm not quite sure what this shape is, but I can see on its face here that it is, it's a six-sided 2D shape. So, that's a hexagon. And this shape is a prism, like a triangular prism. This is a prism, so this shape is called a hexagonal prism. And you may be able to notice another prism on the screen, which this knowledge will help you with that one. So, this is a hexagonal prism, and then it's got one, two faces at the end, three, four, five, six, seven, eight. It's got eight flat faces. I can count the edges. It's got one, two, three, four, five, six on the end. It's got six on the other end as well, that's 12. And then it's got one, two, three, four, five, six around the side. So, that's another six, that's 18 edges. And it's got one, two, three, four, five, six, seven, eight, nine, 10, 11, 12 vertices. Now, a tip for if you're counting them, in a shape like this, it's often helpful to get something like a whiteboard marker which you can rub off just so that you don't count the same face twice, or keep your finger on one face so you know that's where you started and then count around. So, I would like you now to pause the video, and you're going to look up all of these 3D shapes on the screen and see if you can write down the number of edges, vertices, and faces, as well as their name, and if you can think of any examples of the shape in real life. Pause the video now. Okay, so, this is a table of the answers that you should have got. We did the cylinder together, okay? Some more examples. We have the tin of beans. We've also got a loo roll and a glue stick. And then we went onto the next one, which is a triangular prism, And a triangular prism looks like a Toblerone, or it looks a bit like a tent, or it could look a bit like a wedge of cheese. And a triangular prism, this one that I've got here has got a square base, but they can also have a rectangular base. Even if it has a square or rectangular base, the number of faces, edges and vertices are always the same. As you can see on the table, six vertices, nine edges, and five faces. The cuboid, I've got a small one here. The cuboid, you can think about real life examples, there's loads of real life examples of a cuboid. I thought of a brick, a cereal box, a book, but I'm sure you thought of many, many more. And a cuboid has got the same number of vertices, edges, and faces as a cube. It's got eight vertices, 12 edges, and six faces. So, if you were being asked to identify what shape has eight vertices, 12 edges, and six faces, you wouldn't be able to give a definitive answer. You would need a bit more information about the shape of the faces. The next shape was a square-based pyramid, which I have here. And your real life examples would be the pyramids in Egypt, a teepee, which is a type of tent, or the Louvre museum, which is in Paris. Maybe you've been lucky enough to have gone there, and if not, you could have a look at it on the internet. The top of the museum is a big glass square-based pyramid. It's absolutely spectacular, so you should have a look. Now, on the square-based pyramid, we have one, two, three, four, five vertices. One, two, three, four, five, six, seven, eight edges, and one, two, three, four, five faces. The next shape which we looked at earlier on is a triangular-based pyramid, or a tetrahedron. That is the mathematical word, tetrahedron. I really struggled to find real-life examples of a triangular-based pyramid or tetrahedron. One is a Sun Lolly. You may have tried one before, but again, if you haven't, have a look at that on the internet. Another example is, some teabags are tetrahedrons. A tetrahedron has one, two, three, four vertices. It has one, two, three, four, five, six edges, and one, two, three, four faces. The last one, well, we actually looked at this one together, was the hexagonal pyramid. And this one, I, at the weekend, I was eating some Smarties, and I looked at the shape and I thought, oh, this is a hexagonal pyramid. So, there's an example of one in real life. Also, some colouring pencils are that shape, although they're pointed at the top. The actual body of the pencil is a hexagonal pyramid, but you also, not a hexagonal pyramid, a hexagonal prism. You also had a shape that looked like this, and that was, have you guessed it? A pentagon faced? It was a pentagonal prism. And if you had one of these with a seven-sided face, that would be heptagonal prism, and eight-sided would be an octagonal prism, and so on. Great work with that, well done. I hope you managed to find some other real-life examples of those shapes as well. Now we're going to look at identifying 2D faces on 3D shapes. So, here's my question. What 3D shape could this triangle be the face of? I need to start to reason about 3D shapes and think about what I already know about 3D shapes. I know that a triangular-based pyramid is made up of four triangular faces, so it could be the face of a tetrahedron. But I also know some other 3D shapes that have triangular faces. I know that a square-based pyramid has got four triangular faces, so it could be a square-based pyramid. I also know that the triangular prism, which looks like a tent, has got two triangular faces. So, there's three possibilities there, and you may have thought of even more possibilities. So, this one, we can't come up with a definitive answer. We would need more information in order to come to a conclusion about this question. I want you to have a think about these four shapes. What 3D shape could they be the face of? Pause the video and make some notes now. We'll start with the pentagon. We looked at it before. The pentagon could have been the face of a pentagonal prism. Now, the rectangle is slightly more interesting. Well, we know definitely that it could be the face of a cuboid because they have four rectangles, but remember also, a triangular prism can have rectangular faces. And then also, if I think about my hexagonal prism, that's made up of two hexagons, but also rectangle faces. So, there's lots of possibilities here, pentagonal prism as well. Then, looking at the square, well, the first one that comes to mind is a cube which is made up of all square faces, so cube, definitely. Also a cuboid. Two of the faces on a cuboid are square. And then I can also think about, oh, my triangular prism, which had a square face. Could be that. That's got three square faces. But it could also be, I don't have an example of this, but pentagonal prism, if I squish that down, that could have square faces, and the same with the hexagonal prism. And then finally, the circle, that goes back to our initial shape. That's our two flat faces on our cylinder. I think you are ready for some independent learning now, so pause the video and complete your task. And once you finish, click restart. Okay, so your first one was to match the shape to its name. Your number one was a cylinder. Number two was your triangular prism. Number three looked at the hexagonal face to reveal a hexagonal prism. Number four was a pyramid of some sort, and you could see that it had a square base, so it's a square-based pyramid. Number five, the pentagon at the face tells us that it's a pentagonal prism. Number six, we knew it was a pyramid because it met at the top, and this top point, one other thing to note, the top highest point is called the apex. Only pyramids have an apex. Oh, and a cone. I don't think I have a cone though, but you could think of an ice cream cone. The bottom of that, if you turned it the other way up, the top point is called the apex. So, number six was a pyramid. It had a triangular base, and we're using the correct mathematical term, so that's a tetrahedron. Number seven, because it has square faces and rectangular faces is a cuboid. Number eight I don't have an example of, sorry, but that's a cone. And number nine, all square faces is a cube. Question two. You were asked to complete the table with the property shape, with the shape properties, and you had the triangular prism, cylinder, square-based pyramid, and cube. So, you should use these numbers, maybe pause the video, and just check off your answers. For question three, you were asked what shape is each person describing, and it also asked you to sketch a diagram of the shape. The first person, they're thinking of a shape, and when they try to draw the shape, they start with a triangle. So, first of all, straight away, I'm thinking one of these three shapes, one of the pyramids or a triangular prism. So, they start with a triangle. Their shape has four vertices. Okay, so I look at my triangular prism. That's got one, two, three, four, five, six, so it's definitely not that. Then I look at my tetrahedron. One, two, three, four vertices. Okay, could be that. Check with this one, square-based pyramid. One, two, three, four, five vertices. It can't be that one, so it's the tetrahedron. It's got four faces, one, two, three, four, four vertices, and we're being asked, how many edges does it have? One, two, three, four, five, six. Now, remember, if you're doing answering questions about 3D shapes in assessments, you won't have access to 3D shapes, so you have to really try and visualise. That's why it's really helpful to think of real-life, everyday items that are 3D shapes. The tetrahedron one is annoyingly because, very hard to think of anything. So, the second person is saying, "When I draw my shape, "it looks like a triangle, but with a curved side." So, I'm thinking about a 3D shape with a curved side. Well, the only one I've got in front of me is a cylinder. The only other one I can think of is a cone or a sphere. So, I'm thinking of a tin of beans, an ice cream cone, or a football. But does that look like a triangle to you? I don't think it does, so I'm going to exclude that one. And if I think about a football, that one also doesn't look like a triangle, but a cone does. Let me check with the other information. It only has one vertex. That's true of a cone. And remember, because it's the topmost point, we call that the apex. So, what food might I eat out of a shape like this? Oh, we've already thought of it, an ice cream. So, we know that it is a cone, and it's talking about an ice cream cone here. Question four. Raeesa has drawn a 3D shape. His shape has five vertices, eight edges, and five faces. What 3D shape has Raeesa drawn? You could have looked back at your table from earlier, or stopped to think about the different 3D shapes that you've got, and I'm thinking of one that I know has five vertices. Well, I know it can't be a tetrahedron, 'cause that only has four. And I'm thinking about the others. The others all have more than five. I think it might be a square-based pyramid. Let me check. One, two, three, four, five vertices, good. One, two, three, four, five, six, seven, eight edges. That's right. And one, two, three, four, five faces. Raeesa has drawn a triangular-based pyramid. No, he hasn't. He's drawn a square-based pyramid. Okay, Fran has drawn a 3D shape, and her shape has five faces, nine edges, and six vertices. What shape has Fran drawn? So, I'm going to start to work through my shapes so that I can eliminate different ones. I know it can't be a cylinder. That's got three faces. A tetrahedron has got four faces, it can't be that. Actually, a square-based pyramid does have five faces, but as we've just learned, it's got eight edges, so it can't be that. How about a triangular prism? Let's count. So, it's got five faces, one, two, three, four, five. Good so far. Nine edges, one, two, three, four, five, six, seven, eight, nine edges, looking promising. And six vertices, one, two, three, four, five, six vertices. So, Fran has drawn a triangular prism. On to our last question. You were asked to sort the shapes in the Venn diagram into those that had flat faces and curved faces, and using your knowledge of Venn diagrams, you knew that what came in the middle section were shapes that have both flat and curved. So, that was the cylinder and the cone. Now it's time for your final quiz. Pause the video and complete the quiz and then click restart once you've finished. Great work today. In our next lesson, we will be recognising the nets of 3D shapes. I'll see you then.

Coordinates and shapes: To recognise 3-D shapes

Coordinates and shapes: To recognise 3-D shapes

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UnitMaths / Coordinates and shape

Maths