Lesson Video: Edges of 3D Shapes Mathematics • 1st Grade

In this video, we will learn how to identify and count edges and vertices of 3D shapes and how to build shapes.


Video Transcript

Edges of 3D Shapes

In this video, we’re going to learn how to identify and count the edges of 3D shapes. We’re also going to look at their vertices too. And we’re going to learn how to build shapes.

Now, when we use the word edge in everyday life, we often use it to describe the boundary of a shape, the very end of it, its outer limits. So, the edge of a field might have a fence all the way around. It’s where one field ends and the next one begins. If we drew a line around the edge of this screen, it would show the boundary of where the video ends and something else begins. Now, in this video, we’re particularly thinking about 3D or solid shapes. And in maths, the edge of a 3D shape has a certain meaning.

The edge of a 3D shape is where two of its faces meet. Where they touch or meet, it forms an edge. Let’s think about the edges of a cube to begin with. Now, as we’ve just said, the edges of our cube are going to be those places where two of its faces meet. Do you remember what the faces of a 3D shape are? They’re flat surfaces that make up a shape. And the cube’s faces are all squares. And we can only see three of the faces on this cube, and they’re all green. So, it might be hard to know which face we’re talking about. Let’s put some numbers on the faces and turn it into a dice.

There we go. Now, to find an edge on our cube, we need to choose any two of these faces. Let’s choose the one with the number one on it and the one that has the number three on it. Can you see where these two squares or faces meet? It’s this line here. This is one of the edges of our cube. And if we look at the place where the edge with the number three on it meets the face with the number two on it, we can see another edge. There’s also an edge where the number one meets the number two. In fact, all the black lines that make up the picture of this shape are edges.

This brings us onto a question we could ask ourselves. How many edges does a cube have? Now, when we’re working with a video like this, we’re working with pictures of cubes. We haven’t got a cube in our hands to look at. But we have already said that the black lines that make up the outside of our picture are the edges of the cube. How many can you see? There are one, two, three, four, five, six, seven, eight, nine edges on this picture. But as we’ve just said, this is just a picture. We really want to be able to turn this cube around so that we can see the back too because there are some hidden edges that we can’t see at the moment.

Now, this is where building a cube can help us. This is the sort of thing you could do if you had time. Firstly, you’re going to need something long and thin, perhaps cocktail sticks or toothpicks. We’re going to use straws. And then you’re going to need something squashy. You could use fruit gums or marshmallows. Just in case we get tempted to eat them, we’re going to use modeling clay.

Let’s start by making the base of our cube. As we’ve said already, a cube has square faces, so we’re going to need to make a square. Let’s pick up the straws and the modeling clay that we need. There we are, one base of the cube. We’ve used four straws and four blobs of modeling clay to connect them at the corners or vertices. Now, we’re not making a 2D shape, we’re making a solid shape, so we’re going to need to give it some height. Let’s use four more of our straws to do this.

And now, finally, can you see what we need to do to finish our cube off? We need to use our last four straws and four blobs of clay to make a square on the top of our cube. And there we have it. Now, we could call this a skeleton cube. Can you see why? Although it looks like a cube, it doesn’t have any flat surfaces, does it? There are no faces to this cube. If we wanted to, we could put our hands straight through the middle of it.

But using the outline or the skeleton of a cube like this is really helpful to us. This is because it shows us all the edges and the vertices of the cube that we wouldn’t normally see because they’d be hidden around the back. The straws in our model represent the edges of a cube. Let’s count them to see how many edges there are. And as we do, we’ll label them on our green cube, too, so you can match the two up.

There are one, two, three. Wait a moment! How are we going to label this edge? We can’t see it on our green cube because it’s around the back. Well, there is a way to show that it’s there but that it’s hidden away around the back. And that’s by using a dotted line. Often, you’ll see dotted lines on drawings of 3D shapes; it helps us to visualize what they look like. Let’s carry on counting from three. Four, so that’s four edges that go around the square face at the bottom, five, six, seven, eight, and then four more that make up the square face on the top, so that’s nine, 10, 11, 12 straws that we’ve used altogether.

Now as each store represents an edge, we can say that a cube has 12 edges. And not just our green cube here; every cube ever has 12 edges. Maybe you’ve got a building block or a dice that you can look at and count. As we’ve said already, building skeleton models like this are really useful because they also show us the number of vertices that these shapes have. Remember that a vertex is where two or more edges meet. And on our skeleton cube, these are the blobs of modeling clay. There are four around the base of the cube and another four at the top, which makes eight altogether. Cubes have eight vertices. And more importantly, for this particular video, we also know they have 12 edges. And maybe you noticed on a cube, all 12 edges are the same length.

Let’s look at another 3D shape. How many straws would you need to build this shape? In other words, how many edges does it have? Now, just like before, we can’t see all the edges, can we? But we could think really carefully about what this 3D shape might look like all the way around. And we could even draw in some of the edges that we can’t see using dotted lines. What makes up this shape? Well, we can see a triangular face at this end. We can’t see the face at the other end, but we’d expect it to be triangular, too. And then, we have three rectangular faces along the sides. There’s this one we can see. And then, there’s one on the bottom and one hidden away around the side.

By adding the dotted lines, it really helps us to visualize the shape, doesn’t it? Now, let’s use what we’ve just found out to help build the shape. We need to make a triangle at one end. So, that’s three edges, another three edges for the triangle at the other end, and then three more edges to connect them both together. This shape, which is called a triangular prism, has nine edges. We’re going to need to use nine straws to build it. And because we can see that this shape has six vertices, we know that we’re going to need six blobs of modeling clay too.

Now, how good do you think you are at recognizing the edges of 3D shapes? Let’s answer a couple of questions now where we have to put into practice what we’ve learned. And then afterwards, we’ll try a challenge to really test us.

How many straight edges does this shape have?

We can see a picture of a 3D or a solid shape here. Can you think of any objects that are the same as this shape? Looks the same as perhaps a block of wood or maybe a long brick. The name of this shape is a cuboid. We know that it’s a cuboid because it has rectangular faces. It has four of these long rectangular faces all the way around. And then, at each end is what looks like it might be a square face. But we can just call them rectangles because squares are a special type of rectangle anyway.

So, this shape, with rectangular faces along the way around, is a cuboid. But although it’s helpful for us to think about the faces of this shape, the question doesn’t ask us about its faces. We need to say how many edges this shape has. Do you remember what the edge of a 3D shape is? An edge of a 3D shape is the place where two of its faces meet. It’s where the faces touch. So, if we pick two of the faces on this particular cuboid, we’ve got this long rectangular face here and the square face on the end.

Can you see the place where these two faces meet? It’s along here. This is one of the edges of the cuboid. If you imagine this cuboid is a long cardboard box and you open it out and flatten it, we’d be able to see this edge. It would be one of the folds. It’s where two faces meet. Did you notice this edge was one of the black lines that makes up our picture? But unfortunately, because this is a picture of a solid shape, we can’t see all of the edges. Some of them are hidden around the back. Let’s try and visualize what our shape looks like around the back. And we’ll use dotted lines to draw in the extra edges.

Well, from what we know about cuboids, the face on the bottom of this shape is exactly the same as the face on the top. It’s going to be another rectangle. In a way, this cuboid doesn’t really have a top and a bottom because all we’d have to do is turn it upside down; it’d look exactly the same. So, let’s draw in our missing sides of this rectangle on the bottom of the shape, one at the side and one along the back. And the sides of our rectangular face become the edges of this 3D shape.

We’ve got one more edge that’s missing. Can you spot where it belongs? It’s round the back on the left here. And it shows us that the end of our cuboid, there’s a square face. Can you see now that drawing in these dotted lines really helps us to visualize the shape? We don’t need to imagine what it looks like around the back; we can see.

Now that we’ve drawn in all of the edges, let’s count them. There are four straight edges that go all the way around this square face on the right. Then, there are another four edges around the opposite end of the cuboid. And then, finally, there are four more much longer edges that run along the length of the cuboid. So, that’s three groups of four. We know that three times four equals 12. So, we can say that the number of edges that this shape has is 12.

How many edges does the pyramid have?

We know this picture shows a pyramid. And it’s not just because we’re told so in the question. We know it because we know what makes up a pyramid. This particular type of pyramid has a square face as its base and then four triangular faces that all meet at a point or a vertex right at the top. Now, our question asks us, how many edges does the pyramid have? It doesn’t mention faces at all. So, what have the faces of this pyramid got to do with its edges? Well, we know that an edge of a 3D shape is the place where two faces meet. It’s where they touch, where they connect up with one another. And so, knowing what the faces of this pyramid are like can really help us work out how many edges it has.

Remember, we started off by saying that the face at the base of this pyramid is a square. That’s why on this picture we can count one, two, three, four edges around the base. And because we know that the faces around a pyramid are all triangles, they all go up to that point at the top. We know from each of the vertices of this square base, we’re going to have one more edge. And four vertices means one, two, three, four more edges. And four plus another four equals eight. We know that the edges of a 3D shape are those places where two faces meet. And by counting them, we found that the number of edges that this pyramid has is eight.

Now, we did say we were going to end the video with a fun challenge for you to try. You might like to pause the video to have a think about this question or maybe even try building the shape yourself. And the challenge is this. If you have six straws and four blobs of modeling clay, which 3D shape can you build? And because we know what these objects represent when we build a skeleton shape, we could’ve just asked which 3D shape has four vertices and six edges. But perhaps that wouldn’t have been as interesting as doing it this way.

Can you think what this shape might look like? Here’s a clue. This is what the base of the shape looks like. Can you think what to do with your last three straws and one blob of modeling clay? This is the shape, isn’t it? It’s another kind of pyramid, slightly different to the one we saw in the last question because the base of this particular pyramid is a triangle not a square. So, interestingly, not all pyramids have eight edges. Some pyramids have six edges. Why don’t you try making your own 3D shapes out of straws and modeling clay or cocktail sticks and marshmallows? Remember, each straw or each cocktail stick that you use is another edge for your 3D shape.

So, what have we learned in this video? We’ve learned how to recognize and count the edges of 3D shapes. We’ve also learned ways to build 3D shapes and used this to help us learn about their edges.

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