Lesson Video: Matching 3D Shapes to Nets Mathematics

In this video, we will learn how to match pictures of 3D shapes with their nets by analyzing the shapes and the number of faces.

17:59

Video Transcript

Matching 3D Shapes to Nets

In this video, we’re going to learn how to match pictures of 3D shapes with their nets. And we’re going to do this by looking really carefully at the shapes and their faces. Before we start, what is a net? Because in math, it’s got nothing at all to do with catching fish. One way of explaining what a net is in maths is it’s what a 3D shape would look like if we opened it out flat. Another way of thinking about a net is that it’s almost like a plan of a 3D shape. Yes, it’s flat, but it can be folded. And when we fold up a net, it makes a 3D shape. Now, it might be a good idea at this point to see an example.

Here’s a 3D shape, and don’t forget, 3D just means solid. Now remember, a net of a 3D shape is really what it looks like if it was opened out flat. Now, to really help us understand what a net looks like, it would be quite useful if we could somehow flatten this shape. Now there’s an idea. There we go. Now, there are lots more easier ways to make a net than to use an elephant. But it’s quite a fun idea to begin with because it helps us remember this idea of a solid shape becoming flat. And as we can see, what’s left behind here isn’t solid anymore. This is an example of a net.

Now, nets don’t have to be colored. We’re just using colors on this particular example because it’s the first time we’ve seen a net. And it’s gonna help us understand how it folds back together to make a 3D shape. So most often, we might see a net that looks a little bit like this. It seems to be made of lots of shapes put next to each other. And although these look like 2D shapes now, these are just squares, aren’t they? As we fold up our net to make a 3D shape, these are going to become the faces of the shape. And perhaps you remember from your work on shapes, a face is a flat surface that makes up a 3D shape. But in this video, the shapes that make up a net aren’t just faces; they’re clues. We can look at them to get a really good idea of what the shape is going to look like when it becomes 3D.

So what can we tell from the clues we have in front of us? The 3D shape that we make from this net is going to have one, two, three, four, five, six faces. What else can we tell about the faces of this shape? We know that all six faces of the shape we’re going to make are going to be square. And knowing what shape faces are going to be can be really helpful when we’re matching a net to a solid shape. For example, we wouldn’t match the net we’ve got in front of us up with this shape, would we? This is because we can see straightaway this shape doesn’t have all square faces.

Now, as this is the first example, we already know what 3D shape this net is going to make when we fold it, don’t we? But can you see how to get from this net to this 3D shape? We’ll give you a few seconds now to look at the net and practice a really important skill. The long word for this is visualizing. But really it just means imagining a picture in your head. In the next few seconds, look at the net and think to yourself, how would I fold this to make the 3D shape? Hopefully the fact that our net is colored might help you a little bit here. Now there are lots of ways we could do this. And it’s really hard to show in a video, but we’ll have a go.

Don’t know which face you’re going to begin with, but let’s start with this one here, and we’re going to fold it up. There we go. Now, can you spot which face on our 3D shape we’ve just put into position? It’s this one, isn’t it? Now, which face would you choose next? It doesn’t matter. But in this example, we’re gonna choose this one, and we’re going to fold it up again. And we can see by folding this part of the net up, we’ve put another face into position on our 3D shape. Well, you can probably see how all this is going to work now. We just need to take all of this part and fold it up. So this is what we meant when we said that a net of a 3D shape is really what it looks like if it was opened out flat.

And so if we were given this net and asked to match it with one of these 3D shapes, we get as many clues as we could by looking at the net. And we could also use our skills of trying to imagine what the net might look like if we folded it up. And all of this will help us find the correct answer. Now, in the same way that we’ve gone from net to 3D shape in this example, we can also go in the opposite direction. Here’s a 3D shape. Which one of these nets can we match it to? In other words, if we unfolded our 3D shape, what would it look like? Again, we can start by looking for clues, but this time we’re looking at a 3D shape.

Now, we can’t see all of the faces of this shape, but we can see some of them. This shape has some faces that are triangles. We can see one at this end. And although we can’t see it, can you imagine that there’s one at this end too? But this isn’t the only clue we can spot because we can see we’re looking for a shape that has rectangular faces too. Can you see this rectangle on the side? Now, I wonder, can you spot one of these nets that’s definitely not the right answer? We know the top one is wrong, don’t we? Because there aren’t any triangular faces on this net. Perhaps it’s time now to practice our second skill.

We need to start visualizing or imagining. How would we unfold this shape? And what would it look like if we did? Maybe one side down first, then the other, and then the two triangles on the ends. By picturing what this shape might look like if we opened it out, we can guess that it’s going to have two triangular faces and three rectangular faces. And so we can see that the correct net is this one. So do you think you can spot a net when you see one? Let’s try answering some questions where we have to match pictures of 3D shapes and their nets.

This pyramid has four orange faces that are triangles and one blue face that is a square. You can fold a net of a shape to make that shape. This rectangular prism has six faces that are rectangles. Find a net for the rectangular prism.

There are lots of words in this question and some pictures to help us. So let’s go through it really slowly to try to understand what it’s asking us. To begin with, we’re told about a pyramid. Now we know a pyramid is a 3D or a solid shape. Can you see it in the picture? It’s over here. And we’re told that the pyramid has four orange faces that are triangles and one blue face that is a square. Now we know that the faces of a 3D shape are the flat surfaces that make it up. And when we see a picture of a 3D shape like this, it’s sometimes quite difficult to imagine what the shape looks like round the back. We can’t see all of the faces.

So in this question, this description really helps us. Even though we can only see two orange faces, we’re told that the pyramid has four altogether. And we can see a square face underneath, can’t we? This is the base of the pyramid. So just from this information, we can tell something about our shape. It has five faces altogether. The next sentence of our question talks about nets. Now, this is a maths question, so this isn’t fishing nets we’re talking about. A net is like a flat version of a shape; it’s what we get if we opened out a shape to look at it. And this sentence tells us that we could fold the net of a shape to make that shape.

To help us understand what we mean by this, we’re shown a picture of the net of the pyramid. It looks flat, isn’t it? And each of the shapes that makes up this net is the same as one of the faces of the pyramid. We can see there are five shapes altogether, aren’t there? There are four orange triangles and one blue square. Can you imagine how you’d fold the different parts to this net to turn it into a pyramid? We’d have to fold each of the triangular faces upwards: one, two, three, four. We folded the net to make the 3D shape.

Now that we understand about nets, let’s get on to the next part of the question because we’re shown a new shape. And we’re told that this rectangular prism, which is the name of the shape, has six faces that are rectangles. Now, in a way, it’s a good job we’ve got this description because we can’t see six faces if we look at the picture. We can just see one, two, three faces. So we know there must be three more faces underneath round the side and round the back, places that we can’t see on this picture. And the shape of these faces are rectangles, slightly different sizes though, aren’t they? Can you see that the pink faces are longer than the green face on the end? But they’re all rectangles, and the question asks us to find a net for this rectangular prism. In other words, what would this shape look like if we opened it out?

Well, we can use what we’ve learned about pyramids to help. We knew that the pyramid had five faces altogether, didn’t we? And we spotted that there were five different shapes that made up the net, one for each face. So if we know that this rectangular prism has six faces, we’re looking for a net that’s made up of six shapes. The first net that we can see is made up of one, two, three, four, only five faces. This isn’t gonna make the shape we’re looking for, is it? But if you can imagine folding this net up and what it would look like, but it would be almost the same as our picture. But instead of giving us a solid shape, there’d be a hole in one end. It would be similar to our rectangular prism, but it’d be more like a box. This isn’t the right net at all.

Our next net is made up of one, two, three, four, five, six faces. It looks like this might be the right answer. But wait a moment. If we count the faces on our last net, we can see that there are six too. We’re going to have to look for more clues than just the number of faces here. What else do we know about the faces of this rectangular prism? Well, we know that all six of them are rectangles. But this doesn’t help us either. If we look at these two nets, we can see that all of the shapes that make up them are rectangles. Is there anything else that we could use to help us? Well, we did say when we were originally looking at our rectangular prism that some of the faces were longer than the others. Do you remember? The pink faces that made up the sides of this rectangular prism were longer than the green face on the end?

And if we look at this middle net, we can see that all of the shapes that make it up are the same size. This is definitely going to make a shape that has six rectangular faces. But it’s going to make a shape where all of those faces are the same size, and we don’t want that. We’ve used the picture of the 3D shape and also what we were told about it to help us find the net that will make it if we fold it up. The correct net is the one that’s made up of six rectangles, one for each of the rectangular faces in our 3D shape, but also where some of the faces are longer than the others. This is the net that will make the 3D shape.

True or false: The 3D shape, here, can be made from the net, here.

Before we start this question, there’s a word in this sentence that we need to remind ourselves of. What does the word net mean in maths? We could say that a net is what a 3D shape might look like if it was opened up flat. Another way of saying the same thing is that a net folds up to make a 3D shape. And the statement that makes up our question contains a net too. Can you see the picture of it on the end? This is like a plan of a 3D shape. And if we cut this out of cardboard and folded it up, it would make a 3D shape. But what sort of 3D shape? Because our statement shows a picture of a 3D shape and it tells us that we can make this from this net. Now what do you think? Is this statement true or false?

To help us, we could look very carefully at the 3D shape and also at the net to find clues. What can we tell if we look at the 3D shape? Well, probably, the most important thing that we could look for is the faces of this shape. And we can see just by looking that all of the faces of this shape are rectangles. Now you might look at the faces on each end and say, “Well, they look like squares to me.” Well in maths, a square is just a really special type of a rectangle. So because we can’t be sure, we could just use the word rectangles for now.

Now, let’s have a look at our net. What shapes make up this net? This is really important because as soon as we fold our net, these shapes are going to turn into the faces of the 3D shape we make. Well, when we look closely, we can see that this net is made up of three rectangles, so we can say some faces are rectangles. But we can also see two triangles on the ends. This is going to make a 3D shape that has faces that are triangular too. Now we could count the faces. We could also imagine what this net might make if we folded it, but we really don’t need to. We’ve answered the question. The net is going to make a solid shape that has some triangular faces. But the 3D shape in the picture doesn’t have any triangular faces. We can’t make this 3D shape from this net. The statement in the question is false.

Select the net of this shape.

In this question, we’re shown a picture of a 3D shape. It’s solid. Perhaps you know the name of this shape, but it doesn’t matter; it’s not gonna help us answer the question because what we’re being asked to do is find or select the net of this shape. Now we know that the net of a 3D shape is what that shape might look like if it was opened out and flattened. And underneath the picture of the shape, we can see several nets. If we were to cut each one out of paper to fold it, it would make a shape, but only one of them would make the shape that we can see in our picture.

To help us find the right net, we can look for clues in this picture. What can we tell about this 3D shape? Probably the most important thing when we think about nets is to look at the faces of a 3D shape. Don’t forget the faces of a 3D shape are the flat surfaces that make it up. And if we look carefully at this particular 3D shape, we can see something interesting about the faces. They’re all squares, aren’t they? Now if we take a moment and look at the different nets that we have as possible answers, perhaps we can see which one is correct already. Some of the nets are made out of rectangles, and some contain triangles. But there’s only one that’s made up just out of squares.

To check our answer, we could count the number of faces. There’s one on the top, one on the bottom, and then four round the sides. So that’s six faces altogether. And if we look at the net we’ve chosen, we can see that it is made out of six squares. Each one is going to become a square face when we fold them into the shape. Our shape has six square faces. So the correct net that’s going to make this shape is the one made out of six squares.

What have we learned in this video? We’ve learned what a net is. We’ve also learned how to match pictures of 3D shapes with their nets.

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