Lesson video

Hi there, my name is Mr. Tilstone.

I'm a teacher.

I enjoy teaching all of the subjects, but without any shadow of a doubt, the one I like best is maths.

So it's a real pleasure and a real delight to be with you today, teaching you a lesson all about nets.

In today's lesson, we're not really going to be thinking about numbers.

We're going to be thinking about shapes.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can compose 3D shapes from 2D nets and identify the 2D net, which will create a 3D shape.

Our keywords, we've got two.

My turn, net.

Your turn.

And my turn, face.

Your turn.

What do those words mean? Let's have a reminder.

"A net is a 2D representation of the faces of a 3D shape that can be folded up into the 3D object." You might in the past have made the net for a cube, for example.

And faces are the flat 2D surfaces of a 3D shape.

So in that example of cube, the faces are all squares.

Our lesson today is split into two cycles.

The first will be what is a net, and the second will be sketching nets.

So if you're ready, let's begin by thinking about what is a net.

And in this lesson, you're going to meet Alex and Sam.

Have you met them before? They're here today to give us a helping hand with the maths.

This is a three-dimensional or 3D object.

It's a cuboid.

The net of a 3D object is a 2D representation, two-dimensional, of the faces of the object.

So let's have a look at that.

So if you unfold that, this has created a net.

And can you see that net is comprised of 2D shapes? In this case, they're all rectangles.

This is a triangular prism.

That's the 3D shape.

Its net has been formed out of construction materials.

And you might have something like this in your school or your classroom.

And if you have, great, you might want to dig them out and use them.

Which shapes can you see? So they're the shapes that will form the net.

Which ones can you see? How many of them? Well, here we go.

Those two triangles join onto that rectangle.

And the two rectangles join onto the other one.

Now we've got the net.

And that net folds together to make this 3D shape.

"A triangular prism has two triangular faces and three rectangular faces.

Its net is composed of two triangles and three rectangles." Now depending on the size of the triangular prism, the faces might be different sizes.

The triangle might be a slightly different shape.

Some other rectangle of the dimensions might be different, but that's what it needs.

It needs three rectangles and two triangles to form.

Notice how the flat faces are connected along the sides of the shapes.

That's very important.

They're connected along the sides, not the vertices, the sides.

The joins become the edge, the edges of the 3D shape.

So where there's two shapes form the triangle and the rectangle, can you see? There's a join and that will become an edge when it's folded together.

Let's have a look.

Could any of these be the net of a triangular prism? And if not, why not? Well, this one couldn't, could it? What's the problem here? One of the 2D shapes is not even attached to the other so it's not a net.

We can make it attached and we can make it into a net, but at the minute it is not.

What about the next one? Can you see an issue here? That couldn't be a net because the vertex of one of the 2D shapes is touching the side.

It should be the side touching the side, not the vertex touching the side.

So they're not joined.

And what about this one? Well, the side is touching the side, but what's the problem? "The touching sides of the 2D shape should be the same length." And you can see that in the other nets.

Could any of these be the net of a triangular prism? What do you think? Have a good look.

We saw an example, didn't we? We have a triangular prism net.

Could these be the net of one? If not, why not? Well, the first one is wrong because triangular prisms only have three rectangular faces.

That would be one too many.

It would overlap.

And likewise, this one hasn't got enough.

The net needs three rectangles, one for each rectangular face.

That will be a face short.

What about the last one? The wrong shape has being used.

You can have circles in nets, but not in a triangular prism.

So specific shapes are used in specific nets.

Let's have a quick check.

Let's see how you're getting on with your learning.

How do you know that this is not the net for this cylinder? So the cylinder is a 3D shape.

There's a 2D net, but it's not the right net.

How come? Pause the video and have a think.

What do you think? What's wrong with it? "The cylinder does not have any triangulate faces." But the net does, so they don't match.

However, this one does work.

The net of a cylinder is special because it's got two circular faces.

"The rectangle curves around them to form the cylinder becoming a curved surface." So it won't be a flat face.

It'll become a curved surface when it curves around them.

Okay, let's do another quick check.

"Which of these could be the net of a cylinder?" And again, think about why not if it's not.

Pause the video and off you go.

What do you think? Well, C is the one that could be the net of a cylinder.

The rest can't.

There should be two circles for the circular faces, so it's missing a face.

B's got too many faces, one too many faces in fact.

And what about D? What's the issue there? "There's no flat square face on a cylinder." So one of those 2D shapes is wrong and doesn't belong in that net/ Time for some independent practise.

"Explain why each of the nets cannot form the 3D shape." What's the reason? What's wrong with each one? And number two, "If you have any construction materials, use them to create nets for different 3D shapes." Have fun exploring that and I'll see you soon for some feedback.

Welcome back.

How did you get on? Well, number one, "Explain why the nets cannot form the 3D shape." What's wrong with A? The number of 2D shapes on the net does not match the number of faces on the square-based pyramid.

There's not enough in the net.

For B, the 3D shape is a triangular prism but there are no triangles in the net so it can't be.

For C, what's wrong with C? "The net has seven squares but the cube only has six faces." So it doesn't match up.

And then hopefully, you had some construction materials or something similar and you are creating nets for different 3D shapes.

Here are just some examples.

See if you can spot which 3D shape each of them would make.

What about the first one? That would make a triangular pyramid.

What about the second one? That would fold together to make a triangular prism.

And the third one would fold together to make a cube.

There we go.

Time for the next cycle, I think.

This is sketching nets.

"When sketching the net of a 3D shape, all of the faces must be drawn." "Sam has placed a cuboid onto squared paper to draw a 2D representation of its faces for a net." So that's the back of the cuboid, that's the front.

And you can see those on the shape there.

And that's the bottom of the top.

So the bottom is on the paper, touching the paper at the minute.

And there's the top, it's opposite.

And then we've got the right and the left parts of it.

Like so.

So that's all of the faces that are in the cuboid have been drawn as a net.

"Can you explain why this net would not fold to make a cuboid?" Because it seems to have some things that are correct.

It's got the right number of faces, for example.

"The sides of the two touching rectangles are not the same length." Can you see? Just here.

They're not the same length.

So it wouldn't work, it wouldn't fold together to make an edge properly.

There would be gaps in the 3D shape formed from the net, and it wouldn't be a solid shape.

So almost.

"Sam has drawn round one face of a cuboid and then sketches in the other face is to form the net." That's the bottom of the cuboid.

Doesn't matter which face she starts with, but it helps to think of pairs of faces.

So if we've got a bottom, we need a top, et cetera, et cetera.

So we've got the left hand side.

And because we've got the left, we need a right.

That's going to be on the other side.

They're going to be opposite each other.

And we've got a back.

So we're going to need a front and they're gonna be opposite.

And they're the same size as each other look.

as the left and the right are.

And then we need one more.

We need the opposite to the bottom.

Where might she sketch the top face? Where could that go? She's got four choices, and all of them would work.

So let's have look at her four choices.

Last one could put it there.

There or there or there.

There's the four choices.

Let's go for there.

That's where the top is going to be.

And again, it's going to be opposite the bottom.

So pairs of faces.

You can also visualise a net from a 2D representation of a 3D shape.

So visualise, so picture it in your mind.

"What faces can you see and which ones are hidden that you can visualise?" So looking at the angle of that shape, that's a triangular prism.

We can't see all of the faces, but I can imagine them, can you? I can visualise them in my head, I can picture them.

I can imagine if the shape was see through.

Which sides we could see.

Well, you can see a right angled triangle.

Yep, that's visible.

And one of its sides is joined to a rectangle, which you can see.

Another of its sides is joined to another rectangle, the bottom of the prism.

We can't see that one though.

And there's a third rectangular face to complete the prism, but we can't see it.

I can visualise it, I can imagine it, but I can't see it at the minute.

As this is a prism, there will be an identical right-angled triangle on the other side.

We can't see it, but I know it's there.

So let's get sketching that net.

So there's a rectangle and there's the triangle, one of the triangles.

There's the other one.

So one we can see on the 3D shape, one we can't, but there we are.

And there's another one of the rectangles.

And the other rectangle that's the same size, and they would fold together to make that 3D shape.

So that is the net for that triangular prism.

"Look at this 3D shape.

Sketch what the net might look like." Now on this shape, once again, we can see some of the faces, but some are hidden in the position that it's in at the minute.

So you'll have to visualise or imagine them.

Okay, pause the video and have a go at that.

Let's have a look.

What might the net look like? It might have looked a little something like this.

So you can see the pentagon that we can see there, and there's also one that would be on the other side because it's a prism that we can imagine or visualise.

And then all of the rectangular faces, we can see two of them on the 3D shape, and three of them are hidden, well, we can imagine them.

"As this is a pentagonal prism you know there's a pentagon and can see rectangular faces.

You know there are identical faces." You can visualise an identical pentagon on the other side.

This is one of the places it could have been.

It could also have been attached to the other rectangles.

Time for some more practise.

"Complete the nets to make the following 3D shapes." A square-based pyramid.

A triangular pyramid.

So think about how many shapes you need, and think about which shapes you need.

A cuboid.

How many and which ones? And a pentagonal prism, some are there but you need to add some more on.

There is more than one way that you can do these.

Number two, "Sketch a possible net for this 3D shape." What will the net look like? In this case, none of the faces are hidden.

We can see them all.

So that should help when you're sketching it.

And this is the card packaging of a chocolate bar.

It reminds me of a famous chocolate bar, that one.

Hmm.

"Sketch what its net might look like." And on this example, some of those faces at the minute are hidden, so we do need to visualise them.

Number four, "Sketch the net that could be used to make a cereal box." So your cornflakes or whatever your favourite cereal is, think about the box they come in and think about the box unfolded to make a net.

And then number five, "How many 3D shape nets can you sketch?" You may wish to start by drawing around the bottom of the shape and then build onto that.

Good luck with that.

Have fun with that.

And I'll see you soon for some feedback.

Welcome back.

Let's give you some answers or possible answers.

So here's an example.

Yours might be slightly different.

There are different possibilities.

That's a square-based pyramid.

So it's got a square and four triangles, all the same size as each other.

That's a triangular pyramid.

That's made of four identical triangles.

"Does your net have 2D shapes that match the faces of the shape? Can you visualise the nets folding to make that 3D shape?" So in your mind, can you picture them all folding together? And for the cuboid, you're going to need six rectangles.

Four of them the same size as each other and two of them the same size as each other.

And then the pentagonal prism.

Let's have a look.

What shapes will you need? What 2D shapes and how many? You'll need another pentagon and you'll need two more rectangles.

Number two, a possible net for this 3D shape.

"Your net must have the following 2D shapes, but they may be in a different order as long as they would fold together to make the 3D shape." So here we go.

So you need a rectangle.

A trapezium.

An equal size trapezium on the other side.

Another rectangle.

And another rectangle.

And another rectangle.

And they need to join together, fold together, to make that 3D shape.

And "This is the card packaging of a chocolate bar.

Sketch what its net might look like.

Your net must have the following 2D shapes but again, they may be in a different order as long as they would fold together to make that 3D shape." So we would need three rectangles and two triangles.

And number four, "Sketch the net that could be used to make a cereal box." Well, they're usually cuboids, aren't they? Cereal boxes.

So your net must have three pairs of equal-sized rectangles.

So you could think of it as like the front and the back, the top and the bottom, the left and right hand side of your cereal box.

And they would need to fold together to form the 3D shape, the cuboid.

"And then how many 3D shapes can you sketch? Well, you may wish to start by drawing around the bottom of a shape." This is one of many examples, it's a triangular prism.

But there's lots and lots, dozens, hundreds of examples that you could have come up with there.

So well done if you've got one that would fold together to make a 3D shape.

We've come to the end of the lesson.

Today's lesson has been about 3D shapes and how they can be composed from 2D net.

So you've been learning about nets.

And net is a 2D representation of a 3D shape.

It is composed of the faces of the 3D shape.

"Folding the net along certain edges and joining others produces the 3D shape." You can use sketching to create nets of shapes, visualising, so picturing, imagining whether the sides would join together to create the edges of the 3D shape.

Well done today on all of your achievements and accomplishments and your learning successes.

Give yourself a pat on the back.

I hope to see you again soon for some more maths in the near future.

But until then, enjoy the rest of your day, whatever you've got in store.

Take care and goodbye.