# Lesson video

In progress...

Hello, my name is Mrs. Buckmire and today I'm going to be teaching you about nets of prisms. So first, make sure you have a pen and paper.

Remember, you can pause the video whenever you need to.

So, pause when I ask you to, but also if you're not quite sure of something or you want to copy something down and just pause the video, that's fine.

And also, if you're not sure about something, you can rewind the video as well and listen again.

Let's get on with it.

So first task is, I want you to tell me anything about what shape this net will make.

So maybe you're going to tell me the name of the shape.

Maybe you know something about vertices, faces, edges.

Maybe, knowing that it's drawn on a centimetre unit grid, you could tell me about the dimensions.

Hmm, what else could you tell me? Pause the video and have a go.

Okay, I'm sure you have lots of different things to say, but I'm just going to say a few things.

So firstly, I can see there are one, two, three, four, five, six faces.

And then the faces are the flat surfaces or 3D shape.

So what 3D shape is this? Six faces, they're all rectangular.

Ah, it's a cuboid.

Did you get that? Good.

So how many vertices does a cuboid have? Nice.

Vertices are the corners, yeah.

And there were eight.

So there are eight vertices.

And edges, how many edges? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

And you know what? It'd be even easier if we did a little sketch.

So what I'd do is draw a rectangle going forward, like front face, and then one, two, three, four, five to finish up.

Then you know behind it's like one like that.

There we go.

So we have 12 edges.

What else can we say.

Did I mention? So if this is our, let's say this length here.

Oops, this one, is equivalent to kind of this one here.

'Cause it looks like it's quite long.

So that one is one, two, three, four, five, six centimetres long.

So if this is six centimetres, that length there.

So let's say that length is, this one, is four centimetres.

And the height then? Good, it is three centimetres.

You've got more to say? What? You know the volume? Nice.

What's the volume? Good, it's three times six times four.

Six times four is 24.

24 times three? Good, I believe it's 72 centimetres cubed.

Excellent.

Well done if you've got more things written down as well.

Okay.

So that was a net of a prism and that prism was called a cuboid.

It's a rectangular prism.

Now here are some more net examples.

So we've got our rectangular prism there.

I wonder if you know what this one is.

So this is actually a trapezoidal prism.

It looks like that because it has a trapezium at the front.

And this one here is actually a triangular prism.

So it looks like this, right angled even, and like that.

So non-examples here is a pyramid, is the one of the left of the non-examples, a cylinder is this one Wait, are cylinders not prism.

Oh yeah.

Do you remember why? Because it has a circle face and prisms have polygon as the identical faces.

So polygon must have straight sides and a prism has a polygon straight side as identical face on either side.

And so a cylinder is not prism.

And finally this one here is a tetrahedron.

Do you notice anything about the prism nets? What do they all have in common? Hm.

They all have quite a few rectangles, don't they? This one's got three.

This one's got one, two, three, four, and that one's got six, doesn't it? 'Cause it's a cuboid.

They all have multiple.

Now these, at most they have one.

Interesting.

Okay.

So here is an example of a trapezoidal prism.

Okay? So it's like fun stems from the name trapezium because the front face and back face is identical polygons make the trapezium, opposite trapeziums, and we can see that the vertices here do have a straight line segment between them.

Okay? So let's open up and see how it's done.

So we can see this top rectangle here kind of opens up first and then the front goes forward.

The back goes towards like backwards and the right hand side goes down.

So you can see how it opens up to form our net.

And there's one, two, three, four rectangles here.

So let's see what happens as our length change.

Let's change AB.

So that's going to kind of make that trapezium a bit squished.

We can see actually how it doesn't affect.

it effects this rectangle and this rectangle length, but it doesn't change these.

What about if we change the length EF, this here? I wonder if other lengths would change.

Ah, so when we make it smaller, this also becomes small 'cause this is attached to here.

So EA is related to AE, HG here is related to the HG here.

There we can see how that works and there's lots of different things we can do to explore.

If you want to explore as well, go on to GeoGebra and you can Google trapezium net, trapezium prism net, or trapezoidal prism net and you'll be able to explore this as well.

Okay.

So there's one question about sketching a net, two, about actually drawing a labelled net.

So if you've got a ruler, fantastic, otherwise just label what every single side will be.

And three, sketch the 3D shape this net creates.

So I kind of showed a bit how I would sketch a shape so maybe just sketch that front face and think about how it goes backwards, but have a little go.

Okay.

So hoping you had a good go at those questions.

I'm now going to go through some answers.

So to sketch a net for this shape, now I would see that.

So if this is my front and that's my back, so I know I'm going to have kind of a triangle here and a triangle here, and then there's this rectangle which is the base here.

So that's kind of this part in between the base.

And now this slanted right-hand side, that goes down this way.

That would be here and this length and this length would match up.

Whoops, those two lengths.

Base.

And then you've got kind of that left-hand side rectangle there.

So my drawing is horrendous.

So let's actually just show you a better one.

There you go.

Not my ones.

So there you have a net.

Now to draw accurately labelled net of the cuboid.

Now I've just got a generic net of a cuboid here.

So this is the base.

And so that's this bottom bit here.

This is the top.

So the base, there's a top is here.

This is the front.

So that's this part 'cause it kind of bends off the edge of the base.

The left-hand side, right-hand side.

So this is this bit.

Oops.

Right-hand side so that's the front so that means this bit is the back.

Okay.

So what lengths do we know? Let's do this in green.

So the top is six by four.

So we can do six centimetres here by four centimetres.

The right hand side is five by four.

So five centimetres by four centimetres.

Are those the right ones? So five centimetres away from the base.

Yeah, that's right.

The bottom, the back side.

Ah, so this six centimetres is the same so I can write up here if it's easier.

And the left-hand side, the same, five centimetres, four centimetres.

Have I missed any sides? So the back is the same as the front.

So it has a height of five centimetres here.

And this is five centimetres by six centimetres.

The base is six centimetres by four centimetres.

Hopefully that's all of the ones that hopefully got the same.

Okay, it's a sketch in the 3D net this shape creates.

Sorry, 3D shape this net creates.

So I'd start by actually sketching these two faces or at least one of them.

So the front one normally.

So it's like that, so it's a pentagon and then I would just extend it backwards.

And then add it like this.

So if we were going to add dimensions, so the height is four centimetres, so I can just write height here, four centimetres, and the length here is the 10 centimetres.

Well done if you've got that right.

Okay.

So I want to know how many ways can these groups of rectangles be arranged to make the net of a cuboid? Now there's some support on the next slide, but if you think, "Oh, I know how to do this," you go ahead and have a go.

Okay.

So for some support, I've actually just put an outline of a generic cuboid.

So if you have a generic cuboid net, and then what you want to do is like we did in the last independent task, you actually just label different lengths.

So for example, I might decide, and it doesn't matter, this is not to scale in any way, but I might say, "Oh, I want this one to be six centimetres and this one to be six centimetres." So I'm using this one.

I know that the opposite one needs to be the same.

So I've used these two.

Okay? And that's the way to think about which ones are equal.

This one must be equal to this.

Which other ones are equal? Good.

This.

Every front has a base and the top one and this one and this one.

And then you're thinking, then that means which sides must be equal to each other.

So you might have saw a little bit in the independent task, this length, and this length must be equal.

So if this is six, this one must also be six centimetres.

Okay.

You can try and finish up this one, but I'm going to stop there.

Pause it and have a go.

See how many different ways these groups of rectangles can be arranged to make the net of the cuboids.

So don't stop at one.

Keep going.

Try and get two, maybe even three.

Okay.

So I already started with some ideas.

So let me go from the support.

I did this six centimetre and this as six centimetres, which means this one must be six centimetres.

And this one must be six centimetres.

Luckily this one and this one are opposite each other and equal so they need to be the same.

So that means this one could be eight centimetres.

So I've used this six and eight, is that there? Yeah.

I've used these two.

And then this must be six centimetres.

I could even, there's two more, six and eight.

So let's have actually six centimetres, eight centimetres.

And that means this is eight centimetres.

That's six centimetres and that's eight centimetres.

Does this work? Yeah? These match up.

Yep.

And also this one and this must match up.

So they match up as well.

Yeah, it works out.

Okay.

Let's use some different ones.

So we're at five.

So this is five centimetres and this is five centimetre.

Remember not to scale.

That would really be a square but it's fine.

And this is five centimetres 'cause they are opposite each other.

So that means, do we have any five centimetre? Yes, five centimetres, so this one could be eight centimetres then.

And this one must be eight centimetres here and.

Oh, it must be five centimetres here.

Do we have enough for that? Yes we do.

Okay.

So this one's quite similar to the other one as in the two ends are squares and all the other rectangles are equal.

Can we get a different one? Do you have different ones? Hmm.

Let me try.

With this one being six centimetres and this one we have five centimetres.

So no, this is five centimetres.

Let's have this as eight centimetres.

Ah, 'cause now that means this side is not the same.

It's not five, it's six centimetres and this one must be eight.

So here we do have a difference.

So when we have rectangle ends rather than squares, we use different rectangles.

And my length is right? No, this should be five centimetres and this is eight centimetres.

Six centimetres and five centimetres.

Well then, if you've got different answers, maybe you've got another set.

Do check carefully.

So remember that certain ones, for example, this length, let me highlight it.

You just check for yours that this length and this length are the same.

And also can you check that this length matches up to this length and then all the ones along the middle here, these must all be equal as well and the ones going across.

So this length, this length, and this length must all be equal as well.

So do check carefully.

And opposite faces.

A lot of things to check, but hopefully you got it right.

Excellent work today, everyone.

Hope you remember the key points and remember the examples and non-examples and how to name prisms as well.

It'd be really great if you do the exit quiz.

Make sure you do that and that will really test your knowledge and check your understanding.

And I would love to see your work.