# Lesson video

In progress...

Hi, everyone.

Thank you for joining me.

My name is Ms. Jeremy and today's math lesson is all about identifying the properties of 3-D shapes.

Let's start by looking at our lesson agenda.

For our warm up today, we're going to be completing a spot-the-difference task with some of the 3-D shapes that we've been looking at recently.

We'll then introduce new 3-D shapes before sorting 3-D shapes into different categories.

For your independent task today and quiz, we'll be looking at how we can organise and sort 3-D shapes according to their general properties.

For today's lesson, all you'll need is a pencil and some paper and a nice quiet space.

Feel free to pause the video now to find these resources and then once you're ready, press play to begin the rest of the lesson.

A warm up is all about spotting the difference.

So 3-D shapes often have some similarities and of course, some differences as well.

Let's have a look at the shapes on the screen here.

We've got a cube, a cuboid, a cone, and a cylinder.

And our question asks, what is the difference between a cube and a cuboid and how are cones and cylinders alike? We've got two different questions.

I'd like you to have a look at your cube and the cuboid on the screen.

So as you might've noticed, the cube and the cuboid are quite similar in that they have the same number of faces, the same number of vertices and the same number of edges.

However, the main difference they have is that the faces of the cube are always all square.

Whereas the faces of a cuboid are most often rectangular.

They're rectangles with one side that is longer than the other.

Sometimes cuboids will have two faces which are square and the rest will be rectangular, but a square, a cube, sorry, always has all of its faces which are square.

And that means all of the edges on a cube are exactly the same length.

That can't be said for cuboid, which will have edges that are different lengths.

Now looking at the cone and the cylinder, how are these shapes similar? How are they alike? Spend some time having a think about this.

I'm going to give you 10 seconds.

So whilst the shapes look quite different, they are similar in that they both have a curved face.

As you can see, the cone has one flat face, which is this face here at the bottom.

It's a circular, flat face or flat surface.

And then the curved surface is the surface that goes all the way around the rest of the shape.

In the same way, a cylinder has one curved surface which goes around the edge.

If we remember back to my candle holder here, you can see we've got one flat surface, or we've got a flat surface at the bottom here and cylinders also have a flat surface at the top.

And then there is a curved surface all the way around.

So the similarity between a cone and a cylinder is that they both have one curved face.

Let's now look at these shapes here.

Using the language that we were introduced to before, can we describe the properties of these shapes? So we've got the word face, edge, vertex, and then the plural of vertex is vertices.

Choose one of the shapes on the screen.

We'll call them shape A, B, C, and D.

Can you describe those shapes using that language? If you'd like to maybe start with a slightly easier shape, start with shape A.

If you want to give yourself a big challenge, move to shape B instead.

Okay.

Let's have a look at some of the language that we've touched on.

So remember face is either a flat or curved surface of a 3-D shape.

Now in the case of shape A which is a triangular prism, we have got a series of different faces.

We have two triangular faces, one at the front of the shape and one at the back of the shape there and then we've got three rectangular faces.

So overall we have five faces.

Find the vertices.

Let me circle them.

We've got one, two, three, four, five, six vertices there.

We don't have a specific apex.

Remembering an apex is the very top vertex of a shape that is usually opposite the base.

And in this case, we do not have an apex.

Looking at shape B now, to give us a little bit of a challenge.

How many faces do you think shape B has? Well, let's have a look.

I can see that at the very top and the very bottom of the shape, we have got this face here, which we could describe as a hexagon if it was a 2D shape.

A hexagon has six sides.

So we've got a hexagon there.

We've got another face at the bottom, which forms the base here or the other side of the 3-D shape.

So there's two faces there.

And then we've got six faces going all the way around the edge.

One for each of the sides of the hexagon.

So we've got six plus two, which is equal to eight.

We've got eight faces on the shape.

In terms of the number of edges, well let's have a look.

We've got one, two, these are all the straight edges going down, three, four, five, six.

And we know that sounds about right because it's going to have six sides.

And then we've got six edges for this hexagon and six edges for this hexagon.

So we've got six plus six plus six.

That's equal to 18 edges.

That's have a look at the vertices.

I'm going to circle them.

This time, I'll try and circle them in a different colour so that you can see them really nice and clearly.

So in red, let's have a go.

We've got one, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

And that makes sense as well, because we've got a vertex for each of those corner points on our 2D hexagonal shape.

So we've got 12 vertices and no specific apex.

In shapes C and D, we can see we've got apexes just at the top here.

These are opposite the base.

These are the top vertices.

So now that we've understood a little bit more about the terminology that we might use to describe 3-D shapes, let's think about how we could use these properties to sort 3-D shapes into categories.

I've got two circles on my screen here, and that's going to be used to sort out the shapes that are on my right.

I'm going to call these shapes shape A, B, C, D, E, and F.

And what I'd like to do is to create two different categories which I could put these shapes into.

So how am I going to think about which properties we might use? We might think about properties related to the number of faces that the shape has.

Maybe it will have something to do with the vertices, or maybe it will have something to do with the edges of the shape.

Let me show you an example.

I'd like to start with an example where we look at the number of faces the shape has.

Let's say the everything that goes into the first circle is going to be 3-D shapes that have.

Less than seven faces.

And then on the right, we will have shapes that have seven or more faces.

So any shape that has less than seven faces goes into the left circle, any shape that has seven or more faces goes into the right circle.

So looking at shape A, how many faces does shape A have? Can you see? So you should see that it's got eight faces.

This is a hexagonal prism and it's got eight faces so it's going to have to go in this side here.

So I going to put A in there.

B is what we would call a triangular-based pyramid or a tetrahedron, and it's only got four faces.

So it's going to go into this left hand circle just here.

For shape C, how many faces does shape C have? So you should see that it has six faces.

It's got five of its faces, which are the triangles, and then one base face, which is a pentagon.

And so in this case, it has six.

So it's going to go in here.

Shape D.

How many did it have? I'll give you a couple of seconds.

So hopefully you can see it's got seven faces.

So it's going to go to this circle here.

Shape E is a triangular prism.

How many faces does it have? It's got five.

So it's going to go into this circle here.

And shape F, which one? Which of these circles do you think shape F will fit into? It's got seven, so it's going to go just in here.

So you can see that we've managed to separate out these shapes into two different categories according to the number of faces that they have.

So I'd like you to do exactly the same thing.

So here are your labels, A, B, C, D, E, and F.

I would like you to take some time now to find two different categories that you could sort these shapes into.

I sorted them according to categories related to the number of faces they have.

Could you try and use something related to the number of vertices or the number of edges that they have? Spend a bit of time creating your different categories and sorting your shapes.

Pause the video to complete your task and resume it once you're finished.

So how good did you get on with your activity? Did you manage to find two different categories to sort your shapes into? Hopefully that was all fine for you.

Okay.

So let's move on slightly.

Let's have a look at some similarities and differences between these shapes that we're talking about here.

Let's first of all look at the shapes that we have on the screen.

So firstly, this shape here is called a cuboid.

It is made up of typically rectangular faces.

We have just here, a triangular prism which is made up of faces that are either rectangles and faces that are triangles.

So this is a triangular prism.

And the final shape here is also a prism of some kind, but it has, if you look, three, four, five, six sides for one of the 2D shapes at the top and the bottom, and it's a hexagonal prism.

And we call it a hexagonal prism because it's got hexagons on either side of the 3-D shape.

So it's a hexagonal prism.

I want you to have a good look at these shapes.

Now they're all different and we know they have different names, but can you see any similarities between them? What is the same about them? I'm going to give you 10 seconds to see if you can spot anything.

So you might have seen lots of different similarities between these shapes.

You might've noticed that they all have more than five vertices.

You might have noticed that all of these shapes have straight lines as a part of their edges.

You might have noticed that their faces are all flat, rather than curved.

There are lots of similarities you could have found.

Did you notice that every single one of these shapes makes use of a rectangular face, at least one rectangular face? In the case of the cuboid, we have got six rectangular faces with this particular shape.

How many rectangular faces does the triangular prism have? It has three rectangular faces and also got to triangular faces.

And how many rectangular faces does the hexagonal prism have? It has six rectangular faces.

So one of the similarities between these three shapes, is that they all make use of a face that is rectangular.

And you might notice that lots of shapes and specifically lots of prisms make use of faces that are rectangular.

If you just need to have a quick peek at what the rectangular face looks like, that is one of them that I've highlighted just there for you.

That is one of the rectangular faces.

On the triangular prism, this is one of the rectangular faces.

And on the cuboid, this is one of the rectangular faces.

Obviously they've been drawn out on a piece of paper so you can't see their 3-D, their full 3-D format using shape, but you can see that the faces that have been used, some of them are rectangles, which is something that's similar between all of these shapes.

You are going to be finding similarities between the shapes that you can see on the screen.

We've looked at all of these shapes in some format or another today.

What I'd like you to do is see whether you can create a really long chain of polyhedral 3-D shapes where each shape is linked to the next one with one similar face.

So using what we've just spoken about there, I could link my cuboid to my triangular prism and then link my triangular prism to my hexagonal prism, all because they use rectangular faces, at least one similar face.

If I wanted to, however, what I could also do is link my cuboid to my triangular prism because of the rectangles, but then link my triangular prism to my square-based pyramid, because both of them make use of a triangle.

So you can see they've both got a similar face.

You need to try and create a long, long chain, try and use if you can, every single one of those shapes.

I'm not sure whether it's possible so let me know if you do manage to do it.

Can you create the longest chain possible linking each of the 3-D shapes in your chain with at least one similar face each time? Have a go at doing that now.

Pause the video to complete your task and resume it once you're finished.

How did you get on with the activity? Hopefully you've managed to create as long chain as possible.

If you'd like to, you can share it with us.