Lesson video

Hi everyone, thank you for joining me.

My name is Ms Jeremy and today's math lesson is all about problem solving using 2-D representations of 3-D shapes.

So find yourself a nice quiet spot ready for your learning, and then press play once you're ready to begin the lesson.

Let's start with our lesson agenda for today.

We're going to begin with a warm up where we'll recap the 3-D vocabulary that we've been looking at.

We're then going to see how we might represent 3-D shapes using 2-D representations.

We'll introduce the problem that you're going to be solving today and then we'll develop that in our developed learning, before your independent task and quiz at the end of the lesson.

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

Feel free to get those resources ready now pause the video and then resume once you're ready.

So let's start with our warm up.

Let's have a look at our 3-D shape vocabulary.

We've been be having a look at this recently.

And we've been looking at the different ways that we use for capillary to describe 3-D shapes.

Let's say these words together.

My turn, your turn.

Face, your turn.

My turn, edge, vertex, vertices, apex.

Spend a bit of time now and pause video if you'd like to match up each of those purple words that we use to describe 3-D shapes with one of the definitions on the right hand side.

Okay, let's have a look together.

So let's have a look of what a face might be first of all.

Well a face is a flat or curved surface on a 3-D shape.

It describes the surfaces that you see on 3-D shapes like cubes, cuboids, triangular prisms. And on shapes like cubes, the surfaces are all flat, whereas in shapes, like sills or cylinders or cones, you can see some curved surfaces outward.

So now let's look at what edges are.

What an edge of a 3-D shape is the area where two faces meet on that 3-D shape.

And a vertex is the corner.

So a vertex is a corner where edges meet.

If you have more than one vertex, we would refer to that as vertices.

So the vertices are the corners.

And the apex, there's just one apex per 3-D shape.

And some 3-D shapes don't even have an apex.

The apex is the vertex at the very top of the shape, and it is opposite the base.

How did you get on with that terminology? Did you manage to match each of those? Let's use some of the terminology that we can use describing that.

To describe the shape that you can see on your screen.

First of all, can you tell me the name of the yellow shape and the purple shape, maybe three seconds to see if you can remember them.

So you might remember that the yellow shape here we would refer to you as a cuboid.

It is made up of faces which are either rectangular or square, but you have to have at least a few rectangular sides or faces on a cuboid in order for it to be a cuboid not cube.

And here we have a cone, and a cone is made up of one flat face and a curved face as well.

So what I'd like to do is use the same vocabulary to describe and label these shapes.

How would you label the different parts of these shapes? Pause the video now and use your finger to point to the different parts of the shapes and use your words to label them.

So point to the face, point your vertex, point to an apex if there is one on the shape.

Pause the video now to do your labelling and then resume it to see how we might label them together.

Okay, so I'm going to start by pointing to a face on both of these shapes.

This here is a face of the cuboid, and this is the face here of the cone.

I'm pointing to the curb face on the cone and the flat face on the cuboid.

I could also point to a flat face on the cone which is the base of the cone there.

Now looking at the edge, well, an edge, and I'm going to highlight it with the pink here.

An edge is where two faces meet.

So that is an edge there.

And we've got an edge just here on our cone.

And then we've got vertices, which are these points here.

And vertices on the cone where we only have one vertex here, which also is the apex because it's opposite the bases of the very top.

These are vertices.

And if I was referring to just one of them, I would say it was a vertex just like that.

So for the next part of the lesson we're going to be talking about 2-D representation of 3-D shapes.

So you can see here on the screen, on the left hand side, we've got a 3-D shape.

What would you call that 3-D shape if you had to name it? Well I'll call it a cuboid and I know that it's a cuboid because it's made up of faces that are rectangular.

I have got two square faces, one there and one there.

But the rest of the faces the four other faces around the cuboid are rectangular meaning it's a cuboid rather than a cube.

If I just had one of those tins, I would call that a cube.

So if I was to draw, if I were to draw this shape and I wanted to draw it on a flat surface as a 2-D representation, I would have to have four cubes in a row.

So I'm going to draw it on my square piece of paper here.

So I've got one, two, three, four.

Nice and simple.

That is the 2-D representation of my 3-D shape.

Now I need to remember that it's 3-D and rather than it just being four squares in a row, it's a 3-D shape.

If I wanted to, I could extend the top part of my shape and extend this out here to demonstrate that it's 3-D rather than 2-D so you could do this if you wanted to.

However, today we're just looking representing our 3-D shapes in a 2-D format.

We need to remember that these 3-D shapes are 3-D.

And even though we're drawing them on a flat surface, we need to remind ourselves they are three dimensional.

What I'd like you to do is to represent this shape, using a flat 2-D format.

How could we draw this shape on our squared grid using a flat 2-D format? Pause the video now to draw this out and then resume it once you're finished.

So if I were to represent this, I can see that there have been four cubes that have been used to create the shape.

So I'm going to use four cubes and I'm going to do this I'm going to use four squares to represent my four cubes.

I've got one there.

That's my square number one to represent cube number one.

I've got square two to represent cube two.

Square three is going to go here because it's next door it's on the right of cube two.

And then I've got square four just up here to represent cube number four.

That is my 2-D representation of the 3-D shape.

Did you get that one as well? So let's use our understanding of 2-D representations of 3-D shapes to introduce themselves this problem.

We've got letter here from a group of four house who have a bit of an issue that they would like you to solve.

It says, "Dear pupils, we wondered whether you could design us some homes.

Each home should be made out of four cubes.

And we would like 12 different homes designed.

Many thanks, Nevile Lucy, Simon, and Flo." Those are the names of the houses at that was bottom.

So these house would like some different bird homes designed, but the catch is this you can only use four cubes to design the homes.

And you've got to create 12 different designs.

You've got to decide what homes are going to look like.

And then you've got to decide how much they're going to cost.

Let me provide you with a bit more detail here.

So for every one square of land used, there will be a cost of 36 pounds.

So when the home rests on one square of land, you have to pay 36 pounds.

If the home were to rest on two squares of land, how much would you be paying? You'd be paying 72 pounds, 36 times two.

So you have to think about that.

But also there's an extra cost because for every cube face exposed and the word exposed means shown.

So for every cube face that you can see, the paint for that cube face will cost seven pounds.

So lots of math that we need to think about, we're going to be thinking about how we're representing our shapes using 2-D representations.

But we're also going to be thinking about the cost of the land and the cost of the paint for these house.

So let me demonstrate using this shape that we had to look at previously.

Remember when we were drawing the shape out, we represented it like this.

We had our cubes, our squares representing our cubes, and it looked a little bit like this.

That is how you're going to be drawing your shape today.

You're going to be drawing 2-D representations, of the 3-D shapes.

Now looking at the 3-D blue shape that we can see let's first of all work out how many squares of land are used for the shape? What if I think about the land here, I'm going to draw some grass so you can see where the land is.

This is the grass here, apologies that it's in pink rather than green.

And you can see it's resting on one square.

So one square is resting.

One cube square that is resting on the ground.

That means that's going to cost us 36 pounds.

So I'm going to write one square and equals 36 pounds.

So that's good, that's the minimum amount of money that we'd have to pay.

If all of our squares all four squares were resting on the ground and it is a long cuboid that was resting horizontally, we'd be doing 36 times four.

That'd be a much more expensive cost.

That would be the highest cost we could have.

So this is the cheapest cost, which is great.

Now for every cube base exposed the paint will cost seven pounds.

So we've got to work out how many cube faces are shown exposed here? Let's have a look, let me show them in as we go.

So I'm going to start with the ones that we can see.

I've got one, two, three, four, then I've got five.

I've got one under here, which I can't see, but I know it's there, six, seven, eight, nine, one just there 10, 11, another one that I can't really see very clearly 12, 13, and then I've also got the ones around the back.

So I've got four around the back as well.

So the 13 plus four is equal to 17.

So you can see that I've had to work out how many cubes faces there are outwardly facing the kind of area that the home is going to be.

And at this stage, there are 17 cube faces.

Now each cube face is going to cost seven pounds to paint.

I've got 17 of them.

What will my calculation be? I'm going to have to do 17 multiplied by seven to work out the cost.

So 17 times seven, partition out your 17 into 10 and seven, do 10 times seven there and then seven times seven and see if you can add those together in your head.

I'm going to give you five seconds to have a go.

Okay, so you should have seen that seven, 10 times seven was equal to 70.

Seven times seven is equal to 49, 70 plus 49 is equal to 119 pound.

Good is me look at all of that cost, just the paint, just to paint the bird house.

So now we've got to work out the total cost.

So I need to do 119 pounds plus 36 pounds to work out the total cost.

How would I do that? Well, I'm going to use a compensation method around an adjust compensation method because 119 is very close to 120.

So I just pretend that's 120 for the moment and round it up by one pound later on I'll need to adjust for that and take off that one pound.

But for the moment, I'm going to say that that's 120 plus 36.

So 120 plus 36 is equal to 156.

I'm going to adjust for that one pound again.

So my total cost is 155 pounds.

So that home in order to build that home for those house, we would be paying 155 pounds, pretty pricey.

So now it's your turn.

Let's have a look at this home here.

You've got the home that we have represented using a 3-D shape in blue there.

What I'd like you to do first is to represent that home using a 2-D representation just like I did.

Then I'd like you to work out the number of squares of land used and the total cost.

Remember that one square of land costs 36 pounds.

And then I want you to work out the number of cube faces exposed, remembering that one cube face exposed will cost seven pounds to paint.

So how about go at that.

Pause the video now to complete this and then resume it once you're finished.

Can you find the total cost for this bird house to be built? Okay, let's have a look at this together.

So I'm going to just start with my 2-D representation.

So here, I'm going to have my four squares representing my four cubes.

One, two, three, four.

That's my 2-D representation.

Now let's look at the number of squares of land used.

So you should have seen that there was actually just one square of land used just like last time.

So that is going to cost us 36 pounds.

So again, nice and cheap or the cheapest it could have been.

Now let's worked out the number of cube faces exposed.

So let's start with the ones that we can see.

I've got one, two, three, four, five, six, seven, eight, one at the top nine, and then the four at the back, which I can't see 10, 11, 12, 13, and the four on the side, 14, 15, 16, 17.

So there are 17 cube faces exposed.

Now we've already created the calculation for this because we need to do 17 multiplied by seven.

So we should have seen that this would be 119 pounds, and that takes our total cost.

Remembering again, that we're doing 119 plus 36, that should have given you 155 pounds.

So exactly the same cost as our previous shape, even though it was completely different in design.

Really interesting.

So let's move to your independent task.

You're going to, we've created two different birdhouses now.

The one that we did together, the one that you did independently.

Now I'd like you to create a 10 further bird house designs.

They can look, however you would like.

Remember you're only using four cubes and you're representing them using a 2-D shape.

So you might have, for example, one of your designs looks like this.

Like almost like a cuboid itself.

You might have one that is, as we spoke about earlier, a horizontal cuboid.

You might have one that has two at the base, and then one here, and then another one at the base here if you want to, it's your designs, you decide what you want these bird houses to look like.

But remembering you're only using four cubes each time.

Once you've designed each of your designs using your 2-D representation, you need to work out how much they're going to cost.

Remembering that one square land is going to cost you 36 pounds and reminding yourself that one cube face exposed for painting is going to cost seven pounds.

So the same way that we've worked it out the calculations, you need to do the same thing for all 10 of your designs.

And then have a think about which design is the cheapest, and which design is the most expensive.

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

how did you get home with your bird house design? It would be so lovely to see some of them today.

So if you'd like to please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Now it's time to complete the quiz.

Thank you so much for joining us for our math lesson today.

It's been great to have you do join us again soon, bye bye.