Lesson video

Hello there.

You made a great choice with today's lesson.

It's gonna be a good 'un.

My name is Dr.

Rowlandson, and I'm gonna be supporting you through it.

Let's get started.

Welcome to today's lesson from the unit of Plans and Elevations.

This lesson is called "Drawing the Plan and Elevations of a Solid".

And by the end of today's lesson, we'll be able to draw the plan and elevations of a solid.

This lesson will introduce three new keywords.

One of these keywords is plan.

The plan of a solid is the view of it from above.

Another keyword is front elevation.

The front elevation of a solid is the view of it from the front.

And the third keyword is side elevation.

The side elevation of a solid is the view of it from the side.

We'll see plenty of examples of these all the way through today's lesson.

This lesson is broken into two learning cycles.

In the first learning cycle, we're going to be matching points of view to faces of a solid.

In other words, identifying which shape is the plan, the front elevation and the side elevation.

And then the second part of today's lesson, we're going to be drawing those.

We're going to be drawing perspectives of a solid.

Let's start off with matching points of view to faces of solids.

Here we have Aisha, Jacob, Sam, and Laura who are all looking at a pencil sharpener from different points of view.

Let's take a look at what each person can see.

Aisha says, "I'm looking at it from above," and this is what Aisha can see.

Jacob says, "I'm looking at it from the side," and this is what Jacob can see.

Sam says, "I'm looking at it from the front," and this is what Sam can see.

And finally Laura says, "I'm looking at it from a position that allows me to see three faces at once." And this is what Laura can see.

A solid may be represented in two dimensions in different ways, depending on which point of view is being presented.

For example, some points of view allow you to see multiple faces of a solid at once, like this point of view here.

We can see three faces.

However, one problem with this perspective here is that the faces look a little bit distorted.

We know that each face is a rectangle, but if you traced over this, each face would look more like a parallelogram or even trapezium.

And as things are further away, they appear smaller.

With other points of view, you only see a single face at once, like with these points of view here.

But what we can see with these points of view is that it's much clearer that each one is a rectangle or maybe a square.

We can see the right angles more visibly as well when we look at just one face at a time.

When looking at a single face of a solid, each point of view allows you to see a different face.

And these points of view have different names.

The plan is the view from above, and this is what you would see if you looked at the pencil sharpener from above.

You'd see this rectangle or rectangleish-looking shape here.

The front elevation is the view from the front, and this is what you would see from this position.

And the side elevation is the view from the side, and this is what you would see from this position.

Each point of view of a solid can be identified by the shapes seen and their lengths.

For example, here we have a cuboid, which is four units by three units by two units.

And what you need to do, or what we need to do, is determine which rectangle is the front elevation, which one is the side elevation, and which one is the plan for the cuboid from the rectangles at the bottom.

Perhaps pause the video while you think about how we might go about doing this and press Play when you're ready to continue.

Let's take a look at this by first looking at the shape of each one, which we can see as a rectangle, but then by looking at the lengths of each one.

If we start off with this first rectangle, we can see that it's four units by two units.

Which face on the cuboid is four units by two units? It would be this one here.

So this rectangle must be the front elevation.

Now let's look at the next rectangle.

This is three units by four units.

What we may need to bear in mind when it comes to a cuboid is that all edges that are parallel to each other are the same length.

So when it comes to finding a face, which is three units by four units, we can bear that in mind and we can find it here.

This one is three units by four units, and it's the top of the cuboid.

So this must be the view from above, which is the plan.

And then the side elevation is this one here, it's the only one which is left, but we can also double check it.

It's two units by three units.

That must be this face here, the side elevation.

Now in this example, we can see both lengths on each rectangle, but may not always be the case.

The viewpoint can be identified even when some lengths are unknown, so long as there is enough information given to us.

For example, here we have another cuboid, and it's from a slightly different perspective this time.

Let's determine which rectangle is the front elevation, the side elevation, and the plan for this cuboid.

Pause the video while you think about this, and press Play when you're ready to continue together.

Let's do it together now.

And let's start off with a rectangle where we have both of the lengths, three units by four units, and identify that one first on the cuboid.

It's this face here, it's four units along and it's three units up.

That must be the side elevation.

Now we've identified that one, we can take that one off and we know that neither of the other two rectangles will be the side elevation.

It narrows down our options.

So then with the next one, which has a length of three units on it, we can look at the cuboid and remember that all edges which are parallel are the same length.

Now we've already used one of the faces, which is three units by four units.

This one must be three units by six units, which would be this face here, the front elevation.

And then the third rectangle, well, we only have one option left.

That would be the plan, but we can double check it anyway.

We can see that it's four units along and it's six units across.

So yes, it must be the plan.

Here we have Alex who is considering what the front elevation, side elevation, and plan would look like for the cone, which we can see here.

The cone has a radius of three centimetres and a height of eight centimetres.

Pause the video while you think about what you think these might look like yourself, and then press Play when you're ready to continue together.

Let's see what Alex says.

Alex says, "If you looked directly from above at this cone, then you would see a circle.

So, the plan view would be a circle with a radius of three centimetres." That would look a bit like this.

The point in the centre of the circle marks the centre of the circle, but it also shows the point, which is the tip of the cone.

And then he says, "Looking at it from the front, you would see a triangle.

The base of the triangle will be double the radius of the circle." Because, remember, the radius goes from the centre of the circle to the edge.

The triangle would go from one side of the circle to the other, so the front elevation would look something like this, six centimetres by eight centimetres.

Then the side elevation, well, the view from the side would be the same as the view from the front, 'cause the cone's the same all the way around, so the side elevation would look something a bit like this as well.

Let's check what we've learned.

Here, we have a cuboid, and we have three rectangles.

Which rectangle shows the front elevation of the cuboid? Is it A, B or C? Pause the video while you choose, and press Play when you're ready for an answer.

The answer is A.

That's because it's five units by three units, and so it's the front elevation.

Which rectangle shows the plan view of the cuboid? Pause the video while you choose, and press Play when you're ready for an answer.

The answer is C.

The plan view would be a rectangle, which is five units by six units.

Here we have a cylinder.

What shape would the side elevation of this cylinder be? Would it be A, a circle, B, a parallelogram, C, a rectangle, or D, a trapezium? Pause the video while you choose, and press Play when you're ready for an answer.

The answer is C, a rectangle.

Okay, it's all to you now for task A.

This task contains two questions, and here is question one.

Each question shows a solid along with its plan, its front elevation and its side elevation, but you're not told which one's which.

That's what you need to do.

Write either plan, front elevation, or side elevation next to each 2D shape.

Pause the video while you do this, and press Play when you're ready for question two.

And here's question two.

We have four cuboids, and each cuboid has three points of view, which is shown by the arrows labelled A to L.

Also, we have a grid with lots of rectangles joined together on the left.

Let's see how these match together.

Question two says, all but one of the rectangles on the grid match a viewpoint of one of the cuboids.

What you need to do is write the letters A to L inside the rectangles, and put across in the rectangle that does not match any of the letters.

Pause the video while you do this, and press Play when you're ready for answers.

Let's take a look at some answers.

For question one, we need to write either plan, front elevation or side elevation next to each 2D shape.

For part A, this will be the front elevation, this will be the side elevation, and this will be the plan.

For part B, the first one would be the plan, the second would be the front elevation, and the third would be the side elevation.

And for part C, the first shape would be the plan.

The second and third shapes, well, either of them could be either the front elevation or the side elevation, so you could have either way round for those.

And then for question two, we need to write the letters A to L inside each of the rectangles.

And remember that each time we do one, we have fewer rectangles left to choose from.

Let's do this together.

For the first cuboid, we can see that A, B, and C go on these rectangles here.

For the second cuboid, D, E, and F go on these rectangles.

For the third cuboid, G, H, and I go on these rectangles.

And then for the fourth cuboid, J, K, and L go on these ones and that leaves one rectangle left.

It's that one-by-one square, which we can put a cross in.

Okay, so far so good.

Now let's move on to the second part of today's lesson, which is drawing perspectives of a solid.

The front elevation, side elevation, and plan of a solid can be drawn based on the shapes that will be seen from each point of view.

For example, here we have a cuboid, so from each point of view we'll see a rectangle, but we also need to know the lengths.

The lengths of the shapes for the front elevation, side elevation and plan can be obtained from the lengths presented on the solid.

Here the lengths are presented explicitly, but a solid may also be presented on isometric paper.

In this case, the lengths can be obtained from the gridlines.

Let's do this one together.

On a centimetre square grid, draw the front elevation, side elevation, and plan for the cuboid.

We're going to work through this together in a moment, but perhaps pause the video and think about what steps you might take in order to do that.

What things might we need to think about along the way, and then press Play when you're ready to continue together.

Let's now do this together.

And let's start off with the front elevation.

We can see that the front elevation would be a rectangle, which is one centimetre across and two centimetres up, so let's draw that rectangle.

It would look like this.

The side elevation, we'll be able to see this face, which is a rectangle, which is three centimetres across and two centimetres up.

If we draw that, it looks like this, and then if we look at it from above for its plan view, we would see a rectangle, which is three centimetres along and one centimetre across.

It would look something a bit like this.

Here's one for you to try.

On a centimetre square grid, draw the front elevation, side elevation, and plan for this cuboid you can see here.

Pause the video while you do this, and press Play when you're ready to see what the answers should look like.

Here's what your answers should look like.

Your front elevation is four centimetres by three centimetres.

Your side elevation is two centimetres by three centimetres, and your plan is four centimetres by two centimetres.

Here we have a slightly more complex shape.

It is a compound shape constructed with cubes.

On a centimetre square grid, draw the front elevation, side elevation, and plan for this solid.

We're going to do this together shortly, but perhaps pause the video and consider what aspects of this question would make it more difficult than the cuboids we drew earlier.

Why would this be a little bit trickier? And then press play when you're ready to continue.

Well, let's work through this together, and we'll see where those tricky moments are.

Let's start with the front elevation.

If we look at this shape from the front, we'll be able to see two faces.

Each face is a square, and those two faces would appear above each other from our point of view.

It would look something a bit like this.

We know that they are not directly next to each other.

One is further back from the other, but from this perspective, they will just be above each other like we can see.

And then the side elevation, we'll be able to see four squares arranged in an L shape.

It would look something a bit like this.

And then from above for the plan view, we would see three squares.

It would look a bit like this.

Once again, even though those three squares are not all directly next to each other, they would appear like that from above because we wouldn't be able to see the squares that go vertically upwards.

Here we have a solid that's constructed from cuboids.

On plain paper, let's now draw the front elevation, side elevation, and plan for this solid.

Let's do it together.

If we start with the front elevation, we would see these two faces here.

We have a square, which is one centimetre by one centimetre and directly above it we have another square, which is one centimetre by one centimetre.

Also together this would make a rectangle, which is one centimetre and it has a height of two centimetres altogether.

It would look a bit like this.

However, it's not one continuous rectangle.

We would notice the break in between these, so we can draw that break onto our front elevation like this.

And then from the side elevation, we would see a composite rectilinear shape, an L shape.

And then when it comes to the measurements, if we start in the bottom left corner and work our way anti-clockwise around, it would be three centimetres across and two centimetres up.

And then using the back of this shape, we can see it would be one centimetre across going left, one centimetre going down, two centimetres going across again, and one centimetre going down.

It would look something a bit like this, and then the plan view, we would see two faces.

We would see a rectangle that is one centimetre by two centimetres, and down next to it, we would see a square, which is one centimetre by one centimetre.

This would make a rectangle, which is one centimetre by three centimetres, but once again, there'd be a break in this and we can draw that here.

Let's check what we've learned.

On a centimetre square grid, draw the front elevation, the side elevation, and the plan for this solid, which is made from cubes.

Pause the video while you do that, and press Play when you're ready to see what the answer should look like.

And here is what your answer should look like.

Your front elevation should be three squares arranged like so.

Your side elevation and your plan should look the same.

Each of them is four squares arranged in an L shape.

Here's another one to try.

We have a solid which is constructed from cuboids.

And on plain paper, could you please draw the front elevation, the side elevation, and plan for the solid, and label on the lengths as well.

Pause the video while you do this, and press Play when you're ready to see what the answers are.

Here's what your answers should look like.

For your front elevation, you should have what looks like a two by two square with a one by one square cut out at the top right corner.

For the side elevation, you should have two rectangles, one which is one by three centimetres, and above it, a one by one centimetre.

Or you could label it like you can see on the screen here with the two centimetres going upwards instead.

And for the plan, you should have, once again, a compound rectilinear shape in the shape of an L, but it's broken into a square and a rectangle just like the side elevation was.

Okay, it's all to you now for task B.

This task contains three questions, and here is question one.

You have three cuboids, which are presented on isometric paper, and what you need to do is draw the front elevation, the side elevation, and the plan for each cuboid on a centimetre square grid.

The arrow in each case indicates the front of each cuboid.

Pause the video while you do this, and press Play when you're ready for question two.

Here's question two.

You have two shapes which are made from cubes, and what you need to do is draw the front elevation, side elevation and plan for each of these two solids on centimetre square grid.

Once again, the arrows indicate the front of each solid.

Pause the video while you do this, and press play when you're ready for question three.

And here's question three.

Each solid is constructed with cuboids, and what you need to do is draw the front elevation, the side elevation, and the plan for each side on plain paper.

Use a pencil and ruler while you do this, and also label on the lengths after you're done as well.

Pause video while you do this and press Play when you're ready to start looking at some answers.

Let's take a look at some answers.

For question one, for A, your front elevation, side elevation, plan should look like the rectangles you can see here.

For B, they should look like this, and for C, they should look something a bit like this.

Then question two.

For A, your front elevation and side elevation and plan should look like the images you can see on the screen here.

Your front elevation and plan should look the same.

And then for B, the front elevation, side elevation and plan should look like the images we can see now.

One thing which is worth noticing here is even though these two solids are different to each other, the front elevations do look the same.

Can you think why that is? And question three.

With part A, this is what our front elevation, plan, and side elevation should look like.

Hopefully you have the lengths labelled on as well.

They might be labelled in slightly different places, and also hopefully you've shown as well where the breaks would be too.

Then three, part B, this is what our answer should look like.

Our front elevation, plan, and side elevation, with the lengths labelled on and also with the breaks indicated as well.

Fantastic work today.

Now let's summarise what we've learned during this lesson.

A solid may be represented in two dimensions in different ways, depending on which point of view is being presented.

The plan of a solid is the view of it from above, and the front elevation of the solid is the view of it from the front.

The side elevation of a solid is the view of it from its side, and these can be drawn on square grids or they can be drawn on plain paper.

If they're done on plain paper, do make sure you label on any length that you know along the way and use your ruler to help you draw the right angles and also draw the lines accurately as well.

Thank you very much today.

I hope you have a great day.