Lesson video

Hello, my name is Dr.

Rowlandson and I'll be guiding you through today's lesson.

Let's get started.

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

This lesson is called Problem solving with plans and elevations, and by the end of today's lesson we'll be able to use our knowledge of plans and elevations to solve problems. Here are some previous keywords that will be useful during today's lesson, so you might want to pause the video if you want to remind yourself what any of these words mean, and then press play when you're ready to continue.

This lesson is broken into two learning cycles.

To begin with, we'll start by drawing 3D objects to scale, and then we're going to get creative and design our own 3D objects.

Let's start off with drawing 3D objects to scale.

Here we have a photograph of a barn.

Alex wants to make a 2D scale drawing of the barn in this photograph.

He plans to draw its plan and elevations, along with an isometric drawing.

Alex says, "I will need to know some of the actual lengths on the barn." So he obtains these lengths, and here they are.

Let's now use a scale of 1:50 to draw the front elevation of the outline of this building on a centimetre square grid.

Now, we can see that there are windows and doors on the front of this barn, but let's not worry about those.

We just want to focus on the outline of the building.

Alex says, "One centimetre in my drawing represents 50 centimetres, or 0.

5 metres, on the building." So we need to use that in mind when we are calculating how long to draw each line segment in our drawing.

He says, "I'll start by drawing the base and the two vertical edges for the front elevation." The base of the barn is seven metres.

This is 700 centimetres.

So when we divide that by 50, because we're using our scale factor, we get 14.

So the length of the base on our drawing will be 14 centimetres.

Now let's do the vertical edges.

Those vertical edges before it starts to curve are 2.

5 metres on the actual barn.

That is 250 centimetres.

When we divide that by 50, we scale it to 5 centimetres, and the same on the other side as well.

Now we need to do the curved part.

Alex says, "I'll mark the point at the front of the building where the curved roofs meet." So, the curved bits, they do meet above the midpoint of the base of this barn.

And the height of the barn is six metres.

This is 600 centimetres, which when we divide by 50 we get 12.

So we want that point to be 12 centimetres above the midpoint of the base.

We can mark it here.

Alex then says, "Now I'll draw arcs from the top of the walls to this point," like so.

And now we have the front elevation of the barn.

If you look at the photograph of the barn, you can see that the curved roof actually curve outwards again at the bottom of the roof and it sticks out from the sides of the walls.

You could draw those on if you want to, but let's not worry about it for now.

We have the basic outline for this building drawn on our front elevation.

Let's now use a scale factor of 1:50 to draw the side elevation of the outline of the building on this centimetre square grid.

Alex says, "I'll start by drawing the rectangular wall at the bottom." This rectangular wall on the actual barn is 5 metres by 2.

5 metres.

5 metres is equal to 500 centimetres, which when we divide by 50 gives us 10 centimetres for the base of our rectangle.

2.

5 metres is equal to 250 centimetres, which when you divide by 50 gives you 5.

So our vertical height will be five centimetres, and the same on this one as well.

And then we can join up our rectangle, like so.

Alex says, "There are 3.

5 metres from the top of this wall to the top of the building." So we can draw the edge of the top of the building on our diagram by doing 3.

5 metres equals 350 centimetres divided by 50, and we know it needs to be seven centimetres above the last edge we drew.

So that extra line segment we can see there, that's the top of the building.

Alex says, "Even though the roof is curved, this wouldn't show in the side elevation." So, that's the rest of our roof from this point of view.

Let's now use a scale factor of 1:50 to draw the plan for the outline of the building on the centimetre square grid.

Alex says, "The plan view would have the same dimensions as the floor of the building." That would be 14 centimetres on our diagram by 10 centimetres on our diagram.

We've worked these lengths out before and we can complete our rectangle.

Alex says, "I also need to draw the edge where the two curves of the roof meet together," and that is above the midpoint of this line here, which is here.

Let's check what we've learned.

Here we have a picture of a building and its actual measurements.

Sofia is using a scale of 1:500 to draw the front elevation for the outline of the building on a centimetre square grid.

So don't worry about the windows and doors and so on.

How many squares high should her drawing be? Pause the video while you write this down and press play when you're ready for an answer.

The answer is 12 squares.

It would be 12 centimetres in our drawing.

Sofia is using the scale of 1:500 to draw the plan for the outline of the building on a centimetre square grid, so what dimensions should you use for her scaled plan? So what's the length and width of the rectangle? Pause the video while you do this and press play when you're ready for an answer.

The answer is four centimetres by three centimetres.

Use a scale factor of 1:500 to draw the side elevation for the outline of the building on a centimetre square grid, and you can see an arrow pointing where the side elevation would be.

Pause the video while you do this and press play when you're ready for an answer.

And here's what your answer should look like.

It should be 3 centimetres by 12 centimetres.

Let's go back to our photograph of the barn and let's now use a scale of 1:50 to draw the outline of the building on isometric paper.

Let's see what Alex says about this.

He says, "The points on the isometric paper are one centimetre apart.

One centimetre in my drawing represents 50 centimetres, or 0.

5 metres, on the building.

The perspective in my drawing will not quite be the same as in the photo, so it will look a little bit different." He says, "I'll start with the edges that are on the floor." So we've got 14 centimetres as the front of the barn across the floor.

We worked that out earlier by doing 7 metres equals 700 centimetres and divide it by 50.

We won't repeat those calculations again, but that's where that numbers come from.

We can then draw the 10 centimetres going backwards along the floor.

He then says, "I'll now draw the vertical edges, which are parallel and the same length," those lines which are 2.

5 metres on the photograph.

That'll be five centimetres here, here, and here.

Alex says, "I could also complete the rectangular wall at the side." We just need to join it up, don't we? He says, "I'll mark the point at the front of the building where the curved roofs meet," bit like he did earlier.

We need to find the midpoint of that line segment at the front, go above it 12 centimetres and mark the point.

He says, "I'll now draw arcs from the top of this wall to this point," like that.

And the same at the top of the other wall, like that.

He says, "The edge at the top of the roof is five metres and is parallel to the other five metre edges." So we can draw the edge which goes from the top of the roof, like this.

That's 10 centimetres in our drawing.

He says, "I'll connect this to the top of the wall on the right." That needs to be connected with a curve, like so.

And ideally, the curve needs to be as similar as possible to the curve we did earlier.

And then he says, "From this point of view, you would also see a bit of the roof on the left as well." And this is what Alex meant earlier when he said the perspective in our drawing here isn't quite the same as the perspective in the photograph.

We are a little bit higher up in our perspective for this drawing than the photographer was in the photograph.

So we can see a little bit more of that roof.

And there it is.

Okay, let's check what we've learned.

Here we have a picture of that building we saw earlier.

Use a scale of 1:500 to draw the outline of the building on isometric paper.

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

And here's what your answer should look like.

The calculations on the left show you how you work out the length of each line segment on your drawing by using a scale factor of 1:500.

Okay, it's over to you now for Task A.

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

We have a photograph of a building and you're told to use a scale factor of 1:50 to draw the front elevation, side elevation, and plan of this building.

And if you want to, you may use centimetre square grid to help you, or you can do it on plain paper.

Either way, pause the video and have a go at this, and press play when you're ready for question two.

And here is question two.

We have the same photograph again, but this time using a scale of 1:50 to draw the building on isometric paper.

Remember, the perspective that you draw on the paper will not quite be the same as it is in the photograph.

Pause the video while you do this and press play when you're ready to take a look at what the answers should look like.

Okay, let's take a look at some answers and let's start with the front elevation.

It would look something a bit like this.

Now, you may include other details, such as estimates for where the door might be or maybe the curve of the roof as it goes over the door and so on, but you don't have to draw those based on this question here.

The basic outline is what you can see in our answer and those are the measurements as well.

And then for the side elevation it would look something a bit like this.

Once again, you may include other details.

You may have estimated the overhang of the roof and drawn that on either side, but this is the basic outline that you have, and those are the measurements too.

And the plan would look something a bit like this.

Once again, you may include other details such as estimated lengths for the overhang of the roofs, but this is the basic outline and those are the measurements.

And then when we are drawing the building on isometric paper, it should look something a bit like this.

Like we mentioned earlier, it's not quite the same perspective as what you can see in the photograph.

We're a little bit further around to the right in our drawing and we're also a little bit higher up as well.

But here are our measurements if we draw them on.

Great work so far.

Now let's move on to the second part of today's lesson, which is designing a 3D object.

Here we have Jacob.

Jacob is designing a doll's house for a toy-making business.

He says, "I'll start by designing the overall shape of the house, and after that, I'll work on the details." Sometimes we can be really keen to get started with the details 'cause it's always the interesting parts, but it's always helpful to start with the outline first, the overall shape, and worry about the details later.

He says, "I'll start by sketching a rough sketch first of what the shape looks like overall, and this doesn't need to be accurate." And this is Jacob recording some rough ideas to begin with.

Here's what he draws.

Looks something a bit like this.

He says, "I can use this to choose some initial measurements," and this is what he chooses.

Now, Jacob might change his mind on some of these measurements later.

He may tweak them slightly as he gets further down the design process, but this is his starting point.

Jacob says, "I'm now going to create an accurate scale drawing of the object.

So, I need to choose a scale." What scale could Jacob use for his drawings? Pause video and think about what scale you might use and then press play when you're ready to continue.

Jacob uses square paper and isometric paper to produce scale drawings of the doll's house with a scale of 1:5.

You may have thought of something different, but this is what Jacob has chosen to use.

He says, "The front wall is 70 centimetres by 50 centimetres.

This would be 14 centimetres by 10 centimetres in my drawings." So it would look something like this.

On the front elevation we can see a rectangle and we can also see that represented in the isometric drawing.

He says, "The side wall is 50 centimetres by 50 centimetres.

This would be 10 centimetres by 10 centimetres in my drawing." It would look something like this.

Now, the sign elevation is not just a rectangle.

There is a roof as well, which was a triangle.

Jacob says, "The roof is 10 centimetres high.

This would be two centimetres in my drawings." So we need to put that triangle on there.

It would go here.

Jacob then says, "Actually, I want the side wall to go all the way up to the roof.

So, I'll erase a line." Let's go erase those lines there.

He says, "I'll add the front of my roof to my isometric drawing and front elevation," because you can see a bit of the roof from the front, so it would be like this.

He then says, "The remaining line segments in my isometric drawing will be parallel to other line segments." And he can complete his roof like that.

And then finally he says, "I'll now draw the plan for the doll's house," which looks like this.

He says, "Now I've designed the overall shape, I'll add some details to my drawing," things like windows and doors and where the doll's house will open at the front and so on.

Jacob builds the doll's house out of wood, and this is what he's built so far.

He says, "After I completed my scale drawings, I made various small changes to the design before building the actual product.

But the original drawings were a helpful starting point." Can you see how some parts of the actual building he made are slightly different to his initial drawings? Do remember that the photographs at the top are a slightly different perspective to the plan and elevations drawn underneath.

But pause the video and make comparisons between the two sets of images, and then press play when you're ready to continue.

Let's check what we've learned now.

Jacob draws a chimney on his plan.

We can see that on the left side of the screen.

And then next to it we can see three different front elevations.

Which of those front elevations does the chimney match his plan? Pay really careful attention to where the chimney is in his plan and its size.

Pause the video while you choose from either A, B, or C, and press play when you're ready for an answer.

The answer is C.

If we look at why the other two are wrong, with A, that chimney is too narrow.

It's only one square wide, but we can see in the plan that it's two squares wide.

And with B, yes, it's the right size, but that chimney is right next to the edge of the house, but we can see from the plan that it's one square away from the edge of the house.

So it's C.

Here we have the same plan again, but this time we have three side elevations.

In which side elevation does the chimney match the plan? Pause the video while you choose and press play when you're ready for an answer.

The answer is B.

Let's consider why it's not A or C.

In A, the chimney's the wrong size, it's too narrow.

It's only one square wide, but we can see it's two squares wide in the plan.

For C, it's the right size, but it's too far away from the centre of the building.

We can see that on the plan it's only one square away from the very top of the roof, but in C, it's two squares away.

B is correct.

It's the right size and in the right position.

Here are the photos that show the doll's house after the chimney was added.

Okay, it's over to you now for Task B.

This task contains one question, and here it is, and you're going to get creative now.

You need to design a toy building, for example, a doll's house, but it could be something else if you have something else in mind.

Use isometric paper to produce a scale drawing of the building and use a centimetre square grid to produce a scale drawing of its front elevation, side elevation, and plan.

And you need to state clearly the scale that you use as well.

I would start this by drawing a rough sketch of what you want it to look like and then labelling on some measurements onto your rough sketch.

You don't have to do that, but it'd be very helpful for you to do it.

And then consider what it would be once you've scaled it down using a scale factor.

Pause the video while you're doing this and press play when you're ready to start looking at it together.

Okay, let's take a look at what we've drawn.

Answers for this will look different because it's a creative task.

I hope you thought of something really creative in yours.

You may not have done, but either way, I hope you've done something that's accurately drawn as well.

If you're working with other people, I would encourage you to take a look at what other people have done and compare it to your own as well.

Here's what a set of answers could look like.

It's what we saw earlier, the front and side elevations, the plan, and the isometric drawing.

Yours might look like this, it might not do, but we can check it in a similar way.

Please do the following checks for yours.

Check: are all the vertical edges of the building the same height in each drawing? You can do that by counting the squares and counting the grid lines on your isometric paper.

They should be the same height.

Check: is the width of the building the same in each drawing? In the front elevation, the width is going across; in the plan, it's the other direction; and the isometric drawing, it's going a bit of a diagonal.

Check: is the depth of the building the same in each drawing? That should be the side elevation, it should be on the plan, and you should be able to see it on your isometric drawing as well.

If you've done extra details, we need to check those as well.

For example, the door.

Is the door the same size on each drawing? Check it on your front elevation and check it on your isometric drawing as well.

And you can check the same as well in terms of its distance.

How far is that door from the walls or the edges of your building? Is it the same in your front elevation and the same as well in your plan? Other features can be checked in a similar way.

For example, if you've got windows, check 'em the same way as the door.

Check the size and check its position relative to other parts of the building.

And the same with chimneys and anything else you might have drawn in there as well.

Pause the video while you check all these things and then press play when you're ready to summarise today's lesson.

Fantastic work today! Now let's summarise what we've learned during this lesson.

The plans and elevations of a solid can be drawn to scale.

You can combine an isometric drawing with its plan and elevations to find missing information or check that corresponding lengths are equal between the drawings.

And scaling could be indicated by a scale factor or a ratio.

Well done today.

Have a great day.