Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from the unit Maths in the Workplace.

In this series of lessons, we're exploring how maths is used in different careers.

Let's get started.

In today's lesson, you're going to look at some of the ways that maths is used in interior design.

Now, on the screen you can see the keyword area, and this is just a quick recap of what area is.

If you need to, feel free to pause the video while you have a read through.

Our lesson today is divided into two parts, and we're going to start by looking at measurements in interior design.

What areas of maths do you think an interior designer might use? Pause the video and have a quick think now.

Well, I've come up with these.

Area, multiplication and division, conversions, proportion, money, measurements, geometry, scale.

Now, you might have come up with more.

There's quite a lot after all, and during this lesson, we're just going to look at some of these.

So one of the most important elements of interior design is accurate measurements.

Why do you think that might be the case? Well, if measurements are not accurate, then items of furniture may not fit in the space you intended them to go in, you may not buy enough floor or wall coverings, and the visual appearance of a room may not have the desired effect.

Conversion between different units of measure is also important.

Being able to convert between metric and imperial units of length or area is helpful, but also converting using a scale.

Interior designers will often use scale drawings to consider positioning of items of furniture.

Below are sketches of the walls in a room.

A 2.

5 litre tin of paint covers 25 square metres.

The walls will need two coats of paint.

The dimensions of the door are 1.

98 metres by 76 centimetres.

The dimensions of the window are 1.

5 metres by 1.

2 metres.

How many tins of paint are needed to paint this room? Hmm, where do we start? What you might like to do is just pause the video and have a brainstorm about what you think I'm going to need to work out in order to answer this question.

Pause and do this now.

Welcome back.

Let's see if your approach is the same as mine.

Now, there are different ways to do this.

I'm just gonna show one.

So I've started by looking at this wall.

Now, the area of this wall is 2.

72 times 2.

4, and I know that's the case, because both measurements are in metres.

This gives me an area of 6.

528 square metres.

So the total area of both walls is two lots of this, which is 13.

056 square metres.

Now, the dimensions of the door are 1.

98 metres by 76 centimetres.

So the area of the wall, including the door, would be found by working out 3.

78 times 2.

4, and now I need to subtract the area of the door.

Notice how I've converted the centimetres into metres.

Now I have two areas, both of which are in the same unit, so I can subtract, because the area needing to be painted is the area of the wall minus the area of the door, which gives me an area to be painted of 7.

5672 square metres.

Lastly, I have the wall that has a window in it.

So similar working here, I've got the area of the wall including the window, I've then got the area of the window, and then I've subtracted.

Notice how both measurements are in square metres.

This means that I'm subtracting values that have the same unit.

This gives me a resulting area of 7.

272 square metres.

Now, what am I gonna do with all those areas? Well, I'm gonna sum them, and then I'm going to remember that each area has to be painted twice, so I need to double.

So the total area that requires painting is 55.

7904 square metres.

But how am I going to work out how many tins of paint I need? That's right.

I'm gonna do some division.

I need to divide by 25, because that is what one tin of paint covers.

So how many tins will I need? That's right.

I need three tins to paint the room.

Two would not have been enough.

I can see that there.

I actually need two and a bit more, so I have to round up to three.

Quick check that you get this.

An interior designer wants to paint the ceilings in a house.

The coverage is 12 square metres per litre, and tubs are 10 litres.

Each ceiling needs two coats of paint, and the total area of the ceilings to be painted is 88 square metres.

How many tubs of paint need to be purchased? Pause the video while you work this out now.

Welcome back.

How did you get on? Well, I'm gonna go through the working.

See if you match me.

I said the coverage of each tub is going to be 120 square metres, and that might not be your first line of working, but I suspect you've got that somewhere.

I said the area needed to be painted in total is 176 square metres.

Therefore, the number of tubs needed is 176 divided by 120, which gives me 1.

466, and it goes on for a bit, but of course I need to round, so I'll need two tubs of paint.

Well done if you got that right.

An interior designer wants to wallpaper a wall, and below is a sketch of the wall.

The width of a roll of wallpaper is 53 centimetres, and the length of the roll is 10.

05 metres.

How many rolls of wallpaper are needed to paper this wall? Well, easy peasy.

Area of the wall, let's calculate that, so that's 13.

152 square metres.

The area covered by one roll of wallpaper, well, that's 5.

3265 square metres.

So I just need to divide, right? So I'll need three rolls.

Why is that not an appropriate way of calculating the number of rolls of wallpaper that I need? In other words, that's not a good thing to have done, but why not? Surely the maths made sense.

What's wrong here? Pause the video while you have a think.

Welcome back.

Let's see if you came up with the same answer as me.

Well, I've said you're gonna have joins in the lengths.

In other words, if you do this, you're going to get lots of little lines where scraps of one piece of wallpaper meet the edge of another piece of wallpaper.

In other words, we're gonna have all these lines or joins all over our nice wall, and we don't want to see that.

So what we need are strips of wallpaper that are 2.

4 metres in length.

So they can go from the bottom of the wall all the way up to the top of the wall and look lovely and smooth at the end.

So how many widths of wallpaper are needed? Well, we know that the width of a roll of wallpaper is 53 centimetres, so if we turn that into metres, we'll need, well, 11 widths of wallpaper in total.

How many lengths of wallpaper can you get from each roll? Well, let's see.

I can get, ah, four lengths of wallpaper from each roll.

So therefore, how many rolls are needed? I need three rolls of wallpaper.

Now, it is the same number as before, but this time, we know we're being efficient and ensuring proper placement of those strips of wallpaper.

It's time for a quick check now to make sure you've got that.

An interior designer wants to wallpaper a wall.

Below is a sketch of that wall.

The width of a roll of wallpaper is 50 centimetres, and the length of the roll is 10 metres.

How many rolls of wallpaper are needed to paper this wall? Pause the video while you work this out now.

Welcome back.

You should have said that we need four rolls in total, and the working is here on the screen.

So you can see, I took the 5.

62 metre length and divided that by 0.

5, because I converted the centimetres to metres, which told me I needed 12 widths.

I then took the length of the roll of wallpaper, which was 10 metres, and divided by 2.

74, which is the height of the room, to tell me that I get three lengths from each roll.

Well, 12 divided by three tells me I need four rolls of paper.

It's time for your first task.

For question one, you can see some sketches of the walls in the room.

Now, these are not to scale, however the measurements are accurate.

A 2.

5 litre tin of paint covers 25 square metres, and the walls need two coats of paint.

How many tins of paint are needed to paint this room? Pause while you work this out.

Welcome back.

Question two.

An interior designer wants to wallpaper a wall.

Below is a sketch of this wall.

The width of a roll of wallpaper is 52 centimetres, and the length of the roll is 10.

5 metres.

How many rolls of wallpaper are needed to paper this wall? Pause the video while you work this out now.

Time to go through your answers.

For question one, you should have found that we needed five tins of paint.

Feel free to pause the video at this point if you want to check your working against mine.

Then question two, you should have found that you need five rolls of wallpaper.

Again, feel free to pause the video if you want to check your working against mine.

Well done.

It's now time for the second part of our lesson, and we're going to look at finance in interior design.

Earlier, we calculated the total area that needed painting as 55.

7904 square metres.

Now, the paint I'm looking at here covers 16 square metres per litre, and you can see on the table on the right we've got the size of the tins in litres and then how much it costs to buy each tin.

Now, the walls need two coats of paint.

What we're going to do is calculate the cost to paint the room, ensuring that there is minimum wastage.

Well, let's work out the number of litres we need.

Now, remember we needed to paint the area twice, and then we'll need to divide by 16, because that's the area that is covered per litre of paint.

In other words, I'm going to need 7 litres of paint.

Well, let's calculate the cost per litre for each tin.

We need 7 litres, so for the 2.

5 litre size tin, the cost per litre is.

Well, I could round that up and say 18 pounds and 20 pence, but I'm going to leave it like that for the moment, because remember, I'm still calculating.

So here, what about the 5 litre size tin? Well, dividing by 5 gives me a cost per litre of 17.

198, or 17 pounds, 20 pence.

What about the 10 litre tin? Well, we can already see this is going to be nice and cheap.

13 pounds and 10 pence, definitely the cheapest option.

So it's the best value for money, but that's going to leave us with 3 litres of paint that we can't use.

Am I paying for paint that I'm not going to use? That might be wasteful.

I should check.

So, let's have a look.

If I buy one 5 litre tin and one 2.

5 litre tin, that will produce less wastage.

Ah, but it's gonna cost me more money.

Think about it.

The 85.

99 and the 45.

49, when I add those two amounts together, that's going to give me more than the 130 pounds, 99 pence.

So it's gonna cost more, but it's significantly less waste.

However, the extra cost is only less than a pound, so, realistically, given all that wastage, it might actually be better to buy one 2.

5 litre tin and one 5 litre tin.

Let's consider this situation.

Here's a table of prices for different lengths of wood.

Firstly, let's calculate the cost per metre of wood to compare the prices.

So what is 2,400 millimetres in metres? Well, that's 2.

4.

So what I'd like you to do now is just pause the video and quickly convert all the lengths into metres.

Do this now.

Welcome back.

Now we've converted all of those lengths to metres, we can now work out the price per metre.

So for a length that's 2.

4 metres long, the price per metre is 1 pound, 75 pence.

I'm now gonna calculate the cost per metre of the 3 metre length.

In other words, I'm gonna divide by three, and my ratio table's helping me with this.

That gives me a price per metre of 1 pound 75.

It's now your turn.

Can you please calculate the cost per metre of the 3.

6 metre length? Pause and do this now.

Welcome back.

Well, you should have divided by 3.

6, giving us a price per metre of 1 pound 75.

Ooh, it's exactly the same as mine.

It appears that the cost per metre is the same no matter the length of wood you buy, but we'll check the last two lengths to be sure.

Remember, so far it's always been 1 pound 75.

Again, 1 pound 75, and then for the 4.

8 metre length, 1 pound 75.

So the cost per metre is the same for each length of wood, so in this situation, you would definitely want to keep wastage to a minimum, as there is not a value-for-money benefit in buying longer lengths of wood.

So, bearing that in mind, let's consider this problem.

An interior designer wants to construct two of these bookshelves in an alcove.

Below is a sketch of the bookshelf.

Calculate the cost of wood, ensuring minimum wastage.

So let's think about how we do this.

Would it be sensible to start with the longer or shorter lengths do you think? Well, the longer lengths, because off cuts, i.

e where we've cut the wood down to the desired length, may be usable for the shorter lengths.

And let's see what we mean by that.

So, how can we make four 2 metre lengths? So in other words, the sides of our bookshelves, and remember, we have two bookshelves to build.

So in order to make our four 2 metre lengths, we could buy four 2.

4 metre lengths, four 3 metre lengths, four 3.

6 metre lengths, two 4.

2 metre lengths, or two 4.

8 metre lengths.

But which produces the least wastage? Well, let's consider the wastage for each.

In the first scenario, I'd have four 0.

4 metre lengths left over.

For the 3 metre lengths, I'll have four 1 metre lengths left over.

The next case, I'll have four 1.

6 metre lengths.

Now, this one's quite nice, because the 4.

2 metre lengths, I can make two 2 metre lengths out of each of the 4.

2 metre lengths, and that means I'll only have wastage of 0.

2 metres twice.

And then for the 4.

8 metre lengths, I'll have two 0.

8 metre lengths.

So we can see that this option produces the least wastage.

However, the offcuts from this option, the four 3.

6 metre lengths, could be used to form the horizontal lengths.

Remember, they were 1.

2 in length.

So, how can we make our ten 1.

2 metre lengths? So we could buy any of the following options, but which produces the least waste? Well, let's consider the wastage for each.

Well, we can see here, the top option produces the least wastage, 'cause each length can be cut exactly into two lengths, each of 1.

2 metres.

Now, let's take a look at the offcuts.

So remember, this is where we had usable offcuts, and our option where we had the least wastage.

If we use the off cuts, we've got four of our 1.

2 metre lengths, but how many do we still require? Well, we require six more.

And what's the best way to purchase that? Well, either three 2.

4 metre lengths, or two 3.

6 metre lengths.

Both of those options produce zero wastage, and they result in the same price to pay.

So, here are our options of what we could buy.

The first option, where we buy two 4.

2 metre lengths, makes four 2 metre lengths and 0.

4 metres of wastage, and the five 2.

4 metre lengths makes 10 lots of the 1.

2 metre lengths that I want with zero wastage.

So in other words, in the first option, I've got a total wastage of just 0.

4 metres worth of wood.

Now the second option, which was four lots of 3.

6 metres of wood, which resulted in our four 2 metre lengths and four 1.

6 metres of wastage, which, of course, we then turned into four 1.

2 metre lengths with 1.

6 metres of wastage, and then two 3.

6 metre lengths, making six of the 1.

2 metre lengths that I required with zero wastage.

So the first option is the best one.

So we're gonna calculate the cost of option one.

We're gonna buy two 4.

2 metre lengths and five 2.

4 metre lengths.

So the cost of option one is 35 pounds and 70 pence.

Now, bear in mind that option two had wastage.

Would you expect it to cost more, less, or the same than option one? And I want you to justify your answer.

Pause the video and do this now.

Welcome back.

What did you come up with? Well, let's check.

The cost of option two was 37 pounds and 80 pence.

Well, it costs more, and since the price per metre was the same for all lengths, it makes sense this option cost more, because it had more wastage, so therefore minimum wastage is the cheapest.

It's now time for your final task.

For question one, the total area that needs painting in a house is 211.

2 square metres.

This paint covers 16 square metres per litre, and the walls need two coats of paint.

Calculate the cost to paint the room, ensuring there is minimum wastage.

Pause and do this now.

Question two.

I need the following lengths of wood: four 1.

9 metre lengths, six 1.

7 metre lengths, and four 0.

5 metre lengths.

For part A, what is the cost of the wood with minimum wastage? And part B, how much wastage is there? Pause the video while you work this out now.

Welcome back.

For question one, I asked you to calculate the cost to paint the room, ensuring there is minimum wastage.

Well, you should have worked out that you'll need 27 litres of paint, and the closest you can get to 27 litres, being as efficient as possible, is two 10 litre tins, one 5 litre tin, and one 2.

5 litre tin.

The cost is therefore 393 pounds and 46 pence.

Well done if you got that right.

For question two, I asked you what is the cost of the wood with minimum wastage.

Well, I worked out the cost to be 35 pounds and 70 pence, and the wastage total was 0.

6 metres.

You can see how I worked that out.

I took four 2.

4 metre lengths so that I could get four 1.

9 metre lengths, and then I had four 0.

5 metre lengths left over.

At that point, I only had to get the six 1.

7 metre lengths, and I did that by doing three lots of the 3.

6 metres, because that made six 1.

7 metre lengths, and then each of those had a wastage of 0.

2, but there were three lots, that makes 0.

6 in total.

Well done if you got that right.

Let's sum up what we've done today.

An interior designer uses many different areas of maths.

Two examples are calculating the number of tins of paint required to complete a job, and the number of rolls of wallpaper required to complete a job.

Often, an interior designer will want to consider keeping wastage of materials to a minimum, unless they may be able to use the materials on another job.

Well done.

You've worked really well today, and there was some tricky bits of maths going on there.

We had quite a lot we had to figure out.

I really hope you've enjoyed learning some of the ways that maths is used by interior designers.

I look forward to seeing you again for more maths in the future.

Bye for now.