Lesson video

Hello, I'm Mrs. Lashley, and I'm gonna be working with you as we go through the lesson today.

I hope you're ready to make a start.

Our learning outcome today is to be able to apply our area and perimeter knowledge into contextual scenarios.

There's the definition of area and perimeter on the screen.

I'm sure you are familiar with that, but if you wish to pause the video and read them again before we make a start, then please do.

So the lesson we've broken into two learning cycles.

The first one we're gonna look at using perimeter and area in different contexts and the second learning cycle is about costing a design project.

So let's make a start at looking at perimeter and area in different contexts.

So there are many contexts where perimeter and area may be necessary.

First of all, I'd like you to try and think of some contexts where knowing the area is important.

So some examples that you may well have thought of, painting a car wallpapering a wall, top dressing a lawn, or tiling a floor.

Perhaps you've got some more.

And the whole concept here is that the knowing the area, the space that needs to be covered is important in these contexts.

So let's now think about context where the perimeter is needed.

So once again, think about different contexts where you might need the perimeter.

So things that I thought of, maybe you thought of the same ones or different ones.

Painting the lines of a sports pitch, making a frame for a picture, putting coving or skirting around a room, or putting a rubber seal around a window.

So the concept here is that all of these are the boundary of a space.

So that's our perimeter.

So at times deciding whether area, perimeter, or maybe neither of those is required can be the challenge.

Working out the perimeter or working out the area is fairly simple, but just knowing whether to is where the challenge comes in.

So a cricket club is preparing for the upcoming season.

So they've got a big field where the cricket pitch will be.

They need to buy a new boundary rope.

They need to buy grass seed.

They need to paint the site screens, and they also need to get new fencing for the square.

So which of the things the club needs to do will require the perimeter of something? So just have a think about that.

Okay, so the boundary rope, that is the perimeter of the cricket pitch.

If you know anything about cricket, then the boundary is where we get four runs or six runs and that is the edge of the pitch.

So the length of that rope will determine the boundary, and that would be a perimeter.

The fence around the square, so that would be the perimeter of the square.

The fence doesn't stay up during a match, but it's put there at the end of a match most games.

So the perimeter of the square, that's the part that needs to stay protected.

So we put a fence up around it.

So which of the things require area? So this cricket club has got those things to do for the upcoming season, to prepare for the upcoming season, which would require an area.

Well, the grass seed, they need to know the area of the field.

The likelihood is that they will grass seed the majority of the field, not just within the boundary rope, and paint the site screens.

They'll need to know the area of the site screen surface so that they've got enough paint in order to paint them and make them nice and fresh for the upcoming season.

So here's a check for you.

A snooker hall is refilling all their tables.

What do they need to calculate? The perimeter, the area, or neither? So pause the video, and when you're ready to check, press play.

So they're gonna need to know the area.

Depending on what type of table, so it could be a snooker table, it could be an American pool table, it could be an English pool table, they're gonna have different sizes.

So the amount of felt will be different depending on the size of the table.

And so it'll be the area, the surface that needs refelting.

So here we've got Sofia.

And as part of her design and technology project, she's creating a photo frame.

So it's gonna be formed from a sheet of wood, so the backing part, strips of frame moulding, and those moulding have got sort of a detail to them, and a pane of glass.

So Sofia will have perimeter and area calculations to complete to know how much of each material she needs for her project.

So Sofia needs to work out how much of the frame moulding she requires.

And she recognised that the frame is along the perimeter of the glass panel.

So she works out that the perimeter is 40 inches.

So she concludes that she needs 40 inches of the frame moulding, but this is incorrect.

Why is this? So I'd like you to pause the video and if you are with somebody, if you've got a partner, I'd really encourage you to discuss this.

Think about the practicalities of making this frame and why the perimeter of the pane of glass will not give her the length of frame wood moulding that she needs.

So if you were to unfold the frame, the length would be the perimeter of the large rectangle, the external edge, she would need 56 inches.

So here, let's have a look at this.

So if you imagine unfolding the frame, it was 12 inches wide and then that's 16 inches long and another 12 inches and another 16 inches.

So in total that's 56 inches.

The internal perimeter of the pane of glass would not be enough.

It doesn't cater for the cuts.

When Sofia hangs it on a wall, how much of the wall will have been covered? So it'll be covering an area of the wall.

So this calculation is about the area as opposed to the perimeter.

And the area that will be covered will be the largest area, the whole frame.

So 12 by 16, which is 192 square inches.

Here's a check for you.

Sofia's teacher says that there is a piece of glass which has an area of a 100 square inches.

Can Sofia use it for her picture frame project? So pause the video and think about that.

And when you're ready to check, press play.

So it depends.

There is enough area because Sofia needs 96 square inches of glass because it is a rectangle of 12 inches by eight inches.

But if the glass that the teacher has is a 10 by 10 square piece of glass, then it wouldn't fit the gap she has.

So the area is necessary to know, but the dimensions of the rectangle piece is important here as well.

So we're onto the first task of this lesson and it's only one question.

And what I want you to do is go through and decide whether you would need the perimeter, the area, or neither in each of these contextual scenarios.

So you've got painting a door, putting fringe around the edge of a skirt, filling a jug with water, putting string lights around the roof line, carpeting a floor, piping a design on a biscuit in icing, and putting skirting boards around a room.

Pause the video and make your decision whether it's perimeter, area, or neither.

And then when you are ready to check, press play.

So the first one, painting a door would be area where the paint is gonna cover a surface.

So that surface has an area.

If you were painting a door both sides, then you would need to double it 'cause it's gonna have the same area on both sides.

If you were gonna also paint the edges of the door, then you would have to include those to calculate how much paint you need for the area that you are covering.

Part B, putting fringe around the edge of a skirt.

So if you've made a skirt or you've bought a skirt and you want to alter it and make your own sort of customizations and you're gonna put some fringe, so sort of some tassels around the edge of the skirt, then that would be the perimeter.

You would need to work out how much length of fringe is necessary to go around the edge.

Part C is neither, filling a jug with water because you're not covering a surface.

There's an internal surface to the jug, but we are actually filling a space.

So that would be more volume than perimeter or area.

Part D, putting string lights around the roof line.

So this would be the perimeter.

You would need to know how long the roof line is.

If it was a detached property, you would go all the way around the roof line.

That would be a full perimeter.

If you were a terrace house or an end terrace or a semi-detached property, then it wouldn't be actually a perimeter, it would be similar to a perimeter, but you wouldn't be going all the way around the cross section of the property.

Part E, carpeting a floor.

Well you need to know how much area is a surface that you are covering, and so that would be area.

In reality, when you go into a carpet shop to buy some carpet, the carpet comes in fixed widths.

So you do need to know the area that you are covering.

But you'd also need to take into account how how much length of each roll you would need depending on the widths.

So area is important for that contextual, but there's an added issue when you go out to buy a carpet.

Piping a design on a biscuit in icing.

Well, this is neither because depends on the design.

If the design was literally just a piping around the edge of the biscuit, then that would be the perimeter.

But if it's a design on the biscuit, then the likelihood is that it's going over the top of it as well.

So that would be neither.

And then part G, putting skirting boards around a room would be the perimeter.

Once again, it is the perimeter, you're going around the room.

But the likelihood is that room will have a doorway and there won't be skirting along the door.

So part of the perimeter will be missing, but when you are doing your calculations, you would be summing up the lengths of each wall.

Our second learning cycle is looking at costing a design project.

So within these contextual settings, there's an element of cost that needs to be included most of the time as well.

So projects that involve area and perimeter often require budgeting and costing.

So as we've said, painting a room, putting skirting around a room, you would need to know the length or you'd need to know the amount of paint you need.

And then when you go to the shop to buy your materials, there would be some sort of cost, and therefore you might need to make some decisions whether you are going to go for a branded paint or a shop brand, whether you're gonna go for the larger tin or the smaller tin, whether there is a deal on.

And actually it can become more cost effective by taking the smaller parts because they are on a special offer, et cetera.

So costing and budgeting also comes into these sort of contextual problems. So the same items such as paint can come in different quantities.

For example, you can get a 30 millilitre tester pot that would cover 0.

39 square metres of area and cost two pound 45.

But you could also get the same colour, the same make paint in two and a half litres, and that covers 32.

5 square metres of wall or a surface.

And that would cost you 28 pounds.

But you can also get the larger tin of five litres.

It covers twice the amount of area because there's twice the amount of paint.

So 65 square metres, but it doesn't cost you twice as much.

It's 40 pounds.

So that one is better value than the two and a half litre one.

So if the area that is to be painted is 80 square metres and requires two coats of paint, what combination of tins should be bought to be the best value? So this is when that budgeting and costing is coming in.

We've worked out the area of surface which is 80.

We know that we need to give it two coats of paint so we can think about which is the best combination.

So if you buy two five litre cans and one two and a half litre can, that would cost you 108 pounds.

So how much area did we need to actually cover? We needed to cover 160 square metres 'cause we were doing the two coats, and then we needed to figure out the most cost effective way of getting enough paint to cover 160 square metres.

And this way it is the most cost effective.

Another context where budgeting and costing comes in is for bathroom floor to be tiled.

So the tiles can be cut to fit awkward shapes.

The same design of tile comes in two sizes.

One is a smaller square, which is 330 millimetres by 330 millimetres, and the other is a larger square tile of 600 millimetres by 600 millimetres.

The bathroom floor has an area of five square metres.

To work out the number of tiles needed, we need to work out the area of one tile first.

So we know that this is an area problem because we are covering a surface.

That surface is the floor and we're covering it in tiles.

So the units are not consistent.

The tiles dimensions are in millimetres and our area of the bathroom floor has been calculated in square metres.

So which is easier to change? The measures of length, the millimetres, or the measure of area, the square metres? So just think about that for a moment.

Well, it's always easier to convert the measure of length.

The smaller tile, the smaller square tile is 330 millimetres by 330 millimetres.

So if we convert that into metres, that's equivalent to 0.

33 metres by 0.

33 metres.

Therefore we can multiply them together to get the area of one of our small square tiles, which is 0.

1089 square metres.

The other tile, which is the largest square tile, would be equivalent to 0.

6 metres by 0.

6 metres.

And one of those tiles covers an area of 0.

36 square metres.

Because the floor is five square metres, we need to work out how many of each tile is needed.

So this will happen by doing a division.

So the smaller tile, you'd do five square metres, the area of the floor divided by 0.

1089 square metres, which is the area of one small tile.

And that is 45.

914 and some more, so we'd have to round that up to 46 tiles.

So you're gonna need more of the small tiles to cover the floor.

On the larger tile, we do the same idea.

We do the area of the floor divided by the area of one large tile, and that means that rounded up, we need 14 tiles.

So you're gonna need more tiles if they're smaller than if they're larger.

In reality, when you are costing and working out how many of.

How much material you need, there would also be a percentage added to take into account any breakages or any defects on the tile.

That's normally about 10% or 15% extra is suggested that you buy so that you've got those to work with.

So just to check, a wall is going to be tiled.

The amount of tiles needed will be the same regardless of the tile, true or false, and then justify your answer.

The area that needs to be covered by the tiles will be the same.

The size of the tile determines how much of the wall it will cover.

So pause the video whilst you make a decision and then when you're ready to check it, press play.

So that is false, and the reason is, as we've just seen that depending on the dimensions, depending on the shape, each tile will cover a different surface amount.

And so although the wall that is being tiled doesn't change, the area is fixed.

The amount of tiles you need will be determined by the size and shape of the tile.

So once the last task, and this task requires you to cost up for a client their garden plan based on the materials.

So all the necessary ground preparations have been done and you do not need to include any labour costs.

So you are just costing the materials.

The shed is already in existence and in position.

Note, use the conversion that one foot is equal to 30 centimetres.

There is no fence necessary on that edge on the left 'cause that's where the house is.

But fence does need to go around the back of the shed because if the shed was to be ever removed, then we still want there to be fence in place.

So here is the plan that you need to cost up.

Over the next few slides, I'm just gonna go through the costing and the requirements before you make a start.

So the path that is on the plan will be edged using block paving.

The space between will be filled with either shingle or decorative stone chippings to a depth of 30 millimetres.

So you have a choice whether you are going to use the decorative stone chippings or shingle to fill the gap within the path.

So each block is given there, the dimensions, and it's 45 p per block.

And then there is a cost for the shingle or the decorative stone chippings.

So that's the path.

There is a sleeper bed marked on the plan and the sleeper bed will be created using railway sleepers.

Then it will be infield of soil to a depth of 16 centimetres.

Other flower beds will also have soil put in them to the same depth.

So there is another flower bed on the plan that will also need some soil.

So the sleepers, there are the dimensions there and then the soil and how much area it covers.

There is a patio area.

Remember the groundwork has already been prepared.

You're just laying the patio.

The patio slabs that you have a choice of is square ones, which are 450 millimetres by 450 millimetres or larger square ones of 600 millimetres by 600 millimetres.

There's the cost per slab there.

Do not worry about including a percentage in this quote for breakages and defects, just the amount of slabs needed.

Then the fencing.

So remember, a fence will not go along with wall weather houses, but it will go around the outside of the garden.

Each fence base needs a gravel board, a panel, and posts.

The overall heights cannot exceed 6.

5 feet above ground level.

So there will be some dug in some of the posts into the ground.

That's what keeps the structure.

But the overall heights above ground level cannot exceed 6.

5 feet.

But you do need a gravel board and a panel.

Again, there is choice with which ones you go for and pricing for those.

All the posts are four inch square and then nine feet higher.

And that's because there is some below the ground level and some above the ground level.

And then finally, the lawn area needs to be seeded.

There is the cost there for each of those seeds that you can buy.

So here is all of the costs for the materials on one slide.

Remember you have got a lot of choice.

You need to work out how much of each you need and you are trying to come up with a quote for the client.

So they haven't given you a budget, you just need to come up with a quote for the client for the materials to cover all of the work that is necessary in the garden.

Press pause, work through that.

And then when you are ready to go through some feedback for that task, press play.

So the feedback is going to be talking through whether it was perimeter or area that you should have calculated and what they were.

Then I'm gonna show you an example of the quote and the quote will be different depending on what choices you made.

So all the necessary ground works had been done.

There's no labour cost involved, we were just costing up the material.

The path requires the perimeter for the paving blocks and the remaining area for the infill of either the shingle or the decorative stone chippings.

So the perimeter was 32.

6 metres.

And the remaining area, so if you removed the border, there was an area of 10.

64 square metres that needed to be filled by your choice of shingle or decorative stone chippings.

If we then think about the sleepers for the sleeper bed, they are bought in lengths.

So the perimeter is needed to know the correct lengths to buy.

The perimeter for the flower bed that was marked was 10 metres, and then you needed to infill the sleeper bed as well as the flower bed.

So both of them were gonna be filled to 60 metre depths.

So the space that's covers is the area.

So although we are filling it in, and that would be volume, because we're keeping the depth as 16 centimetres, we're removing that dimension.

So we're thinking about just how much area we need to cover.

So the sleeper bed area, once you remove the sleepers, that middle section is 2.

05 square metres.

The flowerbed area, which is running alongside the path, has an area of 9.

24 square metres.

So you need to buy soil that would cover a total area of 11.

29 square metres.

If we think about the patio, or this was an area calculation before working out how many tiles you needed.

So the area of the patio was 21,500,000 square millimetres, which is equivalent to 21.

5 square metres.

So it may be that you converted the measurements into centimetres or into metres and it would be equivalent to those two.

The lawn requires the area of the compound shape.

So the shed was sort of sticking into the lawn, which made it a compound shape as opposed to a rectangle.

And you needed to work out the area to know how much seed to buy.

And the area of that lawn was 47.

83 square metres.

The fencing is close to perimeter, so it isn't a perimeter because you're not going the full way around the garden, but you needed 40.

2 metres of fence in total.

So that was going along one side, along the back of the garden and then back down the other side.

So it was three of the edges of a rectangle.

So here is an example quote.

So the overall cost was 2,256.

85 pounds.

And that is because of the choices that I have made.

So I made a choice of using decorative stone chippings, which were a bit more expensive than the shingle.

So if you'd use the shingle, there's a chance that yours would be lower cost.

And then for the fence, I went for the sort of cheaper fence panels.

So again, if you went for the more expensive fence panels, it would be more expensive.

If you went for the concrete, that would've also been more expensive.

Block paving, you should have worked out that you needed 163 blocks and that was to get the perimeter correct.

The stone chippings, if you went for shingle, this would still have been the cheapest way to get the right amount, which was to buy one jumbo bag and one 20 kilogramme bag.

Soil, the soil should have been the same for all of us because you were putting soil in the sleeper bed and in the flower bed.

And so the most cost effective way would be four lots of 500 kilogramme bags.

The fence panels, we should all agree with how many we need so that you needed 21 panels and 21 gravel boards.

The size of the fence panels and the gravel boards was your choice.

So you may have gone for a one foot gravel board and then you'd have to have gone for a five foot panel to make sure it didn't exceed six and a half feet.

But 21 was needed for both and you would need 22 posts.

The cost will be different depending on which ones you chose.

Sleepers, once again, we needed 10 metres of sleepers.

So the most cost effective way was to buy three lots of the 3.

6 metre lengths.

You'd have a little bit too much there.

You'd have 0.

8 metres too many, but that was the most cost effective way.

There was no reason that you had to do it the most cost effective way.

You just had to make sure you had enough material grass seed.

One five kilogramme bag would've been enough grass seed to cover the area that we needed.

And patio slabs, again, this was a choice whether you went for the smaller square slabs or the larger square slabs.

I went for the smaller ones and I needed 107.

So to summarise today's lesson where we've been looking at perimeter and area in a contextual setting, knowledge of how to calculate perimeter and area is vital when working in many different contexts.

And that includes costing projects.

Before starting any questions that are in context, it's important for you to identify whether it's a perimeter question or an area question, or perhaps it's neither, or maybe it's a sort of liker perimeter as we saw with the fence.

I hope you've enjoyed today's lesson and it's an insight into maybe your future careers where you're gonna be using those math skills that you've learned.

I look forward to working with you again in the future.