Lesson video

Hello there and thank you for choosing this lesson.

My name is Dr.

Rosen and I'll be guiding you through it.

So let's get started.

Welcome to today's lesson from the unit of Maths and the Environment.

This lesson is called Designing a Green Space.

And by the end of today's lesson, we will be able to design a green space whilst considering the community.

Here are some previous keywords that will be useful during today's lesson.

So you may want to pause the video while you remind yourself what these mean and then press play when you're ready to continue.

The lesson is broken into three learning cycles.

We're going to start by planning rooftop agriculture.

An urban area is a region with a high population density of humans.

For example, a town or a city.

An urban environment typically has a high density of the following, buildings, which could be residential, commercial, manufacturing and so on, roads, and with that comes road traffic and carbon emissions, which comes from vehicles, factories and so on.

Urban greening aims to incorporate more greenery into urban environments, for example, with parks and trees.

And this can support biodiversity, promote sustainability and make the area generally more pleasant for its citizens.

Installing green spaces in urban environments is a common initiative for urban greening.

Green spaces could include planting trees on streets or urban green parks such as a park in a city or with rooftop agriculture, for example, growing plants on rooftops.

Let's take a look at the latter of these now.

Here we have a diagram that shows a plan view of a flat rooftop on top of an apartment building.

The diagram is not to scale.

Now the roof could be made into a green space.

Plants could be grown on the unused parts of the rooftop as they have good access to sunlight and rainwater 'cause you're on top of a really tall building.

However, plants cannot be grown on the stairwell or the air vents.

So we can find the maximum area of rooftop that can be used for grown plants based on the information we're given in this diagram.

We could do that with a following calculation.

We could find the area of the entire roof to begin with and then we could subtract the area of the parts that we can't use for growing plants.

So we could subtract the area of the stairwell and then subtract the area of the urban.

So let's do that.

The entire roof is a rectangle, so its area would be 10 multiplied by 21.

The stairwell has a plan that is a square shape, so we could find the area of that by doing three squared.

And then the air vent from a plan of view is a circle.

So we could find the area of that by doing pi multiplied by the radius squared.

So pi times one squared.

If we then perform this entire calculation, we would get 197.

8584 and then there's some more decimals.

Now you may be tempted to round that up to 198 square metres, however, can you think of why that might not be appropriate? In this particular context, it may be more appropriate to truncate the answer to 197 rather than round up to 198 'cause there is not enough space for 198 square metres of greenery.

Therefore we can say that the rooftop has approximately 197 square metres of usable space for growing plants.

If we try and fit more in there, it might not squeeze in.

Now, hang on a minute.

If the entire rooftop was filled of plants, there'll be no space for people to walk on the roof, for example, to tend to the plants.

So we might want to include a walkway along the roof and that means having less greener on there.

So there's a space to walk.

For example, there is 197 square metres of usable area on this rooftop for plants.

If a 1.

5 metre wide walkway is installed, how much space is left for growing the plants? Well, we could work out the area of this walkway by doing 1.

5, which is its width, multiply by 21, which is its length, and that would give 31.

5 square metres.

So that means the remaining area left for plants would be 197, subtract 31.

5, which gives 165.

5 square metres left available for the plants.

So let's check what we've learned.

Here, we have a diagram that shows a plan view of a building with a flat rooftop.

Plants cannot be grown on the stairwell or on the balcony.

So with that in mind, what is the maximum area that can be used for growing plants? Pause right where you start and write something down and press play when you're ready for an answer.

The answer is 144 square metres.

One way you can calculate it is by first working out the area of the entire roof by doing 10, multiply by 20, and then subtracting the total of the parts that you cannot grow plants on.

Four squared is the area of the stairwell, and 2 multiply by 20 is the area of the balcony, and that would give you 144 square metres.

There are other ways you could work that out.

For example, rather than finding the area of the entire roof and the area of the balcony, you could subtract the two metres from the 10 metres to begin with and then find the area of the roof including the stairwell, but not including the balcony.

And then that means you just have to subtract the four squared from a stairwell.

And there are other ways as well you could do it too.

So we've established that the maximum area that can be used for growing plants is 144 square metres.

A planner suggests installing a two metre wide walkway along the length of the rooftop.

So how much area is left for growing plants? Pause video while you work this out and write something down.

Then press play when you're ready for an answer.

Well, we could do 144, which is the maximum area available for growing plants and subtract the area of the walk way, which is two multiply by 20.

And if you do that, you get 104 square metres.

However, looking at the diagram, looking at the stairwell and the balcony, what could be a problem with this design? Pause the video while you write something down and press play when you're ready for an answer.

There are different possible things you could write here, but one example could be, but you can not get from the stairwell, to the balcony without walking over the plants.

So a different design for the walkway is suggested, which you now see on the diagram here, how much areas left for growing plants.

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

Once again, there are plenty of different ways you can work this out, but let's take a look at one way.

You could work out the area of the vertical walkway, which would be 16 square metres.

That's two multiplied by eight.

Could work out the area of the horizontal walkway, which would be 40 square metres, which would be two multiplied by 20.

However, the vertical walkway and the horizontal walkway overlap of each other.

So there's part of that walkway where we've counted the area twice.

The area that crossover is four square metres, which we get from doing two multiplied by two.

So the total area of the walkway would be 16 plus 40.

Subtract the four from the crossover, so we'll only count it once.

That means we get 52 square metres for the tall area of the walkway.

So that means the area available for ground plants will be 144, which is the maximum possible area for growing plants.

Subtract 52, which is the area of the walkway, and that leaves 92 square metres available.

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

This task has one question and here it is.

The diagram here shows the plan view of a rooftop of an office building.

Now the roof has two congruent skylight windows.

The designer wants to use as much roof space as possible to plant greenery.

However, they need to include a border around the edge for drainage, the border is 50 centimetres wide all around.

Could you please calculate the maximum area that could be used for planting greenery? Pause the video while you do this and press play when you are ready for an answer.

Let's work through this together now.

A good place to start could be to work out any unknown lamps and mark them onto our diagram and that would look something a bit like this.

And then, and the next step we could take could be to find the area of the region inside the drainage border.

We could do that in plenty of different ways, but here's one possible way you could calculate that.

You could do 25.

5 multiplied by 3.

5 and then add 29, multiply by 15.

5.

Can you see where that calculations come from? In this calculation, they have split that area by drawing a horizontal line.

So you've got now two rectangles, one above the other, found the area of each and added them together.

And that gives 538.

75 square metres.

But we can't use all of that for greenery because we have those skylight windows.

So we could find the area of each window by doing four multiplied by six.

That gives 24 square metres.

That's for one window.

So to find the area of planting greenery, we could do 538.

75.

Subtract two lots of 24 and that would give 490.

75 square metres.

I hope you found that interesting.

Let's now move on to the next part of this lesson, which is looking at planning a garden or allotment.

Fruit and vegetables can be grown in gardens, allotments, or other green spaces.

However, planning is sometimes required in order to maximise the available space that you have.

Now when it comes to planting fruit and vegetables in an allotment or a garden, people don't tend to just plant them in any random place.

Usually different sections of a green space may be designated for growing different types of plants.

Sometimes this is done by placing barriers around sections of earth so we can see where one thing will grow and where another thing will grow.

Or in smaller gardens, raised beds or large containers called planters may be used instead.

There is often a recommended amount of space to leave around each plant so that they have enough room to grow and the amount of space can vary between different types of plants.

For example, when growing broccoli, it is recommended to plant them at least 80 centimetres apart.

Whereas when growing strawberry plants it is recommended to plant them at least 30 centimetres apart.

Clearly the broccoli needs more space to grow than a strawberry plant.

So here we have Lucas who's planning out his vegetable patch.

He's growing broccoli in it.

He wants to plant the broccoli in rows and columns inside a self-contained garden bed that is four metres by 4.

8 metres.

He should plant the broccoli 80 centimetres apart.

What is the maximum amount of broccoli that he can plant in the available space? Perhaps pause video while you think about how we might go about working out this problem and then press play when you're ready to continue together.

Let's see what Lucas does.

He says to begin with, I could convert the measurements so that they're all in the same units.

That's a very good point.

The length on the garden bed are given in metres, whereas the recommendation for the broccoli is given in centimetres.

So we could convert 'em all into metres or all into centimetres.

Here we converted the lengths of the garden bed into centimetres.

It then says the recommendation to plant 80 centimetres apart suggests that each broccoli needs 40 centimetres of clear space around it to grow.

Therefore, the reason why we plant broccoli 80 centimetres apart must be because they are expected to grow 40 centimetres away from where they first planted.

And if you have two broccoli plants both grown four metres away from where they're first planted, the total distance must be 80 centimetres between them.

Lucas says the set of points that are all 40 centimetres away from a broccoli plant forms a circle with a radius of 40 centimetres.

Now the diagram here shows the closest point to the corner of the garden bed where I could plant a broccoli that is 40 centimetres from the edges.

He then says, I can then plant more broccoli plants in a row, spacing them 80 centimetres apart like this.

There we have six broccoli plants in each row.

He then says, I could repeat the same process working downwards like this and we can see that there are five broccoli plants in each column.

Now the broccoli would form an array that is six by five and it looks something a bit like this.

So it means altogether we have 30 broccoli plants in total.

So we now know that Lucas can plant 30 broccoli plants in this available space.

And Lucas worked this out by taking quite a practical approach to his solution.

How could have Lucas worked this out based on the dimensions of the vegetable patch alone? Perhaps pause video while you think about this and press play when you're ready to continue together.

Well Lucas says each circle has a diameter of 80 centimetres.

So the number of plants in each row can be calculated by dividing 480 by 80, where 480 is the length of the garden bed in centimetres and 80 is the diameter of the circle that would give six.

It then says the number of plants in each column can be calculated by dividing 400 by 80 and that would give five.

So we have the six and we have the five.

The total number of broccoli plants in the array can then be calculated by multiplying six five and that gives 30.

So let's check what we've learned.

Lucas is growing strawberry plants now he wants to plant them in rows and columns inside a self-contained garden bed that is 1.

8 metres by 1.

2 metres.

Please write down these dimensions in centimetres.

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

The garden bed is 180 centimetres by 120 centimetres.

Now Lucas should plant the strawberry plants 30 centimetres apart.

So how far should you plant the first one from the border? Pause video while you write something down and press play for an answer.

The answer is 15 centimetres.

The circle that surrounds the strawberry plant or where it's initially planted has a radius of 15 centimetres.

So how many strawberry plants can he fit along each row? And you can see the second plant is shown on the screen there so you know which direction he's going in.

Pause the video while you word that out and press play when you're ready for an answer.

We could do 180, which is the length of the garden bed in centimetres divided by 30 which is the diameter of the circle surrounding the strawberry plant.

And that would give six so we can fit six along each row.

How many strawberry plants can he fit along each column? You can see now we've planted another strawberry plant below the first one so you can see which direction he's going in there.

Pause the video while you work it out and press play for an answer.

We can get the answer by dividing 120 by 30 and that gives four.

So how many strawberry plants can he fit in the garden bed altogether? Pause way works out and press play for an answer.

We have an array that is six by four.

So when we do six multiply by four we get 24.

Now Lucas says if the garden bed was 195 centimetres long instead of the 180 centimetres like we previously worked out, then I would be able to plant an extra column of strawberry plants.

Is Lucas correct? And please explain your answer.

Pause video while I write something down and press play when you're ready to see an answer.

The answer is no, Lucas is not correct.

We can see why Lucas may have thought that because he's added 15 centimetres onto the length of the garden bed and the circle has a radius of 15 centimetres, but that would put the new strawberry plants right on the border and they won't have room to grow on the other side.

So that means the extra column would not be at least 15 centimetres from the border.

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

This task has one question and here it is.

You have a diagram that shows a plan for a community garden.

It has paths that are 80 centimetres wide and around those paths it has four planting boxes.

Each box is labelled with what the intent to grow in it.

For example, cauliflower in the top left box, you are given some information for how far apart each type of plant should be planted once it's in the garden bed.

What is the maximum number of plants that can be planted in each box? In other words, how many cauliflower plants can they plant in that top left box? How many strawberry plants can go in the top right box and so on.

Pause video while you work this out and press play when you're ready for answers.

Okay, let's work through this together now.

A good starting point with this could be to work out any missing lengths that could be useful along the way like we did in task A.

For example, this length here, the width of the strawberry plant bed.

We could do that by taking 6.

2 which is the width of the entire garden in metres.

And then subtract the length of the cauliflower bed and the 0.

8 which is the width of the path and that'll tell us what's left over and that'll be 1.

8 metres.

We could also work out the length of the broccoli bed by doing 8.

6, which is the length of the entire garden.

Subtract the sum of three and 0.

8, which is a width of the cauliflower bed and the width of the path.

And that leaves us with 4.

8 metres remaining for the length of the broccoli bed.

Now we've got that and we have all the information we need.

We can start to work out the maximum number of plants in each box.

For cauliflower, they should be planted 60 centimetres apart so we can work out how many could go in each row, how many could go in each column and then multiply it together and we'll get 30.

Strawberry plants should be 30 centimetres apart so we can work out the number that can go in each row and column by dividing 180 and 300 both by 30 to get six and 10.

Multiply those answers together.

We get 60 strawberry plants.

Now for broccoli, which should be planted 80 centimetres apart, we can do the same method again.

But this time you may notice that one of your divisions gives you a decimal answer 4.

5.

We can't use that decimal answer in our final calculation because remember what these numbers represent.

They represent the number of broccoli plants.

You can't have 4.

5 broccoli plants and we shouldn't round up to five because there isn't enough space for that fifth broccoli plant in the row.

So that means the maximum number we can fit on that row is four, which is why we do four multiplied by six to get 24 as that final answer for broccoli.

And the same goes with the cabbage plants.

You get a decimal answer for one of divisions get 10.

6 recurring.

You don't have enough space for 11 cabbage plants, which means you can only do four multiply by 10 to get 40.

Okay, I hope you're feeling creative now 'cause we're moving on to the third and final part of this lesson, which is designing a park.

Towns and cities often contain parks and these can vary in size.

Some parks are large enough so that people can go for leisure walks, jogs, or play ball games.

And if there are enough trees in the park, then once people are inside they can no longer see a surrounding roads and buildings.

And this can give people a feeling of being away from the urban area.

However, some parks are just small green spaces within built up areas.

These are sometimes referred to as square gardens or park squares.

However, the shapes are not necessarily squares.

These are often found in areas surrounded by offices, apartments, or townhouses which do not have access to their own private gardens.

So they provide a pleasant outdoor space for people to sit, exercise, walk their dogs and so on.

Let's take this scenario here.

A city is planning to build a square garden between four roads that mostly contain offices.

The space is a 70 by 100 metre rectangle.

The city council hosts a competition inviting children from their nearby schools to design its layout by submitting a scale drawing.

They provide the fallen advice to their children.

One is that large trees should be planted at least 15 metres apart so they have room to grow.

Small trees however, can be planted just five metres apart.

They don't need as much space to grow.

Any footpaths should be at least two metres wide to allow for accessibility and a path that is accessible for vehicles should be at least four metres wide.

So Sophia intends to enter the competition.

Let's see what she does.

The park is 70 metres by 100 metres as a rectangle.

So Sophia plans to construct a scale drawing of the park on an A4 sheet of paper an A4 sheet of paper is 21 centimetres by 29 centimetres once rounded to the nearest centimetre.

So Sophia says I first need to decide what scale to use.

The drawing needs to fit on the paper but not be too small.

What scale could Sophia use? Perhaps pause the video, while you think about some options and press play when you're ready to continue together.

Let's see what Sophia does.

She says if I let one centimetre in the drawing represent four metres in the park, then the length of the paper can represent up to 160 metres in the park.

We can see Sophia's calculations at the bottom of the screen here.

If one centimetre represents four metres, then a 29 centimetre length on the paper would represent 160 metres, which you can get even by multiplying both the numbers at the top by 29 or by multiplying both the numbers on the left by four.

But that's just one measurement of the paper we need to check it fits the other way as well.

She says if I let one centimetre in the drawing represent four metres in the park, then the width of the paper can represent up to 84 metres in the park and that's enough as well, 'cause if we do the same method again, we can see that four multiply by 21 is 84 or we can think of 21 multiply by four is 84.

She says I can write my scale as a ratio by expressing the lens in the same units.

So rather than writing one centimetre represents four metres, we could write one centimetre represents 400 centimetres and now they're in the same units.

We can express that as a ratio.

This scale is one to 400.

So Sophia is using a centimetre square paper and a scale of one to 400.

The park is 70 metres by 100 metres and the A4 sheet of paper is 21 centimetres by 29 centimetres.

Let's see what she does next.

She says I can use division to calculate the length of my drawing.

We could do 100 metres, which is the length of the park and convert it into centimetres, which is 10,000 centimetres and then divide that by 400 from our scale, get 25 centimetres for the length of the drawing.

So let's check what we've learned, what should be the width of Sophia's drawing? Pause video away, work it out and press play for an answer.

Well the width of the park is 70 metres and that is equal to 7,000 centimetres and we divide that by 400 from our scale we get 17.

5 centimetres.

So we can now see that's drawn on Sophia's diagram and makes up the fence of the park.

The council specify that a footpath should be at least two metres wide.

So how wide would this be in Sophia's drawing? Pause video while you work this out and press play for an answer.

Two metres is equal to 200 centimetres and when we divide that by 400 we get 0.

5 centimetres.

So on this centimetre square paper it would be half a square wide.

Sophia draws a footpath, its length in the drawing is 20 centimetres.

How long would this footpath be in the actual park? Please give your answer in metres as well.

Pause video while it works out and press play when you're ready for an answer.

The first step could be to work out the length of this path in park in centimetres by doing 20, multiplied by 400 from the scale that gives 8,000 centimetres and then we can convert it to metres by dividing by a hundred to get 80 metres as a length for the path in the actual park.

So the path is 80 metres long and Sophia wants to place large trees along one side of the path.

They need to be at least 15 metres apart.

So she's drawn where one of them will go.

How many large trees can she fit along the side of the path? Pause video while it works out and press play when you're ready for an answer.

We could do 80, which is the length of the path in metres and divide it by 15, which is how far apart the trees need to be in metres.

That gives 5.

3 recurring, which means we can plant a maximum of five trees along the length of that path.

Here is Sophia's found design and isn't it fantastic? We have a fountain in the middle.

We have large trees and small trees and we can see which ones are which based on the key.

We've got paths.

Some of them look wide enough for a vehicle to get around that, the ones around the outside.

And also there's a path going to the middle, which is wide enough for a vehicle and I think we need that so a vehicle can get to the fountain 'cause the fountain will need maintenance.

We can see that there's a fence around the outside of the park, but there are gaps in that fence to allow people to come in and out through those pathways in the corners of each park.

The key makes clear what everything represents in the diagram.

Also, we have a scale in there so we know how big this diagram is in comparison to what the park will be or how big the park will be in comparison to this diagram.

Do you think about all these features when you plan your own park? 'Cause that's what you're going to do now in Task C, a city is planning to build a park in a residential area.

Please use the information given to you below on the screen here to design its layout and construct a scale drawing.

Now you can either use paper for example, it could be on A4 paper or A3 paper.

It could be square paper if you want to as well.

Or you can use dynamic software such as GeoGebra or Desmos to help you do your drawing, please include a scale on your diagram and a key.

It doesn't matter what scale you use, but it should be appropriate so that the diagram will fit onto your paper but not be too small so you can still see what everything is.

And then there's a question for you to consider in part B.

Pause while you do all this and press play when you're ready to continue.

Okay, I hope you enjoyed that and made something that is both creative and accurate at the same time.

Your answers will vary and so will your scales as well.

For example, if you're using A4 paper, then an example of a scale could be one to 2,500.

In this case, one centimetre would represent 25 metres and that would fit quite nicely onto the paper.

But do check that your diagram has the scale written down somewhere and also a key as well.

For part B, you had to plan a running route along the path to your park and it should start and finish in the same place and calculate the length of the roots.

Now again, your answers will vary depending on the design of your park.

For example, the perimeter of the park will be 2.

2 kilometres altogether.

Therefore, if you have a path that is just about inside the park that is close to its edges, it could be used as a route that is slightly less than 2.

2 kilometres.

However, if you also have some paths going inside the park and you include those in your route, then your route will be longer than 2.

2 kilometres.

Fantastic work.

Let's now summarise what we've learned.

Urban greening is a process of adding green parks, trees, cycle lanes, or other initiatives that improve the sustainability of a town or city, improve the mental wellbeing of its population and reduce its carbon footprint.

When designing green spaces, restrictions are likely to exist, so it's always worth checking what they are.

And a scale model or a map can be a helpful way to visualise the end results of any design, and that's not just with parks and green spaces, it can be with other aspects of design as well.

Well done today, have a great day.