Key Stage 3 Ecomaths


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This is Ecomaths, a brilliant way of looking at

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fascinating, real-life situations

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to understand how maths can be used to help create a sustainable future.

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In the first film we explore renewable energy using algebra.

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Then we look at food production comparing lamb and snails

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using area, fractions and ratios.

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And finally, in a trial of a natural pesticide,

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we calculate volumes and concentrations using standard form.

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VIOLIN MUSIC PLAYS

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Hiya, I'm Stef.

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Now, if you want to keep warm and cook food you need fuel,

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and the oldest fuel known to humans is this stuff - wood.

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You might think that all wood is pretty much the same,

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but what's amazing is that different wood

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contains different amounts of energy, sometimes very different.

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But why does it matter? If we want to get warmer,

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why don't we just stick another log on the fire?

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Well, when we burn any fuel we come across global warming issues

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that affect the entire planet, so it's crucial to understand

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how much energy is in our fuel

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so that we can make the best possible use of it,

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and that's where Ecomaths comes in.

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It's a brilliant way of using maths

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to help make the world a better place.

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'And if you want to know about wood, ask a woodsman.

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'This is Martin Charlton.'

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-Cup of tea.

-Hey, top man!

-There you go.

-So, Martin,

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how come there is energy in wood?

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It's carbon.

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The trees take the carbon dioxide with the sunlight,

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turn it into carbon and oxygen and so it's a carbon fuel.

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So does all wood have the same amount of energy in it?

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Yes, it can. It all depends on the amount of moisture

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you've got in there and the density of the wood,

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but it is the moisture that's the critical thing.

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In an oak tree, for example, you will have 350 litres of water.

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In one of these pine trees there will be anywhere between 15

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and 20 litres of water at any one moment in time.

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So before you can burn it you need to get the water out.

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-So I have here a very damp piece of wood.

-Yup.

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I mean, you can literally see the dampness in it,

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and so, if I put that on the fire, what happens?

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It will only smoulder, it won't burn,

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because the energy in the fire, the heat in the fire,

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is going to dry the wood out first,

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it will drive the water off as steam, before it can actually burn the wood.

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Let's try to understand how much energy is released

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when we burn different types of wood,

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and here's where a bit of algebra comes in handy.

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So, Y. Y is the amount of energy that's contained in the wood

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that can be released when we burn it.

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X is the mass of the wood, the amount of it that we've got.

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But it all depends on the different amounts of moisture in it.

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It's a simple equation. When you double the amount of wood,

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or biomass, X, you get twice as much energy, Y, out.

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The tree - we'll select the tree for various reasons,

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whether it's not suitable for fencing or timber,

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can be used for biomass.

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We will fell it, we will section it up into the proper lengths

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for collecting it in the woods, and then we'll stack it

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in the woods so it starts to lose moisture, and when it gets down

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to around about 40% moisture then we'll come along with a big machine

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and extract it to the roadside or to the place that will chip it.

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Look at this!

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All of that huge amount of wood from the forest has been turned

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into a vast mountain of sawdust. Julian, hi, there.

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-Hello, Stefan.

-What's happened, why does it now look like this?

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It looks like this because what we've done is we have chipped it

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into wood chip and it's important that it's not sawdust.

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It's all to do with how our boilers work.

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And what we're trying to do is turn it into something that flows,

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and can be moved in a consistent way

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to get a consistent amount of energy from it.

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What you're doing is you're increasing the surface area

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of the chip in order for the air to get at it

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and therefore for it to be able to burn effectively.

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How do you work out the moisture level of the wood?

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We can, in the field, use moisture meters,

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which are sort of electronic gadgets really,

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but here at the yard in the farm,

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we can use something as simple as a domestic microwave.

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I don't recommend people do it at home, but you take a certain amount.

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Let's say 100 grams. You put it in the microwave,

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heat it up, for a period, take it out, reweigh it.

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Heat it up again, take it out, reweigh it.

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Once the weight no longer changes, you've got a final weight,

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and you subtract that weight

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from your original weight and you have your percentage in effect.

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The final weight of 73 grams

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is subtracted from the initial weight of 100 grams,

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to give the moisture content. In this case, 27%.

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The energy Y is proportional to the mass X of the wood fuel.

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The gradient function M depends on the moisture.

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The lower the moisture, the steeper the gradient

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and the more energy you can get from the wood.

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So in terms of getting energy out of this stuff,

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what are the other aspects of the equation?

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Clearly you've got to cut the wood down,

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so there's energy in terms of the chainsaws used,

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there's energy in terms of the vehicles that are used

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to actually get it out of the woods,

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to transport it from the woodlands to our yards.

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And clearly also in the chipper,

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and then being transported from here,

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being loaded then transported from here to the customer site.

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-Is that a big part of it?

-Indeed.

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We try to deliver within a 15-mile radius,

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maximum of 30-mile radius, and that gives you

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a sense of the distance it travels.

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Compare that to oil, which has often come halfway round the world

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from Saudi Arabia or somewhere like that, and this is a local product

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produced by local people, it's a local energy resource.

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And this is where the fire is.

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Wow, that's terrifyingly hot.

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And it's amazing to finally see all of the energy that was stored

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in the forest finally being released.

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But this massive biomass boiler doesn't heat some factory.

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It heats this place. It's a school,

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and I'm going to find some experts who can tell me all about it.

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-Hi, Eco-Team, how are you doing?

-ALL: Hi!

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Tell me about this biomass boiler, it's just so cool.

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How much wood chip does it use every hour?

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Well, to work it out we took the measurements of each container.

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This container is six days' worth of wood chip to heat the school.

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The students use the measurements to calculate

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how much they need per hour,

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so they can compare it with other fuels.

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That's 2 metres 35.

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So the amount of wood chips that go through that to heat

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the whole school for one hour is 0.247 cubic metres?

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-Yeah.

-OK, well, that's fantastic,

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so now we know how much wood chip the boiler uses.

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The big question is, really, how does that compare to other fuels?

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So, Natalie, you know about this, don't you?

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Well, with the oil it's 3.4 times more energy

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for every kilogram than biomass.

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-Wow, that's a big difference, isn't it?

-Yes.

-So oil,

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-3.4 times more energy. Per kilo that is, isn't it?

-Yeah.

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So it's a big difference, isn't it? So this, this is heating oil.

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That gives you 3.4 times more energy per kilo.

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-Mm-hmm.

-That's a big difference. OK.

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But what I want to know is how does it compare?

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So let's get some gas on here.

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How does wood chip compare to gas?

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Gas, you get three times more energy per kilogram.

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OK, so a little bit different

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but still a big difference compared to it, isn't it?

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Three times more energy per kilo.

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So there's a huge difference in the energy per kilo,

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but what about the cost, is there any difference?

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Um, biomass is about 10% more expensive than gas.

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-Oh, wow. So there is a significant difference, isn't there?

-Mm-hmm.

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So this is really interesting. There's a huge amount less energy

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per kilo, and it's more expensive, so why would you go for wood chip?

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Because it's not burning any fossil fuels.

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Whereas trees can be regrown, we can't get the fossil fuels back

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and in 30 years they might run out.

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-Yeah.

-So overall it's better for the environment.

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Biomass should stay at quite a steady price

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whereas things like oil should increase more

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because there's less of them.

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It's amazing to use maths to unravel the secret behind wood

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as a biomass fuel, and I wondered if this could be inspiring for you.

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Maybe you could change the way that your school uses energy using maths.

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VIOLIN MUSIC PLAYS

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Hiya, I'm Stef and this is glorious Dorset farmland,

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which produces some of the finest food in the world.

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The trouble is food production

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uses a vast amount of energy, water and land.

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And with the world population increasing so fast,

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land is becoming a huge issue.

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But the earth isn't growing in size, so we need to use land

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in the best way possible to feed as many people as we can.

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Now, I'm going to tackle this problem using maths,

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but this isn't any old maths - this is Ecomaths.

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ICE CRUNCHES

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The best thing to start with is protein, cos it's essential

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to our diet, and we get most of our protein from meat.

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But there are other ways to produce protein.

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Ways that might chill your soul.

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Welcome to the weird and wonderful world of the gastropod.

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Meet Sidney.

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'I'm here to find out whether gastropods, or snails to you and me,

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'could be the future of the burger and save the planet along the way.'

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Easy, now!

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Let's go to meet the man who uses clever Ecomaths to produce

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a large amount of snails on a very small amount of land.

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These are the breeding snails.

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They are enormous! They're terrifying!

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The bigger the snail that we use for breeding,

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the bigger the egg we get from it.

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Snails lay eggs?

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-Yep! About 100 eggs in a batch.

-Wow.

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And with our system we ask them to lay eggs every five weeks.

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Now, these have actually hatched and they're small baby snails

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and they are absolutely tiny.

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These are so sweet,

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-you can see they've got those little tiny antennae!

-Yeah.

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-OK, so that's the first stage of being a baby snail.

-Yeah.

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-So can we have a look at the fatties?

-Yeah, sure.

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-So I've got the feed here.

-Yeah.

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-That's all they need?

-That, for one day, yeah.

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That's enough... That's 100 snails? That is tiny,

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when you think about the amount of food you feed to livestock,

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I think it's an amazing use of resources.

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-This is a batch which is now ready for the market.

-Wow!

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How many snails do you produce every week to send off to the restaurants?

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Around about 6,000 each week.

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6,000 snails? That's a huge amount, isn't it?

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Not really, if you think it's only...

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The average amount of snails in a dish on a menu is six.

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That's only 1,000 dishes.

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Mmm, it's not bad. And how much does each snail weigh?

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They weigh between 12 and 15 grams.

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The big question is how much land do you use

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to produce these 6,000 snails?

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The boxes take up around about 400 square feet,

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which is about 37 square metres.

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So snails are a very efficient use of space?

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-I'd say very efficient, yeah.

-Cos they just stack up higher and higher

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rather than spreading out over big fields.

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Well, if you take seven boxes stacked high,

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you've got 700 snails there.

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And then if you go up to 10, that's 1,000 in each stack.

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But there's one last thing I need.

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How much protein is there in your snails?

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There's no fat at all, and there's about 90% protein.

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90% protein, brilliant. That's all I need to know,

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-I've got all of my facts and figures.

-Good.

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-There's your blanched snails ready to cook.

-Fantastic.

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And there's the live ones. Take care.

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-Ha-ha! You're a star.

-Thanks a lot.

-Thank you very much.

-Take care.

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So how does that compare with figures of land use

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to produce more traditional lamb or beef?

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I know some young people who know all about the Ecomaths

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behind lamb production.

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This working farm is part of Oathall Community College

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and today they're weighing the lambs.

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17.

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It's 43 kilograms.

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We return to the classroom to look at the maths.

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We calculated the mean of their growth weight, of their growth.

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-Is that in kilograms?

-Yeah, that's in kilograms.

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And their breed, so Suffolk, Pedigree Suffolk, Texel, just a few.

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So can you choose certain animals because they're fast-growing

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and other ones for taste?

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Why would you choose a different breed, why do you think?

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It all kind of depends on how well they grow

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and what breed will produce the best meat. You want it to taste nice

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but you also want to make money out of it and make a profit.

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-So, Sam and Freya, can I squeeze in here?

-Yes.

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Tell me what you've been up to here.

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Well, we've been working out the amount of land used by lambs.

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So literally the amount of space you require to produce

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-a kilo of lamb?

-Yes.

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We produce about two lambs each week.

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Each lamb, the bit that we use is about 22.5 kilograms.

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Ten lambs needs 4,048 square metres.

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As the farm produces two lambs each week,

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we have to divide that by five.

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We then take the 809 and divide it

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by the amount of protein produced, and that gives us 25.7.

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That is brilliant, because you've used maths to come up with

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something really useful. We now know it takes 25.7 square metres of land

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to produce one kilo of lamb protein.

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That's pretty good, but I've got a challenge for you.

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Can you use the same maths to work out something about this fella here?

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This is Sidney the snail. Can you work out for me

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how much land you need to produce a kilo of snail protein? OK.

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-That sound like a good challenge?

-Yeah.

-Freya, put your hand out.

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Get to work!

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I left them with the data I collected at the snail farm

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in Dorset, and a few friends I brought with me.

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While these guys are finding out how much protein there is

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in these fellas, I thought it might be a good idea to cook them some.

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And this is how you go about it. First of all, get about 100 snails,

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and boil them up in lots and lots of water,

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then chuck them in a pan with lots and lots of garlicky butter,

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and that way, frankly, anything should taste good.

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To make it fair in the lamb v snail comparison, they took 12 grams

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as the average weight per snail without the shell,

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just as they took 50% to be the useable meat per lamb.

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They also adjusted for the different protein content for the dry meat -

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70% for lamb and 90% for snail.

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Their final figures for land use for kilogram per week

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were really surprising.

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0.57.

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So that's 0.57 square metres to produce a kilo of snail protein,

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compared to 25.7 square metres for a kilo of lamb protein.

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So now that we understand the amount of land needed for snails and

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the amount needed for lamb, how do you relate the two figures together?

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We took the two numbers and we came up with a ratio of 1 to 45.

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Brilliant. So you need 45 times the amount of land to produce

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a kilo of protein from lamb than you do from snail.

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So this is a little bit of snails on toast.

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So, first time for a gastropod?

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-Mmmm.

-Mm.

-They're not bad, are they?

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Do you think that there's something important

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about foods like this that take a lot less land to produce?

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Although lamb does take up more land,

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it's usually land that's unable for humans to use,

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like they're grown on hills.

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I think they are a lot better... way to preserve land,

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but, to be honest, I'd still rather eat lamb!

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STEFAN LAUGHS

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Now, snails might not be your cup of tea but when you use maths

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to take a close look at different types of food

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and look at the energy and land and water

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that goes into the production, you can make some choices

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that could really change the world.

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Everywhere you look, the planet is teeming with life.

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It's called biodiversity and it's simply

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the huge variety of living things that make up the natural world.

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But that variety is getting less and less.

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Who knows what that will mean for the good old human being.

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Time is running out but there are solutions,

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and we need maths to find them -

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but not just any old maths. This is what I call Ecomaths.

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But you don't have to go to the ends of the earth to find living things

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that are under threat, and one of the main culprits

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is this - insecticide.

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It's used by farmers and gardeners across the world to kill pests.

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So, what's the problem?

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That's the problem - harmful to the environment.

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So, what's going on?

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I'm here at Swansea University to find out.

0:20:080:20:11

So, Tariq, explain to me about pesticides.

0:20:110:20:15

OK, Stef. Pesticides are chemicals which control organisms

0:20:150:20:20

which are undesirable organisms. They could be weeds...

0:20:200:20:23

Most of us think of pesticides as controlling insects

0:20:230:20:27

which are pests to crops, but they could also be diseases of crops.

0:20:270:20:31

So what are you doing here?

0:20:310:20:32

We're trying to develop alternatives to conventional chemical pesticides.

0:20:320:20:36

We're trying to exploit natural organisms which occur in the soil

0:20:360:20:41

and in our environment, so we're trying to develop these organisms

0:20:410:20:45

as alternatives to the chemical pesticides.

0:20:450:20:49

'This is where they keep all the pests. Let's take a look.'

0:20:490:20:53

Here, for example, we have weevils. There's a whole range of weevils.

0:20:530:20:57

These can actually devastate a whole range of forest trees.

0:20:570:21:01

They have powerful mouth parts and they chew away and remove bark,

0:21:010:21:05

particularly young saplings. It can be starved and stunted

0:21:050:21:08

and it can actually topple over, and basically, it's killed.

0:21:080:21:11

At the university, they're developing naturally occurring fungi

0:21:110:21:15

that have evolved to attack and kill specific bugs.

0:21:150:21:18

One such fungus, called Metarhizium,

0:21:180:21:21

is proving to be a potent biological alternative to harmful chemicals.

0:21:210:21:26

So you're developing alternatives to pesticides.

0:21:260:21:29

How do you go about proving whether they work or not?

0:21:290:21:33

You have to compare our fungus - this is the agent we're developing -

0:21:330:21:37

with the chemical pesticide.

0:21:370:21:39

It has to show that it's just as good in killing the pest.

0:21:390:21:43

One of the most important things is mathematics,

0:21:430:21:46

because you have to prove to a lot of people

0:21:460:21:49

that this thing is working.

0:21:490:21:51

So, Minshad, what are you preparing here?

0:21:520:21:55

This is the fungus, and I'm going to prepare a test.

0:21:550:21:58

It's called an LC50, Lethal Concentration,

0:21:580:22:01

to kill 50% of the insects.

0:22:010:22:03

'Minshad is doing a vital test

0:22:030:22:04

'to see how effective the fungus is at killing pests.

0:22:040:22:08

'These aren't actually the target pests.

0:22:080:22:10

'They're little larvae called Galleria.

0:22:100:22:12

'They're usually chosen to make sure it's a fair test.'

0:22:120:22:16

-Can I pick this up?

-Yeah. They are quite friendly,

0:22:160:22:19

-and this is used as a model host, worldwide.

-Quite friendly!

0:22:190:22:22

First Minshad takes the fungus, here in this Petri dish,

0:22:230:22:27

and makes up a concentrated solution.

0:22:270:22:30

'The preparation has to be done in sterile conditions.'

0:22:300:22:33

He needs to know how many spores there are per millilitre.

0:22:340:22:38

Believe it or not, he counts them.

0:22:380:22:41

He takes a tiny drop and looks down the microscope.

0:22:410:22:44

He counts the spores in the larger square.

0:22:470:22:50

Then another square.

0:22:510:22:53

He does this five times and takes an average, in this case 40.

0:22:550:23:00

As there are 25 squares, this means that there are 25 times 40 spores -

0:23:000:23:05

or 1,000 - in the sample.

0:23:050:23:08

'Since he knows the volume of the sample,

0:23:080:23:10

'he can calculate the concentration.

0:23:100:23:12

'It's 10 to the 8 spores per millimetre.'

0:23:120:23:15

So the final concentration will be

0:23:150:23:17

one times ten to the power of eight conidia per millilitre.

0:23:170:23:20

So, from this I'm going to make a dilution.

0:23:220:23:25

Now he prepares what's called a serial dilution.

0:23:250:23:28

He takes one millilitre of the concentrated solution

0:23:280:23:32

and adds it to nine millilitres of the wetting agent

0:23:320:23:35

in the second tube.

0:23:350:23:36

This makes the second tube ten times less concentrated.

0:23:390:23:44

Minshad repeats the process from one tube to the next.

0:23:450:23:49

You can see from the labels on the tubes

0:23:510:23:53

that the serial dilution gives you lower and lower concentrations,

0:23:530:23:57

each ten times less.

0:23:570:23:59

The last tube is the control with no spores.

0:23:590:24:02

In the LC50 test, they want to know which of these concentrations

0:24:020:24:06

will kill 50% of the bugs.

0:24:060:24:08

The fungus works by piercing the outer casing and infecting the bug.

0:24:110:24:17

The fungus grows and develops spores,

0:24:170:24:19

so that it can spread to other bugs.

0:24:190:24:22

Because the fungus is naturally occurring,

0:24:220:24:24

birds and other creatures that feed on these bugs are unharmed,

0:24:240:24:28

even if they do fancy a nibble at something distinctly unappetising.

0:24:280:24:33

And here are the bugs in the LC50 test.

0:24:350:24:38

It's day eight, so let's see what's happened.

0:24:380:24:42

This looks pretty gruesome.

0:24:420:24:44

What's going on here?

0:24:440:24:46

This is the LC50 test, where I'm testing the different concentration.

0:24:460:24:51

He counts how many have died and fills in the table for day eight.

0:24:510:24:57

The LC50 test results are that between ten to the six

0:24:570:25:01

and ten to the seven spores are needed to kill 50% of the bugs.

0:25:010:25:06

A computer program allows Minshad to calculate the exact concentration.

0:25:060:25:11

Now, it takes 2.3 million spores to kill half of the insects -

0:25:130:25:18

that's a vast amount of spores.

0:25:180:25:20

Well, it just looks a vast amount of spores,

0:25:200:25:23

but in natural conditions you can find the same number anywhere.

0:25:230:25:28

So where are we going?

0:25:280:25:30

'But where do you collect the fungi? Deepest Africa?

0:25:300:25:33

'The Amazon rainforest? No.

0:25:330:25:36

'This parkland is part of the university campus,

0:25:360:25:39

'and lurking in the soil could be a new fungus strain.'

0:25:390:25:43

This is an untreated area,

0:25:430:25:46

and we're hoping to find a bio-control agent.

0:25:460:25:50

So we're looking to find some fungi?

0:25:500:25:52

Yes, we're looking to find fungi.

0:25:520:25:54

'Earthworms are a sign of the rich biodiversity of untreated soil.

0:25:540:25:59

'That's why Minshad chooses this location

0:25:590:26:01

'to search for promising new fungi

0:26:010:26:03

'for the development of biological pesticides.'

0:26:030:26:06

It's only because of the huge biodiversity of the planet

0:26:060:26:09

that we can find something as amazing as a fungus

0:26:090:26:12

that can help us combat pests.

0:26:120:26:14

But you have to do the maths to prove that it works.

0:26:140:26:17

I'm off somewhere else where they're keeping an eye on the environment.

0:26:170:26:21

Birds are often the earliest indication

0:26:230:26:25

of changes to our environment and their impact on biodiversity.

0:26:250:26:29

These students at Dorothy Stringer High School in Brighton

0:26:290:26:32

are carrying out a bird walk and counting the species

0:26:320:26:35

in the school grounds.

0:26:350:26:37

Can you guys count how many gulls there are

0:26:370:26:40

on the top of the main block over there?

0:26:400:26:43

ALL: One, two, three, four, five.

0:26:430:26:47

-Brilliant. Make a note.

-Are you going to mark them on your sheets?

0:26:470:26:50

STUDENTS CHATTER

0:26:500:26:53

Right, we're now coming to the woodland environment,

0:26:550:26:58

so now I want you to...

0:26:580:26:59

You've got your lists - look up in the trees

0:26:590:27:02

and we'll try to see how many we can identify.

0:27:020:27:04

Most important is that you count the number of each species that you see.

0:27:040:27:08

Each winter for four years, the students have been recording

0:27:080:27:11

the birds, and building a valuable database,

0:27:110:27:14

that contributes to a nationwide survey.

0:27:140:27:17

What have you discovered over the years?

0:27:170:27:19

We've got some data here from the main birds

0:27:190:27:23

that actually are in this area.

0:27:230:27:25

Are there any big changes that you've seen?

0:27:250:27:28

The blackbird - it's gone from, in 2009, seven,

0:27:280:27:32

to 0.5.

0:27:320:27:34

-That's quite surprising.

-Yeah, that's quite a big change.

0:27:340:27:37

There's always a constant with the black-headed gulls

0:27:370:27:40

and the heron gulls. They've always been a big species here,

0:27:400:27:46

but the jackdaws have kind of gone down, but the problem is,

0:27:460:27:49

as the recording isn't always at the same time of year...

0:27:490:27:53

-And that'll have a big effect on the numbers.

-Yeah.

0:27:530:27:56

And this is averaged over quite a few different visits to the woods,

0:27:560:27:59

-isn't it?

-Yes.

-Yes.

0:27:590:28:00

Over the course of the whole of the year.

0:28:000:28:02

I think every class...

0:28:020:28:04

-Pretty much every person would have gone through.

-Yes.

0:28:040:28:07

-A lot of people.

-There's quite a lot of data, then, being averaged out

0:28:070:28:11

-and condensed.

-It should be pretty reliable if it's that many.

0:28:110:28:14

'They're not just collecting data - they're also

0:28:140:28:17

'investing in future biodiversity by planting trees

0:28:170:28:19

'to attract butterflies.'

0:28:190:28:21

-So what are we going to do here?

-We'll plant some saplings.

-Yeah.

0:28:210:28:25

-So, you've got to make a T shape.

-Yep.

0:28:250:28:27

-The bottom bit of the T.

-Yep.

-And then make that the top bit of the T.

0:28:270:28:32

'Come springtime, they'll be back,

0:28:340:28:37

'analysing the results of their efforts using Ecomaths.'

0:28:370:28:41

Subtitles by Red Bee Media Ltd

0:28:510:28:54

A new way of showing how maths is used in the real world to help create a sustainable future.

Stefan Gates meets people using maths to find innovative solutions to the ecological challenges of our age. From local food to food waste, recycling to rainwater harvesting, biofuels to biodiversity, this series highlights how maths is crucial to managing our environment.

In this episode targeted at Key Stage 3, Stefan heads into the woods of Sussex to explore sustainable energy and meets a group of students who use algebra to compare different types of energy. He visits a snail farm in Dorset and compares lamb and snail meat by looking at area, fractions and ratios.

And he explores the maths of scientific discovery using concentrations in standard form and cumulative frequency graphs and interprets longitudinal data in a unique fungus trial at Swansea University.


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