Lesson video

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

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

So let's get started.

In today's lesson, we are exploring agricultural workers, specifically those that work with animals.

So by the end of today's lesson, you will understand just some of the ways that maths can be used by people who work in this profession.

Now, there's a couple of keywords we're gonna be using today, and these should be familiar to you, but if they're not, feel free to pause the video right now and have a read through their definitions.

Our lesson today is broken into two parts, and we're gonna begin by looking at Geometry in agricultural work.

What areas of maths do you think an agricultural worker who is working with animals might use? Pause the video and have a think now.

What did you come up with? Here's some of my suggestions: I said area, multiplication, division, percentages, money, weights and measures, temperature, and time.

During this lesson, we're going to look at quite a few of these.

A farmer has a barn with dimensions of 10 metres by 25 metres.

They want to work out how many of each animal they can safely house in the barn.

Now all animals require a different minimum area in which to live safely and comfortably.

Here's a table showing just some of them.

How many of each type of animal can safely fit into the barn? Let's investigate.

What will the farmer need to do first? Well, they need to know the area of the barn.

What is the area of a rectangular barn measuring 10 metres by 25 metres? That's right, it's 250 square metres.

How many of each type of animal can safely fit into the barn? Well, how's the farmer going to calculate the maximum number of animals the barn can hold? That's right.

They're going to do some division.

So how many cows can the barn safely hold? Well, in order to work that out, we do 250 divided by 10, which means we have 25 cows that can safely fit into the barn.

What I'd like you to do now is calculate the number of chickens, pigs, and sheep that the barn can safely hold.

Pause the video and do this now.

Welcome back.

How did you get on? Well, let's check.

So the number of chickens we can safely hold is 250.

For pigs, it's.

Now, this one's a bit tricky.

It looks like it's 113.

64 pigs.

That's to two decimal places.

But that doesn't make sense.

So we need to round here.

Now, we have to be careful.

We can't round up to 114, even though that's what our rounding rules might tell us.

And that's because 114 pigs won't fit safely into the barn, but 113 will.

Remember there wasn't quite enough space for all 114.

So we need to round down in this case.

And then for the sheep, there's 125 sheep that can fit into the barn.

Well done if you've got those all right.

Now the farmer can get lots more chickens in that barn than he could have any of the other animals.

Does this mean they should use the barn for chickens to give themselves maximum profitability? Well, no, it doesn't.

Now why doesn't it? Well, there are other factors to consider.

What do you think these might be? That's right.

There's the cost to purchase the animals in the first place, the cost of care for these animals, the cost of feeding these animals, and the cost of the bedding.

Don't forget the cost of vaccinating the animals.

We want to keep them healthy after all.

And there is, of course, the price of the produce when we sell it.

We will consider this in the next learning cycle.

It's time for our first task.

For each of the following, calculate the maximum number of each animal which can be safely and comfortably looked after in each of these barns.

Pause the video while you work on this task now.

Welcome back.

How did you get on? Let's go through and mark these answers, then.

So for question One-A, you should have had 150 cows, 1,500 chickens, 681 pigs and 750 sheep.

For part B, we should have 250 cows, 2,500 chickens, 1,136 pigs and 1,250 sheep.

And then for part C, we should have 140 cows, 1,400 chickens, 636 pigs, and 700 sheep.

Well done if you've got those all right.

It's now time for the second part of our lesson where we're going to look at costs and percentages.

What I'd like you to do now is take some time to research how much it costs to keep and care for each of the following animals in the UK.

So that's dairy cows, chickens, pigs and sheep.

Pause and do this now.

Welcome back.

What did you find out? Now, I'm gonna share with you what I found when I did my research.

Now, you are very welcome to use the figures that I found, or you can use your own for the next parts of this lesson.

Bear in mind, if you're using your own, you'll obviously get different answers to me, and that's absolutely fine.

Just check that your working matches.

So here are the animals, and this is the cost of care I found.

Now I've got costs per day, per year, per month for these different animals, depending on what I was able to find out.

Now, what might it be useful to do so that I can compare these costs? And you might have already done this if you found your own figures.

That's right.

I need to work out the cost per the same amount of time for each animal.

So I'm gonna go with per year here.

So I'm gonna start with the cows.

What do I need to do to calculate the cost per year of caring for one cow? Well, I have the cost per day, therefore, I need to multiply this by the number of days in a year.

So 3.

75 pounds x 365 gives me 1,368 pounds and 75 pence.

Now I've updated my table.

So let's look at the chickens.

Now, what do I need to do to calculate the cost per year of caring for just one chicken? That's right.

I have the cost per year for four chickens.

So I need to divide by four to find the cost for one chicken.

So that's 50 pounds.

So let's update my table.

There we go.

Now let's do the pigs.

What must I do to calculate the cost per year for caring for one pig? That's right, I have the cost per month, so I need to multiply by 12.

So that's 240 pounds for the year.

And finally, the sheep.

What do I have to do to calculate the cost per year for caring for one sheep? I bet I didn't catch you out.

I have nothing to do because I've already got that.

It's 95 pounds.

So this must mean that it's best to keep chickens.

What do you think? Take a moment and chat with the person next to you or have a think for yourself.

Welcome back.

So do you agree? Is it best to keep chickens? Well, now remember, a different number of each animal can fit into the barn.

So I need to find the total cost to care for all of those animals.

Bear in mind, I also haven't considered the cost to purchase and the price that any produce would sell at.

So it's still quite a lot to work out here.

So what I've done is I've updated my table and added a column for the number of animals that could safely fit into the barn.

So the total cost now for the cows is going to be 34,218 pounds and 75 pence.

What I'd like you to do now is work out the total cost for the maximum number of chickens that I could safely house in the barn and the pigs and the sheep.

Pause the video while you work this out now.

Welcome back.

How did you get on? So let's see if you've got the same totals as me.

For the chickens, I have 12,500 pounds, for the pigs, 27,120 pounds.

And for the sheep, 11,875 pounds.

Well done if you've got those all right.

I've now got my total cost of care per year for the number of animals that could safely fit into the barn.

Well, now it looks like it's best to keep the sheep.

What do you think? Am I right? Explain your answer either by writing it down or by talking to the person next to you.

Welcome back.

So what did you say? Well, I hope you pointed out that I also need to consider the price at which any produce is sold at.

So far, I'm paying out a lot to keep these animals, but I'm not actually making any money.

Hmm.

It's not gonna help me in the long run.

So let's start with dairy cows.

Well, what do dairy cows produce? Well, they produce milk.

So what information do I need so that I can work out the profitability of a dairy cow? I need to know the amount of milk a cow produces per day and what price I can sell it for.

Well, how many litres of milk do you think one cow produces in a day? Well, on average, a cow in the UK produces 22 litres of milk per day.

Remember, I've got 25 of those cows, and each cow produces an average of 22 litres of milk per day.

We'll assume the selling price of a litre of milk is 37.

6p.

So what's the total income for our barn of cows? Well, let's start by working out the number of litres of milk produced by one cow during a year.

So what calculation do I need to do? That's right.

22 x 365.

So one cow is producing 8,030 litres of milk per year.

But remember, I've got more than one cow.

I have 25 cows.

So what's the total number of litres for our whole herd? What do I need to do? That's right, that's that 8,030 from before multiplied by 25, meaning that my herd of cows is producing 200,750 litres of milk per year.

So let's work out the total income I receive.

In other words, from my cows, I'm receiving 75,482 pounds over the course of the year.

And what about those chickens? Well, each chicken produces an average of 300 eggs per year.

We'll assume the selling price of a dozen eggs, so remember a dozen is 12, is 143 pence per dozen.

So what's the total income for our barn of chickens? Well, the number of eggs produced in a year by all the chickens in total is 75,000.

So what's the total number of dozens I have? What calculation must I do? Remember, I'd reminded you that a dozen meant 12.

So that's 75,000 divided by 12, meaning I've got 6,250 lots of dozen.

So to find the total income I receive, I have to multiply this number of dozens by the 1.

43 pound that each dozen sells for, meaning my income is 8,937 pounds and 50 pence.

Now for the pigs, I'm assuming that the average pig carcass has a mass of 90 kilos, and the selling price of a kilo is 2.

06 pound.

So for the barn of pigs, what's the total income? Well, the total mass of the entire herd of pigs is what calculation? That's right.

113 x 90.

Then, now that I've got the total mass of the herd of pigs, I can work out the total income received.

It means that my pigs generate 20,950 pounds and 20 pence.

It's now your turn.

Can you please tell me what the total income for the barn of sheep is going to be? Pause and do this now.

Welcome back.

Let's see how you got on.

Well, the total mass of our sheep is 2,250, and the total income received is 13,000 and 5 pence.

Well done if you got that.

So what I've now got is an updated table showing the total cost of care per year and the total income per year.

What do you notice? Which of the animals are making a profit? That's right.

It's the dairy cows and the sheep.

Which one of those though is the most profitable? That's right, it's the dairy cows.

The difference between the income and the cost of care is greater than it is for the sheep.

Now, if the farmer decides that they want to keep chickens, what could they do so that the eggs become profitable? Well, they could decide to sell them directly to the buyer instead of sending them to a retailer.

Remember, the retailers are going to mark up the price of an item so that they themselves are making some money.

So it's unlikely the farmer's gonna get as good a price as if they sell directly, but it does mean they've got to do a bit more of the work.

So the farmer looks up the cost of a dozen eggs from different retailers and finds these prices.

So what should the farmer charge for a dozen eggs? Well, what they decide to do is use the mean average price.

So in other words, they're not going to try and be cheaper than all four, but equally, they're not gonna try and be more expensive.

So what is the mean price? It's 3.

48 pounds, and that's what the farmer decides to charge.

So will the farmer now make a profit if that's what they sell a dozen eggs for? What's the total income going to be? That's right.

It's 6,250 multiplied by the 3.

48 pound, meaning it's 21,750 pounds.

So do those chickens now make a profit? Yes, they do because the income is now greater than the cost of care.

Now, the farmer has decided they're not gonna consider keeping pigs.

So which of the other animals are the most profitable? Well, what's the percentage profit in each case? My percentage profit for cows is 120%.

So let's go through one together.

Let's calculate the percentage profit for the chickens.

So I filled in my ratio table, 100% percent is equal to the cost of care per year.

So in other words, the 12,500.

And then the income has gone underneath in the money column.

What's the multiplier that turns 12,500 into 21,750? There's my multiplier.

So remember, it's a ratio table, things have to be in proportion to each other.

So the same multiplier leads to 174.

In other words, the percentage profit is 74%.

Because 21,750 is 174% of 12,500.

It's now your turn.

Please calculate the percentage profit for the sheep.

Pause the video and do this now.

Welcome back.

Let's see how you got on.

So you should have found that, for the sheep, we've got a profit of approximately 9.

5%.

So which of the other animals are most profitable? We'd thought as much from before because we could see there was a big difference between the cost of care and the income.

But this just proves it.

The cows are indeed the most profitable.

However, have we considered all the costs? Well, we didn't consider how much it cost to purchase the animals in the first place.

Cows may be far more expensive to buy upfront than chickens or sheep.

We also didn't consider things like processing and packaging or paying people any wages.

We are assuming, after all, that other people work on the farm with us, rather than just us ourselves.

We didn't consider the fact that costs and selling prices change constantly, which also makes it really hard to ensure that animals are profitable.

I think you'll agree that an agricultural worker who works with animals uses a lot of maths.

It's now time for your final task.

So a farmer decides they want to give their cows more space.

The cost of care for one cow per day is 4.

00 pounds, and each cow is going to be given 12 square metres.

You should assume that each cow produces 20 litres of milk a day, and that the selling price per litre of milk is 38 pence.

I'd like you please to calculate the following: Part A, the number of cows that the barn can house, part B, the cost of care for the cows per year, part C, the income from milk production, and Part D, the percentage profit.

Pause the video while you work this out now.

Welcome back.

Let's look at question two now.

The farmer decides they want to keep chickens.

They're going to give each chicken an area of 15 square metres.

The cost of care for a chicken per year is 50 pounds, and each chicken produces 0.

8 eggs on average per day.

They decide to sell the eggs themselves, selling one dozen for 3.

20 pounds.

Please calculate the following: Part A, the percentage profit, and part B, the farmer wants to make a 60% profit.

How much do they need to charge for a dozen eggs? Pause the video and work this out now.

Welcome back.

Let's go through our answers.

So the number of cows the barn can house is 125.

The cost of care for the cows per year is 182,500 pounds.

The income from the milk is 346,750 pounds, and therefore the percentage profit is 90%.

For question two, you had to calculate percentage profit.

You may wish to pause the video right now and look at the working I have on the screen and check that you have the same figures as mine.

Remember, if you are using your own figures that you found at the start of this learning cycle, then you may get a different answer, and that's fine if that's the case.

For these figures though, the percentage profit is approximately 55.

7%.

Part B, remember, we wanted a 60% profit.

So what I've done is I've worked out the cost of care per year, the number of dozens per year, and then said, "Oh, well, what income do I need for a 60% profit? Well, I need 8,000 pounds per year.

So dividing that by the number of dozens tells me how much I can charge for a dozen eggs.

In other words, to get a 60% profit, I should charge approximately 3.

29 pounds.

Well done if you've got that all right.

It's now time to sum up what we've been looking at today.

So people that work with animals use many areas of maths.

And during this lesson, we looked at ensuring that animals have the correct amount of space to live in safely and how the cost and selling price can affect our profit margins.

Well done today.

I hope you found it interesting, learning about some of the ways that maths can help in this particular career.

I look forward to seeing you again for more maths.

Bye for now.