Lesson video

Hi, I'm Mrs. Warehouse.

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're going to be looking at agricultural workers who work specifically with crops, and how they use maths as part of their everyday role.

So by the end of today's lesson, we're gonna understand just a little bit of the math that's used.

Now, there are some keywords you're gonna need for this lesson.

And you can see them right now on the screen.

Now they should be familiar to you.

But if they're not, feel free to pause the video right now and have a read through those definitions.

Now, our lesson today is broken into two parts.

I'm gonna begin by looking at using conversion in the agricultural industry.

So what areas of math do you think an agricultural worker who's working with crops might use? Why don't you pause the video now, and either have a chat with the person sitting next to you or brainstorm yourself.

Welcome back.

What did you come up with? Well, you might have come up with some of the following.

You might have said area and volume.

Or multiplication and division.

Perhaps estimation.

Money, weights and measures.

Temperature, time.

Conversions, standard form.

In fact, you may have come up with some others too.

And that's great if you did.

Now during this lesson, we're not gonna have time to look at all of these, so we're gonna focus on just some of them.

Can you think of any units of measure for area? Well, you might have come up with square centimetres, square metres, square kilometres.

Now these are units that you are familiar with.

When working with land, sometimes other measurements are used.

Do you know any units of measure for land? Well done if you came up with any of the following.

So acre or hectare.

Now, acres are an imperial unit of land measure.

And hectares are a metric unit of land measure.

An acre is equivalent to 43,560 square feet.

And a hectare is equivalent to 10,000 square metres.

Which is larger, do you think? An acre or a hectare? Well, one foot is approximately 0.

3048 metres.

So let's think about how we convert that.

So what I've done is I've drawn a square.

And each side of the square is one foot in length.

Which means that the area is one square foot.

But if we change those measurements, so instead of saying one foot, it says 0.

3048 metres.

Then I know what I need to multiply in order to find the area.

Multiplying those two values gives us, or squaring those values, gives us 0.

092, et cetera, square metres.

So one square foot is approximately 0.

092, et cetera, square metres.

Which means that an acre, remember, is approximately 43,560 of this.

Which means that acre is approximately 4046.

86 square metres.

Again, this is only approximation.

Because it depends where I stopped in my value.

But what it does tell me though, is a hectare is larger.

Let's do a quick bit of conversion checking now.

I'm going to convert 2.

3 acres into square metres.

I know that one acre is approximately 4046.

86 square metres.

So I can use a ratio table to help me with this conversion.

To change one into 2.

3, I need to multiply by 2.

3.

So I've used the same multiplier, because remember, the multiplicative relationship has to be preserved.

So multiplying by 2.

3 gives me 9307.

778.

And that's how many square metres are in 2.

3 acres.

It's now your turn.

Please convert 5.

2 acres into square metres.

Pause the video and do this now.

Welcome back.

Let's see how you got on.

Did you use a ratio table like I did? It's absolutely fine if you didn't, but you may find it easier if you did.

It makes it really clear to see the multiplier.

I have to multiply by 5.

2.

So when I do that, I discover that 5.

2 acres is approximately 21043.

672 square metres.

Now, in the UK, crops are sold in tonnes.

But in the US, crops are sold in bushels.

It's important for farmers to be able to convert between tonnes and bushels so they can compare the markets.

Since bushels are a measure of volume rather than mass, different crops have different conversion factors.

Here's a table to sum up these conversion factors.

In other words, one bushel of barley is equivalent to 0.

021772 tonnes.

However, we can see that for oats, one bushel is equal to 0.

014515 tonnes.

Soybeans and wheat have the same conversion rate.

So what we've got here is our table showing us the conversions between bushels to tonnes.

We've also got that $1 is equal to 78 pence.

We've got the selling price per bushel in dollars, and the selling price per tonne in UK pounds.

Are farmers in the US or farmers in the UK getting a better rate of pay for their wheat? Well, let's investigate.

First of all, I need to select wheat from my table, and work out how many bushels of wheat are in one tonne.

Well, there's approximately 36.

7 bushels of wheat in a tonne.

To find the pricing dollars of a tonne, I multiply by $5.

86, and this tells me that I'm getting roughly $215.

You'll notice on the screen, I've been careful to use exact values.

Well, as exact as I can be, when I've been carrying on future calculations.

So even right now, I haven't actually rounded my value on the screen.

I'm still trying to use the most accurate value I can.

I'm gonna convert that to pounds.

And when I do that, I get that it's approximately 167 pounds and 95 pence.

And that's approximately what a farmer in the US is getting for selling a tonne of wheat.

Whereas in comparison of selling a tonne of wheat in the UK, the farmer is getting 173 pounds.

So in other words, the farmer in the UK is getting a better rate of pay.

Let's do a quick check to make sure that you've got this.

I've given you the important information on the screen.

And what I want to know is, am I getting a better deal if I'm selling in the US? Or if I'm selling in the UK? I've claimed that the price is better in the US.

But I want you to do some quick calculations to tell me if that's true or not.

Use your calculations to justify your answer.

Pause, and do this now.

Welcome back.

How did you get on? Well, you should say that it's true.

The price is better in the US.

It's time now for your first task.

For question one, I want to know which farmer is getting the best price for oats.

Farmers in the US? Or farmers in the UK? Pause now while you work this out.

Welcome back.

Time for question two.

What is the minimum selling price per tonne of corn in the UK to make the UK price better? Please give your answer to the nearest pound.

Pause and do this now.

Welcome back.

For question three, what is the minimum selling price per bushel of soybeans in the US to make the US price better? Please give your answer to the nearest cent.

Pause and do this now.

Welcome back.

Let's go through our answers.

So for question one, you should have been able to show that the farmer in the UK is getting a better rate of pay.

Now, if you need to, do pause the video now, so that you can check your working against mine.

Question two.

What's the minimum selling price per tonne of corn in the UK so the UK has a better price? You can see my working here on the screen.

And what I've done is shown the minimum selling price is 117 pounds per tonne.

Remember, I've given my answer to the nearest pound, and I couldn't round down.

I needed to round up, so it was definitely better.

Well done if you got this right.

Then for question three, the minimum selling price per bushel of soybeans in the US to make the US price better.

Again, remember, I had to round up to make it better, is $5.

34 per bushel.

Well done if you got those all right.

It's now time for the second part of our lesson.

Well we're going to be looking at how estimation is used.

In order to predict income from crops, farmers use estimation.

To estimate the yield of a crop, they will take one square metre sample from various places in the field.

Then they find the mean of these samples to give an average number of plants per square metre.

This means they can then work out an estimate for the number of plants on their land.

They will also select a plant and count the number of grains per ear to generate an estimate.

What does that actually look like? Well, let's have an example.

A farmer has a 12 hectare wheat field.

Below are the number of ears of wheat in five different square metre samples.

And here are the number of grains on each ear of wheat from one plant.

The first thing the farmer needs to do is to calculate the mean number of ears per square metre, and the mean number of grains per ear.

How do you calculate the mean? That's right.

We have to find the total number of ears and divide by the number of samples.

So what is the total number of ears? Well, let's sum our five values.

When we do that, we get 2,300.

Well, that's not where we end, is it? The next thing we need to do is we need to find the mean number of ears per square metre, and we do that through our division.

2,300 divided by five is 460.

In other words, the mean number of ears of wheat per square metre sample is 460.

So here's the number of grains on each ear of wheat.

What is the total number of those grains? Pause the video while you work this out now.

Well done if you said the total was 480.

Well, we need to divide by the number of ears of wheat.

So we divide by 10, which gives us 48.

A farmer has a 12 hectare wheat field.

The mean number of ears per square metre is 460, and the mean number of grains per ear is 48.

The average mass of a grain is 50 mg, so that's milligrammes.

And the selling price per tonne is 173 pounds.

Now 12 hectares remember, is 120,000 square metres.

Which means that the total number of grains per square metre is 22,080.

And the total number of grains therefore, in the field is, oh, goodness me, it's a good thing we're using standard form here.

Otherwise, that's going to be an extremely large number.

So what I've got here is when I calculated 120,000 multiplied by 22,080, I then converted my number to standard form to give me 2.

6496 times 10 to power of nine.

So the total mass of grain in the field is that value multiplied by 50.

Which means that the total mass of grain in the field is 1.

3248 times 10 to the power of 11 milligrammes.

Now I convert that into tonnes.

And when I do that, I have 132.

48 tonnes, which is a lot easier to look at that number in tonnes, isn't it? Now I know what the selling price is per tonne, so I can multiply this by 173, to get that the income from the field is 22,919 pounds and four pence.

So it's your turn.

Let's see if you can calculate the income from the barley field using the information you can see now on the screen.

Pause and do this now.

Welcome back.

How did you get on? Well, I'm gonna put up the key bits of information that I found when I did my working, so you can compare it to your values.

The total number of grains in the field is 1.

9375 times 10 to the power of nine.

The total mass of the grain would have been 89.

125 tonnes.

And therefore the total income is 13,903 pounds and 50 pence.

Well done if you got that right.

It's now time for our final task.

For question one, calculate the total income for a 15 hectare field of oats.

There's a lot of information there on the screen.

Make sure you read it carefully, and find any values that you need so that you can do some future calculations.

Pause and do this now.

Welcome back.

Time to go through this.

So I started out by working out what the mean number of panicles was.

So in order to do that, I summed up the number of panicles per square metre, and got 2075, then divided it by the number of samples, which was five, giving me a mean of 415 per square metre.

To calculate the mean number of grains per panicle, I summed up the numbers I got from my sample, which gave me 235, and then divided by five, which gave me 47.

The total number of grains, remember, is the mean number of panicles multiplied by the mean number of grains per panicle.

I then also had to multiply by the number of square metres that were in my field.

I had a 15 hectare field, so that means 150,000 square metres.

So the total number of grains was 2.

92575 times 10 to the power of nine.

To find the total mass of the grain, therefore, I multiplied this by 41.

3 milligrammes, and then converted to tonnes, giving me 120.

8, et cetera, tonnes.

Now remember, I didn't round that value at that point.

That's why you can see the dot dot dot on the screen, to show the number does continue.

I then took that value and multiplied by 274 pounds, 'cause that's what I get per tonne, to give me an income for the field of 33,108 pounds and 37 pence.

Well done if you got that right.

If you didn't, but you were very close, then maybe check that you didn't use a rounded figure when you should have been using as close to the exact one as you can.

Remember, your calculator can store working values, and that's a really handy way of making sure you're using the value the calculator generated and not a rounded value too early.

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

Working with crops requires you to have a really good understanding of how to convert between different units.

For example, converting between acres and hectares, converting between hectares and square metres, and converting between different currencies.

Estimation is an essential part of working with crops.

It allows a farmer to predict the yield of their crops, and therefore how much income they're likely to make.

Well done.

You've worked really well today.

And I hope you enjoyed learning about some of the ways maths is useful in the world of work.

I look forward to seeing you again for more maths.

Bye for now.