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 look at how maths can be used in the catering industry.

So let's get started.

Now, on the screen, you can see some keywords that we're going to use in our lesson today.

Now, these words should be familiar to you, but if they're not, feel free to pause the video now while you read through the definitions.

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

What areas of maths do you think a caterer might use? Why don't you pause the video now and have a discussion with the people around you or have a think for yourself? Welcome back.

What did you come up with? Well, here are some suggestions.

Measures, money, conversions, proportion, percentages, ratio, temperature.

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

Maybe you came up with some others and you might even see a bit of it used as well in this lesson.

Now, here on the screen, we have a chocolate brownie recipe.

Now, recipes may sometimes be written in US terms. A caterer needs to be able to convert these measures into metric units.

So let's look at how we do this conversion.

We're going to begin with the conversion rate that one gramme is approximately 1/14 of a tablespoon.

One teaspoon is equivalent to five millilitres and one tablespoon is equivalent to around three teaspoons.

Now, is there enough information on the screen now to convert all of the measurements into metric units? That's into grammes or into millilitres.

What do you think? That's right, there isn't enough information yet.

The teaspoon and tablespoons can be converted, but not the cup measurements we have.

So, what other pieces of information do we need in order to convert the cup measurements into metric units? Well, we need some information about what the capacity of a cup is.

A cup is equivalent to 16 tablespoons.

Is there enough information now to convert all of the cup measurements into metric units? That's right, there is now.

So let's convert all of the cup and spoon measurements into metric units.

Now, I'm going to go through this in the video, but if you want, you could pause now and have a go at doing this yourself.

Right, let's go through this together.

So, which of our ingredients need to be converted into grammes and which into millilitres? What are grammes a metric measure of? That's right, they're a metric measure of mass, in other words, our solid ingredients.

What do millilitres measure? That's right, they're a metric measure of capacity, which is our liquids.

So, which of the brownie ingredients will we measure in grammes? Pause the video and have a discussion now.

Welcome back.

Did you say the following? Butter, the sugar, the cocoa, the sea salt, the flour, and the nuts.

We don't have to convert the eggs after all because two large eggs is exactly the same in the US and in the UK, they're still just large eggs.

Which of the brownie ingredients will we measure in millilitres? Was there anything left over? That's right, the vanilla extract.

So starting with the measures for mass, let's convert all of the cup and spoon measurements into grammes.

Now, remember, these are all going to be approximate because one gramme is approximately 1/14 of a tablespoon.

This means that one tablespoon is effectively 14 grammes, but again, it's an approximation.

A teaspoon, therefore, is 4.

7 grammes.

So in other words, roughly 1/3 of a tablespoon.

One cup would be 16 tablespoons, which is approximately 224 grammes, half is eight tablespoons, which is 112 grammes, 1/4 is four tablespoons, 56 grammes.

And 3/4 is 12 tablespoons or around 168 grammes.

Now measures for the cup split into thirds.

Why might this cause a slight hesitation? That's right.

Our 16 tablespoons, remember, are equal to a cup.

That's so far so good, but three is not a factor of 16, so 1/3 in 16 is not as easy as we might initially think.

Now, that's not a problem, of course, 'cause we know how to do this, but it just means that we're not going to get perhaps the same level of exactness we got when we did it before.

So, what would be a solution to this problem? Well, let's use teaspoons rather than tablespoons.

Remember there are three teaspoons in one tablespoon, so that's equivalent to 48 teaspoons or 225.

6 grammes.

Then 2/3 would be 32 teaspoons or 150.

4 grammes, and 1/3 of a cup would be 16 teaspoons or 75.

2 grammes.

Now, let's see what happens if I use the fact that we know one cup is 224 grammes.

Oh, look at those measurements.

Why are they slightly different, do you think? Well done if you remembered.

They're slightly different because of that approximate symbol.

Remember one gramme is approximately 1/14 of a tablespoon.

So we have approximate values here.

Let's think about what the most appropriate measurement to use would be.

Well, if we look at the cup totals, we've got 225.

6 grammes and 224 grammes.

A pretty good measurement to use, therefore, would be 225 grammes, that's pretty easy to measure on scales.

And then 2/3 of a cup would be 150 grammes and 1/3 would be 75.

They're definitely gonna be a lot easier to measure out and they're close enough that it's unlikely that slight variation is going to affect our baking or cooking, depending on what we're making.

Now let's look at capacity.

Let's convert all the cup and spoon measurements into millilitres.

While a tablespoon is approximately 15 millilitres and our cup, therefore, is 240 millilitres, we can then work out half the cup to be 120, 1/4 of the cup to be 60, and 3/4 to be 180.

Now, for the cup split into thirds, remember 240 was our total, but this is quite easy to third.

So we have 160 millilitres for 2/3 and 80 millilitres for 1/3.

Cups can be converted into grammes or millilitres, and the conversion rate we've used is just one of the available conversion rates.

However, it is worth noting that the conversion rate can differ depending on what we are measuring, and it's important to be aware of this.

So in other words, different substances have different conversion rates, so it's not a one size fits all.

Let's do a quick check.

Please fill in the missing measurements using the table below.

So in other words, all the information you need is in this table to help you fill in the other missing measurements.

Have a go now.

So pause the video and I'll see you soon.

Welcome back.

How did you get on? Up on the screen now you can see what you should have put down.

Now again, some of these are approximate and some of them I've allowed multiple answers.

You'll notice that two of them I've left as improper fractions, and that's because I'd have always have to round, so I've left it like that just to say this is what you should get.

And of course, if you've given it as a decimal, just check that this would've been the value you got before you converted it to a decimal.

Well done if you've got these all right.

Now we know our conversion rates, we can convert the ingredients in the recipe.

So our butter becomes 140 grammes.

Sugar becomes 280 grammes.

The cocoa is 196 grammes.

The vanilla is five millilitres.

The sea salt is 1.

25 grammes.

The flour is, well, 112 or 112.

5 grammes, and the nuts are 150.

Do we now have all the information we need to bake the brownies? What do you think? Well done if you said no.

Ovens in the UK use degrees Celsius, not degrees Fahrenheit.

We've got to do that conversion too.

So to convert degrees Fahrenheit into degrees Celsius, we subtract 32 and then multiply by 5/9.

So we start with the 325 degrees Fahrenheit, subtract 32, and then multiply by 5/9.

This gives us 163 degrees Celsius to the nearest integer.

So let's do a quick check.

I'll do one first and then it's your turn.

To convert degrees Fahrenheit into degrees Celsius, we subtract 32 and then multiply by 5/9.

So let's convert 260 degrees Fahrenheit into degrees Celsius and give our answer to the nearest integer.

So 260, subtract 32, and then multiply the result by 5/9, gives me 127 degrees Celsius.

Now it's your turn.

Please convert 450 degrees Fahrenheit into degrees Celsius and give your answer to the nearest integer.

Pause and do this now.

Welcome back.

You should have got 232 degrees Celsius.

Quick check now.

True or false? 420 degrees Fahrenheit is equal to 402 degrees Celsius to the nearest integer.

Is that true or is that false? Pause and make your choice now.

Welcome back.

You should have said false.

But the question is, what mistake do you think was made? Pause the video while you work out what you think the mistake was.

Did you spot it? It's the order of operations that's incorrect.

When inputting into a calculator, we should have 420 minus 32 in brackets.

If we don't put the brackets there, then the calculator says that we should do the multiplication first before we do the subtraction, and that's the wrong order.

It's time now for your first task.

You'll see two recipes on the screen, a pancake recipe for part A and a scone recipe for part B.

Please convert the following recipes and oven temperatures into UK units of measure.

Pause and do this now.

And on the screen are your answers.

Now, please feel free to pause the video and just check these against what you have.

If you are very, very close, just check that conversion, 'cause remember, they were approximate measurements used earlier, so do just be careful.

Well done if you've got these right.

It's now time for the second part of our lesson, which is percentages in catering.

Up on the screen you can see a pineapple chicken recipe.

Now, some foods need preparing before they're used in a recipe.

Do you think that any of the ingredients for this recipe would produce any wastage? Well, I think the red pepper, the chicken thighs, the garlic, and the pineapple chunks would all produce some level of waste.

Let's think about what we mean by that.

So although the garlic and the pepper produce wastage, for example, we don't use the stalk of the pepper, and for garlic, we don't use the skin on the outside of it.

So although that is a bit of waste, this doesn't affect our recipe, but the wastage of the chicken and the pineapple do need to be considered.

Now, caterers use percentages to work out how much of a particular item they need to buy for the recipes.

So once a product is cleaned, trimmed, and portioned, it is called the edible portion or EP.

The EP is important because it reflects the true quantity needed and the true cost of the food.

Caterers use percentage yield values to calculate the EP.

For this, we're going to use the fact that percentage yield for chicken thighs is 79%, and for pineapple, 52.

So there are tables that chefs and caterers can use, which give an average percentage yield, but many calculate their own based on the intended use of the ingredients, the quality of the ingredients, the equipment, and their own skill levels.

So, how do you think a percentage yield is calculated? Well, we weigh the mass of the purchased product, we prepare the product, and then we reweigh it.

The percentage yield is the mass of the prepared product divided by the mass of the purchased product and then multiplied by 100.

So a chef prepares five kilos of kale.

The prepared product has a mass of 3.

7 kilos.

What is the percentage yield? Well, we do 3.

7 divided by five multiplied by 100.

Our percentage yield is therefore 74%.

Let's do a quick check here.

What's the percentage yield for a chef that purchases 20 kilos of sweet potatoes and, after preparation, has 16 kilos of sweet potatoes? Well, that's 16 divided by 20 multiplied by 100, or 80%.

It's now your turn.

Can you work out the percentage yield for a chef that purchased four kilos of mushrooms and, after preparation, has 3.

88 kilos of mushrooms? Pause and do this now.

Welcome back.

You should have done 3.

8 divided by four multiplied by 100 to give 97%.

That's a really good percentage yield.

So let's go back to our recipe of our pineapple chicken.

A 79% yield means that only 79% of the purchase weight is usable.

So, what weight of chicken thighs needs to be purchased so that we are left with 450 grammes after the preparation is done? Well, remember, the edible portion was 79% of the purchase mass.

In other words, 450 grammes, which is what we want to end up with, is equal to 0.

79 multiplied by the purchase mass.

Or we can use our inverse operations here.

450 divided by 0.

79 gives us a purchase mass of 569.

6 grammes to one decimal place, which means that we need to buy at least that amount.

So we could buy a bit more, but we certainly can't afford to buy less.

What weight of pineapple needs to be purchased to be left with 250 grammes after the preparation is done? We have to be careful here because this time the percentage yield is 52%.

In other words, 250 grammes is equal to 0.

52 multiplied by the purchase mass.

So inverse operations leads us to a purchase mass of 480.

8 grammes to one decimal place, which we might obviously round to the nearest gramme.

Let's do a quick check.

I'll do one and then it's your turn.

The percentage yield of a butternut squash is 66%.

The restaurant needs 10 kilos of butternut squash to make soup.

So, how many kilogrammes of butternut squash do they need to buy? And we're gonna give our answer to one decimal place.

Well, we need 10 kilos to go into the soup, and the percentage yield was 66%, so we're gonna multiply the purchase mass by 0.

66.

Inverse operations leads us to say that our purchase mass is 15.

2 kilos to one decimal place.

It's now your turn.

Please can you read the question on the screen and then calculate how many kilogrammes of onions I need to buy so that I have the five kilos I need to make the soup.

Pause and do this now.

Welcome back.

What did you get? Well, by calculating five divided by 0.

89, you should have got to one decimal place that I need to buy 5.

7 kilos of onions.

Now, you'll have noticed that initially it said 5.

61 and that might make you think you need to round down.

However, it's how much do I need to buy so that I'll definitely get my five kilos.

If I bought 5.

6 kilos of onions and then calculate 89%, I'm not going to get the five kilos I need, so I needed to round up here.

It's now time for our final task.

For question one, calculate the purchase mass in order to guarantee that we have one kilogramme of each food listed in the table.

Please give your answers to the nearest gramme.

Pause and do this now.

Question two.

We've got here a recipe for some soup, and what you can see is the amount I need for five servings.

On the left, we've got a table displaying the different types of vegetables along with their percentage yield and their cost per kilo to buy.

Part a, calculate the mass to the nearest gramme for each vegetable that the restaurant needs to buy to ensure they can make 50 servings of soup.

Pause and do this now.

Part b, assuming the cost is proportional to the mass, what is the cost to buy the necessary vegetables? Please round up to the nearest penny.

Pause and do this now.

Part c, how much do you think the restaurant should charge for a bowl of soup? Now, that's an interesting one.

You might want your answers to part a and b here.

Pause and do this now.

Let's go through the answers.

Question one.

You can see the mass to purchase in the table displayed on the screen.

For the ones that I've put an asterisk by, that's to show that you needed to round up, even though the calculation might make you think you need to round down.

Now feel free to pause the video so you can check my answers against your own.

Well done, let's look at question two now.

Part a asks you to calculate the mass to the nearest gramme for each vegetable that the restaurant needs to buy to ensure they have enough servings of soup.

Now, they wanted to make 50 servings, so the first thing I did was I scaled up my recipe.

In other words, I took the measurements that were for five servings and multiplied by 10.

So the restaurant will need 5.

6 kilogrammes of chopped onions, which means they have to purchase more than that.

So once I'd worked out the amount of the vegetables that I needed to make 50 servings, I then calculated how much I needed to purchase.

So the final answers that you are looking for are in the table on the left of the screen.

So for example, for cabbage, I've got to purchase 16.

076 kilogrammes, carrots, 3.

609 kilogrammes, celery, 6 kilogrammes, onions, 6.

293 kilogrammes, and potatoes, 7.

655 kilogrammes.

Well done if you've got that all right.

In part b, I said to assume the cost was proportional to the mass, so what's the cost to buy the necessary vegetables? Now, what I've done is I've written in the table a total cost for each of the vegetables when you buy the total amount you need, and then I've written the total cost at the bottom.

In other words, when you sum that final column, you should get 67 pounds and 11 pence.

Then in part c, I said, well, how much should the restaurant charge for a bowl of soup? Now remember, we can make 50 servings, so 67.

11 divided by 50 gives us a cost per portion of one pound and 35 pence.

Now, that's to make sure that we've definitely got enough to break even.

However, this does not take into account the other ingredients, staff, and energy costs, or the amount of profit you wish to make.

Remember, that's only just covering the expense of buying those five types of vegetables.

I suspect we need to charge a lot more for a bowl of soup if we're actually going to be able to cover other costs and make some profit.

So as long as you said a value in excess of that, well done.

Let's sum up what we've learned today.

It is necessary to convert between US and metric units of measurement when using recipes.

US recipes tend to use cups and spoons as their units of measurement and UK recipes use the metric units of grammes and kilogrammes.

You may even see some old UK recipes using pounds and ounces.

Caterers use percentage yields when calculating products to buy as these consider the wastage of the product.

Well done, you've worked really well today, and I hope you've enjoyed learning about some of the ways maths is useful for the people who work in the catering industry.

I look forward to seeing you next time for some more maths.

Goodbye for now.