Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from our unit of lessons on financial maths education.

I'm really looking forward to exploring some of the ways that we use maths in order to help out with our personal finances.

So let's get started.

By the end of today's lesson, you'll be able to compare the overall cost and benefits of a range of goods and services.

Well, I'm gonna be using the phrase direct proportion today, and you can see the definition for direct proportion on the screen now.

Feel free to pause the video if you want to have time to read through this.

Our lesson is broken into two parts.

We're gonna begin by determining value for money based on price.

A shop sells the same range of eggs in two different sized boxes.

How could we determine which option is better value for money based on their prices? Pause and have a quick discussion now.

Welcome back.

What did you say? Well, Jun says, "Buying two small boxes would result in the same number of eggs as buying one large box.

So we could compare the cost of two small boxes with the cost of one large box." Is that what you said? Well, let's do that.

And two small boxes will cost us 3 pound 60.

So if we want to buy 12 eggs, it would be cheaper to buy one large box rather than two small boxes.

"Therefore, the large box is better value for money," says Jun.

Now could you justify this in a different way? And maybe this is what you did.

Aisha said, "We could consider the price per egg." Well, if six eggs cost 1 pound 80, that means that one egg costs 30 pence.

For a box of 12, they cost 3 pound, and that means that one egg costs 25 pence.

"The price per egg is cheaper in the large box.

So, the large box is better value for money." Let's compare Jun's method with Aisha's.

What's the same, and what's different? Pause the video while you discuss this now.

Welcome back.

What did you come up with? Well, here's an example of a difference.

Jun has used multiplication whilst Aisha has used division.

Something that's the same is that both methods compare the price for the same number of eggs for each option.

So in Jun's case, he was comparing the cost for 12 eggs under both different options, whereas Aisha compared the cost for one egg for both options.

Let's do a quick check on that.

A shop sells two different sized containers of water.

Which is the best value for money? Pause the video and work this out now.

Welcome back.

Which option did you go for? Let's consider comparing if we were buying three litres under each option.

So for the smaller container of water, if I wanted to buy three litres, I'd need three containers, which will be 1 pound 65 in cost, but the other one costs 1 pound 50 for three litres.

So the three-liter container is better value for money.

Back to our example with eggs.

This time, though, we've got the same range of eggs in two different sized boxes, and this time the larger box has got eight eggs in it, not 12, and the price has changed.

How could we determine which option is better value for money based on the prices of these eggs? Well, Sam says, "24 is a common multiple of six and eight.

So, I could calculate the cost of 24 eggs with each option." Absolutely, Sam, you absolutely could do that.

So, let's do that.

Four boxes of six cost us 7 pounds 20.

But for the box of eight eggs, I would need three boxes, and that would cost 7 pounds 80.

So if we want to buy 24 eggs, then it would be cheaper to buy four boxes of six eggs.

The boxes with six eggs are better value for money therefore.

Could you justify this in a different way? Of course you could.

You could work out the price per egg, and that's what Lucas is going to do.

Six eggs cost 180 pence, which means that one egg costs 30 pence.

Here with our eight eggs costing 260 pence, we have that one egg costs 32.

5 pence.

The price per egg is cheaper for the box of six eggs, so that's the box that's better value for money.

Can we justify this in a different way? Well, Laura says, "I could work out the price per egg in the smaller box and then add the price of two eggs to the 1 pound 80." Ah, interesting.

So Laura works out that one egg costs 30 pence.

So eight eggs would cost us 2 pounds 40.

And this shows that the box of six eggs is better value for money, even though this isn't actually a practical solution because I can't buy exactly eight eggs using boxes of six.

Let's do a quick check.

A shop sells two different sized containers of water, a two-liter container and a three-liter container.

Which is the best value for money? Pause the video while you work this out now Welcome back.

Which one did you go for? Well, you should have picked the two-liter container.

That's better value for money.

Six is the lowest common multiple of two and three.

So if I bought three two-liter containers of water, it would cost me 2 pounds 85 pence, whereas if I bought two three-liter containers of water, it would cost me 3 pounds.

Three shops are selling watermelons.

Two of the shops have offers on.

The watermelons are the same size and quality in each supermarket, and it's important to know that.

So what I'd like to know is which shop offers the best value for money.

Pause the video while you have a discussion now.

Welcome back.

Which one did you go for? Well, let's explore these and find out.

We could calculate the cost of buying different quantities of watermelons in each shop, and this can be done using a spreadsheet.

So for shop A, it's 3 pounds 50 each.

So what I need to do is simply add on 3 pounds 50 for every additional watermelon I buy.

For shop B, they're 4 pounds each.

When I've bought two, I get the third one at half price.

So to buy two watermelons will cost me 8 pounds, but to go to three watermelons, I'm only gonna add on 2 pounds this time 'cause remember the third one's half price.

And then another 4 pounds to buy four and another 4 pounds to buy five.

For shop C, they're 4 pounds 50 each, but I buy four for the price of three.

So I'm adding on 4 pounds 50, but when it comes to that fourth watermelon, that's free.

And then we go back to increasing by 4 pounds 50.

So now we can see for different amounts of watermelons what that's gonna cost for each of the shops.

So which shop offers the best value for money? What Alex points out, it does depend on how many you want to buy.

And this is what you might have said.

"To buy one or two watermelons, Shop A is the cheapest, but if I want to buy three, Shop B's offer means that that shop is the cheapest.

When buying four watermelons, Shop C's offer makes that shop the cheapest.

But when buying five watermelons, Shop A is once again the cheapest.

So for the quantities in this table, the shop that offers the best value for money differs depending on the quantity I need.

This doesn't show what happens when buying more than five though.

For larger quantities, we may find that one shop always offers the cheapest price." Let's do a quick check then.

So we're gonna continue extending our table.

In which shop would it be cheapest to buy six watermelons? Pause and work this out now.

Welcome back.

What did you say? Well, in the table, I've written down the three values you would get for each shop, and we can clearly see that shop B would be the cheapest.

It's now time for your first task.

Question one: A shop sells the same range of tomatoes in two different sized boxes.

Which box is the best value for money? And justify your answer with reasoning.

Question two: A shop sells the same range of pears in two different sized packs.

Which pack is the best value for money? Justify your answer with reasoning.

Pause the video and work this out now.

On the screen you can see three different shops along with the price to buy pineapples there.

And you can see that some of the shops have offers on.

In which shop is it cheapest to buy the following numbers of pineapples? Pause the video and work this out now.

Welcome back.

It's time to go through your answers.

So for question one, you should have said the large box of 24 tomatoes is the best value for money.

And you can see on the screen one example of a justification, but you could have done an alternative approach, and it's absolutely fine if you did.

Question two, which pack is the best value for money? You should have said the small pack of pears is the best value for money.

And again, you can just see one example of a justification here.

Alternative approaches were absolutely fine too.

Question three: In which shop is it cheapest to buy the following numbers of pineapples? Well, part A was shop A.

For B, it was shop B.

C, it was shop C.

D, it with shop C, and E, shop C.

It's now time for the second part of our lesson, and that's on value for money as a personal concept.

So based on price, the large box of eggs is better value for money than the small box of eggs.

But why might someone choose a small box rather than large box? Pause and have a quick discussion now.

Welcome back.

What did you say? Well, Jun says, "I'm unlikely to eat 12 eggs before they go off.

So if I buy a large box, then some eggs will end up being thrown away.

That means the extra cost would be a waste of money." The same item of food is sold in two quantities.

So which is the best value for money based on their price? Well, we can see here that if there's 500 grammes for 1 pounds 20, then a kilo will cost 2 pounds 40.

If we've got five kilos for 8 pound, then one kilo costs me 1 pound 60.

Therefore five kilos for eight pounds is the best value for money.

But what else might someone consider when deciding which option to choose? So context is important when deciding which option is best.

How might the type of food affect someone's decision in each case? So let's consider if tomatoes were being bought or if it was pasta.

Well, Andy says, "Based on price alone, the larger quantity is best value for money." So I should five kilos of tomatoes and five kilos of pasta.

However, Andy correctly points out that "I'm not gonna eat five kilos of tomatoes before they'd go off, so smaller quantities would be better.

The pasta of course keeps for a while, and therefore buying five kilos might be the best option, so long as we can store it." Now, special offers in shops can make it cheaper to buy multiple quantities of the same product.

Why might shops use offers like the ones below? So for example, we've got buy two, get a third half price, and buy four for the price of three.

Sofia points out, "With each offer, it is tempting to buy a third watermelon," because in offer two, I'll get a free one if I do that.

And in offer one, my third one's only half price.

Sofia points out, "What if I don't want to buy a third watermelon? That could be a waste.

It seems like these offers are trying to tempt me to spend more money rather than save money." She's got a point.

Let's do a quick check.

A cinema is showing two films. The entrance price to each film is 6 pounds 50.

Film A is 90 minutes long.

Film B is 120 minutes long.

Lucas says, "Well, the 120-minute film is better value for money." Explain why Lucas may not be correct.

Pause the video and do this now.

Welcome back.

Did you say something along the lines of, "It depends on the quality of the film"? Also, am I even interested in film B? Maybe it's not something I don't really like, and so I wouldn't want to see that film.

Let's look at this one.

A shop has an offer on pineapples, buy one and get an extra one half price.

Sam says, "I can save money by buying two pineapples at a time." Explain why Sam may not be correct.

Pause and do this now.

Welcome back.

Well, Sam might not eat the second pineapple, meaning it would be a waste of food and money.

It's time for our final task.

Question one: Aisha is buying some milk, and the shop sells milk in four different sized cartons.

And you can see them on the screen now.

For part A, starting with the worst value for money, sort the options in order of value for money based on their price.

And part B: Why might Aisha not buy the option which is best value for money? What other factors might she consider when making her choice? Pause the video and work this out now.

Question two: A shop has a buy one, get an extra 1/2 price offer on the following items. For each item, consider whether it would be worth buying an extra one for half price.

Explain any factors other than price that should considered.

Pause and do this now.

Question three: Sam and Jun are planning to play some games of pool.

There are two options for payment to play on the table.

Option one is 2 pound per game, and option two is 10 pounds per hour with unlimited games during that time.

Sam and Jun are considering which option would be cheaper for them.

What factors should they consider? Pause and work this out now.

Let's go through our answers.

So for question one, I said to sort the options in order of value for money based on their price, starting with the worst.

Well, here's the price per pint, and therefore the order is one pint, two pints, four pints, and six pints.

Now, although the six pints might be the best value for money, why might Aisha not buy that option? Well, milk usually goes off within a week, so if Aisha's not going to use six pints of milk in a single week, that might not be a good option for her.

So she should consider how much milk she typically uses in a week.

Question two, would it be worth buying an extra one for half price for each of these items? Well, bread usually goes off within one to two weeks, so it depends on how much you'd eat in that time.

You might not want to buy the extra loaf.

It's likely to go to waste.

However, some people are happy to freeze bread until they need it.

Now soap does not expire, or there's a very, very long time before an expiry date.

Soap runs out with usage and will need to be replaced.

Therefore, buying an extra bar of soap for half price could save money in the long term.

Now, the newspaper.

You are unlikely to want two copies of the same newspaper unless you're buying a copy for someone else.

Therefore, it would not be worth buying an extra copy.

Now let's look at question three.

Well, you might have said, "How long they want to play for." That's one of the factors they might consider.

So for example, if they're only gonna play for 30 minutes, option one might be better.

You might have also said, "How long it normally takes 'em to complete a game," and maybe that's the second factor.

So if their games typically last less than 10 minutes, then they could play six games in an hour.

Therefore option two would be cheaper than option one.

But if their games usually last around 15 minutes, then they're only gonna be able to play four games in an hour, and therefore option one would be cheaper than option two.

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

There are different ways to calculate value for money, and price is only one factor.

Mental calculations and technology can help determine value for money, and value for money is a personal concept.

When presented with offers that incentivize buying extra items, it can be helpful to decide whether you want or need the extra items by considering whether they are likely to go to waste.

Well done.

You've worked really well today.

I look forward to seeing you for more lessons in the future.

Goodbye for now.