Lesson video

Hi, thanks for choosing to learn with me today.

In today's lesson, we're gonna be looking at how maths can help us with our everyday lives.

Let's get started.

In today's lesson on understanding advertising, we're going to look at analysing promotions and marketing claims. Now here are some keywords we're gonna use in our lesson today, proportion and unit.

Now if these words are familiar to you, feel free to carry on, but if they're not, you might like to pause the video now and have a read through.

There are three parts to our lesson today.

We're gonna begin by comparing promotions.

We can use our proportion skills to help us make decisions about value for money.

So for example, a supermarket offers 330 millilitre cans of lemonade in two different size packs.

How can we work out which is better value for money? Pause the video and have a think now.

Well, we need to compare the prices of the same number of cans.

Laura suggests working out the cost for 24 cans under each offer.

Why do you think she chose 24? That's right.

24 is the lowest common multiple of eight and 12.

Aisha, on the other hand, is going to work out the cost for four cans under each offer, and Lucas is going to work out the price per can.

Which of these methods do you think is gonna be the easiest? Well, let's consider each one.

We'll start with Laura.

If eight cans cost four pounds 10, well then I know that I can multiply by three to work out the cost for 24 cans, which is 12 pounds 30.

Under the second offer, I know that 12 cans is six pounds 20.

So doubling gives me the cost for 24 cans, which is 12 pounds 40.

So which one is better value for money? Well, the same number of cans is cheaper if you buy in packs of eight.

So the packs of eight are better value for money.

Now we should see the same thing here, but let's make sure.

So the cost for four cans each.

Well, to get from eight cans to four cans, I need to half.

So you do the same for the money.

That means two pounds and five pence.

And for the 12 pack, well what am I going to divide by this time? That's right, by three.

Well, six pounds 20 divided by three, oh doesn't work out nicely.

It's two pounds and then, oh, I've got that six pence recurring.

Well that doesn't make any sense.

Hmm.

It seems likely it's gonna be two pounds and probably seven pence, but it doesn't really matter.

even if it's two pounds and six pence.

I can still see that the first deal is better value for money.

Now we can't actually buy four cans 'cause they're impacts of eight or 12.

But we compare relative prices per four cans.

Now I don't know about you, but I don't particularly wanna be standing in the supermarket trying to do this in my head.

So I'd probably need to grab out my calculator, or you know, use a calculator app on my phone.

Let's have a think about what Lucas is going to do.

Well if eight cans is four pounds 10, dividing by eight gives me the price per can, which is oh, 0.

5125.

Okay, so around 51 to 52 pence.

What about under the 12 pack deal? Well, dividing by 12 tells me that that's 0.

516 recurring.

It's a little harder to see which one's better value for money here, but still possible.

Now we refer to this method as the unitary method because you're finding the price per individual unit.

Again, pretty tricky without using a calculator, and the price per can does look so similar.

Let's do a quick check.

I'd like you please to put these in order, starting with the deal that is the best value for money.

Pause and have a go at this now.

Welcome back.

Let's start by comparing their prices.

So what I've done is I've looked at the price per donut.

Now remember with the last one, although it's 50 P per donut, the third one is free.

So what I've done is gone, well, the cost for three donuts is a pound and that let me work out the price per donut.

I've now put these in order.

So you should have had C, D, and A, and B.

Lucas wants to buy crisps for his class's end of term party.

There are 15 pupils in his class, and he wants everyone to get one pack each.

So which of these deals is better value for money? Well, we'll start by finding the price per pack.

Oh, that looks like the 24 pack then is the best value for money.

Lucas says, however, I don't want any packs left over.

So can I get 15 packs in another way that ends up being cheaper? If he wants 15 packs of crisps, he could buy three of the five pack deal.

That's gonna cost him five pounds and 25 pence.

And already we can see that's cheaper than just buying one 24 pack.

So even though the price per pack was the best value for money for a 24 pack, because we don't need that many packets of crisps, it's not necessarily the deal we want to go for here.

Laura can see an even cheaper way though.

Have you spotted what Laura's seen? Pause and have a think now.

That's right, Lucas could buy a 12 packet of crisps and a five packet of crisps.

This cost is only five pounds and 10 pence.

Now, shops will use promotions to encourage customers to buy more.

Most of the time, the promotions do offer better value for money.

However, it's always good to check yourself and remember how much you actually need versus how much you could get.

So here we've got some deals.

What might be wrong with each of these promotions? Pause the video and have a go now.

Right, let's look at the cereal one first.

If you look here, we look to what a normal bag cost and then we multiply by 1.

5 to see what the cereal with 50% extra would cost normally.

And that's five pounds 40.

So actually, you're not saving any money here.

It's costing what it would cost anyway.

On the deal for jam, three jars at one pound six each is actually four pounds and 80 pence.

So in other words, it's cheaper to buy three jars individually, rather than using the promotion.

And then for the shampoo, well five bottles will cost us 11 pounds and 50 pence.

So you'll save 50 P in total if you buy five bottles.

However, you end up spending 11 pounds on shampoo just to save 50 P.

Depending on how much shampoo you'll use, it's really up to you if that saving's actually worth it.

Bear in mind, you've got to store those bottles too.

Let's do a quick check.

Laura wants to buy 10 apples.

What's the cheapest way for her to do this? Pause the video while you work this out now.

Welcome back.

What did you come up with? Well, we worked out the price per apple for the six pack.

It's definitely better value for money than buying the apples individually.

Well, two six packs definitely gives me enough apples.

It's gonna cost me three pounds and 98 pence.

What about if I buy just one six pack of apples and then the four apples individually? Well that only costs me three pounds and 67 pence.

So in other words, to get the 10 apples, Laura should buy one six pack and then four individual apples.

It's now time for our first task.

Question one, use two different methods to show that the packs of six rolls are better value for money than the packs of four rolls.

Pause and do this now.

Question two, Aisha needs 500 grammes of mushrooms for a recipe which feeds two people.

And you can see the different options for what she can buy on the screen.

Part A, for each pack, what is the price per hundred grammes? Part B, what would be the cheapest way to buy enough mushrooms to feed two people? Part C, what would be the cheapest way to buy enough mushrooms to feed four people? And part D, what would be the cheapest way to buy enough mushrooms to feed eight people? Pause and do this now.

Question three, which of these promotions are good value for money? Make sure to explain your answer.

Pause and do this now.

Question four, Lucas sees this promotion in a supermarket.

Does this promotion offer a better deal than the price Lucas saw last week? Pause while you work this out.

Time to go through our work.

So for question one, you needed to use two different methods.

What you see on the screen is an example of one of the methods.

So in this one, I found the lowest common multiple of four and six, which is 12.

And then compared the cost for 12 rolls under each deal.

I saw that packs of six were better value for money.

I've also used the method for finding the unit price.

And again, the pack of six is cheaper.

You may, of course, have used a slightly different method.

For example, you might have found the price for 24 rolls.

It doesn't matter, as long as you use two different methods.

Question two, for each pack, what's the price per a hundred grammes? And you can see the three answers on the board.

Underneath, what I've done is I've done a little bit of rounding just to make it a little bit easier to compare.

Part B, so what's the cheapest way to buy enough mushrooms to feed two people? Well, the cheapest way to get 500 grammes is to buy one pack of 600 grammes, costing you one pound 80.

What's the cheapest way to buy enough mushrooms to feed four people? Well, that means you need a thousand grammes of mushrooms. Buying one pack of 600 grammes and one pack of 400 grammes is the cheapest.

And in fact, you have no leftovers here.

Part D, what's the cheapest way to buy enough mushrooms to feed eight people? Well that means you need 2000 grammes of mushrooms. The 400 gramme pack is the best value for money.

And buying five is exactly 2000 grammes.

So there's no wastage whatsoever.

This will, therefore, cost her five pounds and 50 pence.

Now, which of these promotions are good value for money? Well, let's look at the pears first.

Under the deal, you save 17 P when you buy three pears.

Well that seems like a reasonable saving if you're going to eat the three pears before they'd go off.

For the ice cream tubs, you save 20 pence when you buy four tubs.

Well, even though this is a higher saving than the pears, it's a much higher cost.

You've also got to find the space to store and then use four tubs of ice cream.

It's not necessarily, therefore, a good promotion.

For the veggie sausages, well, three of those is going to cost six pounds 90.

The promotion's more expensive than the original price.

That is definitely not good value for money.

And then our final question, does the promotion offer a better deal? Well, let's have a look.

At last week's price, two bottles cost Lucas two pound 60.

Under this deal, it'll cost two pound 70.

The promotion does not offer a saving compared to last week's prices.

Well done if you've got those all right.

Let's move on now to the second part of our lesson, which is on unit pricing.

Items and shops often have the unit pricing written underneath.

Sometimes this is a price per item or a price per gramme or a price per a hundred grammes.

So for example, you can see here, I've got strawberries for 600 grammes costing three pounds 40, but the unit prices underneath, and this is a price per a hundred grammes.

And the same is true for the strawberries where it's 400 grammes.

Which of these is better value for money? The unit pricing makes this easy.

We can see that the 600 gramme pack is cheaper per a hundred grammes.

Let's check if the unit pricing is correct though.

Well, if 600 grammes cost three pounds 40, then I can see that a hundred grammes will cost, well, 0.

56666 recurring.

Hmm.

Well it's been rounded up 'cause they've written 56.

7, but that is approximately correct.

What about for 400 grammes? When divided by four, gives me 0.

625 and this unit pricing is correct.

What's wrong with the unit pricing for these chocolate bars? Well, firstly, the units are very wrong.

Without doing any calculations, we know that each chocolate bar is not going to cost less than half a pence.

Let's have a quick look at what they have done then.

Two pounds 15 divided by five gives us 0.

43.

Ah, they've got their units wrong here for money.

We can also see the values have been rounded.

The five pack is definitely better value for money.

But when rounded to the nearest 10 pence, they look like they're the same.

Now we've corrected them, and they are easy to compare.

Although we should probably notice that the five pack does save us less than a pence per chocolate bar.

So it might not be worth it.

Now Laura saw this label the other day, and she doesn't understand what the 0.

8 P each is referring to.

Lucas reckons it's probably the price per bag because it's a six pack of crisps.

Do you think he's right? Without calculating, we can see this is not a sensible price for a bag of crisps.

Costing less than a penny each, how on earth is that gonna make one pound 35 for six? Lucas thinks, well, maybe they got the units wrong, and it's 80 pence per bag.

Well let's check.

One pound 35 divided by six is 0.

225.

Hmm.

So that's not 80 pence per bag.

That'd be 22 and a half pence per bag.

So it's not that.

What do you think it's referring to? Laura points out sometimes the unit pricing is cost per gramme or a hundred grammes or one kilo.

Ah, let's consider that, therefore.

Well, six packs of 30 grammes each is 180 grammes.

Let's therefore, take the price in pence and divide by 180.

And that gives us 0.

75.

Rounding to one decimal place is 0.

8 pence.

So this is the price per gramme of crisp.

Hmm, doesn't seem like that's a particularly useful way to compare.

So when we're comparing unit prices, we need to check those units and what it is that they're actually telling us.

Let's do a quick check.

Which of these is better value for money? Pause the video now while you have a go.

Welcome back.

The bottles are 500 millilitres each for the first one.

So we've worked out the price per a hundred millilitres here.

Let's change the price to per a hundred millilitres for the others as well.

Well, it was already done for the second one, and you can now see how it works out for the third one.

In other words, I've got 17 pence per a hundred millilitres, 12 and a half pence per a hundred millilitres, and 15 pence per a hundred millilitres.

So the 800 millilitre bottle for one pound is the best value for money.

Well done if you got that.

Remember, your reasoning could have been different, but you should still have got to the same conclusion.

It's time now for our second task.

For the first question, I'd like you to check which of these unit pricings are correct.

Pause and do this now.

Question two, which of these deals is the best value for money? Pause and work this out now.

Here are the answers to question one.

Now you might like to pause the video while you have a quick read through this and check your working.

And in question two, which of these was the best value for money? Well, both the six pack of crisps and the four pack of crisps are the best value for money because their unit pricing works out to be the same.

Well done if you got that right.

Time for the final part of our lesson now.

And that's on analysing adverts.

Adverts are designed to persuade people to make a purchase.

Statistics are a powerful tool in advertising.

It's important to understand some of the ways statistics can be manipulated.

Let's look at this premium anti-aging cream.

90% of customers saw fewer wrinkles.

Hang on, there's an asterisk there.

Let's read what that says, "Of 48 surveyed." Hmm.

Why do you think this advert uses this statistic? Well, 90% sounds like an impressive number.

I admit when I first read that, sounded good to me.

It does make it sound more scientific, as if research has proven that this works.

And people are far more likely to buy it if they think it's recommended by others.

Now there are ways this statistic can be misleading.

Well, we surveyed 48 people.

So what is 90% of 48? 43.

2 people? Uh, that's not an integer.

It's impossible for exactly 90% to have seen fewer wrinkles.

This is likely to have been rounded.

So for example, if 41 out of our 48 people answered positively, well, that gives us 85.

41%.

Well that does round to 90% to one significant figure.

But you might be thinking like I am, personally rounding to 85% would make more sense here.

Not if you're an advertising company.

You're technically correct to round to 90% to one significant figure, but you're not really giving me the full picture, are you? There are other things, of course, to consider.

A sample size of 48 is quite small.

Is this because not many people responded, or because the company wanted to manipulate the data? We don't know who was surveyed.

If it was young people who don't have many wrinkles, this could be quite misleading.

And the people who are most likely to respond to the survey are people who regularly use and like the product.

We don't know how the question was originally phrased or the time period it was tested over.

Let's look at another advert.

Carl's cars is the fastest growing car brand in the UK.

Join the new craze, buy a Carl's car.

Well, why do you think the advert is using this claim? Well, if the brand is growing fast, it suggests it's a good company which people like.

It appeals to people's sense of not wanting to miss out on something everybody else has.

And it makes the brand sound like it's new and innovative, and it may have something that other brands do not.

So to back up their claim, Carl's cars use these figures.

Now, it does initially look quite impressive.

Those numbers are indeed increasing.

But Aisha's here, and she's done her research.

She's found another car company whose customers increased from 400,000 to 480,000 last year.

So is Carl's car's claim false? Well, the issue here is with the difference between numerical increase and percentage increase.

We can see from Carl's car's table, that in year two, there was an increase of another 5,770 customers.

And then again from year two to year three, the numbers increased by 17,290.

In comparison, let's look at what Aisha found.

Well she found a company where their sales increased by 80,000.

So the company Aisha found got more new customers last year than Carl's cars.

So does that mean that Carl's car's claim is false? Well, let's consider the percentage increase.

Carl's cars saw an increase of 202%.

And then in year two to year three, they saw an increase of 201%.

So broadly similar.

They're currently growing at a rate of 200% a year.

That's a pretty big increase.

In comparison, the company Aisha found is only growing at a rate of 20% per year.

Now of course there are other things to consider.

Carl's cars looked to be a new company, and it's easier to get a large percentage increase if you start on a very small number.

And it was only in its third year.

It's unlikely this growth rate is going to continue.

Companies, of course, are likely to pick the statistic that looks the best, and that could be a raw figure or a percentage.

Let's do a quick check.

A company surveyed 40 people and claimed 95% of people would recommend them.

How many people is that actually? And then give me a reason why this claim may not be as convincing as it initially sounds.

Pause and do that now.

Welcome back.

Well, what is 90% of 40? It's 38.

In other words, 38 people.

Now give a reason why this claim may not be as convincing as it sounds.

Well, if this is a national or global product, sampling just 40 people is tiny.

We don't have any information about who was surveyed and we don't know how the question was asked.

Certain phrasing or asking people in person can lead to more positive answers.

Let's consider this one.

A company's profits rose from 24,000 in year one to 28,000 in year two.

What is this as a percentage increase? And then a company's profits fell from 15,000 in year one to 13,500 in year two.

What is that as a percentage decrease? Pause the video and work this out now.

Welcome back.

You should have got 16.

7% increase for the first question and that has been rounded.

And then for the second question, you should have got a decrease of 10%.

It's time now for your final task.

Question one, we're comparing a low sugar box of muesli, which advertises it has 20% of sugar to the normal muesli.

Part A, how much sugar would be in a hundred grammes of the low sugar muesli? Part B, if a teaspoon is 4.

2 grammes, how many teaspoons of sugar are in a 30 gramme serving of the low sugar muesli? And then part C, a different brand advertises 5.

5 grammes of sugar per 40 grammes serving.

Which muesli has the least sugar? Pause and work this out now.

Question two, Roy's rides makes and sells motorbikes.

Their advert claims, "Our motorbikes hold their value much better than our competitors." Part A, the average depreciation of the value of a motorbike in its first year is 20%.

What would a motorbike worth 2,500 pounds new be worth after one year? And now you can see some figures for the value of motorbike from Roy's rides and a motorbike from their nearest competitor.

So for part B, give a statistic to support the claim made by Roy's rides and in part C, give a statistic which does not support their claim.

Pause and do this now.

Welcome back.

Let's go through our answers.

Part A should have 16 grammes and in part B, we worked out that there's one and one seventh of a teaspoon of sugar in a 30 gramme serving of low sugar muesli.

In part C, we wanted to know which muesli has the least sugar and you should have been able to justify that the different brand has a lower sugar content.

In question two, I asked what would a motorbike worth 2,500 pounds new be worth after one year if it followed the average depreciation? And that means it would be worth 2000 pounds.

Part B, you had to give a statistic to support the claim made by Roy's rides.

Well, if you just look at the numerical difference, there's a smaller decrease in value for the motorbike at Roy's rides than their competitor.

Part C, you had to give a statistic which did not support the claim.

So now we're looking at a percentage change, and we can see that for Roy's rides, there was 25% decrease, but for their competitor, there was only a 15% decrease.

Well done if you've got those all right.

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

Proportion skills can be used to compare prices, and promotions do not always offer the best value for money.

Shops often display unit prices to help you compare products, but these are not always in the same units.

Advertisements often make use of data, and the validity of that data and any conclusions should not be assumed.

Well done.

You worked really well today.

I look forward to seeing you again.