Lesson video

Hello, I'm Mr. Tilstone and I'm delighted to be teaching you a lesson all about money.

So, if you're ready to begin, let's go.

Our lesson outcome is I can apply tools and strategies to solve problems involving money, including finding change.

So you're going to be combining a lot of the skills that you might have been learning recently, all about adding and subtracting money.

We've got some very important mathematical vocabulary today.

Some keywords, which I'm going to introduce to you, using my turn, your turn.

Ready? Represent, representation.

And here's what those words mean.

A representation is a way of showing a mathematical idea.

So concrete objects, pictures and symbols can all be used to represent mathematics.

So these are all some representations that you might have seen before that relate to 3 + 4 = 7.

So today, in our lesson about money, we're going to be representing the money in lots of different ways.

There are two parts to our lesson today, two cycles.

The first is reasoning about word problems and the second is solving more complex word problems. So, if you're ready to begin, we'll start by reasoning about worded problems. In today's lesson, you'll meet two characters who may be quite familiar to you by this point.

So we've got Jun and Izzy here to help us today.

So let's use that word representing them.

Worded problems are a way of representing maths.

When you solve problems with money, sometimes they will include mixed units.

So, let's have a look at this example, see what you can spot about the money.

Izzy goes to a funfair.

She has 10 pounds to spend.

She spends 2 pound 30 on a drink.

She pays 50 P to play hook-a-duck.

She pays 30 P for a lucky dip.

She wins 1 pound 50 on a game.

How much money does she have now? Now before we go about solving that problem, let's think about the money.

You may have noticed that those were represented in different ways.

Some were decimal numbers and some were in pence.

So let's see if you can see which is which.

Well, the first amounts, neither is, just showing a number of pounds, so 10 pounds.

The second one is using a decimal number.

So 2 pounds 30, 2 pounds and 30 pence.

We've got another one of those as well.

The 1 pound 50 that uses a decimal point too.

And then we've got two money amounts that are in pence.

So that's 50 pence and 30 pence.

All of those are correct, they're just different.

It might be helpful to change them so that they're in the same unit to help you with your calculations.

You could change them all pence or all to pounds and pence.

But let's have a go at changing them all to pounds and pence.

So instead of saying 50 P or 50 pence, we could say zero pounds and 50 P.

And instead of saying 30 P, we could say zero pounds and 30 p.

And now that looks similar to the 2 pounds 30 and the 1 pound 50, they're in using this same unit.

The alternative would be to turn everything into pence.

So the 50 P and the 30 P are already in pence, but we could change the others into pence too.

So we've got 2 pounds 30 becomes 230 pence.

1 pounds 50 becomes 150 pence and 10 pounds becomes 1,000 pence.

Now everything's in pence and calculating should be easier.

Shall we do a quick check to see if you've understood that concept? So remember, we're not looking at working out the answers yet, we're just thinking about making sure that the money amounts are all in the same unit.

So look at the worded problem and rewrite all the values so that they're in the same unit.

Let's read it.

John has 4 pounds 70 left of his pocket money.

He spends 2 pounds 90 on a magazine.

He spends 80 P on a packet of sweets.

As he walks home, he finds a 50 pence piece.

How much money does he have now? So I can see two amounts that use decimals and two amounts that use pence.

Can you convert them so that they're all the same? Maybe you could do it in two different ways.

Pause the video and we'll do some feedback shortly.

Well, you could have turned them all into pence.

That would be one option.

But the other option that we've gone for here is to turn them all into pounds and pence.

So instead of 80 P, zero pounds and 80 and instead of 50 P, zero pounds and 50, now all of them use decimals.

Let's start to untangle some problems now.

When you solve problems with money, you need to decide what operation to use.

Sometimes there will be more than one step with different operations.

So we need to decide is this an addition problem for example, is it subtraction? Is it a combination of operations? The language in a worded problem can help us to decide on the operation to use, but it can also sometimes be a bit confusing as we'll soon see.

But Jun here has got an example of where he knows the meaning of a word and what operation that might be.

So altogether.

So when you see the word altogether, it often means an addition question.

So he's using that as a clue to help him out.

Likewise, he says, "Seeing 'how much more' usually means I need to subtract." So Jun understands that how much more means there's a difference and that we use subtraction for difference.

And Jun says, "If it says how much change, I usually have to find the difference." So change problems are usually about finding the difference.

So we do use subtraction for that.

But yes, sometimes the language can be misleading or it can trip you up a bit or lead you down the wrong path.

Let's look at an example.

So Izzy and Aisha are collecting money for the same charity.

They've collected 145 pounds 65 altogether.

Aisha's collected 70 pounds 90.

How much has Izzy collected? Let's have a think about that.

So the problem includes the word altogether, which if you remember from earlier, Jun knows often means adding.

Can this word problem be represented by 145 pounds 65 plus 70 pounds 90? Well no, that's not what's being asked here.

You do not know how much Izzy has collected.

What you actually need to do is find out the difference between the total and Aisha's amount.

So it's actually a subtraction problem, so be careful.

Let's have a look at another one.

Izzy and Aisha are collecting money for the same charity.

Aisha collected 17 pounds 50 more than Izzy.

Izzy collected 67 pounds 90.

How much has Aisha collected? This problem includes the words more than, so that suggests we're looking at the difference in subtraction.

So can this worded problem be represented by 67 pounds 90 take away 17 pounds 50? Well, once again, no, that's not quite what's being asked.

You don't know how much Aisha's collected, but you do know the difference.

What we actually need to do here is to sum, to add the two amounts.

So when tackling any kind of word problems, including those involving money, make sure that you fully understood the context and the problem.

Take some time to really think about it.

Use the language as clues, but be careful.

It might not be asking what you think it's asking.

So do be careful and do have a good think before you start tackling the problem.

Your turn, now let's check your understanding so far.

What's the equation and what word here might mislead us? What might trip us up? What might send us down the wrong path? So Jun bought some treats at the shop and paid with cash.

He spent 3 pounds 47 and got 1 pound 53 change.

How much money did he pay for his treats with? So pause the video and have a think.

What's the equation? What's being asked here? You don't necessarily need to solve this one, but what's the equation? Well, we could use this equation.

3 pounds 47 plus 1 pound 53 equals.

But if you hadn't fully understood that word problem, what word there might of trip you up a little bit? What might have made you think that maybe this was a subtraction question.

Which word? The word change.

The word change could make us think this worded problem requires subtraction, but it didn't.

So we needed to think about the problem really carefully before we started.

So when you solve word problems, including with money, you need to decide what operation to use.

You can think about what is known and what is unknown.

And bar models can be used to represent a worded problem.

And often when we represent something with a bar model, it becomes obvious whether we need to add or subtract or both.

So when Jun's tackling word problems, he asks himself some questions.

What do I know? What don't I know? And can I draw it? So let's consider those questions with this problem here.

So let's start by thinking what do I know and what don't I know.

What's known and what's unknown? So Izzy and Aisha are collecting money for the same charity.

They have collected 145 pounds 65 altogether.

Aisha collected 70 pounds 90.

How much has Izzy collected? So let's consider what's known and what's unknown about this word problem.

Well first of all, what's known is that the girls have got 145 pounds 65 altogether.

So that is their sum.

So think about a bar model, picture a bar model.

Whereabouts could you put that on the bar model? Hmm.

The other thing that we know is that one part of it is the 70 pounds 90 that Aisha has collected.

So that's part of that total.

So where could we put that on a bar model? That's what we know.

What's about what we don't know? We don't know this.

We don't know the other part, which is how much Izzy has collected.

Bar models can be used to represent a worded of problem.

We could do that with this one as well.

So here we go.

The 145 pound 65 can go on the top of the bar model.

That's how much they've collected altogether.

70 pound 90 is what Aisha's collected.

We need to know the difference now.

We need to know how much Izzy's collected.

Now when we represent it like that, we can treat the 145 pound 65 as a minuend and the 70 pounds 90 as a subtrahend.

If we subtract the subtrahend from the minuend, it will give us the difference.

So that's what we're going to do.

We're going to do 145 pounds 65, take away 70 pounds 90.

And that will give us Izzy's amount, that will be the difference.

So once again, the bar model before we start this calculation shows what is known and what is unknown.

Let's continue to think about those two questions.

What is known and what is unknown, as we think about this new problem.

So it's over to you for a quick check.

Jun bought some treats at the shop and paid with cash.

He spent 3 pounds 47 and he got 1 pound 53 change.

How much money did he pay for his treat with? So think about that.

What is known, what is unknown and could we possibly represent that with a bar model so that we can see what we need to do with those numbers? Pause the video and have a go.

Well let's investigate.

So we know that one part is 3 pounds 47 and that's how much Jun spent.

We know that another part is 1 pound 53, which is Jun's change.

What we don't know is the whole of what Jun had to begin with.

So can you start to picture that in terms of a bar model, we've got a part and another part, we just don't know the total.

So where would each of those three parts go? Well, let's look at that bar model, shall we? So here we go.

So we've got that one part on the bottom, how much was spent, we've got the other part, how much change we had, what we don't know is the total.

So you can see now we've represented that what we need to do with those two money amounts, we need to add them, we need to add them together.

So we've spent some time thinking about the language used in word problems and how sometimes it can be helpful but sometimes unhelpful or lead you down the wrong path.

We've also considered what is known about a word problem, what is unknown and how that can be transferred into a bar model to help us really see what calculation we need to use and what operation we need to use.

So let's put all of that into practise now.

Task A, use an efficient strategy to solve each problem.

You may want to represent each one using a bar model.

Certainly I find that very helpful to help you choose the right calculation.

So here we go.

Number one, Izzy goes to a funfair.

She has 10 pounds to spend.

She spends 2 pounds 30 on a drink.

She pays 50 P to hook-a-duck.

She pays 30 P for a lucky dip.

She wins 1 pound 50 on a game.

How much money does she have now? There's quite a lot going on there, isn't there? I would recommend reading that two or three times and really thinking about it before you start.

But do consider what do you know and what don't you know.

What is known, what is unknown.

And for number two is Izzy and Aisha are collecting money for the same charity.

They've collected 145 pounds 65 altogether.

Aisha collected 70 pounds 90.

How much has Izzy collected? So once again, think about the language, think about what's known, think about what's unknown.

Number three Izzy and Aisha are collecting money for the same charity.

Asia collected 17 pound 50 more than Izzy.

Izzy collected 67 pounds 90.

How much has Aisha collected? What's known? What's unknown? Number four, Jun has 23 pounds 75 on Wednesday.

On Thursday, Jun buys lunch which costs 4 pounds 55 and spends 1 pound 99 on some football stickers.

On Friday, he finds 1 pound in his pocket and 50 P under his bed.

How much money does he have by Friday? Number five, Aisha's has 37 pounds 50, Jun has 7 pounds 5 more than Aisha.

Izzy has 12 pounds 80 less than Jun.

How much money does Izzy have? So be careful and think about what is being asked there and what is the unknown part and how you can use the other parts to help you to work that one out and decide on the right operation.

These questions are definitely going to take some thinking about.

So don't rush.

Have a good think about what's being asked each time and use all of those different skills that you've got at your disposal.

Pause the video and I'll see you later for some feedback.

Okay, how did you get on with that task? Let's have some feedback.

So for number one, lots of different ways you could have tackled this, but we could have done this 10 pounds, take away 2 pounds 30, take away 50 P, take away 30 p, and then add that 1 pound 50 back on that she won.

That gives you 8 pounds 40.

So well done, if you've got 8 pounds 40, whatever method you used.

Number two, we could have done 145 pounds 65, takeaway 70 pounds 90.

And that will give us a difference of 74 pounds 75, very well done if you got that.

Number three was an addition problem.

So 67 pounds 90 plus 17 pounds 50 equals 85 pounds 40.

And number four had a combination of operations.

We needed to do some addition and some subtraction.

But the final answer is 18 pounds 71 and very well done if you got that.

There was a lot going on with that question.

Finally, for this cycle, number five, Jun has 44 pounds 55, and Izzy has 31 pound 75.

Let's move on now to the second and final cycle of the lesson.

And that is solving more complex problems. So money can be represented in different ways.

Sometimes we use numerals, sometimes we use coins.

So here we've got 3 pounds 46 first represented with numerals and the second with coins.

But they both mean the same thing.

These representations have the same value.

Remember, not all amounts are represented by a coin.

So for example, we don't have a 6 pence coin, so we could use a 5 pence and a penny.

Different coins can be used to represent the same sum of money, but the representations are still the same.

Now, were you very eagle eyed, did you spot the difference between this representation and the previous one? There was something different about the coins.

Do you want another look? Here we go.

So that 2 pound coin became two 1 pound coins, but they still both represent 3 pounds 46.

Let's do a quick check, write or draw exactly 5 coins that you could use to make 4 pounds 53.

There is more than one way to do this by the way.

So if you found one, maybe you find another one and another one, pause the video.

Good luck.

Well, how about this? This is one possible solution.

You could use a 2 pound coin, a 2 pound coin, a 50 P coin, a 2 P coin, and a 1 P coin.

And altogether that would make 4 pounds 53 using exactly five coins, well done if you've got that solution.

And well done if you've got a different one too.

And now how about using exactly eight coins to make 4 pounds 53, quite the challenge.

Well here's one way.

So if you count those coins, you'll see there's 8 of them and we've got 1 pound, 1 pound, 1 pound, 1 pound, 50 P, 1 P, 1 P, and 1 P.

And when we add all of those together, that gives us 4 pounds 53.

but it's not the only way.

How about this one? A 2 pound, a 1 pound, a 50 P, a 50 P, a 50 P, 1 P, 1 P and a 1 P.

So we've still got eight coins, but eight different coins, but it still gives us 4 pounds 53.

So as we've already discussed, money can be represented in different ways.

So I've looked at it in terms of decimal notation, in terms of coins, but it can also be represented in a bar graph as you can see below.

So let's take a little time just to interpret this graph, see what it's all about.

Let's first of all look at the title.

The title is "The Money Raised by Each Class From Non-Uniform Day." Okay, got that.

Let's look at the axes.

So the X axes tells us the different classes.

Okay, I can see that.

I can see six different classes and I can see the names of them.

And the Y axis tells us the money raised.

So we can see it goes from zero pounds to 40 pounds.

Okay, so I feel like I've got a bit of information about what this graph's all about.

Now let's start to delve a little bit deeper with this graph.

So question, which class raised the most money from the non-uniform day? Well, the tallest of all the bars is class 3 G.

So the bar that represents class 3 G, is the tallest and this means that most money.

Okay, a different question, which classes raise the same amount of money? So let's look at that.

Let's see which bars are the same as each other.

And we can see that the bars for class 2 A and class 6 F have the same height.

So they have the same value of money.

The bars are representing the value of money that those classes have.

So let's do a quick check, over to you.

Which class raised the least amount of money and how do you know? Pause a video and have a think about that.

Let's see, 4 C raised the least.

The bar representing 4 C is the shortest.

That might be something that you said as a response to that question.

Over to you again, a quick check, how much money did 3 G raise? Pause the video, see if you can figure it out.

3 G raised 40 pounds.

And we can see that by reading across in a straight line from the top of 3 G's bar.

Do you feel ready to put those skills into action? Put them into practise? Well let's see, shall we? So for task B, number one, Izzy spend some money.

She paid with a 5 pound note and received four different coins as her change.

How much could she have paid and how much change could she have had? Now a key word to consider there when you tackle that problem is the word different? So those four coins are all different.

That's something that we know.

So Jun asks us, what could a change be and what could it not be? And for B 2, you're going to use the graph to answer the questions.

A order the amounts raised by each class in descending order.

Descending order, can you remember which way that is? Is that going up or going down? Have a think.

How much more did class 1B raise compared to class 2A? So you've got a how much more question.

Think about what that's asking.

Be careful with the word more.

Might not be what you think it means.

And class 4 C, we're aiming to raise 40 pounds.

How much more would they need to meet their target? So do be careful with that language when you tackle those questions.

And this is the graph that you will be using to answer those questions.

So pause the video, good luck and I'll see you soon for some answers and some feedback.

How did you get on with that task? Let's find out.

Let's have some feedback.

So Izzy spend some money.

She paid with a 5 pound note and received 4.

Remember 4 different coins as her change.

How much could she have paid and how much change could she have had? There are lots and lots of different answers to this question, but here's one.

You may have said Izzy received 1 P, 2 P, 5 P, and 10 P in her change? So that's 4 different coins.

Add those together and you get 18 P.

And if it's 18 p change, that means she spent 4 pounds 82, because that's a difference.

18 P is the difference between 4 pounds 82 and 5 pounds.

Let's have a different response.

You might have said she received 2 P, 5 P, 10 p and 20 p.

So still 4 coins, still 4 different coins.

This is 37 P.

In that case, you must have spent 4 pounds 63.

There are many possibilities and well done to you if you listed lots and lots of them.

Perhaps you use some kind of system to find out all of the possibilities.

Well done if you did.

Question 2A, when we we order the amounts raised by each class in descending order.

Remember descending going down, it goes 35 pounds, 32 pounds 50, 31 pounds, 30 pounds, and 28 pounds 50.

How much more did class 1 B raise compared to class 2 A? So that's a difference question we're looking for there.

So that needs subtraction.

So 6 pounds 50 is a difference between 35 pounds and 28 pounds 50.

And the class 4 C we're aiming to raise 40 pounds.

How much more would they need to meet their target? Again, that's a difference question.

The answer this time is 9 pounds.

And so we've come to the end of our lesson, which has been all about solving a range of problems, including finding change.

When solving problems involving money, it can help to make all the values the same unit.

So for example, all pence or all pounds and pence.

Strategies can be used to solve problems, including thinking about what is known and unknown.

And representing a problem with a bar model can help you see the operation and steps.

It can really help you to picture and to visualise and to see what operations needed.

I can't recommend bar models enough.

They're brilliant.

Money can be represented in different ways, including with coins and in graphs.

But problems can be solved in the same way.

And when you are solving problems, remember to look out for the language used.

It can be helpful, but sometimes it can lead you down the wrong path.

There's been some really challenging maths today and I hope you've enjoyed that.

It's been a great pleasure spending this lesson with you.

Well done and goodbye.