Lesson video

Hello there, I'm Mr. Tilstone.

Money may already play a big part in your life, but if not, it certainly will do when you get older.

So I'm really excited to be talking to you today about the subject of money.

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

Our lesson outcomes, so, our target if you like, by the end of the lesson, is, "I can calculate change when purchasing more than one item".

So you may have had recent experience of calculating with change, but what about when it's more than one item? And our keywords are subtrahend.

So I'll say that you say it back.

My turn.

Your turn.

Subtrahend.

And minuend.

Just a little reminder of what those words mean.

And minuend is the number being subtracted from.

And the subtrahend is the number subtracted from another.

So in the example is seven takeaway three equals four.

Seven is a minuend and three is the subtrahend.

Our lesson is going to be split into two parts.

The first will be using subtraction to calculate change, and the second using addition and subtraction to calculate change.

So if you're ready, let's begin with cycle one, using subtraction to calculate change.

In this lesson, you'll meet Andeep.

You may have met Andeep before.

He is going to be helping us out today.

So here's Andeep.

Andeep had one pound, he bought a pencil for 20p and a pen for 50p.

How much money does he have left? So we're going to start with some fairly gentle arithmetic, 20p and 50p, and we're going to use a bar model to represent the information that's known and unknown.

So at the moment we've got three pieces of known information, the one pound, the 50p, and the 20p and one piece of unknown information.

So let's see if we understand what each part of the bar model represents.

So what's the pound? The pound is what Andeep's got.

What's 50p? 50p is the cost of the pen.

And what's 20p? 20p is the cost of the pencil.

Now I'm going to think of the pound in a different way and you may have thought of it this way before in recent times.

Instead of one pound, I'm going to think of it as 10, 10 Ps and that'll become clear why in one moment.

So here we've got a reduction story.

A story where the numbers are going to reduce.

So we've started with one pound or 100p, and Andeep has bought a pencil for 20p.

So we're going to reduce that amount by 20p.

Here we go.

One pound or 100p take away 20p equals 80p.

So already Andeep's got less money than what he started with.

He spent some money on something.

Now let's move on to the pen.

The pen costs 50p.

So let's subtract 50p from what remains.

So the 80p that we had take away 50p more gives us 30p.

And 30p is how much money Andeep's got after he's bought the pencil and the pen.

He's bought more than one item and we've subtracted and subtracted again.

And this has left a difference.

We've subtracted 70p from one pound or 100p and that's left us with a difference of 30p.

So this is one of the strategies that we're going to be focusing on today.

It involves subtracting one subtrahend and then another subtrahend.

And we could use that to subtract another subtrahend if need be.

So let's look at that word problem again, this time without the bar model and without the coins to represent it.

So Andeep had one pound, then he bought a pencil for 20p and a pen for 50p.

How much does he have left? So we start with one pound take away 20p gives us 80p.

And then the 80p that's left, we subtract 50p from to give us 30p.

So that's how it would look as an equation.

This is a useful mental method if the subtrahend are quite easy to subtract and they were in this case.

They were multiples of 10p.

So subtracting and subtracting again can be a useful strategy.

Okay, let's try a different problem.

This time Andeep's got five pounds instead of one pound.

He bought a sticker book for two pounds 40, and a pack of stickers for 30p.

So already you can see the subtrahends are different, the arithmetic's a little more challenging this time, but we're gonna use that same strategy again.

So how much money does he have left? So Andeep could calculate like this.

He could do five pounds, take away two pounds 40, so that's the cost of the sticker book, equals something.

And then whatever he's left with, subtract the 30p, that's the cost of the pack of stickers and that will give you how much money he's got left.

So let's see if you can maybe figure out the missing numbers from those equations.

Five pounds take away two pounds 40 gives us two pounds 60.

And then two pounds 60 take away 30p gives us two pounds 30.

So that's how much money he's got left.

Can you think of a different way that Andeep could have subtracted and subtracted again? Well he could have swapped the subtrahends and subtracted those in a different order.

So instead of doing five pounds, takeaway two pounds 40, he could have started with five pounds, takeaway 30p.

So he could have started by subtracting the cost of the pack of stickers and then whatever that gave him, he could have subtracted the two pounds 40 or the cost of the sticker book, and that would've given him a money total that he had left.

So let's see if we can figure out what the gaps would be this time.

So five pounds take away 30p equals four pounds 70.

And then four pounds 70, subtract two pounds 40, equals two pounds 30.

Personally I found the first way a bit easier, but they gave us the same answer either way.

So we've looked at a couple of examples using subtraction and subtraction again.

Time for a check for understanding.

Let's see if you've understood that.

Here's what you're going to do.

Draw a bar model and use subtraction to calculate.

Andeep had two pounds.

So a new amount of money this time, a new minuend.

Two pounds.

He bought a pencil sharpener for 20p and a pencil topper for 60p.

How much change does he have left? If you've completed that, maybe you could try it in a different order.

Pause the video and good luck.

How did you get on with that? Shall we have a look? Well, here's our bar model.

So two pounds is the minuend.

He bought the pencil sharpener for 20 pence so he's going to take that away from that.

And the pencil topper for 60 pence.

So it doesn't really matter what order that was going on the bar model, but we're going to take them away and that's going to leave us with one pound 20.

So that's what it looks like as a bar model.

Here's what you could have done.

You could have done two pounds take away 60p equals one pound 40, and then one pound 40 take away 20p equals one pound 20.

I think there was one more way we could have done that using subtraction and subtraction again, but keeping the same minuend.

How about two pounds, take away 20p, take away 60p? It would still give the same answer.

So we've had a little go at using the subtraction and subtraction again strategy.

Are you ready to put that into practise? Well let's find out, shall we? So Task A, number 1, you're going to draw a bar model and use subtraction to calculate.

And here's the problem.

Andeep had five pounds.

So we've got a new minuend, five pounds this time.

He bought a biscuit for 30p and a drink for 50p.

How much change does he have left? So we want a bar model and we want a way of subtracting those two subtrahends.

Number two, Andeep makes a call from a telephone box.

He has two pounds in coins.

He uses these four coins to make the call.

How much money has he got left from the two pounds? So this time we've got four subtrahends.

Can you still use that same strategy of subtracting, subtracting, subtracting and subtracting in this case? Pause the video, good luck, and I'll see you shortly for some feedback.

So how did you find using that strategy? Well, let's have a look at at some answers.

So the bar model for question one might look a little bit like this.

You might have the bottom part of the bar model in a different order and that's fine.

But the calculation is five pounds take away 30p equals four pounds 70.

And then four pounds 70 take away 50p equals four pounds 20.

You might have started by doing five pounds take away 50p and that's fine too.

But the answer that we're looking for here is four pounds 20 and a big well done if you've got that.

And for Task A, 2.

So you had four subtrahends for this one, but they're all multiples of 10 pence.

So the subtraction and subtraction again strategy is a good one.

So he had two pounds in coins and he used these four coins.

Now he might've used them in any order.

He might've put the 10p in first, the 20p, we just don't know.

So whatever order you subtracted your subtrahends doesn't matter.

So here's just one example.

You could've done this.

Two pounds, take away 10p is one pound 90.

One pound 90 take away 50p is one pound 40.

One pound 40 take away 20p equals one pound 20.

And then one pound 20 take away 10p equals one pound 10.

Again, that might have been done in a different order, but the answer we're looking for is one pound 10.

That's how much has got left.

Well done if you got that.

So that first strategy involved just using subtraction but multiple times.

The next strategy is going to use a combination of addition and subtraction.

So we're going to use addition and subtraction to calculate change.

Are you ready? Fantastic! Let's go.

So we're already quite familiar with Andeep's problem, so we'll use that same context again but with a different strategy.

So he's got one pound, remember, and he bought a pencil for 20 pence and a pen for 50 pence.

And we want to know how much money he's got left.

We're using the exact same bar model as before to represent this problem.

So on the top of the bar model we can see the one pound, that's how much money he's got to start with.

And on the bottom of the bar model are two subtrahends, our 20 pence and our 50 pence.

And just like before, I'm going to treat the one pound as 10 10p's Previously our first step was to subtract one of the subtrahends, but what if we didn't do that? What if we added both of those subtrahends together first? 50 pence, which is the cost of the pen, and 20 pence, which is the cost of the pencil equals 70 pence.

So what we've done there is combine those two subtrahends together to make one subtrahend, which we're now going to subtract from the minuend, from the pound.

So we're going to do one pound take away 70p.

You could subtract that, so one pound take away 70p, or you could count on.

And that's what Andeep is going to try.

You can count on from 70p to one pound to calculate how much money he's got left, how much change.

So here we go.

On the left hand side of the number line, we've got the 70p, which is our new subtrahend.

And on the right hand side, one pound, which is the minuend, and we're gonna count from one to the other.

That's fairly straightforward to do.

That is a jump of 30 pence.

So that's how much money he's got left.

That's the difference.

But Andeep says this, he says, "I didn't need to draw a number line because I know my number bonds to 100.

I knew that 70 plus 30 equals 100".

So he used that in the context of 70 pence plus 30 pence equals 100 pence, or a pound.

So if you're good with your number bonds, you may not need to draw a number line.

So let's just recap what we've done there.

We've added together all the subtrahends.

In this case there were two subtrahends, 50p and 20p, and then we've subtracted that new subtrahend, the total from the minuend, in this case one pound.

So we've added first, subtracted second.

Let's look at that just as an equation without any number lines or any coins to represent the problem.

So what we did is add first.

So we added 20p and 50p, the cost of the two items, and that gave us 70p.

And then we did one pound take away 70p, and that gave us 30p.

And that's how much money he's got left.

So adding first, subtracting second, it's a good strategy.

Andeep had five pounds.

He bought a sandwich for one pound 45 and a drink for one pound 32, how much money does he have left? So you might notice the arithmetic's not quite as gentle this time.

We've got a bit more work to do here, but we are still going to use that same strategy of combining our two subtrahends to make one subtrahend and then subtracting that from the minuend, which in this case is five pounds.

So here we've got one pound 45, the cost of one of the items, plus one pound 32, the cost of the other.

And that's given us 2 pounds 77.

So our new subtrahend is 2 pounds 77.

That is what we're going to subtract from the five pounds.

So five pounds take away two pounds 77, which is the total cost of his items, equals two pounds 23.

So adding first, subtracting second.

And I really do recommend this strategy.

So let's see if you can use the strategy of adding first, subtracting second.

Let's do a check.

An apple costs 55 pence and a drink costs 72 pence.

How much change will I get from two pounds if I buy both? Calculate this using addition and then subtraction.

Draw a number line to support if you need to.

Pause the video and very best of luck.

Let's see how we got on with that one, shall we? Okay, so if we add together our two subtrehends, and remember, we could do that in any order.

It doesn't matter if we start with the 55p or the the 72p, but one example being 55p plus 72p equals 127p, which we could change into something looking a bit more familiar, which is one pound 27.

And then two pounds take away one pounds 27.

We could count on using a number line from one pounds 27 to two pounds.

And that is a 73p difference.

So that is how much change you would get.

Congratulations if you've got that, you're on track, you're doing really well.

I like this strategy.

Do you? Well, let's see if we can change it up a little bit.

Let's see if we can make the arithmetic a bit more complicated.

Let's see if we can change the number of subtrahends.

Let's try a new problem.

The class has raised 100 pounds, we've got a much bigger minuend this time, to spend on a party.

They spent 25 pounds 49 on pizzas, 13 pounds 85 on drinks, and 18 pounds 75 on decorations.

So this time we've got three subtrahends, three different items that they bought.

How much do they have left to spend on entertainment? So we're representing that first of all with a bar model.

So on the top of the bar model, our minuend, how much we had to start with, that was 100 pounds.

And on the bottom of the bar model, we've got three knowns and one unknown.

The three knowns are the three different money amounts, the 25 pounds 49, the 13 pounds 85, and the 18 pounds 75.

It wouldn't really matter what order those went in, but the question mark, the difference between those and the minuend is what we're going to try and establish.

So Andeep says, "If I subtracted all of these I'm bound to make lots of mistakes".

It's right, isn't it? I don't think subtracting, subtracting and subtracting is gonna be very wise on this occasion.

I think it will be better to add first.

So good instinct there, Andeep.

He says, The arithmetic isn't as easy this time", and it's certainly not.

There's no way that I could do all that in my head.

"I think I will need to use a written method.

But I can still add the subtrahends first".

So do you have a written method for adding together different amounts of money? Hmm.

What about the column method? When we add together those three subtrahends, it gives us 58 pounds and nine.

And just note that we paid attention to the regroups.

We made sure that those were being added on.

So is that the answer to our problem? Is 58 pounds nine how much they have left to spend on entertainment? No, it's not.

That's only the first part of our problem.

We've got one more step to go.

We've done all the adding, we haven't done the subtracting.

So as Andeep rightly says, "That's how much the class have spent".

But that's not the question.

Now to work out what's left of the 100 pounds.

So we're going to need to subtract that subtrahend from our minuend of 100 pounds.

And you can see that on the bar model.

Now, do you think it would be a good idea to use column subtraction for this? Hmm, let's have a look at that.

Let's have a think about that.

I don't think it would be.

And the reason being, there's going to be lots of placeholders, lots of zeros, and that's going to mean lots of regrouping.

It's gonna turn into a very complicated calculation.

So I think there's a better way.

And so does Andeep.

He's used a number line and he's used the counting on strategy.

So his calculated 100 pounds take away 58 pounds nine by counting on, counting on from the 58 pounds nine, our subtrahend, to 100 pounds, which is our minuend.

And he shows the steps on a number line.

And again, I couldn't do this in my head.

I need a number line to help me scaffold my thinking.

So he's gone from 58 pounds nine to 58 pounds 10, so that's a one p jump.

And then he is done another jump from 58 pounds 10 to 59 pounds, that's a a 90 pence jump.

And then another jump from 59 pounds to 60 pounds, which is a one pound jump and then one final jump from 60 pounds to 100 pounds, which is a 40 pound jump.

You might have done that in fewer jumps, but that's just one way to do it.

That's still not quite the answer yet though.

We still need to combine those.

So we're going to work backwards.

So 40 pounds, plus one pound, plus 90p, plus 1p, gives us 41 pounds, 91.

And that is the answer.

That is how much they've got left.

So as Andeep says, "We spent 58 pounds nine and so we have 41 pounds 91 left to spend on entertainment".

And you can see that in the bar model, that's a difference between 58 pounds nine and 100.

So let's just reflect on that.

There were a few minuends and the arithmetic wasn't too straightforward.

So column addition was definitely a good way to add together those subtrahends.

The new subtrahend wasn't really easy to subtract from the minuend.

So we did need a written method.

We decided against using the column subtraction because of all the regrouping that would take place and instead we used a number line and that worked really well.

So this time it took a bit of time, but we got there using the exact same method of combining together our subtrahends and then subtracting the new subtrahend from the minuend.

And to put that simply, we added first, subtracted second.

So let's see if you can apply that strategy now of adding first and subtracting second.

Here's a problem.

Another class has raised 120 pounds to spend on a party.

They spend 32 pounds 55 on food, 21 pounds 79 on drinks and 38 pounds 50 on entertainment.

So just like the other problem, they've got three different subtrahends there, but a different minuend and this time 120 pounds.

How much do they have left to spend on party games? So again, it's another context where we need to find out the difference.

What we want you to do is tell your partner the steps needed to solve the problem.

Not looking for the answer as such, but how would you go about it? So pause the video, have a think, and have a chat to your partner.

Here's something you might have said.

First, add together the subtrahends, and in this case that was 32 pounds 55, 21 pounds 79, and 38 pounds 50.

And then subtract the total from the minuend, which is 120 pounds.

And they're the steps that would help you to achieve that calculation.

It really is a great method, very useful.

So let's see if you can put that into practise now yourself.

So we've got a couple of word problems here for you.

A banana costs 65p and a bar of chocolate costs 83p.

How much change will I get from two pounds if I buy both? Draw this as a bar model and then solve using the adding first method.

So you've got two different subtrahends to add together there.

The second question.

The class has raised 200 pounds to spend on a party.

They spend 32 pounds 79 on pizzas, 24 pounds 50 on drinks, and 13 pounds 85 on decorations.

How much do they have left to spend on entertainment? Solve once again using that adding first method.

So how many subtrahends can we see here? Well, pizzas, drinks and decorations.

That's three.

So you've got three subtrahends to add together there.

Looking at that first example, you may or may not be able to work the subtrahends out using mental methods, with the second one, definitely not.

You're going to need written methods for that.

And then for B 3.

Andeep has got 350 pounds in his bank account.

He pays for a new video games console, cost him 129 pounds 95.

He buys two games, each costing 38 pounds 50, and he buys an extra controller costing 49 pounds 25.

How much is left in his bank account? So have a little think about this one.

This is a bit of a special problem.

Have a good think about how many subtrahends that is.

So pause the video and good luck with that.

I'll see you soon for some feedback.

How did you get on with that? Should we give you some feedback? So a banana costs 65p and a bar of chocolate costs 83p.

When we combine those two subtrahends it equals one pound 48.

So now we've got a new subtrahend, what we're going to do is subtract that from the minuend, which is two pounds.

We're gonna work out the difference between those two values.

I would recommend doing the counting on method to do that.

So two pounds take away one pound 48 gives us 52p.

Well done if you got 52p.

For number two, this time we had three different subtrahends and when we combine them together, it gives us 70 pounds 79.

So that's what we're going to work out.

The difference between that and 200 pounds, our minuend.

200 pounds take away 70 pounds 79.

Again, I wouldn't recommend using column subtraction for that because of all those zeros that you're going to need, all the placeholders.

It's gonna mean a lot of regrouping.

But I would recommend using the counting on strategy.

When we count on from 70 pounds 79 to 200 pounds, it gives us 129 pounds 21.

Big congratulations if you got that.

For Andeep's problem there's a couple of ways you could have approached that.

So we've got the 129 pounds 95, that's his video games console.

We've got 38 pounds 50, which is one game, 38 pounds 50, which is another game, 49 pounds 25, add those altogether and you get 256 pounds 20.

But let's just pause on that for a second because there was another way to do it.

That's four subtrahends that we've combined together, but I can think of a way to make that into three subtrahends.

What if we combined the cost of the two games together to make that one subtrahend? Then you'd have three.

But either way it would still give us 256 pounds 20.

So that's our new subtrahend that we're gonna subtract from our minuend.

350 pounds take away 256 pounds 20.

Again, I would use counting on method for that, but it gives us 93 pounds 80.

There was a lot of arithmetic in that, a lot of different steps, a lot to do.

So very well done if you got that.

That was a really meaty, challenging question.

You've been amazing if you've achieved that one.

So well done.

We've come to the end of our lesson.

Our lesson today was calculating change when purchasing more than one item.

And we've looked at two different strategies.

Our strategies were as follows.

We looked at subtracting and then subtracting again.

That's a useful strategy if both subtrahends, or however many subtrahends you've got, are easy to subtract, such as multiples of 10.

That works quite nicely in that case.

However, where multiple subtrahends are more complex, the strategy of adding the subtrahends before subtracting from the minuend is often more efficient.

And that's the one I'd really recommend.

It will work every time.

So add first.

So add those subtrahends together and then subtract from your minuend.

Take care, and goodbye.