Lesson video

Hello, there.

My name is Mr. Tilstone.

Today's lesson is all about that all important topic of money and I'm very excited to be teaching you.

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

Now you may have had some recent experience of adding some different money totals together.

Today's outcome is I can use and explain the most efficient strategies when subtracting quantities of money.

We've got some important mathematical vocabulary today, some keywords, and I'm going to introduce them in a my turn/your turn style.

So are you ready? So we've got minuend, subtrahend, and difference.

Let's go over the meanings of those words, shall we? So a minuend is the number being subtracted from, a subtrahend is the number being subtracted from another, and the difference is the result after subtracting one number from another.

So let's look at that.

So in 7 take away 3 equals 4, seven is the minuend, three is the subtrahend, and four is the difference.

Our lesson today is split into two parts or two cycles.

The first is going to be using the column subtraction method in the context of money.

And the second method is going to be exploring efficient methods of subtracting quantities of money without using a column method.

So let's begin with using column subtraction.

Are you ready? Let's go.

In this lesson, you will meet the following three children.

They're going to be here to help me out.

So we've got Lucas, Sofia, and Jun.

So we've got a bar model here.

And again, you may have had some recent experience of using bar models in the context of addition.

I can see four different facts from this bar model, two addition and two subtraction.

So let's explore those, shall we? I can see 1 pound 37 plus 2 pounds 45 equals 3 pounds 82 and I can swap those addends over and see 2 pounds 45 plus 1 pound 37 equals 3 pounds 82.

But crucially, and this is what we're looking at today, I can see two subtraction facts.

So if we treat 3 pounds 82 as our minuend, we've got 3 pounds 82 take away 1 pound 37 gives us 2 pounds 45.

And again, keeping 3 pounds 82 as our minuend, we've got 3 pounds 82 subtract 2 pounds 45 equals 1 pound and 37.

Let's put those into a context.

So I buy two magazines, one of them costs 3 pounds 82 and the other costs 2 pounds 45.

What's the difference in price? So we start off with our minuend, the number that we're going to be subtracting from.

And just like when we're doing column edition, we're going to make sure everything's lined up, including the decimal points.

We're also going to be representing it initially with a bar model.

So we've got 3 pounds 82, our minuend, at the top of our bar model.

You may have noticed that just as we do with column addition, we've started with our most expensive items. So in this case, that's 3 pounds 82.

Now we're going to put our subtrahend underneath it, so the number that we're going to subtract from that is going to go underneath it.

So now we've got in the column 3 pounds 82 subtract 2 pounds 45, and we're going to also put that into our bar model.

So essentially what we're doing is subtracting the least expensive item from the most expensive item.

Now we're going to find the difference.

And just like with column addition, we're going to start by considering the least significant digit or the pennies.

So we're starting off with 2 subtract 5.

So 2 one ps take away 5 one ps.

And you might notice we've already hit a bit of a snag.

And our issue is that 5 p is greater than 2 p, so we're going to need to regroup.

We can't just swap them over like we can with addition.

So let's begin our regrouping.

We've regrouped one of those ten ps for 10 one ps and you can see that in the column subtraction.

So instead of eight ten ps, we've now got seven ten ps, and we've also got 12 one ps altogether.

So now we can do 12 one ps subtract 5 one ps, which can be calculated.

12 one ps take away 5 one ps is 7 one ps.

Now over to the ten p column.

There are now seven ten ps and we can subtract four ten ps.

We don't need to do a regroup here.

No regrouping required.

So just a 7 take away 4 is 3.

7 ten ps take away 4 ten ps is 3 ten ps, or if you like, 70 p take away 40 p is 30 p.

And finally onto our most significant digit, which is the pounds and 3 one pounds subtract 2 one pounds is 1 one pound.

So that was quite straightforward, no regrouping required there at all.

So that gives us 3 pounds 82 take away 2 pounds 45 is 1 pound 37 and 1 pound 37 is the difference.

So let's add that to our bar model.

So 3 pounds 82 was our minuend, 2 pounds 45 was the subtrahend, the money total that we were subtracting from that.

And then when we did that, that gave us a difference of 1 pound 37.

So once again, let's go over those three parts of the column subtraction, so we've got the minuend, the subtrahend and the difference.

My question to you is can the minuend and subtrahend be swapped and still give the same answer just like you can swap add-ins over? What do you think? Well, the answer's no.

Whilst add-ins can be swapped over in addition questions, the minuend and subtrahend cannot be swapped in subtraction questions.

It will give a different answer and it will give the incorrect answer.

Okay, let's change the numbers.

Let's increase the numbers, in fact.

They're going to be over 10 pounds this time.

And let's change the context as well.

So we're still looking at a difference, but this story's all about how much more is needed.

So the game I want to buy costs 29 pounds 50 and I have saved 18 pounds 94.

How much more do I need to save? So once again, we're looking for the difference.

So in this case, 29 pounds 50 is our minuend and 18 pounds 94 is our subtrahend.

And when we subtract 18 pounds 94 from 29 pounds 50, it will give us the difference between those two prices or how much more we need to save.

So it's still a difference context.

And once again, just like before, we can set this out as a bar model.

A slight change though is that this time our minuend is greater than 10 pounds, so that extra column has been needed, but it's going to be the exact same process as before.

And that bar model, if you look at the bar model, it's showing a difference.

There's a difference between those two prices and that's what we're going to calculate.

So I've made a start here.

I've set everything up, I've included my minuend, I've got my subtrahend, my decimal points are all lined up, and I've begun by starting with my least significant digits.

So so far, so good.

And I've got 0 take away 4 equals 4.

Hmm, "Can you spot the mistake?" wonders Lucas.

Yeah, I think he spotted something wrong.

Can you see it too? That's not right.

The zero cannot be ignored.

0 p subtract 4 p is not 4 p.

A regroup needs to occur.

So be very careful.

Check if your subtrahend has got a digit that is greater than your minuend, you're going to need to do some regrouping and that's what's necessary here.

We're going to need to regroup from the ten ps.

And that's what we've done.

So we've regrouped one of those ten ps.

So instead of 5 ten ps, it's got 4, and we've regrouped it for 10 one ps.

So now we've got 10 p take away 4 p is 6 p.

And we carry on in that fashion going from right to left and that will give us the answer 10 pounds 56, so remember to do your regrouping.

So our minuend was 29 pounds 50, our subtrahend was 18 pounds 94, and that's given us a difference of 10 pounds 56 and we can show this on the bar model.

So I need to save 10 pounds 56 more.

That's a difference between what I've got and what I need.

Let's change the context slightly.

There's going to be something a bit different about this one.

See if you can spot it.

I need 12 pounds 50 to enter a swimming competition, but I only have 7 pounds 8.

How much more money do I need? So once again, just like before, we are looking at a difference problem and a how much more problem.

But there's something a bit different about this one.

Have you spotted it? Our subtrahend and our minuend have got a different number of digits, but can we still use the method? Yes, we can.

A placeholder zero can be added if it's helpful.

It won't change the outcome, but it sometimes helps to have the same number of digits in the minuend and the subtrahend.

And when we complete the calculation, it gives us 5 pounds 42, so I need 5 pounds 42 more.

And you might notice that I've remembered to do my regrouping as I've gone along.

Time for a quick check for understanding.

So I've saved 6 pounds 53 and my brother has saved 4 pounds 38.

How much more have I saved than my brother? So let's have a think, what's the minuend there? What's the greater number? What's the subtrahend? What am I going to subtract from it? And then we need to find out the difference.

That's what's totally unknown at the minute.

That's what we need to calculate.

So you need to do two things.

Represent that with a bar model, please, and then calculate it using column subtraction and remember to do your regrouping.

Pause the video and I'll give you some feedback very shortly.

Let's see how you got on.

So that is that problem represented in bar model form.

And here is the column subtraction that gets you there.

So the difference is 2 pounds and 15.

Do you think you might be starting to get the hang of column subtraction? Do you think you might be ready to do some practise questions? Let's find out, shall we? So number one, complete the calculation and fill in the bar model.

And we've set that out for you, we've lined everything up, so you've got a nice example.

All you've got to do is finish it off and add it to the bar model piece.

So you're looking to find the difference.

You've got the minuend, you've got the subtrahend, we just need the difference, please.

Number two, complete the calculations using column subtraction.

So this time, they haven't been set out for you, so you need to do that.

So please do remember to keep your digits lined up and use those decimal points.

And, crucially, remember your regroups.

So red trainers cost 12 pounds 75 and the blue ones cost 27 pounds 40.

How much more do the blue ones cost than the red ones? So ask yourself, what is my minuend here? What do I need to put on top of this calculation? What's my subtrahend? What am I gonna put underneath it? Remember to line them up.

Remember to use your decimal points.

Remember to do your regrouping.

Pause the video, good luck, and I'll see you soon with some answers and some feedback.

Well, let's have a look.

So we had two regroups for the first question and that gives us the answer 4 pounds 62.

That's the difference.

And then when we use the bar model, that's what it looks like.

So 8 pounds 47 is our minuend and 3 pounds 85 is our subtrahend, which we've got on, got on the left here, and 4 pounds 62 is our difference.

Sometimes the difference can go on the left, sometimes on the right.

And hopefully you set these up properly and got the answers, 10 pounds 95, 14 pounds 65, and 8 pounds 55.

And now our final question in this cycle, red trainers cost 12 pounds 75 and the blue ones cost 27 pounds 40, so we need how much more? So what's the difference between them? And that is 14 pounds 65.

So we've looked at using column subtraction as a strategy, but it's not the only strategy and sometimes other ways can be quicker if you have a think about it before you do the calculation.

So let's explore some alternative methods.

Okay, so here's Lucas.

He's a big football fan.

Lucas has bought a football shirt for 17 pounds 99 and he's paid with a 20 pound note.

How much change did he get? Now Lucas is getting used to this column subtraction method and that's what he's done.

He set it out as a column subtraction.

I'm not sure that's the most efficient way though, hmm.

Sofia says, "Hang on, Lucas, that's going to require a lot of regrouping.

It is, isn't it, when you think about it, 'cause we need to regroup that first zero and then we're going to need to regroup the second zero and the third zero.

And there's something about those numbers that makes me think that column subtraction might not be the best method.

Have you spotted it? Look at the Subtrahend.

Look at 17 pounds 99.

Is there something special about that? I think there is.

Sofia says, "I can count on to find the difference." I've shown my steps on a number line." So let's have a look at that, shall we? So here's our number line, just draw a straight line, simply as that.

So on the left-hand side, she's got the subtrahend, 17 pounds 99.

And on the right-hand side, the minuend, and we're going to go from the subtrahend to the minuend by using counting on.

So if we take a little jump of 1 p, that will take us to 18 pounds.

And then one more jump will take us from 18 pounds to 20 pounds, which would be? Two pounds, so all we have to do now is combine those together, 2 pounds plus 1 p is 2 pounds 1.

Now how much quicker was that than using column subtraction and no regrouping required? Now Sofia's chosen to use a number line to do that and it was quite quick to do it, but you might even be able to do it in your head too.

Sofia's got a 20 pounds voucher and she's downloaded a movie for 11 pounds 98.

She's used that voucher.

How much money has she got left, 'cause she's not spent all of it, has she? So we're looking again at the difference between those two values, between the minuend and the subtrahend.

So when the minuend has lots of placeholders, which 20 pounds does, so that's potentially got two extra placeholders where the pennies are, it can be more efficient to use count on to find the difference.

So here we go.

So we're going from 11 pounds 98 to 12 pounds, that's a two pence jump.

And then from 12 pounds to 20 pounds, that's an 8 pound jump.

Combine them together and we've got 8 pounds 2 and that would take so much less time than doing it as a column subtraction.

So we've got Sofia again.

She was given 50 pounds as a birthday present and she wants to buy a new pair of trainers for 35 pounds 99.

Now let's think about that subtrahend, 35 pounds 99, it's very close, isn't it, to a multiple of one pound? Very close, it's got that 99 on the end.

How much will she have left afterwards? So straight away I'm thinking to myself, I don't think column subtraction's the best method for this one.

I think it's going to be a counting on one.

So how much will you have left afterwards? So we're looking to find the difference between the minuend and the subtrahend.

So just like before, we're going to use a number line and we're going to use counting on.

Column subtraction would take way too long, there'd be way too many regroups.

Okay, so let's draw our number line.

On the left-hand side, we're going to put our subtrahend, our lower value, that's 35 pounds 99.

On the right-hand side, our minuend, our higher value, and then we're going to work out the difference by counting on, using the counting on strategy.

So we can do this in lots of different ways, but we could do it like this.

One p would take us up to, what do you think? To 36 pounds, so that's our first jump.

And then you can either do two jumps, so you could jump to 40 pounds and then to 50 pounds from there.

Or if you're good with your number pairs and your number compliments, you might realise that 36 plus 14 equals 50, so you could in fact do it in one jump and we're going to do just that.

So all we need to do now is combine those together and that gives us 14 pounds and 1 pence.

Jun's impressed with Sofia's strategy but he's got a different one.

Let's investigate his strategy.

So back to the Lucas problem with the football shirt.

He bought a football shirt for 17.

99 and he paid with a 20 pound note.

How much change did he get? Let's have a look at a different way to do it then, an alternative way.

This is called adjusting.

So Jun says, "If we adjust both the minuend and the subtrahend by a penny," so in this case make them both one penny more, "the difference is still the same, but it's much easier to subtract." Let's see that in action.

So instead of 20 pounds and 17 pounds 99, it's going to become 20 pounds 1 and 18 pounds.

Now this time there's absolutely no regrouping required.

We can easily see the difference between those and easily work it out.

So we need to add 2 pounds 1 to get from 18 pounds to 20 pounds 1 And I did that in my head very quickly with very little effort.

So that's the difference, 2 pounds 1.

We can also use Jun's strategy to adjust the minuend and the subtrahend the other way by making them both smaller by the same amount.

So let's have a look at something else.

So Jun had saved 34 pounds 65 of his pocket money and he spent 12 pounds 5 on a meal combo.

How much does he have left? So we've got a reduction problem here, but that will still give us a difference.

Okay, we need to adjust both the minuend and the subtrahend by five pence.

The difference is the same, but it's much easier to subtract.

What do you think that's going to turn into then? It would make them both five pence smaller.

Should we have a look? So 34 pounds 65 would become 34 pounds 60 and 12 pounds 5 would become 12 pounds.

Now it's become very easy to subtract one from the other.

So 34 pounds 60, take away 12 pounds gives us 22 pounds 60.

And again, I found that fairly easy to do in my head and it involved no regrouping.

I think it's time we did a little check.

So you're gonna start by thinking about Sofia's counting on strategy.

So remember she likes number lines and counting on to solve this problem.

Sofia bought a bag for 15 pounds 95 and she paid with a 20 pound note.

How much change did she get? So can you draw a number line and use that counting on method to work out that difference? Pause the video and good luck.

Let's have a look.

So using that counting on strategy, we're going to go from the subtrahend, 15 pounds 95, to the minuend of 20 pounds.

And we could use the following two steps.

5 pence would take us to 16 pounds and 4 pounds would take us up to 20 pounds.

Combine those together and we've got 4 pounds 5.

Big well done if you've got 4 pounds 5 and you didn't even need to use column subtraction to get there.

Okay, let's think about Jun's strategy.

He likes adjusting.

So use Jun's adjusting strategy to solve this problem.

So Jun has 15 pounds and he buys a game for 8 pounds 99.

How much does he have left? So could you adjust both the minuend and the subtrahend there to make that easier? Pause the video.

Have a go.

Let's see how you got on with that one.

So the 15 pounds could become 15 pounds 1, so we're adjusting by a penny.

So therefore the 8 pounds 99, again, needs to be adjusted by a penny and increased, in fact, by a penny, to make that nine pounds.

Now we can work those out fairly easily without any regrouping required.

So the difference between 15 pounds 1 and 9 pounds is 6 pounds 1.

Congratulations if you got that.

And once again, you didn't need to use a column subtraction, so there are other ways.

I think it's time for the final practise of the lesson.

So have a good at solving these problems, so you've got a few strategies at your disposal now.

You've got column subtraction, you've got adjusting, you've got counting on, you've got all sorts of different things you could do.

So choose the best one, have a little think about it before you start each one.

Well, let's see how you got on.

So the first one then, 15 pounds take away 12 pounds 99 gives you 2 pound 1.

Now whatever method you used, if you got that right answer, well done.

But you might've said, I chose the counting on method, because 12 pounds 99 is close to 13 pounds.

So I certainly wouldn't have used the column method for that one.

The second one, 13 pound 5 take away 2 pound 10 is 10 pound 95.

And again, you can use any strategy, but maybe adjusting's a good one for that, because 13 pounds take away 2 pounds 5 is easier to work out in my head.

So we've adjusted both by 5 pence, turning one of them into a multiple of 1 pound.

50 pound 70 take away 8 pound 95, well, you may have chosen the adjusting method, because 50 pound 75 take away 9 pounds is easier to work out in my head.

And finally, 36 pounds 85 take away 14 pound 5, so the answer's 22 pounds 80, so that's the important part.

Maybe you chose the adjusting strategy to turn it into 36 pounds 80, take away 14 pounds, and therefore you didn't need to do any regrouping whatsoever.

We've come to the end of our lesson.

So today's lesson's been all about using and explaining the most efficient strategies when subtracting quantities of money.

So you've got a few different methods at your disposal now.

We started by looking at column subtraction.

It's a useful strategy, it's a great strategy, and it will work lots of the time, but it's not the only strategy.

Other strategies can be more efficient, so these include counting on and adjusting.

So the first example of, we can see counting on, to find out the difference between 17 pounds 99 and 20 pounds.

We've counted on, we used a number line.

And in the second example, we've done 34 pounds 65, take away 12 pounds 5 by adjusting both the minuend and the subtrahend and in this case by five pence, turning it into 34 pound 60, take away 12 pounds.

So my advice is take a short amount of time to ponder and consider which strategy is best before you begin each calculation.

So look before you leap.

That way you're going to be fluent and efficient.

It's been huge fun and a huge privilege for me today to be teaching this math lesson all about money.

And hopefully I will see you again soon for another math lesson.

Take care and goodbye.