Lesson video

Hello there, I'm Mr. Tilstone.

There's an old saying that goes, "Money makes the world go round." Well, it certainly is very important.

We use money to pay for goods and services and we receive money for the jobs that we do.

So it's my great pleasure today to teach you a lesson all about money.

So if you are ready, let's begin.

Our lesson outcome today, so our aim for today's lesson is I can use and explain the most efficient strategies when adding quantities of money.

So today's lesson's going to be all about adding.

As always, we've got some keywords, some important mathematical vocabulary which I'm going to introduce to you now using My Turn, Your Turn.

Are you ready? So addend, altogether, regroup/regrouping.

Some of those words may already be familiar to you and some may not be, but let's just go over them just in case.

So an addend is a number added to another number, simple as that.

And the word altogether is another way of saying in total.

The process of unitizing and exchanging between place values is known as regrouping.

In money, ten 1 p coins can be regrouped for 10 p and that might be something you've explored quite recently.

One 10 p coin can be regrouped for ten 1 p coins.

Our lesson today is going to be split into two cycles.

The first is using column addition when adding quantities of money.

Perhaps column addition is something that you've been exploring before, something you're getting quite confident with, let's see if we can apply those skills in the context of money.

And the second cycle is considering when opportunities might arise where we don't have to use the column addition method, where perhaps something more efficient can be used instead.

So if you are ready, let's have a look at using column addition when adding quantities of money.

I've got a couple of helpers with me this lesson and you might have seen them before.

So here's Sofia and Jun.

Let's begin by considering how a bar model may be used to represent addition.

So let's look at this example, which has got some money totals in.

What can you see here? What sorts of things can you see? What addition facts and what subtraction facts? Well, we can see 1.

37 pounds plus 2.

45 pounds equals 3.

82 pounds.

We can use the commutative law to see that 2.

45 pounds plus 1.

37 pounds equals 3.

82 pounds.

So there are the two addition facts I can see.

I can see some subtraction facts as well.

So starting with that top bar, I can see that if I've got 3.

82 pounds and I take away the first bar, which at the bottom is 1.

37 pounds, I've got 2.

45 pounds.

And likewise, if I start with 3.

82 pounds and take away the second part of the bottom bar that's 2.

45 pounds, that gives me the equation 3.

82 pounds subtract 2.

45 pounds equals 1.

37 pounds.

But it's the addition facts that we're going to particularly focus on today.

So let's put that into context, shall we? I buy two magazines.

One costs 1.

37 pounds and the other costs 2.

45 pounds.

How much do I spend altogether? So looking at the bar model, what we don't know is the total.

So the top part of the bar model is missing, but we do have two addends there.

Whilst the order of the addends will not affect the final total, it's most common to put the highest amount first.

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

2.

45 pounds is higher than 1.

37 pound.

So that's what we're going to put at the top of our column addition calculation.

And then underneath that, we've got our second addend, which is our 1.

37 pound.

We don't need to write the pound sign in the column addition, but do notice that everything is lined up.

The decimal points crucially are all lined up.

When completing column additions, we start with our lease significant digits.

So the digits on the right and it's the same is true when we're adding money totals.

So here we've got 7 pennies plus 5 pennies equals 12 pennies.

And we need to do some regrouping here.

We can regroup 10 pennies for one 10 p.

So that's how we express the 12: 12 p equals 10 p plus 2 p, and you can see both of those values in the column addition.

So now we're going to move on to the 10 p column.

There are no regroups this time because the total is within 10.

So we've got four 10 p's plus three 10 p's plus that regrouped, one 10 p.

So 4 plus 3 plus 1 equals 8 10 p's.

You must remember to add the regrouped 10 p at the bottom.

Then, we move on to the 1 pound column.

There's no regrouping here either.

So this calculation has involved one regroup.

So here we've got two 1 pounds plus one 1 pound equals three 1 pounds.

So now we've got not only our two addends, but the total that we get when we combine those addends.

So we've got 1.

37 pounds plus 2.

45.

equals 3.

82 pounds.

So I spend 3.

82 all together, and the column addition method really helped me to calculate that.

In the previous example, both of the addends were within 10 pounds.

So let's go a bit further, shall we? Let's have two addends beyond 10 pounds.

So I want to buy two games, one for 24.

55 pounds, and one for 17.

82 pounds.

How much will I spend altogether? So Jun is starting by considering, can I estimate the total? Well, 24.

55 pounds is about 25 pounds and 17.

82 pounds is about 20 pounds.

So we are looking for something in the ballpark of 45 pounds.

It won't be exactly that but something quite close to that.

It's useful to estimate because if we end up with an answer that's wildly different to that, we might realise we've done something wrong in the calculation and need to try again.

So as Jun has correctly worked out, the total will be close to 45 pounds.

So let's see if it is.

So we're going to do all the same things that we did before.

Only this time, we're going to need one more column for the 10 pounds.

And apart from that, we're going to use exactly the same process as before, starting with the least significant digit, the pennies.

Both of our addends are in our column addition sum now.

So we've got 24.

55 pounds plus 17.

82 pounds.

And remember, the decimal points are lined up and that's really important.

It will give us a different answer if they're not.

This time we're starting quite simply because there's no regrouping.

So five 1 p's plus two 1 p's equals seven 1 p's.

5 plus 2 equals 7.

But we do have a regrouping and I could tell that from the start because I could see in the 10 p's that it was going to go over 10.

So this time regrouping occurs when adding the values in the 10 pence column.

So we've got five 10 p's or 50 p, plus eight 10 p's or 80 p, and that gives us 130 p or thirty 10 p's.

So 130 p equals 1.

30 pound or 1 pound and 30 pence, and you can see that represented in the column addition.

I could see before we started this calculation that there was going to be at least one more regrouping as well and it was going to occur in the 1 pound column because that exceeded 10.

So we're going to regroup there too.

So we've got four 1 pounds plus seven 1 pounds, plus that regrouped one pound.

So 4 plus 7 plus 1 equals 12 or 12 pounds.

12 pounds is regrouped for one 10 pounds and 2 pounds.

So 12 pounds equals 10 pounds plus 2 pounds.

And again, you can see that in the calculation.

And finally to move on to the most significant digit, the one on the left-hand side, that's the 10 pounds.

So we've got two 10 pounds or 20 pounds plus one 10 pound plus that one 10 pound that was regrouped.

So 2 plus 1 plus 1 equals 4, so that's 40 pounds.

So I spend 42.

37 pounds altogether.

And Jun was quite close, wasn't he? With his estimation.

So we've looked at two examples now of column addition.

One where both hddends were under 10 pounds and one where they were both over 10 pounds.

Let's see if you are ready for a little check for understanding, shall we? You're going to complete this partly finished column addition example.

So we've got 24.

63 pound plus 37.

89 pound.

We've set it out for you.

All you've got to do is finish the calculation.

So pause the video, give it a go, and don't forget about that regrouping.

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

So the answer is 62.

52 pounds and they were three regroups there.

So well done if you've got that, you're on track.

So let's continue to use column addition.

But there's going to be something a little bit different about this example and I want you to see if you can spot what it is.

I want to buy a book that costs 5.

60 pounds and a game that costs 27.

5 pounds.

How much will I spend altogether? So have a look at those two addends.

What do you notice? Well, they're different.

In the first example we looked at, both of the addends were under 10 pounds, and in the second one, both over 10 pounds.

In this one, one's under 10 pounds and one's over 10 pounds but we can still use the same strategy.

And just like before, we're going to start by putting the addend that's got the highest value at the top of our column addition.

So here we go, everything's set out.

The 27.

5 pounds has got the highest value, so that's going to go on top.

The 5.

60 pounds is underneath it and we've used decimal points all lined up, so everything's good to go.

Aligning those decimal points will help to ensure that the digits go into the correct place value column and help us to get the correct answer.

Now this next part's optional, but for a lot of people, they find it quite useful to use a placeholder zero.

That way, both of the addends have got the same number of digits, but that's up to you.

Five 1 p's plus zero 1 p's equals five 1 p's and no regrouping there.

Zero 10 p's plus six 10 p's equals six 10 p's, still no regrouping.

Seven 1 pounds plus five 1 pounds equals twelve 1 pounds.

So that's where we've got our first regroup.

So remember to include the digits for the regrouping and remember to add them on to the next part.

Two 10 pounds plus zero 10 pounds plus that one 10 pounds that was regrouped gives us three 10 pounds.

So altogether, that gives us 32.

65 pounds.

And just to reiterate, you must remember about the regrouping.

Time for knowledge check.

We've got two examples here of column addition and I'd like to know which of these correctly shows 23.

65 pounds plus 4.

72 pounds.

But the one that's not correct, I wonder if you can spot what's gone wrong with it.

Pause the video, have a go.

Let's check, well, the one that was correct there was a, everything's been set out correctly there.

That's the correct answer.

And b was wrong, and the thing that was wrong with b, the error that had been made was that the 13 had been written as 31.

So be careful when expressing your regrouping.

I think you are really getting the hang of using column addition for money.

So let's do one more example, still using column addition.

There's going to be something different about this and I wonder if you can spot what it is before I tell you.

I bought a chair for 50.

35 pounds, a desk for 83.

25 pounds, and a lamp for 25.

10 pounds.

How much did I spend altogether? So first of all, did you spot what was different this time? Well, it's got three addends instead of two.

Can we still use column addition? Absolutely, all of the same principles are going to apply.

Remember to put the addends in order from greatest to smallest.

So we've skipped ahead a little bit, we've actually worked out the answer to this and it's 158.

70 pounds.

Now Jun's having a look at that and he's saying the column addition looks different.

It does, doesn't it? Can you spot, apart from the fact that we've got three addends, something that's a bit different about this? Have a look.

The number of 10 pounds has exceeded 10.

So we needed another regroup at the end of it.

So ten 10 pounds are regrouped for 100 pound.

That meant we needed another column on the left-hand side.

So fifteen 10 pounds equals 150 pounds or 100 pounds plus 50 pounds.

So remember when carrying out your column addition, you may sometimes need an extra column on the left if there's going to be one final regroup.

But 83.

25 pounds plus 50.

35 pounds plus 25.

10 pounds equals 158.

70 pounds.

And I've remembered to include my regroups.

Time for one final check, I think, before we do the practise.

Spot the errors in the following calculation.

And then, can you correct it? So somebody's had a go at adding three addends together, three money totals together, but they've made some errors and it's given them the wrong answer.

So pause the video, find the mistakes, and correct them, please.

Okay, let's check, shall we? How many did you spot? Were you able to put it right? Well, if it's supposed to be 45.

60 pounds, then a zero's missing.

Can you see that? So that may be what the money total should have been.

However, it might have been 45.

06 pounds in which case the placeholder zero is missing again, but just in a different place.

And the pence after the decimal place is always represented using two decimal places.

Please remember that.

Not only that.

The digits have not been lined up properly.

You can see that, can't you? The decimal points should be in line in there.

The means they're not.

So the 8 pounds is currently showing as 80 pounds.

It's in the wrong column.

The regrouped values have not always been included, so they haven't always added those up.

It's an easy thing to miss.

So make sure that you're including them.

So there are two possible correct calculations and bravo if you've got either of these.

So either 90.

07 pounds or 89.

53 pounds.

I think you are ready to start putting these skills into practise.

What do you think? Let's have a look, shall we? So we've got some column addition to do.

For task one, we've already set it out for you including keeping those decimal points lined up.

So all you've got to do is add them together.

So a couple of things there.

Remember to start with the least significant digit, that's the pennies.

And remember about your regroups, remember to include those and add those.

For number two, we haven't set those out so you've got to do that.

So remember to keep your digits lined up, your addends lined up.

Remember to use the decimal points and keep those aligned.

And then number three, we've got a bit of a word problem.

I want to buy three games, one for 24.

55 pounds, one for 20.

52 pounds, and the other for 17.

82 pounds.

How much will I spend altogether? So you've got three addends there.

Once again, remember to keep them lined up.

Remember to line up those decimal points.

Remember to include and add your regroups.

So pause the video, very best of luck.

I think you're going to be amazing and I'll see you soon for some feedback.

Okay, let's give you some feedback for task A.

So number one, 4.

25 pounds plus 2.

53 pounds is 6.

78 pounds and that involved no regrouping.

And 3.

73 pounds plus 5.

19 pounds is 8.

92 pounds.

That did involve regrouping with the pennies.

And for A2, using column addition, you would've got for the first one, 5.

47 pounds; the second one, 9.

33 pounds; and the third one, 33.

88 pounds.

And then for number three, when we add those three addends together and we remember all our regroups, it will give you the answer, 62.

89 pounds.

So a big well done to you if you've got some of those right and especially well done if you've got all of those right.

You are definitely on track and ready for the next lesson cycle.

So now let's consider other methods because you don't always have to use column addition.

Sometimes it's quicker and more efficient to use something else.

So let's explore some possibilities.

So we've got two money amounts here, two addends.

We've got 32.

78 pounds plus 22.

99 pounds.

Now Sofia has noticed something.

She says: Hmm, looking at that question, you could use column addition, it would work.

You could do it, it would give you the answer, but I think there's a much quicker and more efficient way.

The trick is to notice if there's anything special about either of the addends.

And I think there is, look at those two addends.

One of them has got something special about it, something different about it.

It's the second addend, 22.

99 pounds.

It's really close, isn't it? It's really close to 23 pounds and I think we can use that.

So what might you do to find the sum instead of using column addition? Hmm, let's have a look.

So it's that 99 p that's quite special.

And you might have had some recent experience of adding 99 p.

So Sofia says we could use the strategy of rounding and adjusting.

So turn the 99 p or round it into 1 pound, and then adjust back.

So we could do 32.

78 pounds plus 23 pounds, which I can actually do in my head, can you? Take away 1 p.

So that will give us 55.

77 pounds.

So once again, we've not added 22.

99, we've added 23 pounds, and then subtracted a penny.

We've broken into two smaller, easier steps.

Jun's looked at the same two addends and he's got a different idea.

He's got a different strategy.

He says we could also use compensating.

Make the first addend 1 p less and the second addend 1 p more.

And again, you might have had some recent experience of using this compensating strategy.

So we've taken 1 p from one of the addends and added it to the other one.

It hasn't affected how much money there is altogether, but it's made them easier to add together.

So we've changed 32.

78 pounds into 32.

77 pounds, taking that penny away.

And we've added that penny onto 22.

99 pounds to make it 23 pounds.

So the calculation now for Jun has become 32.

77 pounds plus 23 pounds.

And again, I can do that in my head.

That involves no regroups whatsoever.

That gives us 55.

77 pounds.

So well done, Sofia, and well done, Jun.

They didn't need a column addition strategy.

They were very efficient.

They were much quicker with their methods.

Let's do a quick check for understanding.

Let's focus on Sofia's method to start with.

So hers remember was the rounding and adjusting strategy.

So she's adding together these two addends, 38.

50 pounds plus 49.

95 pounds.

Now one of those addends is pretty special 'cause it's pretty close to a multiple of 1 pound.

So can you have a go at rounding that, and then adjusting it using the same strategy that Sofia used? Pause the video and have a go.

How did you get on? Let's have a look.

Well, I'm going to keep my 38.

50 pounds the same.

But the addend that I'm going to adjust is going to be the 49.

95 pounds.

I'm going to round it up essentially by 5 p to 50 pounds.

So that then becomes 38.

50 pounds plus 50 pounds, which is easy, I can do that.

That's 88.

50 pounds.

Take away the 5 p that I adjusted.

So 88.

50 pounds take away 5 p is 88.

45 pounds.

Really well done if you got the answer to that and you didn't need to use column addition to get there.

Jun just loves the compensating strategy and he thinks you can tackle this one in the same way.

So 38.

50 pounds plus 49.

95 pounds, we could use compensation for as well.

So in this case, if we make one addend, the 49.

95 pounds, 5 pence more, that would take it to 50 pounds.

But if we do that, we've got to make the other addend, five pounds less.

So that would take that down to 38.

45 pounds.

So then the calculation becomes 50 pounds plus 38.

45 pounds, and that gives you 88.

45 pounds.

And once again, we didn't need to use a column addition and it was much quicker without it.

Okay, let's have a look at this example then.

We've got 3.

28 pounds plus 2.

40 pounds.

So two addends under 10 pounds.

Now looking at those, are either of those addends really close to a multiple of 1 pound? And they're not really, are they? So do we need to use column addition? Hmm, well, let's think about that 'cause if we don't have to and we've got a quick away, that's what we should do.

Well, Sofia has noticed something again.

She's really good at noticing things.

She doesn't leap straight into calculation.

She has a little think before she does to see if she can save time in the long run.

She's done it again.

So, hmm, looking at that question, you could use written column addition, it will get you there.

She's right, but I think a different way might be more efficient.

She says neither of the addend is close to a multiple of 1 pound.

So I don't think adjusting will work.

I don't think compensating will work.

However, I've noticed that there will be no need to regroup.

Well, let's just check that.

Okay, the pennies, no, no regrouping there.

The 10 p's, no, no regrouping, that stays under 10.

And the 1 pounds, again, won't cross 10.

So you can easily add the two addends going from left to right this time, going from the pounds to the pence, without using a column.

So we've got 3 pounds plus 2 pounds equals 5 pounds.

20 p plus 40 p equals 60 p and 8 p plus 0 p equals 8 p.

So the sum is 5.

68 pounds and no column addition was needed.

So what Sofia did is I partitioned each addend and jotted down my working out.

It was more efficient than a column method.

Well done, Sofia.

Jun had a slightly different approach, although he also didn't use column addition.

He partitioned just one of the addends.

So in this case, he's kept the 3.

28 pounds as it is, and then added the other addend on in parts.

So he did 3.

28 pounds plus 2 pounds equals 5.

28 pounds.

5.

28 pounds plus 40 p equals 5.

68 pounds.

So the sum is 5.

68 pounds.

Unlike Jun, you might need to do a bit of jotting to do that or you might even be able to do that all in your head, but it's much more efficient than writing it down in a column addition sum.

Let's have a quick check.

What strategy or strategies might be used for adding 5.

84 pounds and 3.

97 pounds efficiently? So look at both of those addends and ask yourself if there's anything special about any of them.

Okay, so we don't want the answer as such, just which methods could be used.

So could you a, use column addition, a written strategy? Could you b, do that mentally, mental edition? Could you c, use the compensating strategy? Or could you d, use rounding and adjusting? And I think there's more than one answer there.

So pause the video, have a think which options would work there.

Well, let's go through that one at a time.

So column addition, written strategy.

Well, yes, it would work but it wouldn't be efficient.

So you'd get the answer, but I think it would take too long.

What about b, mental addition? No, no, I wouldn't go for mental addition because there will be at least two regroups that's going to make it really difficult to keep track of everything.

So I wouldn't recommend using mental addition.

I don't think I'd be able to do that.

What's about compensating then? So making one of the addends slightly bigger and making the other one slightly smaller by the same amount.

Yeah, that would work, wouldn't it? So that would turn into 5.

81 pounds plus 4 pounds because the 3.

95 pounds is really close to 4 pounds.

So we've taken 3 pence off one and added it to the other one.

5.

81 pounds plus 4 pounds equals 9.

81 pounds, no need for column addition.

And then rounding and adjusting, could we use that? Yeah, we definitely could.

5.

84 pounds plus 4 pounds.

Take away the 3 p, gives you 9.

81 pounds, and I can do those two small steps in my head.

Let's see if you are ready to try some of these problems and apply some of those strategies.

For each question, a strategy has been suggested.

You don't have to use it but it's recommended.

So for A, I buy a book that costs 3.

60 pounds and a game that costs 27.

05 pounds.

How much do I spend? See if you can use a mental partitioning strategy for that one.

B, I buy a DVD player that costs 42.

45 pounds and a DVD that costs 4.

98 pounds.

And hmm, I think there's something about the 4.

98 pounds there.

How much do I spend? Try using the rounding and adjusting strategy, the one that Sofia likes.

And C, my friend and I are putting our money together to donate to a charity.

I give 23.

52 pounds, and my friend gives 19.

98 pounds.

How much do we give altogether? Hmm, 19.

98 pounds, something special about that addend, isn't there? Try the compensating strategy, the one that Jun likes.

For task two, choose two items and find the total cost.

Complete as many totals as you can.

Sometimes you'll need to use column addition.

Sometimes you'll be able to use a mental strategy such as rounding and adjusting or compensating.

Say which strategy you've used each time.

So the challenge after that is to choose three items, so three addends, and do the same thing.

So before you get stuck in, remember to ask yourself each time, do I need to use column addition here? And if you do, you do.

But if you've got a quicker way, use that.

Okay, pause the video and I look forward to seeing you soon with some feedback and see how you got on.

Welcome back, how did you find that? Well, let's find out, shall we? Let's give you some feedback, some answers.

So for A, we got 30.

65 pounds.

So whatever method you used, if you've got 30.

65 pounds, you've done well.

For B, that's 47.

43 pounds, and for C 43.

50 pounds.

And there's lots and lots of possible answers for the next task.

If adding two addends, let's look at the example of 2.

70 pounds plus 99 p gives you 3.

69 pounds, that's using rounding and adjusting.

You maybe did 15.

75 pounds plus 23.

55 pounds, which I would use column addition for because there's regrouping.

And then for the three addends, maybe you did 15.

75 pounds plus 5.

87 pounds plus 99 p.

And for that, I can use a combination.

I can use column addition first, and then some compensating afterwards.

And so we've come to the end of the lesson.

Let me tell you, I've had really great fun today exploring all of the different methods that we can use when adding money amounts together.

Written strategies can be useful way of adding money totals, especially if there are more than two addends or if regroups are necessary.

So often column addition is best, but not always, written strategies are not always the most efficient way to calculate.

They're not always the quickest.

Rounding and adjusting, compensating and partitioning can be more efficient depending on the calculation.

So my recommendation is look before you leave, have a little thing before you start calculating what's the best method that I've got to tackle this problem.

You've been fantastic and hopefully, I'll see you again soon for more maths.

Take care and goodbye.