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I can use knowledge of addition to add commonly used prices efficiently

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Prices are often 1p or £1 lower than the next whole number of pounds so £2.99 not £3.00
A number line supports rounding and adjusting strategies
You might round one addend or all the addends
Adjust the answer according to the rounding

Common misconception

Pupils use inefficient calculation strategies such as always using columnar methods.

Promote efficient mental strategies and model clear examples of the use of these.

Keywords

Addend - An addend is a number added to another number.
Round - When you round a number, you are making a number less accurate, but keeping it close to its original value.
Adjust - When you adjust a number you make a small change to it.
Redistribution - Redistribution is where part of one addend is moved to another addend.

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Hello there, I'm Mr. Tilstone.

I'm very excited to be working with you on today's lesson, which is all about money.

So if you are ready, let's begin.

The outcome of today's lesson is I can use knowledge of addition to add commonly used prices efficiently.

We've got some useful vocabulary today, some keywords, so my turn, your turn, addend, round, adjust, redistribution.

And let's find out what those words mean shall we? An addend is a number added to another.

When you round a number, you are making a number less accurate, but keeping it close to its original value, it makes it easier to use.

For example, 39 rounds to 40 to the nearest multiple of 10.

When you adjust a number, you make a small change to it.

For example, adjusting 99 p to one pound.

Redistribution is where we take part of one number and add it to a different number.

For example, 19 plus 34 can be redistributed so that it's 20 plus 33.

Our lesson today is going to be split into three parts.

The first part we'll be using the redistributing strategy when adding money.

The second will be using the adjusting strategy with one addend.

And the third part will be using that same adjusting strategy with two addends.

So let's start by using the redistributing strategy when adding money.

We've got two special helpers with this for today's lesson, and that's Aisha and Laura.

Okay, let me begin by asking you a question.

Have you ever noticed this, when you go to shops, have you noticed that lots of prices end with a nine or a 99? So let's have a look at some examples and I'll show you what I mean.

So you might see, for example, this bicycle on sale for £399, or you might see this pair that's 49 pence or these headphones that are £39.

99.

I've noticed that happens quite a lot, have you? Have you also noticed that sometime prices end with 95 too? So for example, this cake might cost £4.

95.

Have you ever wondered why that is? Well, the answer is it's a little psychological trick that retailers use.

So if we take this example, £4.

95 seems less than five pounds, which it is, but it seems a lot less because it's four pounds something instead of five pounds something.

Now, I'm sure that you've had lots of experience with rounding before, so let's see if you can use and apply those rounding skills to change these money totals back up to a rounded price.

So let's begin.

The bicycle, if you were to round it back up to an approximate price, what would it be? Well, 399 is very, very close to 400 pounds.

So it costs around 400 pounds.

What about the pear 49 pence? Can you round that back up to a more rounded figure? Let's try, shall we? 49 p rounds to 50 p.

What's about the headphones? £29.

99 is almost a very round number, isn't it? What number is that? That's 30 pounds.

So the headphones cost around 30 pounds.

And what's about the cake? So that's £4.

95, which is almost five pounds.

That skill of rounding is going to come in very handy, in a moment.

Aisha and Laura have got some money.

Aisha's got 55 p and Laura's got 29 p.

And the question is, how much do Aisha and Laura have altogether? And you might notice something particularly about Laura's total.

So the girls want to find out how much they've got altogether, and Aisha starts to use the column method to find the total.

But Laura says, \"Hang on Aisha, we can calculate this in a quicker, more efficient way.\" So let's explore that, shall we? Laura says, you can use a strategy called adjusting to combine the two addends.

She says, \"If you give me one p, you'll have 54 p and I'll have 30 p.\" So both of their money amounts have changed slightly.

They've adjusted them.

So that then becomes 54 p plus 30 P, which is 84 p.

And as Aisha says, \"Oh yes, that's much easier to calculate than 55 p and 29 p.\" It becomes something that's very easy to calculate mentally.

54 p plus 30 p equals 84 p.

I don't need a written method for that.

So the total amount of money that the girls have got has not changed, it was just adjusted and it became easier to work out when one of the numbers, in this case Laura's, was a multiple of 10 when we rounded it back up.

Let's try that skill again, shall we? But let's change the money amounts.

So this time Aisha has got 49 p, and this time Laura's got 36 p.

Now have a little think, which of the girls, Aisha or Laura, has got the money amount that's close to a multiple of 10? This time it's Aisha.

She's got 49 p, which is very close to 50 p.

Can they still use the redistribution strategy, do you think? Well, the answer is yes they can.

I'm sure you've learned lots of times before that it doesn't matter what order the addends go in, it will still give you the same sum.

And it's the same here with the money amount.

So the order of the addends doesn't matter at all.

So 49 p plus 36 p will give you the same as 36 p plus plus 49 p.

And what we're going to do now is adjust those money amounts.

So if Laura gives Aisha one p, Aisha will have 50 p and Laura will have 35 p.

The total's the same, just like before, but the calculation is easier.

That's now become 50 p plus 35 p, which I can do in my head.

That's 85 P.

The adjusting strategy is very useful, don't you think? This time it's not in pennies, it's in pounds and pennies.

Can we still use that redistribution strategy, do you think? Well, the answer is yes, we can.

So have a little think.

Which of the girls, Aisha or Laura, has got the money amount that's close to a multiple of 10? Hmm.

The answer is, it's Laura, 19 is very close to 20.

So if we add one penny to Laura's total, that means we need to take away one penny from Aisha's total.

So what will the new totals be? Let's have a look.

So it's now become 63 p plus 20 p equals 83 p.

So even though the notations changed, we can still use that same useful redistribution strategy.

Over to you now, let's see if you've understood the learning so far.

We've got a quick check for understanding for you.

It's a true or false.

So true or false, 59 pence plus 37 pence can be calculated by using 60 pence plus 38 pence.

So is that true or is that false? And I'd like you to justify your answer, please.

And you've got two options.

Option A, the 59 p has been adjusted to 60 p, and you also need to increase the other addend by one p.

Or option B, the 59 p has been adjusted to 60 p, so you need to decrease the other addend by one p.

So pause the video and see if you can work out whether that's true or false and how can you justify it.

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

Well, it's false.

And the reason for that is that the 59 p has been adjusted to 60 p.

So you need to decrease the other addend by one p.

So one of them is increased by one p, meaning you need to decrease the other one by the same amount.

Well, you are doing really well and I think it's time to put those skills into practise.

So for task A, number one, you're going to add together these items using that redistribution strategy.

So the first one is 59 p plus 37 p, and you've been given a little hint there.

We've told you what to do.

So we've changed the 59 p to 60 p and change the 37 p to 36 p.

So we've redistributed the money to make it easier to work out.

So work that one out.

And then for B, you've got to think yourself, how do you redistribute? What are you gonna add to what? What are you gonna take from what? So what could 65 p plus 29 p become? And the same for C.

You might notice something about the order of the addends there.

So 19 p plus 74 p, can you use the redistribution strategy? And then for number two, you're going to add together these prices using the redistribution strategy.

Now remember to look out for the one that's close to a multiple of 10.

So we've got 62 pence plus 19 pence, 29 pence plus 43 pence, 42 pence plus 39 pence, 49 pence plus 26 pence.

Even though the notation is different, it's still saying that.

And then 44 pence plus 49 pence.

You might notice with that one the notation is mixed on both examples.

So good luck, pause the video and we'll see you very soon.

So how did you get on using the redistribution strategy? Let's look at some answers.

So for number 1, 59 p plus 37 p becomes 60 p plus 36 P.

So all you had to do is add those together and that gives us 96 pence, which I can do mentally.

I can do all of these mentally when I use the redistribution strategy.

65 pence plus 29 pence, if we redistribute becomes 64 pence plus 30 pence.

And now one of my addends is a multiple of 10, so it's easier to calculate mentally.

So that's become 94 pence.

And then 19 pence plus 74 pence, I've changed to 20 pence plus 73 pence.

So one addend has been increased by a penny and one's been decreased by a penny.

It hasn't changed the total, but it's now far easier to work out because one of them is a multiple of 10, and that's 93 pence.

And for number 2, 62 p plus 19 pence, what did you change that to? I redistributed that so that it became 61 pence plus 20 pence, which is 81 pence.

What's about 29 pence plus 43 pence? Well, I changed that to 30 pence plus 42 pence, which is 72 pence.

For C, 42 pence plus 39 pence.

Well, if I use my redistribution strategy, that becomes 41 pence plus 40 pence, which is 81 pence, 49 pence plus 26 pence, let's change that to 50 pence plus 25 pence, which is 75 pence.

So there's two different ways that you can represent that.

And then 44 pence plus 49 pence, that 49, so close to 50, so let's make it that.

Let's change it to 43 pence plus 50 pence.

And they're fairly easy to add together because one's a multiple 10 and that becomes 93 pence.

And just like before, there are two different ways to express that.

How are you feeling so far, that cycle one complete? Shall we get on with cycle two? Well, let's go.

So for this cycle, we're going to be using a different strategy, this time adjusting, and we're going to focus on one of the addends.

Have a look at this problem.

So we've got a lemon costing 55 pence and a pineapple costing 99 pence.

Now we could use the strategy that we've just been using, the redistribution strategy, that would work for that because 99 pence is very close to one pound, but we're going to try a different strategy this time.

It's quite hard to add 99 pence, but it's not as hard to add one pound.

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

We're going to change, temporarily, the cost of the pineapple from 99 pence to one pound.

So we're going to change the value of that addend, but we're going to keep the value of the other one in this strategy the same.

So 99 p is the second addend, what we're going to do is add a pound and then subtract a penny, which is the same thing as adding 99 pence.

So we're doing it in two small easy steps.

So instead of 55 p plus 99 p, it's going to be 55 p plus one pound, take away a penny.

And those are quite easy steps.

But let's see that on a number line.

Let me show you what I mean.

So here we've got our 55 pence and we're going to add on a pound to start with.

Here we go.

55 p plus a pound.

That's fairly easy.

That's £1.

55.

And then take away one penny gives us £1.

54.

So I broke that up into two small simple steps.

So you might write the equation 99 p plus 55 p equals for this example.

Does that mean you need to use a different strategy? Well no, addition is commutative, so you can sub the addends in any order you like.

You can swap them over.

So here we've got 55 p plus one pound, take away one penny, equals £1.

54.

So it doesn't matter which way we express them, we can still use the same strategy and it's a useful strategy too.

In a different shop, Aisha notices the prices are written differently, so the pound sign has been used in these cases.

Does that mean she needs a new strategy? Hmm, what do you think? No, the exact same strategy can be used as before, even though the notation is different.

Remember £0.

99 is the same as 99 p and it's still one p less than one pound.

So we can still use that strategy of adding on to one pound and taking one penny away, even though the notation is different.

Now in those examples, both of the addends were under one pound.

Would the strategy still work if one of the addends was more than one pound? The answer is yes.

So let's have a look at one example, now.

A toy car costs £3.

45.

So you can see already we've got an addend that's greater than one pound.

A toy lorry costs 99 p more than the car.

So we've got the other addend that's the same as before, 99 pence.

How much does the lorry cost? So have a think to yourself, what equation can you write for that? What plus what equals what? So 99 p is the second addend.

So just like before, we can add one pound and then subtract one penny, which are both fairly simple steps.

So in terms of an equation that be £3.

45 plus 99 p, which is the same as £3.

45 plus one pound, take away one p.

And once again, we can see those steps on a number line, £3.

45 plus one pound, take away one penny.

Number lines are easy to draw and they're a good way to scaffold your thinking.

So let's go through the process that got us there.

So first you add one pound.

One pound is one p more than the addend, which is 99 p.

So we adjust by subtracting one p.

So we've now looked at a couple of examples where one of the addends is 99 p.

What if it was greater than 99 p, but still close to a multiple of one pound? Let's investigate that.

So even when both of the addends are greater than one pound, you can still use that adjusting strategy.

Let's look at an example.

Aisha buys a small salad pot, which is costing £3.

45 and a cup of tea for lunch.

And the cup of tea is costing £1.

99.

So which of those two addends is close to a multiple of one pound? The cup of tea.

£1.

99 is very close to two pounds.

So how much does she spend altogether? So which addend could she adjust? The £1.

99.

What could she adjust it to? £1.

99 is very close to two pounds.

So we're going to first of all, temporarily adjust it to two pounds.

Essentially all we're doing is doing some rounding and then adjusting.

So as an equation that becomes £3.

45 plus £1.

99 equals, so is the same as, £3.

45 plus two pounds, take away one penny.

And that has become a calculation that I can do in my head.

But let's make sure that we really understand that number line because that's what I'm seeing in my head when I'm using this strategy.

So that becomes £3.

45 plus two pounds, which takes us to £5.

45, take away one penny, which takes us to £5.

44.

So once again, that's two small easy to take steps.

Two pound is one p more than the addend, which is £1.

99 and then you adjust by subtracting the one penny.

Let's make a little change.

Even when both addends are greater than one pound, you can adjust as we've just seen.

See if you can spot something slightly different about this example.

So we've got the salad bowl again, which is costing £3.

45, just like before.

This time the cup of tea's a different price, it's £2 98.

Hmm.

So do you think we could still use that same strategy of rounding and adjusting? Well, the answer is yes, we can.

We're just going to adjust it slightly differently.

Which addend is being adjusted? Well, just like before, it's the £2.

98, because it's very close to a multiple of one pound, it's very close to three pounds.

£2.

98 is two pence away from three pounds.

So you need to adjust this time by two pence, not one pence.

So we rounding to three pounds and then adjusting.

So £2.

98 is the second addend, so we can add three pounds and then subtract two pence.

So that becomes as an equation, £3.

45 plus £2.

98 equals, is the same as, £3.

45 plus three pounds, take away two p.

So once again, let's see those steps on a number line.

We start with £3.

45, our first addend, plus three pounds takes us to £6.

45, fairly straightforward.

Take away two pence, takes us to £6.

43.

So we weren't subtracting one p this time, it was two p, but it was still the same idea.

Aisha buys a toy car and a pair of scissors.

So the toy car costs £3.

45, and the pair of scissors cost £2.

95.

Hmm.

So not 99 p this time.

And not 98 p, but £2.

95.

Do you think we could still use that adjusting strategy? And if so, how? What would we do? Well, the answer is yes, we can.

So we're going to take the addend that's close to a multiple of one pound, that's £2.

95, and we're going to round it accordingly.

£2.

95 is five p away from three pound.

So you need to adjust at this time, not by one p, not by two p, but by five p.

So let's think about the steps to solving this calculation.

We'll use a stem sentence first.

You add mm plus mm equals mm.

So have a think about that one.

What are we adding and what are we adding to? Well, £3.

45 is our first addend, plus three pounds takes us to £6.

45.

So that's our first step complete.

That's our rounding.

And then we need to adjust.

So mm subtract mm equals mm.

Let's have a look, shall we? So £6.

45, take away five p this time, that's what we've rounded, that's what we need to adjust, equals £6.

40.

So what we've essentially done is take an addend that's quite difficult to add, which is £2.

95, and turned it into an addend that's very easy to add, three pounds, and adjusted it by an amount that's easy to take away, five P.

So looking at that altogether we've got, first you add £3.

45 plus three pounds, equals £6.

45, and then adjust £6.

45, take away five p, equals £6.

40.

Your turn.

Let's check your understanding so far.

You're going to complete that same stem sentence with a different example.

And then draw a number line to show how adjusting can be used to find the total.

So your question is this: A sticker book costs £4.

35 and a pair pack of stickers cost £1.

99.

How much do they cost altogether? So we've got this stem sentence.

First you add mm plus mm equals mm, and then adjust, mm take away mm equals mm.

So pause the video, have a go at that.

Good luck.

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

Let's give you some feedback.

So that completed stem sentences.

First you add £4.

35 plus two pounds equals £6.

35, and then you adjust.

£6.

35 take away one p equals £6.

34.

And the number line that represents that equation looks like this.

Are you ready to put that new skill into practise of rounding and adjusting? Well, here's what you're going to do.

So task B number one, filling in the stem sentence to calculate £5.

55 plus £3.

99.

And you will notice that one of those is very close to a multiple of one pound.

So first you add mm plus mm equals mm, and then adjust, mm take away mm equals mm and then draw a number line to go with it, just like in the check for understanding.

For number two, you're going to draw number lines to represent the strategy to sum each pair of prices.

And remember each time to look out for the addend that's close to a multiple of one pound.

So 65 pence plus 99 pence, 99 pence plus 74 pence.

And you might have noticed there're, the different representation, the different notation.

C, £3.

25 plus 95 p.

And D, £4.

76 plus £2.

98.

And for number three, complete these calculations.

This time try it without using a number line.

See if you can do it in your head using the same steps.

So we've got £4.

86 plus 99 p.

£4.

86 plus £1.

99, so one of the addends is the same as the previous question.

And the same with C, £4.

86 plus something, equals £7.

85.

You're going to need to do a little bit of thinking about that one.

And then something plus £3.

99 equals £8.

85.

That's quite tricky because we're giving you the addend that's close to a multiple of a pound, but not the other addend.

So pause the video, very best of a luck and I'll see you shortly.

Okay, how did you get on with that? Let's have a look.

So number one, that stem sentence becomes £5.

55 plus four pounds equals £9.

55.

And then adjusting that, that's £9.

55 takeaway one penny equals £9.

54.

And that's what it looks like on a number line.

For number two, they become 164 p or £1.

64, £1.

73 or 173 p, £4.

20 or 420 p, and then £7.

74 or 774 p.

All of those are acceptable answers.

And that's what the number lines look like.

And how did you get on with number three? Completing the calculations without using a number line? Well, A became £4.

86 plus 99 p equals £5.

85 B becomes £4.

86 plus £1.

99 equals £6.

85.

And then C, the missing addend was £4.

86 plus £2.

99 gives us £7.

85.

And then D, the first addend was missing and it's £4.

86 plus £3.

99 equals £8.

85.

Very well done if you got that.

Some of those were tricky towards the end.

And so we move on to the final of our three lesson cycles, and that's using the adjusting strategy that we've just used, but this time with two addends.

So you're going to do two adjustments.

Let's look at the first example.

See if you can tell me something about those addends.

So we've got the cup of tea costs £1.

99, and the pineapple 99.

Do you notice anything? Hmm? Have a little think.

Well, both of those addends are close to a multiple of one pounds.

So we could adjust both of them to help us find the total.

So let's try that.

Let's try rounding both addends and then adjusting both addends.

So £1.

99 is one p away from two pounds.

So you need to adjust that one by one p.

And then 99 p is one p away from one pound.

So we also need to adjust that one by one p.

So essentially our calculation is very close to two pounds plus one pound, which is a very easy calculation to solve.

So first we add two pounds plus one pound equals three pound, and then we adjust and we're going to do two adjustments.

So three pounds, take away one penny.

That was the penny we adjusted from the tea.

Take away one penny.

That was the penny we adjusted from the pineapple, equals £2.

98.

Let's have another go at using that strategy of adjusting both addends.

So we'll keep the cup of tea £1.

99, but this time let's add a book to it.

So it's going to be £1.

99 plus £2.

99.

So we've got a stem sentence.

So it's first you add mm plus mm equals mm.

And then adjust, mm take away mm equals mm.

So take a few moments just to think about what the gaps will be in that stem sentence, how we can fill them up.

So first you add, that's two pounds plus three pounds equals five pounds and then we adjust.

Now before we did it in two different steps, but I think we could do that in just one step.

So instead of doing five pounds, take away one penny take away one penny, we can just do five pounds takeaway two p.

So that's £4.

98.

Laura says this, see what you think.

She says 99 p plus 99 p equals one pound plus one pound.

Is that correct? Is that right? Hmm.

Take a moment to think about it.

No, that's not correct, is it? 'cause equals means it's the same as, and they're not the same.

So she's done the first part, which is to round them, but she's not done the adjusting part, so she can't use the equals sign.

The two parts of the equation are not equal, but we could make it so that they are.

99 p plus 99 p equals one pound plus one pound, take away two p.

And now we can use the equality sign.

Now Laura is correct.

Okay, over to you for a quick check, tell your partner using the stem sentence how you'd calculate this.

So £4.

99 plus £3.

99 equals what? So first you add mm plus mm equals mm and then adjust, mm take away mm equals mm.

Pause the video and have a go.

So that was five pounds plus four pounds equals nine pounds.

And then adjusting that, nine pounds take away two p equals £8.

98.

I think you are ready to apply that skill of adjusting both addends.

So let's have a go.

So C1, is to fill in the gaps, use a number line if you need to, but you might not need to.

And if you don't need to, that would save time.

And then for number two, we've got some different money amounts and you might notice something about those money amounts.

And then we've got some questions.

What costs about one pound? Which two items together cost about four pounds? What did you buy if you spent £4.

98? So that'll be more than one item.

What three items could you buy for less than 10 pounds? Can you do it more than one way? And could you spend exactly £5.

98? What would you have bought? Pause the video.

Very best of luck.

Off you go.

How did you get on? Let's give you some feedback.

We have reached the end of our lesson and haven't you done well? So our lesson today has been using knowledge of addition to add commonly used prices efficiently.

So remember, prices often ending near multiples of 10 p and one pounds.

So 59 pence, 95 pence, 99 p, 49 pounds, that kind of thing.

So we can apply mental strategies to add these numbers to other amounts of money.

We've got two strategies at our disposal.

We could use the redistribution strategy, which is where we adjust one addend by increasing it and then adjust another one by decreasing it by the same amount.

So in the example here we've got 55 p plus 39 p is the same as 54 p plus 40 p, which is 94 p.

And when we adjusted, it became easier to do.

And then finally, we can also use the adjusting strategy, which we've done with both one addend and two addends.

So let's look at an example here.

£3.

85 plus £1.

99 is the same as £3.

85 plus two pounds take away one p, and that's £5.

84.

You've been absolutely amazing.

It's been a real pleasure spending this lesson with you and I hope to see you again soon.

Goodbye.

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