Lesson video

Hello there, I'm Mr. Tilston.

I'm a teacher and I absolutely love maths.

So, I'm really excited to be here with you today teaching you a lesson all about rounding.

Now, maybe you've had some recent experience of rounding.

Do you know, for example, any rounding rules? Maybe you've used a number line, to help you round, something like that.

Well, today we're going to take that even further.

So, if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is, I can round a 4-digit number to the nearest hundred and ten.

And hopefully, you've had some recent experience of rounding a 4-digit number to the nearest thousand.

Our keywords today.

My turn, rounding, Your turn.

My turn, multiple, your turn.

I'm sure you know those words, but let's have a little reminder, shall we? Just in case.

Rounding means making a number simpler, but keeping its value close to what it was.

For example, to the nearest hundred, 623 rounds to 600.

And as I said before, maybe recently, you've rounded a number to the nearest thousand.

A multiple is the result of multiplying a number by an integer.

For example, multiples of 100 are 100, 200, 300, 400.

We could go on.

Our lesson today is split into two cycles.

The first will be rounding to the nearest hundred.

So, we'll really focus on that and the second will be rounding to the nearest ten.

There will be some similar skills between the two, but let's start by rounding to the nearest hundred.

In this lesson, you're going to meet all of these wonderful children.

You're going to meet Alex, Aisha, Sophia, Izzy, Andeep, and Lucas.

Have you met them before? They're here today to give us a helping hand.

They're all in Class 4, and Class 4 at Oak Academy are learning about distances from London to other European cities.

So, that sounds like an interesting geography lesson.

They've each been given a card with an airport on, and it's distance from London Heathrow Airport.

They use a STEM sentence to stand on a large line in between the correct multiples of 100.

We'll see that in a minute.

And they've got this STEM sentence.

My distance is, mm, kilometres.

The previous multiple of 100 is, mm, kilometres.

The next multiple of 100 is, mm, kilometres.

You might have used a similar one to that before with multiples of 1,000.

So here we go.

This is Sophia, she's got Krakow in Poland, which is 1,410 kilometres away from London, 1,410.

So, she's got that STEM sentence and she's going to use it.

Let's see if you can fill it in before she does.

What's the number that's given? What's the previous multiple of 100? What's the next multiple of 100? Let's have a look.

So, "My number is 1,410 kilometres.

The previous multiple of 100 is 1,300 kilometres," she says.

And, "The next multiple of 100 is 1,500 kilometres," she says.

Hmm, I'm not sure either.

Something didn't seem right there.

Is that correct? Hmm.

Well, the number would be somewhere in between those multiples of 100.

So, no, her number lies between 1,400 and 1,500.

So, she was almost right with that STEM sentence.

She needs to make a little adjustment.

That's better.

Now, he says, "My number is 1,410.

The previous multiple of 100 is 1,400." Well done, Sophia.

And, "The next multiple of 100 is 1,500 kilometres." So, Sophia stands in between the correct multiples of 100, which are stuck to the wall.

So, she's not going to worry about being exact, just somewhere in between them.

There we go.

That's somewhere in between those two multiples of 100.

So, this is Alex.

Hello, Alex.

Alex has Vienna, Austria, which is 1,279 kilometres away from London.

Again, see if you can beat him to it.

Can you use that STEM sentence before he does? "My distance is 1,279 kilometres.

The previous multiple of 100." What do you think that is? The previous multiple of 100.

Where would he stand? Where would he go in between those? It's 1,200 kilometres and the next multiple of 100.

What comes after? "1,300 kilometres," is what he says.

Is he correct? Yes, he is.

His number lies somewhere between those numbers.

1,200 and 1,300.

So, he stands in between the correct multiples of 100, just like Sophia did.

Where's he going to stand? Just here.

Somewhere in between those two multiples of 100.

Aisha has Nice in the south of France, which is, now, this is quite a difficult one to say.

Do you think you know how to say this, 'cause it's got no hundreds in? How do we say that? That's 1,040 kilometres away from London.

What do you notice about the hundreds? Well, as we just said, there's no hundreds, but the STEM sentence still works.

Let's try it.

What do you think she'll say? "My distance is 1,040 kilometres.

The previous multiple of 100 is," what do you think? 1,000? 1,000 is a multiple of 1,000, but it's also a multiple of 100.

You can count in one hundreds to get there.

The next multiple of 100 is what? 1,100.

Aisha stands in between the correct multiples of 100.

Where she's going to stand? Just here, and then she notices something.

Have you noticed anything yet about these numbers? Let's see what she notices.

She says, "The hundreds digit tells you what the previous multiple of 100 is." Hmm.

Okay, I think I know what you mean, Aisha.

Maybe say a bit more though.

Let's have a look.

So, Aisha's going to use what Aisha's noticed to help her describe her number without a number line to help.

She's got Turin, Italy, which is 1,129 kilometres away from London.

And this is what Aisha said.

"The hundreds digit," what's the hundreds digit here? One.

".

tells you what the previous multiple of 100 is." Hmm.

So, my distance is 1,129 kilometres.

So, what we're saying is that hundreds digit will help us with the next part, 'cause it's the same.

The previous multiple of 100 is 1,100.

I see what she means.

So, the next multiple of 100, 100 more than that is, 1,200.

You don't really need a number line for that, do you? I can sort of picture one in my head.

Right, here's a check for understanding.

Where should Izzy stand, in between which two multiples of 100 should she stand? Pause the video and have a go.

What do you think? You've got a few options there.

Where should she stand? Izzy's number is in between 1,100 and 1,200.

So, she should stand between those two numbers.

She's going to stand just there.

So, well done, if you said that.

You're on track.

Question for you.

What numbers exist at these points between 1,400 and 1,500? Have a look how many equal parts it's split into for starters.

Well, the difference between 1,400 and 1,500 is 100.

So, there's 100 in between those two numbers.

And then 100 is divided into 10 equal parts, and that is 10.

So, we're going to count along in multiples of 10.

Are you ready? Let's go.

So, we've got 1,400, that's a multiple of 10.

What's next? 1,410.

What's next? 1,420.

I think you're getting this now, aren't you? One more.

What's next? 1,430.

I think we can count together now, don't you? Let's go.

1,440, 1,450.

What do you notice about that number? 1,460, 1470, 1480, 1,490, and 1,500.

And that is a multiple of 10.

The Class 4 teacher has challenged the pupils to round the distances to the nearest 100 kilometres.

So, we've thought about what two multiples that lies in between, but now let's see if we can round it as well.

So, just a little reminder from Sophia, she had, my number 1,410.

The previous multiple of 100 is 1,400.

The next multiple of 100 is 1,500.

But what's it closest to? Now, we're going to have a look at the tens for a clue, and the tens have been highlighted there is one, one ten.

Hmm.

So, what are we going to do? We're going to go to the previous multiple or the next multiple.

Going to consider that tens digit.

You can ignore the ones, there's no ones in this case, but it doesn't matter.

It's not going to affect how the number is rounded.

The tens will affect it.

So, here we go.

That's 1,410.

It's pretty close isn't it? To 1,400, but it's really far away from 1,500.

So, we need to think about which one is closest to, 1,410 is 10 away from 1,400, and nine tens away from 1,500.

So, it's closer to 1,400, by quite a lot in fact.

So, we can complete the STEM sentence.

That's what it rounds to.

Okay, what about this one for Alex? "My number's 1,279.

The previous multiple of 100 is 1,200." We've established that already.

"The next multiple of 100 is 1,300." But what's it closer to? Again, let's have a look at the tens for a big clue.

That's going to be what tells us which one it's closest to.

It's seven, seven tens.

Hmm.

Does that mean it's closer to the previous multiple or the next multiple? Well, here we go.

That's how far away it is from the previous multiple of 100, quite a bit.

Seven tens away or 70.

And that's how far it is from the next multiple of 100, not too much, three tens or 30.

So, Alex is number is seven tens away from 1,200 and three tens away from 1,300.

So, that means he's closer to 1,300.

That's what it rounds to.

We can say 1,279 rounded to the nearest a 100 is 1,300.

Aisha's number has four tens.

So, it is four tens away from the previous multiple of 100 and six tens away from the next multiple of 100.

So, what's it closer to? It's closer to 1,000 kilometres.

Something special about this one.

1,040 rounded to the nearest 100 is 1,000.

What's special about that do you think? Aisha has got it.

1,040 rounds to 1,000 to the nearest 100, but it also rounds to 1,000, the nearest 1,000.

So, it's quite a special number.

The pupils move from in between the multiples of 100 to the multiple of 100 to which the number rounds based on the number of tens it has.

So, look at the number of tens each time and think where they would stand.

So, we've got Aisha, she's got 1,040, so that's four tens.

So, she's gonna stand at 1,000.

And then we've got Izzy, she's got 1,129, that's got two tens.

So, she's gonna stand on 1,100.

And then we've got Alex, he's got 1,279, that's got seven tens.

So, he's gonna stand on the next multiple of 100.

There we go.

And then we've got Sophia.

She's got 1,410, that's got one ten.

So, she's going to stand on the, hmm, you tell me.

Pause the video.

What do you think? Is she standing on the previous multiple of 100 or the next multiple of 100.

So, it's got one ten.

One ten means it's the previous multiple.

So, that's where she stands, 1,400.

Well done, if you got that.

Here's Lucas and he's got a special one.

So, hello, Lucas.

He's got Lisbon, Portugal, which is 1,450 kilometres away from London, right? There's something special about this.

It's that number five.

We can do this bit quite easily.

"My number's 1,450 kilometres," but there's going to be a bit of a problem here and I wonder if you can see what it's going to be.

"The previous multiple of 100 is 1,400." That's not the problem.

"The next multiple of 100 is 1,500." That's straightforward too, but what does it round to, and why is that tricky? Well, have a look at this.

Hmm.

Can you see the problem? It's five tens away from 1,400, and it's also five tens away from 1,500.

So, it's exactly in the middle.

It's not closer to either of them.

And what do we do then? There's a rule in rounding.

You might remember this.

If the digit in question is five or above, so 5, 6, 7, 8, or 9, round to the next multiple of the number you are rounding to.

So, that number five is just a special rule that we have in maths.

1,450 rounded to the nearest a 100 is 1,500.

Now, Class 4 are looking at the distances between London, Heathrow and some further out destinations.

So, we've got New York, Jerusalem, and Shanghai.

I've been to two of those places.

I've been to New York and Shanghai.

So, let's start with New York.

What's the previous multiple of 100? 5,500.

What's the next multiple of 100? 100 more than that? 5,600.

So, that number's somewhere in between those two, but what does it round to? That four will help us.

Four means it's the previous, so that's 5,500.

Let's have a look at Jerusalem.

Previous multiple of 100? 3,600.

Next multiple of 100, 3,700.

What is it closer to? It's got a three.

So, is that going to be previous or next? That's previous.

Shanghai, what's the previous multiple of 100? 9,200.

What's the next multiple of 100? 9,300.

Now, it's got six tens.

So, are we going to round to previous or the next? The next, that's 9,300.

Aisha's noticed something.

She's always good at noticing things, isn't she, Aisha? Have you noticed that? She says when rounding to the nearest 100, the thousands don't change.

Hmm, I wonder if she's right.

Let's have a look.

Well, that is true of New York.

5,548 kilometres and it rounds to 5,500.

So, the thousands didn't change there.

And it's true of Jerusalem too, look.

3,000, 3,000.

And it's true of Shanghai, look.

9,000, 9,000.

She might be right, or is she? She's almost right, almost.

That's usually the case.

But let's have a look at Sri Lanka, and that's 8,952.

So, remember, Aisha was saying that the thousands digit isn't affected.

Well, the previous multiple of 100 is 8,900.

The next multiple of 100, what's 100 more than that? 9,000.

So, the thousands has changed there.

And the nearest multiple of 100, well, it's a five.

So, what does that tell you? Use that special rule.

We round to the next multiple of 100, so that's 9,000.

So, in this case she's not quite right, but almost.

Here's the rule.

If the last three digits are 950 to 999, the next multiple of 100 is also the next multiple of 1,000.

Let's do a check.

When rounding a 4-digit number to the nearest hundred, what's the most important digit to consider? Is it the thousands, is it the hundreds, is it the tens, or is it the ones? Pause the video and if you can, have a discussion about that.

Did you come up with an agreement? Which one is it? It's the tens.

The tens digit helps us to decide how to round a number to the nearest hundred.

If the tens digit is five or more, the number rounds to the next multiple of 100.

It's time for some practise.

So, for the first one, you're going to use a STEM sentence or sketch a number line to run the numbers to the nearest hundred.

Number two, complete the table a bit like we did before, showing distances from the United Kingdom.

Got some new countries there.

For number three, use the following digits.

5, 7, 6, and 4.

How many numbers can you make that round to 6,500? There's quite a few.

And number four, what are the smallest and largest whole numbers that went rounded to the nearest a 100 give a value of 8,400.

You're going to need to do some thinking about that one.

Good luck and I'll see you soon for some feedback.

All right, let's give you some answers then.

So, number one, 2,872, the seven tells us to round to the next multiple of 100.

So, that's 2,900.

2,504, that's got zero for the tens.

So, we round to the previous one, 2,500.

2,700 is 2,700 when rounded.

So, that number remains the same.

2,010, that's got a one.

So, that rounds the previous one.

That's 2,000.

2,650, that's got a five.

So, you need to apply a rule, round to the next multiple, which is at 2,700.

So, two numbers here round to that.

And 2,999, that's got to nine.

So, that's going to round to 3,000.

And number two, here are the answers.

Number three, use the following digits.

How many numbers can you make that round to 6,500? Well, in systematic order, the possibilities are 6,457, 6,475 and 6,547.

And the smallest and largest whole numbers that when rounded to the nearest a 100 given value of 8,400.

Well, if you put that on a number line and put 8,400 in the middle, it makes it a bit easier to see that the smallest would be 8,350 and the largest would be 8,449.

If it was 8,450 one more, it would run to the next multiple, which would be 8,500.

Okay, rounded to the nearest ten, we're going to use a similar system.

So, the Class 4 teachers challenged Alex to round his number in a different way.

This time for the nearest multiple of 10.

That STEM sentence has been tweaked a little bit.

The previous multiple of 10 is 1,270.

What about the next one? The next multiple of 10 is 1,280.

But what is it closest to? Well, let's think about what numbers exist at these points between 1,270 and 1,280.

Well, the difference between those numbers is 10 and there's 10 equal parts.

So, that must mean each part's worth one.

So, we can count along in ones.

And here's Alex's number 1,279.

You can see it's quite a long way from 1,270, but it's very close to 1,280.

So, Alex's number is nine ones away from 1,270 and just one away from 1,280.

So, we can say 1,279 rounded to the nearest 10 is 1,280.

Aisha thinks she can round the various distances from London to the nearest 10 kilometres by visualising the positions of the numbers on a number line between multiples of 10.

And she's really focusing on that one digit.

So, she thinks you don't need the number line.

Let's see if you can do the same.

So, it's Krakow, that's 1,410.

So, the ones digit is zero, but let's think about the previous and next multiples of 10.

That's 1,410, the same number.

The next one's 1,420.

That must mean it rounds to, because it's the same 1,410.

For Prague, that's got a five.

We need a rule there, but let's think about the multiples of tens that it's between.

It's in between 1,280 and 1,290, but that five tells us that we round the next multiple, which is 1,290.

And then 1,198.

Well, the eight tells us we need to round to the next multiple, but let's think about what is in between.

It's in between 1,190 and what's 10 more than that? In this case, the final two digits meet the 95 or above rule that we looked at before.

So, the next multiple of 10 is also a new multiple of 100.

This will affect the hundreds digit as well as the tens and ones.

So, there we go.

So, 10 more than that's 1,200.

What's it closer to? The eight will tell us.

That's the giveaway.

That tells us that we round to the next multiple.

So, that's 1,200.

Let's do a check.

Round these distances from London to the nearest 10 kilometres.

Pause the video.

Let's see.

So, New York is in between 5,540 and 5,550, but the eight tells us that it's closer to 5,550.

Jerusalem is in between 3,630 and 3,640.

The zero tells us that the number doesn't change.

It's 3,630.

Shanghai is in between 9,260 and 9,270.

And the six tells us that it's closer to 9,270.

And Reykjavik, that 1,895.

So, what's that in between? That's in between 1,890, and 10 more than that? 1,900.

What's it closer to? Well, think about the five that will give you a clue.

The five, the special rule is be rounded to the next multiple.

The ones digit this time is five.

So, the rounding rule needs to be applied.

The next multiple of 10 also happens to be a new multiple of 100.

So, this is the only example of the four where the hundreds digit changes as well.

In all other examples, because the final digits are below 95, the other digits remain unchanged.

So, it's closer to 1,900.

Brilliant, if you've got all of those.

Let's do one more check.

When rounding a 4-digit number to the nearest 10, what's the most important digit to consider? Is it the thousands, hundreds, tens or ones? Pause the video.

So, rounding to the nearest 10.

So, we need to think about the digit after that.

That's ones.

The ones digit helps us to decide how to round the number to the nearest 10.

If the ones digit is five or more, the number rounds to the next multiple of 10.

Time for some practise.

Number one, use the STEM sentence or sketch number line to round the numbers to the nearest 10.

A bit like you did before.

Complete the table.

This time we're thinking about rounding to the nearest 10.

And number three, the smallest and largest whole numbers that give a value of 8,450 when rounded to the nearest 10.

Good luck with that.

Work with a partner if you can, and I will see you soon for some answers.

Welcome back, let's have a look.

So, here are the numbers when rounded to the nearest 10.

Well done, if you got those.

And here are the numbers when rounded to the nearest 10.

Again, first of all, thinking about the previous to next multiples and that's what it rounds to.

Well done, if you've got those.

Number three, the smallest and largest whole numbers that when rounded at the nearest 10 give a value of 8,450.

Again, using the number line and putting that number 8,450 in the middle, I think is really helpful.

The smallest digit will be 8,445 and the largest digit will be 8,454.

One more would take us to the next multiple and we don't want to do that.

We've come to the end of the lesson.

The lesson today has been rounding a 4-digit number to the nearest hundred and ten.

When rounding, a 4-digit number to the nearest hundred, consider the tens digit.

If it's 0, 1, 2, 3, or 4, round to the previous multiple of 100.

And if it's 5, 6, 7, 8, or 9, round to the next multiple 100.

When rounding a 4-digit number to the nearest ten, consider the ones digit.

If it's 0, 1, 2, 3, or 4, round to the previous multiple of 10.

And if it's 5, 6, 7, 8, or 9, round it to the next multiple of 10.

Very well done.

Rounding can be quite a tricky concept, but I think you are definitely starting to get there.

Practise will make perfect.

Hopefully, I'll get the chance to spend another maths lesson with you in the near future.

But until then, enjoy the rest of your day.

Take care, and goodbye.