Lesson video

Hi, there, my name is Mr. Tilston.

I'm really excited to be working with you today on this lesson, which is all about rounding.

Rounding is probably a brand new concept for you, so I'm looking forward to exploring that with you.

So if you are ready, I'm ready, let's begin.

The outcome of today's lesson is I can explain what rounding is and round a four-digit number to the nearest thousand.

And in the future we'll look at rounding in different ways, but today let's just focus on the nearest thousand.

Our keywords today are, my turn, rounding, your turn.

My turn, multiple, your turn.

What do those words mean? Let's have a look.

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

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

So it's pretty close by.

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

So for example, multiples of 100 are 100, 200, 300, 400.

What do you think the multiples of 1000 could be? We'll come back to that.

Our lesson today is split into two cycles: previous and next multiples of 1000 and rounding to the nearest 1000.

So if you're ready, let's start by looking at previous and next multiples of 1000.

In this lesson, you're going to meet Alex, Aisha, Sofia, Izzy, Andeep, and Lucas.

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

Class four at Oak Academy are learning about mammals.

They have each been given a card with a mammal on and it's mass in kilogrammes.

They need to use the stem sentence to stand on a large number line in between the correct multiples of 1000.

And the stem sentence is this.

My number is mmm kilogrammes.

The previous multiple of 1000 is mmm kilogrammes.

The next multiple of 1000 is mmm kilogrammes.

So they're going to say that stem sentence and fill in the blanks with different values.

So here's Sofia.

She's got the hippopotamus, which has a mass of 3750 kilogrammes, so big mammal.

So she's going to use her stem sentence, my number is mmm kilogrammes.

The previous multiple of 1000 is mmm kilogrammes, and the next multiple of 1000 is mmm kilogrammes.

That number is 3750 kilogrammes.

The previous multiple of 1000 is, what do you think she's going to say here? She says 2000, and the next month 1000 is, what do you think she'll say? 4000, is she correct? Is that what you would've said? She's not actually quite right there.

She's half right.

That's where her number would be.

Somewhere in between 3000 and 4000.

Is the previous multiple of 1000, 2000 though? That's not what that's in between is it? No, a number lies somewhere between 3000 and 4000.

So instead of saying 2000 for the previous multiple, it's actually 3000.

You can see that using the number line.

Sofia stands in between the correct multiples of 1000, which is stuck to the wall.

So here she is, somewhere in between the 3000 kilogrammes and the 4000 kilogrammes.

This is Alex.

Alex has got the northern elephant seal, which has a mass of 1600 kilogrammes.

Right, do you think you could do that stem sentence? Let's have a look at what he says.

My number is 1600 kilogrammes.

What's the previous multiple? Where would that be? What's that in between? 1000 kilogrammes he says.

The next multiple of 1000 is 2000 kilogrammes.

Would you agree? Is that right? Is that correct? Yes, that's where his number lies.

Somewhere in between those two multiples of 1000.

So he stands in between the correct multiples of 1000.

Here he is, 1600 is somewhere between 1000 and 2000 kilogrammes.

This is Aisha.

She's got the Javan rhinoceros, which has a mass of 2150 kilogrammes.

Help her to complete the stem sentence.

Pause the video, and off you go.

Did you have the chance to practise that? Did you get the chance to say it to your partner? Let's have a look.

So my number is 2150 kilogrammes.

The previous multiple of 1000 is 2000 kilogrammes.

The next multiple of 1000 is 3000 kilogrammes.

So it's somewhere in between those numbers.

Aisha stands in between the correct multiples of 1000.

There we go.

She notices something, hmm.

Have you noticed anything yet? She says the thousands digit tells you what the previous multiple of 1000 is.

All right, yes.

So Alex, his thousands digit was one and his previous multiple of 1000 was 1000.

Hmm, Sofia, her thousands digit was three, and the previous multiple of 1000 was 3000, ah.

So 2150 kilogrammes, a thousands digit is two.

So the previous multiple of 1000, according to Aisha, is 2000.

She's right.

Izzy, he's going to use what Aisha's noticed to help her describe her number without the number line to help.

She has the Asian elephant.

Okay, see if you can do that first.

So she's got 3178 kilogrammes.

She's going to think about the previous multiple of 1000 using Aisha's method and the next multiple of 1000.

Let's have a look.

The thousands digit tells you what the previous multiple of 1000 is, yep.

So my number's 3178 kilogrammes.

The previous multiple of 1000 is 3000 kilogrammes.

And the next multiple of 1000 is 4000 kilogrammes.

Right, let's do a check.

Where should Izzy stand? She's got 3178 kilogrammes.

What two multiples should she stand in between? Pause the video and have a go.

Where would you place her? Let's have a look.

Izzy's number is in between 3000 and 4000, so she should stand near Sofia.

So they're in the same part, they're together.

They're both in between 3000 and 4000.

Both of their numbers start with a three in the thousands column.

It's time for some practise.

I think you're ready.

Number one, join the numbers to their correct previous and next multiples of 1000.

You may wish to sketch a number line to guide you.

Number two, use the following digits.

How many ways can you complete the stem sentence? You've got 5, 7, 6, and 4.

My number is mmm.

The previous multiple of 1000 is 6000, and the next multiple of 1000 is 7000.

How many four digit numbers can you make that fit that criteria? Pause the video, have fun, and I'll see you soon.

Welcome back.

So joining the numbers then, 4872.

Previous, 4,000, next, 5,000.

3500, 3500, so previous, 3000, next, 4000.

2700, previous, 2000, next, 3000.

4010, previous, 4000, next, 5000.

So there's two in that category.

3650, previous, 3000, next, 4000.

1999, previous, 1000, next, 2000.

And then the possibilities for this question in systematic order from smallest to greatest are as follows.

6457, 6475, 6547, 6574, 6745, and 6754.

Well done if you've got any of those, but especially well done if you've got all of those.

Are you ready for the next cycle? I think you probably are.

There's rounding to the nearest 1000.

Have you ever heard of that term rounding before? Rounding numbers, hmm.

Rounding a number means turning it into a number which is similar but simpler.

It gives the number a value which is approximate, so a rough number.

It can be helpful to group similar numbers together.

That's why we round.

For example, if a person has a mass of 62 kilogrammes and another has a mass of 57 kilogrammes, both of those could be rounded to the nearby mass of 60 kilogrammes.

They're both about approximately 60 kilogrammes.

Would you agree? So both have a mass of approximately 60 kilogrammes.

They're roughly the same.

If a different person has a mass of 71 kilogrammes, it wouldn't be fair to say they've got a similar mass to the others.

It's quite close to a different multiple of 10 though.

It rounds to 70 kilogrammes.

So that's what we mean by rounding.

Let's explore that a bit more.

What numbers exist at these points between 3000 and 4000.

So it's equally spaced.

There's 10 intervals in between those.

What do you think? Well, the difference between 3000 and 4000 is 1000 and there's 10 equal parts.

1000 divided into 10 equal parts is 100.

So each of those intervals is worth 100.

So can you count in 100 from 3000? Count along with me in multiples of 100.

So we've got 3000, 3100.

What's next? 3200.

What's next? 3300.

Got it, should we keep going? 3400, 3500, 3600, 3700, 3800, 3900, and 4000.

So we've got a new number line look.

So the class four teacher has challenged her pupils to round their mammals masses to the nearest 1000 kilogrammes.

So here we go.

We've got part of this stem sentence already.

My number is 3750 kilogrammes.

The previous multiple of 1000 is 3000 kilogrammes.

Remember this from before.

The next multiple of 1000 is 4000 kilogrammes.

But what is it closer to? Hmm.

To do this, the pupils are now going to consider the hundreds digit and that has been highlighted on Sofia's number.

The hundreds digit is seven for her.

They can ignore the tens and ones.

They're not going to affect how the number is rounded.

So we're going to really focus on the hundreds digit to tell us how to round the thousands.

Here we go.

So that's 3700, and that's how far it is from 3000, the previous multiple, and that's how far it is from 4000, the next multiple.

Well hopefully, you can see really clearly which one it's closer to.

It's closer to what? Well, it's seven hundreds away from 3000 and three hundreds away from 4000.

So therefore it's closer to 4000.

So she can complete the stem sentence, it's closer to 4000 kilogrammes.

Or, we could say that 3750 rounded to the nearest thousand is 4000.

That's what we mean by rounding.

Sofia moves from in between the correct multiples of 1000 to the multiple of 1000 that her number rounds to.

So which one was it closer to? Remember that seven hundreds, that tells us it was closer to 4000.

So look, she's moved.

She's now standing straight underneath that number, not in between it.

Okay, my number's 1600 kilogrammes is annex.

The previous multiple of 1000 is 1000 kilogrammes.

The next multiple is 2000 kilogrammes.

But what's it closer to? Right, look at the hundreds.

Think about where that would be on the number line.

The number line's there for you and which is it closer to? There we go.

It's that far from 1000 and it's that far from 2000.

Which is it closer to? Alex's number is six hundreds away from 1000 and four hundreds away from 2000, so it's closer to 2000.

We could say 1600 rounded to the nearest thousand is 2000.

Alex's number rounds to 2000, so that's where he is going to stand.

Just there, look, underneath the 2000.

Let's have a check.

So you're going to help Aisha.

This was her value, 2150 kilogrammes.

The one has been highlighted to give you a little bit of a clue.

Help her to round her number to the nearest 1000 and say that stem sentence please.

Pause the video.

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

My number is 2150 kilogrammes.

The previous multiple of 1000 is 2000 kilogrammes.

The next multiple of 1000 is 3000 kilogrammes.

And it's closer to, that one tells us doesn't it? Not far is it from 2000? Very close.

It's a long way from 3000.

So it's closer to 2000 kilogrammes.

And we can say 2150 rounded to the nearest thousand is 2000.

Well done if you got that, you are on track.

Okay, where should Asia stand then? So at the minute, she's not stood in the correct place.

She needs to stand where the number rounds to.

2150, does she stand on 2000 or 3000? She stands with Alex.

Both of their numbers round to 2000 kilogrammes.

Even though Alex's number was less than 2000, and Aisha's number was more than it, they both round to 2000 kilogrammes.

Their mammals could be grouped together as their masses are similar.

Yeah, you can say those two mammals have got a similar mass because they round to the same number.

Izzy thinks she can round her number to the nearest 1000 without a number line to help.

I like her confidence.

So she's got 3178.

So we're looking at that 100 to help us round to the nearest thousand.

My number is 3178.

The previous multiple of 1000 is 3000 kilogrammes.

The next multiple of 1000 is 4000 kilogrammes.

What's it closer to? Do you think you know? Well, 3100 is 100 away from 3000 and 900 away from 4000.

So it's closer, much closer in fact, to 3000, 3178 rounded to the nearest 1000 is 3000.

Andeep's mammal has a mass of 1075 kilogrammes.

Now what do you notice this time? This is a little bit tricky for Andeep.

Can you see why? What is it about his hundreds? Well, his number's 1075 kilogrammes.

The previous multiple of 1000 is 1000.

The next multiple is 2000.

What's it closer to though? Hmm, bit different this time.

Well, it's a long, long, long way from the next multiple of 1000, but it's actually already on the previous multiple.

So it's zero hundreds away from 1000, but 10 hundreds away from 2000.

So that means it's closer to 1000.

In fact, it's already on it.

So we can say 1075 rounded to the nearest 1000 is 1000.

Okay, what about Lucas? His mammal has a mass of 1500 kilogrammes.

Previous multiple is 1000.

The next multiple is 2000.

What's it closer to? You might spot a problem here, let's have a look.

So that is the distance from 1000.

That's the distance from 2000.

What do you notice? Can you see a problem or an issue? It's not as easy this time is it? Can you see why? It's five hundreds away from 1000 and it's five hundreds away from 2000.

So you can't say which one it's closest to 'cause it's right in the middle, exactly halfway between the multiples of 1000.

There's a rule in rounding.

If the digit in question is five or above, round to the next multiple of the number you're rounding to, not the previous one.

So whenever you see a five, go to the next one, not the previous one.

So instead of saying which one it's closer to, we go and say which one it rounds to and it rounds to 2000 kilogrammes, even though it's the same distance from each multiple of 1000, it rounds to 2000.

And that's a rule in maths.

1500 rounded to the nearest 1000 is 2000.

If the hundreds digit in a four-digit number is five, the number rounds to the next multiple of 1000.

Let's look at two more examples of that.

So we've got 2500.

That rounds to the next multiple of 1000, which is 3000.

And then 3500, what's that going to round to? The next multiple, which is 4000.

So 3500 rounds to 4000.

If the hundreds digit in a four-digit number is 0, 1, 2, 3, or 4, the number rounds to the previous multiple of 1000.

If it's 5, 6, 7, 8, or 9, it rounds to the next multiple of 1000.

So five is that cutoff point.

When rounding a four-digit number to the nearest thousand, what is the most important digit to consider? Is it thousands, hundreds, tens, or ones? Pause the video, chat to your partner.

Can you explain why? So when we are rounding to the nearest thousand, what's really important to focus on is the hundreds.

The hundreds digit helps us to decide how to round a number the nearest thousand.

If the hundreds digit is five or more, the number rounds to the next multiple of 1000.

It's time for some final practise.

Use the STEM sentence that you can see there or sketch a number line to round the numbers from Task A to the nearest thousand.

So again, you're joining them.

Number two, use the following digits, same ones, again.

How many numbers can you make that round to 5000? And how many numbers can you make that round to 6000? See if you can be systematic again and get all the possibilities.

Number three, what are the smallest and largest whole numbers that, when rounded to the nearest thousand, give a value of 8000? Smallest and largest.

That's tough, have a good think about that.

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

Welcome back, how did you get on with that? Do you think you're getting the hang of rounding? Let's have a look.

So rounding these numbers, 4872, well the 800 tell us we round the next one, that's 5,000.

3500 would need to use that rule.

It's five, so it rounds to the next one, that's 4000.

2700, again, that rounds to the next one, that's 3000.

4010 already on that previous multiple, so that's 4000.

And then 3650, the six is more than five, so it rounds to the next multiple of 1000, that's 4000.

And 1999, it's really, really close to 2000, and that 900 tells us we need to round to the next multiple.

And then how many numbers can you make that round to 5000.

Well here are all the possibilities, in order, from smallest to greatest.

And how many can you make that round to 6000? Here are those possibilities.

Well done if you've got any of those.

Well done if you've got lots of those.

And put a big, special well done if you manage to get all of them.

Number three, the smallest and largest whole numbers that, when rounded to the nearest 1000, give 8000.

Well, here's a number line to help.

Got 8000 right in the middle.

So the smallest number that would round up to that would be about here, and that's 7500.

If it's before that, it would be 7499 and that would have 400, so round the previous one.

So this has got 500, so that's the first number.

And then the greatest one, 8499.

Because if it was 8500, that would mean it would round to 9000.

So that's the very largest whole number.

We've come to the end of the lesson.

I've had lots of fun today, I hope you have too.

Explain what rounding is and round a four-digit number to the nearest thousand.

So here we've got an example, 3750, and we can represent that on a number line.

And that 700 tells us that it's closer to 4000.

So when rounding to the nearest thousand, the important digit to consider is the hundreds digit and whether it is closer to or rounds to the previous or next multiple of 1000.

Remember, if the hundreds digit is five, that's special.

That means you round it to the next multiple of 1000.

So try to remember that.

There's lots of ways you might want to remember that.

So, let's look at this example.

My number's 3750.

The previous multiple of 1000 is 3000.

The next multiple of 1000 is 4000, and it's closer to 4000, so it rounds to 4000.

You've done really, really well today.

Give yourself a pat on the back.

It is well deserved.

I hope you have a lovely day, whatever you've got in store, and I hope to see you again soon for some more maths.

Maybe we'll be rounding some different numbers.

Take care and goodbye.