Lesson video

Hello there.

I'm Mr. Tilstone.

I'm a teacher, and I'm going to be teaching you a lesson today that's all about rounding.

Rounding may not be a new concept to you, perhaps you've had some recent experience of rounding.

Can you think of any rounding rules? Can you remember using a number line to help you round? We're going to do a bit more of that today.

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

The outcome of today's lesson is, I can round a four digit number to the nearest thousand, hundred and ten, and perhaps you've done all three of those things before, well today we're going to combine them.

Our keywords today, just the one, my turn, rounding, your turn.

So that's what this lesson is all about.

You may know what rounding is, but let's give you a reminder anyway.

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

So for example, the nearest hundred, 623 rounds to 600, it's pretty close.

Our lesson today is split into two cycles.

We're going to start by rounding a four digit number in different ways, and then we're going to do some problem solving with rounding.

So if you're ready, let's start by rounding a four digit number in different ways.

In the lesson, you're going to meet Sofia.

Hello Sofia.

She's here today to give us a helping hand with our maths.

Sofia is rounding 4,735 in different ways by sketching number lines.

The nearest thousand, she's sketched the number line.

The answer she's saying will be a multiple of 1,000.

So it will end in at least three zeros, she's right.

So it's in between 4,000 and 5,000, yeah.

The seven hundreds tells me it's closer to 5,000.

So she's not going to worry too much about exactly where it goes, but she knows that it's going to be roughly roundabout there.

4,735 round to the nearest multiple of 1,000 is 5,000.

Now she's going to do the same thing for the nearest hundred.

So she's got a sketched number line, and she's going to round to the nearest hundred, so she's got to think about the multiples of 100 that it lies in between.

And she says the answer will be a multiple of 100.

Yes, it will.

So it will end in at least two zeros, yes it will.

So what's that in between, do you know? That's in between 4,700 and 4,800.

Now what's she going to look at this time? The tens.

The three tens tell me that it's closer to 4,700.

So it would be roughly there on the number line, somewhere like that.

So 4,735 rounded the nearest multiple of 100 is 4,700.

This time she's rounding that same number to the nearest 10.

She says the answer will be a of 10, yes.

So it will end in at least one zero.

Yes.

So what two multiples of 10 is that in between, do you know? That's in between 4,730 and 4,740.

But what's it going to be closer to? Now this is going to be tricky, can you see why? It's got five ones.

So you've got to apply that rule because it's exactly halfway in between.

So what's that special rule in maths that we use? 4,735 rounded to the nearest multiple of 10 is 4,740.

So the five told us to round the next multiple.

Now she's rounding 7,995.

What do you notice? What do you think is going to happen here? Well, this is it to the nearest thousand.

This is it to the nearest a hundred.

And this is it to the nearest 10.

Hmm.

In all three cases the answer's going to be 8,000.

Which of these numbers could be the result of rounding a whole number to the nearest hundred, 5,000, 5,200, 5,280, or 5,309? Pause the video and see if you can figure that one out.

Let's have a look.

So 5,000, could something have been rounded to the nearest hundred and given the answer 5,000? Yeah, any number from 4,950 to 5,049 would round to 5,000 for the nearest hundred.

What about 5,200, is that possible? Yes.

Any number from 5,150 to 5,249 would round to 5,200.

What's about 5,280? Hmm, 280.

No, it's not a multiple of 100, so it can't be.

What about 5,309? No, same reason.

It's not a multiple of 100.

Let's do another check, round this four digit number to the nearest 1,000, 100 and 10, and if you can do this, you're ready for the practise tasks.

Let's have a look.

So 2,507 to the nearest 1,000, it was in between 2,000 and 3,000, but the five told us that it rounds to 3,000.

The nearest hundred, so that's zero is what's important.

Let's have a look.

That's 2,500, that rounded to the previous multiple of 100.

And to the nearest 10, let's have a look at the seven for a clue.

Seven tells you it rounds to the next multiple, so that's 2,510.

And if you've got those three answers right, well done.

You are ready for the next set of questions.

And these are those, draw lines to round 7,852 in different ways to the nearest a thousand, hundred and ten.

Number two, give Sofia some feedback.

She says 6,352 rounded to the nearest 100 is 6,452.

Is that right? Is that wrong? Is that a little bit of both? Number three, round these four digit numbers, to the nearest 1,000, 100, and 10.

And then number four, list some numbers which round to 3,000 to the nearest 100 and 3,000 to the nearest 1,000.

Pause the video, if you can work with somebody else, please do, and I'll see you soon for some feedback.

Welcome back.

So number one then.

7,852 rounded to the nearest 1,000 is 8,000.

That eight told us to round the next multiple.

The nearest 100, it's 7,900, we had to use a special rule for that five.

And to the nearest 10, it's 7,850.

The two told us to round to the previous multiple.

And let's give Sofia some feedback on what she said.

She's got some bits right, she remembered that the five tens means that the number rounds to the next multiple of 100.

However, the answer is not a multiple of 100.

The correct answer is in fact 6,400.

So well done if you said something like that.

And number three, let's round these four digit numbers in different ways.

And that last one's interesting, isn't it? Because to the nearest 1,000 and to the nearest 100 and to the nearest 10, 2,004 rounds to 2,000.

And then number four, some numbers which round to 3,000 to the nearest 100 and 3,000 to the nearest 1,000.

Well you might have had lots of possibilities there, but anything from 2,950 to 3,049.

I think you're ready for cycle B, that's problem solving with rounding.

Okay, here's a problem.

And you might need to read this twice and you might need a little bit of time to understand it and digest it and get to grips with it, that's fine.

The difference between two four digit numbers is five.

So let's think about that, so far we've got two four digit numbers and whatever they are, the difference between them is five, five ones.

When each number is rounded to the nearest 1,000, the difference between them is 1,000.

So they might round to different multiples of a thousand.

In fact, they must do.

What could the two numbers be? Hmm, okay, let's begin to unpick that.

A systematic approach will help to find all of the possibilities.

That's what good mathematicians do, they use systems when they can.

So we're going to start with the possibilities where the thousands digit is one, that's the lowest possibility for the thousands digit.

So let's use our trusty number line, and let's put 1,000 on one side and 2,000 on the other side.

Okay.

So that's going to be the difference between them being 1,000.

If we think about the middle part of that, that'll be 1,500, that's the very lowest number that will round the next multiple of 1,000, because one less than that would've rounded to 1,000.

So that's the lowest number that rounds to 2,000.

Now remember it says a difference between those numbers is five.

So you've gotta think what's five less than 1,500? Hmm.

Five less than 1,500 is 1,495.

And 1,495 rounds to 1,000.

So let's have a look, let's have a little check.

Is the difference between those two numbers five? Yes.

When rounded to the nearest 1,000, is the difference between them 1,000? Yes.

One rounds to 1,000, one rounds to 2,000.

So it satisfies both of those criteria.

So we've got ourselves a possibility, but it's not the only one.

Keep increasing the numbers by one until the statement is no longer true.

So we've got this time 1,501, and then 1,496.

So very similar to the last one, just one more.

And they still round to different multiples of 1,000 with a thousand in between them.

And then let's do the same again, let's increase it by one more.

So those two numbers have got a difference of five.

And when rounded to the nearest 1,000, there's a difference of 1,000.

Do you think there's any more? Could we do another one? What would happen if you increased it by another one? Yeah, that would work.

Those two numbers have a difference of five.

And they round to different multiples of 1,000 with a difference of 1,000.

What about if we did another one, what would that be, would that work? Yes, it would.

Those two numbers have got a difference of five and they round to different multiples of 1,000 with 1,000 difference.

What about if we did one more, would that work? Wouldn't would it? Because one more than 1,499 is 1,500 and we've already established that that rounds to 2,000.

So no, so that's all of our possibilities.

Now those same possibilities can be explored with numbers where the thousands digit is two.

So we've got a lot more possibilities as well.

Let's have a look at that.

So this time it's 2,000 and 3,000.

And again, just like before, we're gonna start right in the middle of those, because that's the lowest number that rounds to the next multiple.

So that's 2,500.

Now remember the difference is five, what's five less than 2,500? 2,495.

So that's another pair of possibilities.

So the possibilities where the thousands digit is two, are as follows.

Those two, those two, those two, those two, and those two.

And one more, the would be 2,500 and that would round up so that's not a possibility.

So that's all the possibilities, where the thousands digit is two.

Do you think there's going to be more? What about where the thousands digit is three? Would that work? Hm, you tell me.

Pause the video and have a go.

So when the thousands digit is three, what could it be? Well, 3,495 and 3,500 is the lowest possibility.

But we could also have 3,496 and 3,501.

We could have 3,497 and 3,502.

We could have 3,498 and 3,503, and we could have 3,499 and 3,504.

Well done if you've got all of those possibilities.

And you could repeat all of that for the thousands digit of 4, 5, 6, 7, 8, and 9, so lots of possibilities.

There are five possibilities each time.

That makes 45 possible answers to the question.

Time for some practise, use rounding skills to answer the following question.

Think about which digit you need to consider each time.

There is 1,750 millilitres of juice in a jug.

What's this rounded to the nearest litre? The mass of Sofia's Labrador is 3,207 grammes.

What's that to the nearest one kilogramme? In a year, Oak Academy raises £2,457 for charity.

And class six raised an additional £128 from a cake sale.

Rounded to the nearest £10, how much has been made for charity? Number two, the difference between two four digit numbers is three.

When each number is rounded to the nearest 10, the difference between them is 10.

So it's a little bit similar to the question you've done already.

The numbers have a thousands digit of three and a hundreds digit of four.

So lots to think about here.

What could the two numbers be? And give as many possible answers as you can.

Maybe you could be systematic just like we showed before, start with the lowest possibility.

Number three, using each card only once, how many different ways can you fill the boxes? Can you be systematic and find all of the possibilities? So we're looking for a number that rounds to 1,400 to the nearest 100.

And then a number that rounds to 4,000 to the nearest 1,000.

So there's eight blank spaces, and there's eight cards.

So you can use them each once only.

See how many possibilities you can find.

Pause the video, good luck with that and I will see you soon for some feedback.

Welcome back.

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

So number one then 1,750 millilitres of dew to the nearest litre, well, you needed to know a bit of information for that, didn't you? You needed to know that there's 1,000 millilitres in a litre.

So the seven hundreds tells you that's closer to 2,000 millilitres, or two litres.

And the mass of Sofia's Labrador is 3,207 grammes.

What's that to the nearest kilogramme? Well, you needed to know that there's 1,000 grammes in a kilogramme.

3,207 is closer to 3,000, or three kilogrammes.

And then Oak Academy raised 2,457.

Class six raised an additional £128, rounded to the nearest £10, how much has been made? So we needed to do a little bit of adding first and maybe used a column sum for that.

That gave you £2,585, and then rounded to the nearest £10, well, we needed a rule for that because it was a five in the one's place, so we needed to round to the next multiple of 10.

And that's £2,590.

And then the difference between two four digit numbers is three.

When each number's rounded to the nearest 10, the difference between them is 10.

The numbers have a thousands digit of three and a hundreds digit of four.

What could the two numbers be? So using a systematic approach, the possibilities are as follows.

Starting with this one, it could be a 3,402, and 3,405.

And here are the full range of possible answers.

Well done if you've got some of these, and a very well done, big special well done if you got all of them.

Here's some.

Here's some more, and more.

You notice we're going up in tens each time.

And that's all the possibilities.

So a massive well done if you've got all of those, that was tricky.

So for number three, as long as no card is used more than once, the top number can be anything from 1,350 to 1,437.

And the bottom number can be anything from 3,502 to 4,367, so lots and lots of possibilities.

Well done if you've got lots of them.

We've come to the end of the lesson.

It's been a really challenging one, but I hope you've enjoyed that challenge.

We've been rounding a four digit number to the nearest thousand, hundred and ten.

Any four digit whole number can be rounded to the nearest 1,000, 100 or 10.

It may be helpful to sketch a quick number line to help with the rounding.

Number lines are brilliant when it comes to rounding.

Although you may know to visualise a number line in your head, or even apply rules about rounding numbers such as if it's five it rounds to the next multiple.

These skills can be applied to problem solving scenarios about rounding numbers, and you've just had some experience of doing some of those.

Very well done on your massive achievements today.

I think you definitely need to give yourself a pat on the back.

Hopefully I'll get the chance to spend some more time with you in the near future on a math lesson.

Maybe not about rounding, maybe about something else.

But in the meantime, have a great day.

Take care, and goodbye.