Lesson video

My name's Mrs. Harris and we're going to be looking at rounding to a required degree of accuracy.

Here's what we'll do in the lesson.

We'll start by thinking about why we estimate and round before we round to the nearest multiple of 100,000, followed by the nearest multiple of 10,000 and then I have an independent task for you.

You're going to need a few things.

Let's take a look.

You're going to need a pencil, maybe a rubber.

Rulers are always handy.

Some paper or a book to write on.

So if you don't have those things, pause the video now and go and find them.

Right, got everything we need? Let's get started then.

This is where we're going to consider why we estimate and round.

So we would estimate and round when we want to know roughly how many or much much of something we have.

When we want to know roughly how many people live in London.

Or roughly how much is 502,452 plus 487,312? We'd get a quick estimation of that, wouldn't we? And then we'd know if our answer was kind of right before we sat and worked it out properly.

We'd want to know may roughly how many people are in your class compared to another.

And that might be just a more or less comparison.

But we'd still get an idea.

Also, when we estimate or round numbers, they're easier to communicate.

They don't have so many digits that we have to say.

We can just focus on the ones that really matter.

The ones that have a greater magnitude.

So let's have a think about rounding to the nearest multiple of 100,000.

Populations are great to round to the nearest 100,000.

Here's the population of London in 2016.

It was 8,787,892.

But populations, they're not static.

They change all the time.

So reporting a statistic like this to this degree of accuracy, I'm not sure it's very helpful.

Have a think, would there be a reason that we'd need to know to round a seven-digit number to the nearest multiple of 10? I guess it depends on the degree of accuracy we need with the data.

If we're comparing with something else, and that is the deciding factor that makes the difference, then yes, we would need to round to that.

But it doesn't really serve much purpose here.

We can use a bead string to help us with our rounding.

Before we do though, we need to consider what each group of 10 beads is worth.

Just have a look at the bead string.

What is the value of each group of 10 beads? Okay, have you got it? Each group of beads is worth 10,000.

So if each group of 10 beads is worth 10,000, what is each individual bead's value? Okay, so each bead has a value of 10,000.

Great, now we know that, we can use our bead string to represent the population of London on it.

Just have a look, where would you put the population of London in 2016 on this bead string? Okay, so what we want to be looking for is the 8,787,000 on the bead string, don't we? And that lies just there.

By doing this, we can see quite clearly what multiple of 100,000 it's nearest to.

Yeah, it's closest to the 800,000 multiple, isn't it? There's the population written in and we can see how close it is to the 800,000 multiple.

We would round it up.

Well, we round it up 'cause we can see it's closest but it's also past the halfway mark, isn't it? It's past 8,750,000 mark.

I had to think there.

If it was below that, we'd round it down, wouldn't we? So I want you to have a quick go at rounding these populations.

Remember, if they're past the halfway mark, the 50,000 mark, they round down and if they're above, they would round up.

When you've done that, I'd like you to plot them on the number line.

So pause the video and have a go now.

Okay, got it? Let's have a look at the answers together.

So we would round the first one, we'd round down and we'd round it to 9,400,000.

Then we'd round the second one up or down to the nearest 100,000? Oh, I plotted it first, sorry.

I plotted it there on my number line.

Then I plotted Tehran there with my rounding down.

So let's find out did we round the last one up or down? We did, we rounded it up.

And that shows the population is greater than the others.

Now, having the whole figure wouldn't really have added anything.

We would have still really plotted them in just about the same place.

And we can still make the comparison between the populations of the countries even though we don't have all the digits in the figure.

In fact, it's easier to report without all the digits, isn't it? Now we're going to consider rounding to the nearest multiple of 10,000.

Now, the 10,000 digit is going to have a different place in the number compared to the 100,000.

So we're going to need to be careful to identify it in each number.

I've got some numbers here for you that I'd like you to round in a second to the nearest multiple of 10,000.

Let's just take a quick look at them.

Have you quickly identified where the 10,000 multiple is? Good.

Because that's one of the mistakes we might make.

And by identifying that, hopefully we can avoid it.

So pause the video now and round to the nearest multiple of 10,000.

Welcome back.

How did you get on with rounding these numbers to the nearest multiple of 10,000? Let's have a look at the answers together and how I would approach the problem.

So I've written them out ready.

And I've used a symbol here.

It looks like this.

And it means approximately equal to.

So I'm going to use that one as I report my rounded numbers to the nearest multiple of 10,000.

Now, the first thing I wanted you to do was identify which was my 10,000 digit in a number.

So I have my one million.

I had my 100,000.

We would have used that earlier.

So this is my 10,000 digit.

Ah.

So 1,970,847 is approximately equal, when rounded to the nearest multiple of 10,000 to 1,970,000.

Okay, that's one down.

In the next one, where was my 10,000 digit? That's right, my 100,000, this one was my 10,000 digit.

Now, because this one is above, well, it is five, 'cause five and above we round up.

This one would be approximately equal to 190,000.

Where was the 10,000 digit? The multiple of 10,000 in our final number? It was the first one, wasn't it? And again, this one's going to round up.

The digit next to it, its adjacent one is a six.

So we round up.

So 46,761 is approximately equal to 47,000.

And there are your answers to your rounding these numbers to the nearest multiple of 10,000.

Hello, everyone.

Miss Jones here.

Now, I don't know if you noticed but I think Mrs. Harris here has made a deliberate error for you to try and spot.

You might have seen it already.

If not, have a look at her whiteboard.

Can you spot any mistakes? That's right, on that last one, 46,761, she didn't round to the nearest multiple of 10,000.

47,000 is not a multiple of 10,000.

So let's think about that carefully.

I'm going to use a number line just to visualise this.

And I'll draw it here.

I need to be rounding either down to 40,000, which I know is the multiple of 10,000 before or up to 50,000.

Now, I know that 46,761 is nearer to 50,000 than it is to 40,000 because I know that 6,000 is closer to that next multiple of 10 there.

So I need to be rounding up to 50,000, not 47,000 if I'm looking at the nearest multiple of 10,000.

Now, we did ask you to think about what mistakes you might make, and you can see, it's very easy to make a little error when we're doing lots of rounding.

So always make sure you check what multiple of 10, whether that's 10, 100, 1,000 or 10,000 that you're rounding to.

And if you need to, visualise or draw a quick number line to really think about this and check your answers afterwards as well.

Okay, I'll hand you back over to Mrs. Harris to finish the lesson off.

I've got another problem for you that I want you to take a few seconds to look at.

And it says always, sometimes or never.

So that's what you're going to tell me when you come back.

Always, sometimes or never.

But that won't do.

I'm going to need convincing.

So always, sometimes, never.

Rounding a number to the nearest multiple of 100,000 will give a different result to rounding the same number to the nearest multiple of 10,000 or 1,000.

So pause the video, leaving this problem on the screen so you can see it and convince me.

Is this always true, sometimes true or never true? Pause it now.

Okay, welcome back.

What did you decide? Did you decide that rounding a number to the nearest multiple of 100,000 will give a different results to rounding the same number to the nearest multiple of 10,000 or 1,000 always? Sometimes? Or never? I decided on sometimes.

It'll sometimes give a different number.

Usually.

But there are occasions where it will give the same number and to convince you, I wrote it down.

So if we had the number 299,999, if we rounded it to the nearest multiple of 100,000, we would get 300,000.

If we rounded it to the nearest multiple of 10,000, we would get 300,000.

And if we rounded it to the nearest multiple of 1,000, we would get 300,000.

Did you convince me of your answer? It's time for your independent learning now.

You can show me everything that you know about rounding.

So pause the video and navigate to the worksheet to find all the numbers and their degree of accuracy that you need to round to.

See you soon.

Welcome back.

Thanks for having a go at the independent learning.

Your first challenge was to round each number to the nearest multiple of 1,000.

Here's your answers.

Our first answer when we rounded 765,432, we would round it to 765,000.

Our next number, you had to be really careful to notice the decimal point.

76.

543 would simply become zero.

That's its nearest multiple of 1,000.

7,654 would be rounded up to 8,000.

And 765 would also be rounded up but just to 1,000.

When we looked at the next set of numbers and rounded them to the nearest multiple of 1,000, 234 became rounded to zero.

2,345 was rounded down to 2,000.

We rounded 23,456 down as well to 23,000.

And we rounded the last one up to 235,000 from 234,567.

So well done if you got them right.

If you didn't, just try and have a little look about how I've got my answers and why they're different to yours.

Then you have a table to complete.

Now, this had the same number each time but it needed rounding to different degrees of accuracy.

I've got the answers here.

So our answers, reading from top to bottom, are 700,000, 700,000, 695,000.

And then we have 20,000, 20,000, it's a bit like our always, sometimes, never, isn't it? And we then finish on 20,500.

I'll give you a second just to look at them.

Okay.

So we have reached the end of our lesson.

If you've got any work you'd like to share with me and everybody at Oak National, you can ask a parent or carer to pop some examples on Twitter for us, tagging @OakNational.

There's just one little job for you to do now and that is to complete the quiz.

Bye.