# Lesson video

In progress...

Hi, everyone.

Thank you so much for joining me.

My name is Ms. Jeremy.

And today we are looking at a math lesson based on rounding five digit numbers.

Let's start by looking at our lesson agenda.

We're going to begin by looking at some number lines and before looking at how we round to the nearest 10 000 and later on how we round to the nearest 1000.

All right.

After that we'll have our independent task and our quiz at the end of the lesson.

So for today's lesson, you are going to need a pencil and some paper and a nice quiet space free from any distractions.

Get yourself sorted with those resources, pause the video and when you're ready, come back and begin the lesson.

So we're going to begin with a warm up.

We've got a number line just here and it asks us what are the missing numbers on our number line? We've got to work out if we know what those numbers are.

Initially, we've got 32 400, 32 500, 32 600.

We've got to work out what the next number is.

The best way of doing this is to work out what those intervals are.

An interval is a space on a number line.

So we can see it is going up in.

Can you work it out? It's going up in hundreds.

So I can see that it's the hundreds, the digit in the hundreds column that is changing each time.

That means that if I've got to 32 600, the number that I'm looking at changing is this one here it's the one in the hundreds place.

So I'm on 32 600.

The next number on our number line must be 32 700.

Can you work out which number comes next? I'm going to give you five seconds.

Great.

So you might have worked out.

The next number on our number line will be equal to 32 800.

And we can carry on counting up using our hundreds.

Always remembering the intervals are always equal.

If they start off being a hundred spaces apart, they will always be that throughout your number line.

Okay.

Moving on to our main lesson.

So the first thing I want to talk about is the reasons why we round.

When we round, we find an approximate number, a rough number that is close to the number that we're speaking about.

So the question I want to ask you is why do we do this? Why is it important to round? Well, let me give you a few examples of why we might be rounding in everyday life.

For example, has anyone ever asked you the time? And you've had a look at your watch and you've seen that it's nearly half past four for example, you could say it's 27 minutes past four right now, and be really, really accurate with your description.

Or you could provide, provide a rounded answer.

You could say it's nearly half past four.

It's approximately half past four.

Rounding helps us talk about numbers, helps us be quite general with the numbers that we're using.

And that helps us with calculations as well.

Similarly, if you're talking about, let's say a concert or going to see something where lots of people are attending.

In so saying there are 2 198 people exactly in the stadium, you might say there are approximately 2000 people in the stadium.

And actually rounding often helps us when we're calculating.

It's much easier to calculate something using the number 2000, than a very very and accurate specific number like 2 193.

So rounding helps us with talking about numbers.

It also helps us with calculating with numbers as well.

So we are going start by looking at rounding to the nearest 10 000.

When we round a number to the nearest 10 000, what we're doing is looking at the closest multiple of 10 000 other that number is nearest to.

So we have a couple of steps that we need to follow in order to do this.

The first thing that we need to do is identify the closest smaller multiple of 10 000.

I'm going to start by looking at number 21 450 it's just here.

And I need to think about the smaller multiple of 10 000, that that number is close to.

And I can see that when we're talking about 10 000, we're looking at our 10 000 columns.

That digit is there and I can see that 20 000 will be the smaller number.

The next thing I need to do is identify the closest larger multiple of 10 000.

So I'm counting 10 000 up and I can see that that would be 30 000.

So 21 456 is somewhere between 20 000 and 30 000.

And my job is to work out.

Is it closer to 20 000 or is it closer to 30 000? And a number line really helps us with this.

The third step on our success criteria is to identify the halfway point.

And that's really helpful for me because if it goes on this side of our halfway point, we know it's rounding up to 30 000.

Whereas if it goes on this side of our halfway point, we know it's rounding down to 20 000.

That's why the halfway point is so crucial.

In this case, the number that is halfway between 20 000 and 30 000 is 25 000.

Now, the last thing I need to do is to place 21 450 on my number line and workout which multiple is closest to.

Well I know 20 000 is at the end, 21 450 would be approximately roughly around here.

So I'm going to put it onto my number line, just here.

And straight away without any hesitation I can see 21 450 is much closer to 20 000 than it is to 30 000.

So what I can do is I can write 21 450 rounds to 20 000.

And you might have noticed this little way, the equal sign here, that sign means approximately.

You know, a straight equal sign that looks like this obviously means that both sides are equal.

Whereas when we make it a symbol like this, that tells the person who's looking at our equation, that we have got an approximate value there.

So we can say the 21 450 when rounded to the nearest 10 000 is approximately 20 000, it rounds down.

So let's look at another example of rounding to the nearest 10 000.

This time we've got the number 45 327.

Again, following the same success criteria that we have been up to date.

So first of all, let's identify the closest smaller multiple of 10 000.

In this case, it is 40 000.

Then let's look at the closest larger multiple.

So we're looking 10 000 up, which is a 50 000 in this case.

And the number that is halfway between 40 000 and 50 000, I'm going to give you five seconds to work out what that is.

Okay.

So the halfway point between 40 000 and 50 000 is 45 000.

Now we're ready to place our number on the number line and work out whether it's closer to 40 000 or whether it's closer to 50 000.

So I know the 45 327, it's just past 45 000.

It's probably around that.

And even though it's just past that halfway point, it is past it.

So therefore we are rounding up.

That means the 45 327 rounds up to 50 000.

And I can write that in just like that, using that approximately sign that we've used before.

So then we've shown how to round to the nearest 10 000 using our success criteria, using our closest multiples of 10 000 on either side of our number line.

So now it's your turn to have a go, we've got the number 73 299.

What I'd like you to do is to use our success criteria to work out the closest smaller multiple of 10 000, the closest larger multiple of 10 000, the halfway point, and then whether or not this number rounds up or down.

Pause the video to complete your task, using a piece of paper, draw out your number line, and then resume it once you're finished.

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

So you should have seen that your closest smaller multiple of 10 000 on this side would be 70 000.

I'm going to write that in just here and your closest larger multiple would have been 80 000.

I'll just put that here for you.

The halfway point was 75 000 and 73 299.

Well let's work out approximately where it goes.

This would be 71 000 72 000 73 000.

So 73 299 I would place approximately there.

And you can see straight away that actually, because I placed it there, it's rounding down 73 299 rounds down to 70 000.

So now that we've had a go rounding to the nearest 10 000 I wonder whether we can have a look at rounding to the nearest 1000.

In this case, we follow the exact same success criteria, but we're not focusing on that digit in the 10 000 anymore, we're instead looking at that digit in the 1000 column.

We're going to be looking at whether we're rounding down to the smaller multiple of 1000 or up to the larger multiple of 1000, depending on whether it crosses the halfway point or not.

So looking at our number for rounding to the nearest 1000, our number is 45 327.

First, I'm going to work out my closest smaller multiple of 1000.

And in this case, my closest smaller multiple is 45 000.

My closest larger multiple of 1000 is 46 000.

And the number that is halfway between 45 000 and 46 000, I'm going to give you five seconds to work out what it is.

Okay.

If you got it.

The halfway point is 45 500.

So now I'm ready to place my number 45 327 is going to be placed.

Well, let's have a look.

This is will be 45 100, 45 200, 45 300, I would say it would be around here, 45 327.

So you can see in this case, my 45 327 rounds down to 45 000, because it's closer to 45 000 when we're rounding to the nearest 1000.

It's before my halfway point, I round down.

So let's have a look at another example.

This one is for you to have a go at.

We've practised rounding to the nearest 10 000 and I've shown you how to the round to the nearest 1000.

What I'd like you to do is to round 65 561, firstly to the nearest 10 000 and then drawing another number line rounding to the nearest 1000.

You will need two number lines to do this because your multiples will be different for each number line.

Your first number line will have the multiples of 10 000 on it whereas your second number line will have the multiples of 1000.

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

So first of all, I'm rounding to the nearest 10 000.

So firstly, I've got to find my closest multiples of 10 000 on either side.

Well in this case, my closest multiple of 10 000 here is 60 000.

And on the other side, I've got 70 000.

My halfway point is 65 000.

And so 65 561 it goes over 65 000.

It's past the halfway point.

I placed it around here and you can see it's going to round up to 70 000.

It's only just over the halfway point, but any number that goes over the halfway point rounds up to their next multiple of 10 000.

It rounds to 70 000.

Now when I'm rounding to my nearest 1000, I'm going to have to rub out all of these numbers because my multiples change.

This time, I'm going to have my multiples of 1000 on either side.

So again, I'm focusing on that number digit, that is in the thousands column.

So I can see in this case, my number, my multiple here, my smaller multiple will be 65 000.

My larger number multiple will be 66 000.

My midway point would be 65 500.

And in this case 65 561 again it only just goes over that 65 500 that midway point, but it does go over.

And so I would be rounding up again.

I'm rounding to the next multiple of 1000.

I round up to 66 000.

So now it's your turn to have a go at this independent task.

You're going to use the number line method that we've been practising to round each of these numbers to the nearest 10 000 and then to the nearest 1000.

I would recommend creating two number lines per question, because for the first one you're going to need to have your closest multiples of 10 000 and for the second one, you're going to need to have your closest multiples of 1000.

How did you get on? Let's have a look at some of the answers together.

But as you can see here, I've written out the answers for rounding to the nearest 10 000 and then rounding to the nearest 1000 with a forward slash just between so you can tell the difference between the answers.

But I did decide that we would maybe go through one of the examples together.

I want us to try the most challenging question together, which was question F.

Question F said can we round 55 000 to the nearest 10 000 first of all.

So again using our success criteria, we've been using up to date.

I going to put in my closest multiples of 10 000.

I've got 50 000 on this side.

I've got 60 000 on this side.

I've got my midway point 55 000 and I'm ready to place my number.

But here is where I get a little bit stuck because 55 000, which is the number I'm rounding is exactly the same as my halfway point.

And what I've told you up until now, is there any number that goes past that is greater than your halfway point it rounds up.

Any number that is less than your halfway point rounds down, but what about if your number is exactly on your halfway point? Well, the rule in this case, and you might already know this, is that if your number is exactly on your halfway point, it rounds up.

So 55 000 rounded to the nearest 10 000 rounds up to 60 000 in this case.

So let's have a go at rounding now to the nearest 1000.

I'm going to have to rub out these markings because I'm changing my multiples.

For 55 000 the smaller multiple of 1000 is 55 000.

That's on this side here.

The larger multiple is 56 000 The midway point is 55 500.

And again, this one is a little bit different to the ones we've looked at in the past because 55 000 is exactly the same as my starting point.

So actually no rounding really needs to take place here.

I know already that because it's exactly the same, 55 000 rounds down or stays exactly where it is at 55 000 when rounded to the nearest 1000.

So hopefully you got on okay with our learning.