Lesson video

Hi everyone.

Thank you for joining me for another maths lesson.

Today we are focusing on rounding six digit numbers to the nearest multiple of 100,000, and then the nearest multiple of 10,000.

So get yourself sorted with a nice quiet space and press play when you're ready to begin your lesson.

Let's begin by looking at our lesson agenda for today.

We're going to begin with a warmup where we'll be counting up in 100,000s and 10,000s.

Then we're going to look at rounding to the nearest 100,000 before looking at rounding to the nearest 10,000.

And we'll finish at the end with an independent task and quiz.

For today's lesson you will need a pencil and some paper and a nice quiet space.

So get yourself sorted with these resources and once you're ready, press play to begin the lesson.

So let's begin with our warmup.

So we've got this question here.

It says, how would we count up in 100,000s and 10,000s? We've got the starting number and I'd like just us to say the starting number together after three.

One, two three, 429,000.

And the first thing I'd like us to do is think about how we would count up using our 100,000s.

So the digit that I am looking at, the digit that I'm focused on, is the digit that is in the 100,000s column.

At the moment it's a four so that is equivalent to 400,000.

And what I want to know is what features next on my number line if we were counting up in 100,000s.

So it's that digit four that is going to change, it's going to go up by one.

So instead of 429,000, it will be 529,000.

The next number will be 629,000.

Your turn.

The next number will be, 729,000.

So remember when we're counting up in our 100,000s we are focused on that digit that is in the 100,000 column.

We might need to regroup at times, but in this case, we were able to focus on that digit without the need for regrouping.

Okay, let's have a look at the next part of the question which asked us, how do we count up in 10,000s? This time, we're not going to be focused on the digit in the 100,000s column.

What will we need to do in order to count up in 10,000s? I'm going to give you three seconds to work it out.

So hopefully you've seen that actually we need to focus on the digit that is in the 10,000s column.

At the moment it's that digit two.

And we'll be looking at that digit two changing as we count up in 10,000s.

So we're going to start 429,000.

The next number would be 439,000, then 449,000.

The next number would be 459,000.

So you can see depending on what we're counting up in, whether we're counting up in 100,000s, 10,000s, 1,000s, 100s, 10s we are looking at the digit in that particular column that is changing, primarily we may need to regroup other columns if necessary.

But not in the case that we've seen today.

So the first thing that we're going to look at for the rest of our lesson today is rounding to the nearest multiple of 100,000.

And I've got this question to start us off.

The question says, why might it be useful to round to the nearest multiple of 100,000? I'd like you to think about a reason why we might decide to do that? Why might we decide that it's useful strategy to round a number like 298,000 to the nearest multiple of 100,000 to say that it's approximately 300,000? I'm going to give you five seconds to have a think of a reason why we might decide to use this scale.

Okay.

Have you thought of one? Let me give you an example of my own.

So let's imagine that we are thinking about the number of people attending a sporting event.

So lots and lots of people going to visit this sporting event.

Now we could describe the number of people being there as saying there are 298,871 people in attendance.

That's very exact, it's very precise.

It tells you the exact number of people that are present at this event.

That's useful, but we could also say this.

We can say there are approximately 300,000 people there.

There in that case, we've rounded to the nearest multiple of 100,000.

And we've actually given a very rough approximation of the number of people present.

The reason that this is useful is that it's much easier to talk about the number 300,000 or to calculate using the number 300,000 than it is to use the number 298,871.

So rounding offers us an approximate value that's close to the original value that helps us with talking about numbers and calculations with numbers as well.

So that gives you a bit of a reason why we might decide to round to the nearest multiple of 100,000.

So let's have a go at rounding to the nearest multiple of 100,000 ourselves.

This is the way that we would go about it.

We've got four steps to success.

The first thing we need to do is identify the closest smaller multiple.

Then identify the closest larger multiple.

Then identify the halfway point.

And if our number, our original number that we're rounding, is greater than our halfway point, we round up to the larger multiple.

If our number is less than our halfway point, we round down to the smaller multiple.

I'm going to give you an example now so we can see how we might do this.

We've got this number here.

It's 721,345.

And I've underlined that digit that's in the 100,000s column Because that is the digit we're focusing on, where you need to work out whether we rounding up or down for that particular digit.

So let me look at my first step to success.

The first thing I need to do is identify the closest smaller multiple.

In this case, my closest smaller multiple is 700,000 because, I know that the actual number that I'm rounding 721,345, it comes after that closest smaller multiple.

So that is the closest smaller multiple.

Now, what I want to do is count 100,000 up to get to the closest larger multiple.

That's on the other side of our number line.

The closest larger multiple in this case is 800,000.

So I'm going to write it just here, at the other end of my number line.

Now let's look at success point number three.

I need to identify the halfway point.

The number that comes halfway between 700,000 and 800,000.

I'm going to give you three seconds to work out and say what it might be.

Okay, the number is 750,000.

So I'm going to put that just in the middle there.

And the next thing I need to do is place my actual number 721,345, somewhere on this number line in the correct position so that I can see whether it's greater than the halfway point i.

e it would round up or whether it's less than the halfway point and it would round down.

So I know my number line is going up, the small intervals of my number line are going up in intervals of 10,000.

So this will be 710,000.

This is 720,000.

So 721,345 is around there.

And I can see straight away that it's far closer to my smaller multiple, and therefore it's going to round down to 700,000 rather than rounding up to 800,000.

So I can say 721,345 is approximately equal to 700,000.

And if I wanted to I could also use my approximately sign, which looks like this, it's like a wavy equal sign to show that I've got an approximation and an approximate value there.

So now it's your turn to have a go at rounding to the nearest multiple of 100,000.

This time you've got the number 279,113.

I'd like you to draw your own number line, like we've got there with your 10 intervals and your halfway points.

And use our steps to success to identify which multiple of 100,000 we would round this number to.

Pause the video to complete your task and resume it once you're finished.

Okay.

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

So first of all you needed to work out your closest smaller multiple.

In this case, the closest smaller multiple was 200,000.

Remember we're focusing on that digit, that is in the 100,000s place.

Our closest larger multiple was 300,000.

Our halfway point was 250,000.

And we needed to identify where we would place this number on our number line and to see whether it went over or it was greater than our halfway point or whether it was less than a halfway point.

What I can see straight away again, my number line is going up in intervals of 10,000, for the small intervals.

So I can start 250,000.

This is 260,000, 270,000, and I've got 279,000 which I'm going to place around that, just before 280,000.

Straight away hopefully you can see that we will be rounding up because my number is closer to 300,000 and I'm going to use my approximately sign.

I can say that 279,113 is approximately equal to 300,000 because it rounds up.

So hopefully you can see there, how we would use our number line to identify how to round six digit numbers to the nearest multiple of 100,000.

So let's move on.

Let's try and round to the nearest multiple of 10,000.

This time we've got our six digit number, but we're not rounding to the nearest multiple of 100,000.

This digit now is going to stay the same because we're actually not worried about that digit at the moment and we're not worried about rounding to the nearest 100,000.

We are thinking about our 10,000s digit, and you can see that I've underlined that just there, in this example, we want to work out whether we're going to round 832,172 up or down.

Exactly the same method is used.

The only difference is that we use different multiples on either end of our number line.

What we need to use is our closest smaller, multiple of 10,000, our closest larger multiple of 10,000 and then our halfway point.

Let me show you an example.

So in this case, our closest smaller multiple of 10,000 for this number is 830,000.

Our closest larger multiple of 10,000 is 840,000.

And our halfway point, I'm going to give you five seconds to see if you can work out what it is.

The halfway point is 835,000.

I'm now going to put my number 832,172 onto the number line.

This time, the small intervals on my number line are going up in 1,000s rather than 10,000s.

So I'm going to count up to help me out.

There's 830,000.

That would be 831,000.

That's 832,000.

So 832,172 is around that point there.

Which means that it would be rounding down.

I can see that it's far closer to 830,000 than it is to 840,000.

So when rounded to the numerous, multiple of 10,000, 832,172 rounds down to 830,000.

So hopefully you can see exactly the same success criteria has been used.

All we've done is changed the points on our number line, our starting point, our ending point and our halfway point.

So once again, I'd like you to have a practise of this.

Remember we're rounding to the nearest multiple of 10,000.

Use this number line here.

Draw it out onto your piece of paper and identify the closest smaller multiple, larger multiple, halfway points before deciding whether this number rounds up or down, Pause the video to complete your task and resume it once you're finished.

Okay, let's have a look at this together.

So we've got the number 655,120.

Again, just following that success criteria like we've always done, we're identifying the closest smaller multiple, in this case it is 650,000.

The closest larger multiple is 660,000.

And our halfway point is 655,000.

Now I've got to place my number on the number line.

And it's interesting because actually my number is incredibly close to my halfway points.

The number I want to place is 655,120.

My halfway point, as you can see here, is 655,000.

So my actual number is only a tiny bit bigger, tiny bit greater than my actual halfway points.

It is still greater though.

And we know that numbers are greater or equal to the halfway point always round up.

So in this case, when rounding to the nearest multiple of 10,000, we would identify that 655,120 rounds up to 660,000.

So hopefully you managed to get that too.

So let's move on to your independent task.

What I'd like you to do is use the number line method that we've practised already in this lesson to round each of these numbers below, A to F, to the nearest multiple of 100,000, and then also to the nearest multiple of 10,000.

I'd like you to use the number line method for these, these questions.

You might need to draw two different number lines out for each of your examples because you will need to use different multiples of 100,000 and 10,000 at the end of your end number line, Pause the video to complete your task, but don't forget to join us and resume once you're finished to check through your answers.

Okay, so let's go through the answers to the questions that you have completed for your independent task.

You can see they're written here on the screen.

The numbers that written on the left hand side of the answer are the numbers that are rounded to the nearest 100,000.

And on the right hand side, are the numbers rounded to the nearest 10,000.

So quickly spend a bit of time now to just mark your answers that you've created.

And we are going to have a quick look at question F together.

So let's have a little peek at question F and see what we might have done to solve this.

So, first of all remember we were rounding to the nearest multiple of 100,000.

So what I'm going to do is start by putting my closest multiples of 100,000 in this corner here on this side, I've got 300,000.

Because remember we're focusing on that digit in the 100,000s column.

Over here, I've got 400,000.

My midway point is 350,000.

And in this case, I can see that 355,000, if I'm looking at exactly the placement of where this would go, I'm putting it around here, which demonstrates that it would round up.

So 355,000 rounded to the nearest multiple of 100,000 is equal to 400,000.

Now lets try and round this to the nearest multiple of 10,000.

So when I rub out the markings that we've got on the screen here.

And remembering that we need to change our closest, smaller multiple and our closer larger multiple 'cause this time we're looking at the digit that is in the 10,000s column.

So this time my closest smaller multiple of 10,000 is 350,000.

My closest larger multiple of 10,000 is 360,000.

And my midway point is 355,000.

And here in lies a slight issue.

As you can see, 355,000 is my halfway point, but it's also the exact location of the number that I'm trying to round, which makes it challenging because we know that if a number is greater than the halfway point, we round up.

If it's less than the halfway point, it rounds down.

But in this case, our number is exactly the halfway point.

Now you might remember that actually when a number is exactly on the halfway point, it always rounds up.

So in this case, 355,000 rounded to the nearest multiple, all but 10,000 is 360,000.

How did you get on with those? So what would be lovely is if you'd like to please ask your parent or carer to share your work on Twitter, tagging @OakNational and hashtag #LearnwithOak.

We'd love to see what you've created during the lesson today.

Anything left to do is to complete your quiz.

Thank you so much for joining me for another maths lesson today.

It was great to have you.

Do come back and join us again soon.

Bye bye.