Lesson video

Hello, how are you today? I hope you are looking forward to your math lesson.

I know I am looking forward to learning with you.

My name is Dr.

Shorrock and I'm here to guide you through today's lesson.

Today's lesson is from our unit: Rounding and Solving Problems with Numbers with up to Seven-Digits.

This lesson is called Rounding Seven-Digit Numbers to the Nearest Million.

As we progress through the learning today, we will revisit what it means to round a number and we will consider why we need to round, why is it so important, and then we will have a look at how we round these seven-digit numbers.

Now, sometimes new learning can be a little bit tricky, but it is okay I'm here to guide you and I know if we work really hard together, then we can be successful.

Should we get started then? Let's look at how do we round seven-digit numbers to the nearest million? Our keywords for the learning today are round, midpoint, multiple, and critical.

It's always useful to practise saying keywords aloud.

Let's have a go at this together.

My turn, round.

Your turn.

Nice.

My turn, midpoint.

Your turn.

Lovely.

My turn, multiple.

Your turn.

Fantastic and my turn, critical.

Your turn.

Well done.

When we round, we're making a number simpler, but actually we're keeping it value very close to what it was.

The result is less accurate, but it is easier for us to use.

The midpoint is the middle of something.

In this case, it's the middle of two points on a number line.

It's a point halfway between two things or numbers.

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

So for example, 2,500,000 is a multiple of 100,000 and 25.

And something that is critical while it has crucial importance.

Let's get started on our learning today then, shall we? We're gonna start by thinking why do we round? In our lesson today, we have Aisha and Lucas to help us and Aisha and Lucas are looking at some headlines and statements from some websites.

The first one, the Earth's circumference is approximately 40,000 kilometres.

The average mass of a blue whale is 140,000 kilogrammes.

A new intercity high speed railway is estimated to cost 50 billion pounds.

What do you notice about these headlines? That's right.

The precise value has not been given, has it? The Earth's circumferences approximately 40,000 kilometres.

It's not the actual value, is it? It's not a precise value.

This approximate value is rounded and it's rounded to make it simpler for us to understand.

If we look at this one, the average value is rounded.

We've got the average mass is 140,000 kilogrammes that's rounded and it's rounded isn't because it's not an exact value, it is an average.

Our next headline, the new intercity high speed railways estimated to cost 50 billion pounds and it's an estimated value and it's a rounded value because the exact figure is not known.

Let's check your understanding with that.

Which of these statements include rounded values? Option A, A charity event recently raised approximately 1,200,000 pounds.

B, the maximum length of a professional football pitch is 105.

2 metres or C, it costs an estimated 25,000 pounds a year to go to university.

Pause the video while you have a think about which of those include rounded values.

Maybe talk to someone about it and compare your answers.

When you are ready for the answer press play.

How did you get on? Well, part A, we've got the approximately word.

It's not a precise value, so that's definitely a rounded value.

Part B, no, we've got an exact value there, haven't we? 105.

2, so that's not rounded, but part C is because we've got an estimated value.

It's rounded because we're not sure exactly how much it costs.

How did you get on with those? Well done.

It's your turn to practise this concept now about why we round.

Could you use either a computer to research or looking at a newspaper? Could you find some statements that have used rounded values, either as approximations estimates or averages? If you can, discuss with someone why the numbers are rounded.

Pause the video while you do that and when you are ready to discuss your answers, press play.

How did you get on? So you might have found some statements like I found these.

A famous comedian, Jo Bland, recently raced approximately 2,900,000 pounds for charity.

The average mass of a T-Rex was 5,000 kilogrammes.

The cost of Oxford Rover's new football stadium is estimated to be 150 million pounds.

You might have discussed with someone that these numbers are rounded numbers.

They are rounded to make the amount simpler to understand, or because an exact amount is not known.

How did you get on with those? Did you find any interesting ones? I'd like to have known what you found.

Well done.

So fantastic learning so far.

I hope you really have an appreciation now of why we round.

We're going to move on now and think about how we round.

How do we round seven-digit numbers to the nearest million? Let's have a look at this number line.

What do you notice about this number line? Where is it starting? Where is it ending? What are the intervals? How is it increasing? And then what can we say about the value of the letter A? Well, we've noticed that the number line is increasing in 1 million, starting at zero and finishing at 10 million.

And we can say that A is greater than two million, but smaller than three million.

And we can say this because A is positioned between two million and three million.

We can say the previous multiple of one million is two million and the next multiple of one million is three million.

We can say that A is nearer to three million than two million, and we can say A then is three million when rounded to the nearest multiple of one million.

We can show this information about A with an inequality.

two million is less than A and A is less than three million.

So the previous multiple of one million is two million, and the next multiple of one million after A is three million.

And we can say that A is three million when rounded to the nearest multiple of one million.

That's the one millions multiple that it's closest to.

Let's check your understanding with that.

Could you complete the sentences to describe the letter 'B'? So think about where is it positioned on the number line? So 'B' is between mm and mm.

The previous multiple of one million is mm.

The next multiple of one million is mm.

'B' is nearest to mm, 'B' is mm when rounded to the nearest multiple of one million.

Pause the video while you have a go at that and when you are ready for the answer, press play.

How did you get on? Did you say 'B' is between six million and seven million? The previous multiple of one million is six million.

The next multiple of one million is seven million, 'B' is nearest to six million, so 'B' is six million when it's rounded to the nearest multiple of one million.

How did you get on with those? Well done.

Now instead of a letter, we've now got a number.

What can we say about the number 2,783,450? Well, we can say that 2,783,450 is between two million and three million.

You can see there where it's positioned.

on that number line.

We can say the previous multiple of one million is two million and the next multiple of one million is three million.

But which is it closest to? That's right, 2,783,450.

Well, it's nearest to three million, isn't it? So that means 2,783,450 is three million when it's rounded to the nearest multiple of one million.

And we can share this information with an inequality, two million is less than 2,783,450, which is less than three million.

And we can say that 2,783,450 is three million when it's rounded to the nearest multiple of one million because it's closest to three million than it is to two million.

Let's check your understanding with that.

Could you complete the sentences to describe 7,683,102? So the sentences are 7,683,102 is between mm and mm.

The previous multiple of one million is mm.

The next multiple of one million is mm.

7,683,102 is closest to mm.

7,682,102 is mm when rounded to the nearest multiple of one million.

Pause a video while you have a go at completing those sentences.

When you're ready to go through the answers, press play.

How did you get on? Did you notice that 7,683,102 is between seven million and eight million.

The previous multiple of one million is seven million, and the next multiple of one million is eight million.

7,683,102 is nearest to eight million.

You can see that from the position on the number line.

And then we can say 7,683,102 is 8 million when it's rounded to the nearest multiple of one million.

What do you notice about these numbers? We've got 5,192,012.

5,811,159.

What do you notice? Well, both numbers are between five million and six million, aren't they? We can see where they're positioned on the number line.

5,192,012 is nearest to five million, but 5,811,159 is nearest to six million.

We can say 5,192,012 is five million when it's rounded to the nearest multiple of one million.

But 5,811,159 is six million when rounded to the nearest multiple of one million.

So both those numbers were between five million and six million, but they rounded to different multiples of one million.

So both of these numbers had five whole millions and they both were positioned between five million and six million on the number line, but they round differently.

Can you explain why? Let's look at both of these numbers positioned on the number line again.

Can you see that 5,192,012 sits before the midpoint of five million and six million? Whereas 5,811,159 sits after the midpoint.

That means that they both rounds differently.

5,192,012 was nearer five million because it's before the midpoint, whereas 5,811,159 rounds to six million because it's nearer to six million because it's after the midpoint.

Let's revisit these numbers.

What do you notice? So these are the numbers that we have looked at so far.

2,783,450.

Well that rounded to three million.

5,192,012.

Well that rounded to five million.

5,811,159 rounded to six million and 7,683,102 rounds to 8 million.

Lucas has noticed that when we round to the nearest million, this 100,000 digit is the critical digit.

It's of crucial importance.

It can really help us with our rounding.

If it is four or less, we round to the previous multiple of one million.

So can you see where we rounded to the previous multiple of one million with 5,192,012? That 100,000 digit was a one.

It's less than four.

So we round to the previous multiple of one million, which was five million.

If it's five or more so in the other examples, we round to the next multiple of one million 'cause it means that after that midpoint.

Let's check your understanding with that.

By looking at the critical 100,000s, can you determine which multiple of one million 3,099,523 rounds to and complete the sentences? The critical 100,000s digit is a mm.

This means we rounded the mm multiple of one million.

3,099,523 is mm when rounded to the nearest multiple of one million.

Pause the video while you have a go and when you're ready to go through the answer, press play.

How did you get on? Did you notice that the critical 100,000 is a zero and this is less than five? So it means we round to the previous multiple of one million.

So 3,099,523 is three million when we round to the nearest multiple of one million.

Your turn to practise now.

Can you round these numbers to the nearest multiple of one million? You could use a number line, or you could look at the critical digit and use the STEM sentences that we have been learning about to help you.

Question two, Lucas is thinking of a number.

His number rounds to three million to the nearest multiple of one million.

Part A, what's the smallest integer, so that's a whole number that his number could be? And part B, what is the greatest integer or whole number that his number could be? Question three, using the given clues, could you match the number to the child? So Aisha's number rounds to three million to the nearest multiple of one million.

Lucas' number rounds to four million to the nearest multiple of one million.

And Izzy's number will also rounds to four million to the nearest multiple of one million, but it's smaller than Lucas' number.

Pause the video while you have a go at those questions.

When you're ready to go through the answers, press play.

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

For question one, you need to round these numbers to the nearest multiple of one million.

We've got the part a 9,810,000 while the previous multiple of one million is 9 million and the next multiple is 10 million.

Going to look at that critical digit, it's an eight.

So 9,810,000 is 10 million when rounded to the nearest multiple of one million.

Part B 9,180,000, well, the previous multiple of one million is 9 million and the next multiple is 10 million.

The critical digit is a one.

This means we rounded the previous multiple of one million.

So 9,180,000 is 9 million when rounded to the nearest multiple of one million.

Part C, 4,500,000.

Well the previous multiple of one million would be four million.

The next multiple of one million would be five million.

The critical digit is a five and this means we round to the next multiple of one million.

So 4,500,000 is five million when rounded to the nearest multiple of one million.

Part D 4,499,999, the previous multiple of one million is four million.

The next multiple of one million is five million.

That critical digit is a four.

This means we round to the previous multiple of one million.

So 4,499,999 is four million when rounded to the nearest multiple of one million.

Part E, 1,000,001.

Well the previous multiple of one million is one million, and the next multiple of one million would be two million.

The critical digit is a zero.

This means we round to the previous multiple of one million.

1,000,001 is one million when rounded to the nearest multiple of one million.

For question two, we needed to think of what Lucas' number could be.

We were told his number rounds to three million to the nearest multiple of one million.

Now, you might have reasoned that his number would have to be greater than or equal to the midpoint of two million and three million, but smaller than the midpoint of three million and four million.

This means that the smallest his number could be is 2,500,000.

The critical digit is a five, which means 2,500,000 would round to the next multiple of one million, which would be three million and the largest his number could be is 3,499,999.

The critical digit is a four, so that means this number rounds to the previous multiple of one million, which would be three million.

For question three, you had to use the clues to match the number to the child.

Aisha's number rounds to three million to the nearest multiple of one million.

If we look at the first number, well that's more than four million, so the smallest that could round to is four million, so it can't be that one.

If we look at the second number, 3,550,692, the critical digit is a five.

So that number will round to the next multiple of one million, which would be four million.

So Aisha's number must be the third number.

The critical digit is a four.

So this will round to the previous multiple of one million, which is three million.

So Aisha's number is 3,498,300.

We've determined that the other two numbers round to four million, but Izzy's number we're told is smaller than Lucas's number.

So Izzy's number must be 3,550,692 and Lucas's number 4,100,509.

How did you get on with those questions? Well done.

Well done today.

I can see how hard you have tried and how you have progressed your learning with understanding how we round seven-digit numbers to the nearest million.

We know that sometimes numbers are rounded as approximations to remove unnecessary detail.

We know they make the number appear simpler, and we know that rounded numbers are also used to give an estimate or average.

We know that when we round to the nearest multiple of one million, identifying the previous and next multiples of one million and the midpoint between them supports us to be successful.

We know when we round to the nearest multiple of one million, the critical digit is the 100,000th digit.

If this is a four or less, we round to the previous multiple of one million.

If it's five or more, we round to the next multiple of one million.

You should be really proud of how hard you have tried today.

I know I am proud of you.

I've had great fun, and I look forward to learning with you again soon.