Lesson video

Hello, how are you today? My name is Dr.

Shorrock and I'm really excited to be learning with you today.

You have made a great choice to learn maths with me and I'm here to guide you through the learning.

Today's lesson is from our unit, understand place value within numbers with up to eight digits.

This lesson is called Read and Write Numbers Up to 10 million.

As we move through the learning today, we are going to deepen our understanding of how our numbers are structured and how we can use the structure to help read and write numbers.

Now, sometimes it can be a little bit challenging when we learn new things, but don't worry, I'm here to help you.

And I know if we work really hard together, then we can be successful in our learning.

Let's get started then, shall we? How can we read and write numbers up to 10 million? Our key words for the learning today are million and separator comma.

You may have heard those words before, but it's always good to practise saying them aloud.

Let's have a go.

My turn, million.

Your turn.

Nice.

My turn, separator comma.

Your turn.

Fantastic.

One million is composed of 1000 thousands and is written by a one followed by six zeros and ten one millions make 10 million, and a place value separator comma.

Well, that's what we use to partition longer numbers to help us read them efficiently.

So let's get started with today's learning, shall we? We are going to start by looking at the structure of larger numbers.

And we have Laura and Jacob to help us in our learning today.

Laura and Jacob find a calculator and type some numbers in.

If you can find a calculator, it might be fun having a go at this.

How do we read such a large number though, Jacob is saying.

Can you see the number in the calculated display? The digits are two, five, six, nine, two, four, one.

How do we read that? And Laura knows that we need to identify the number of millions, thousands, and hundreds, tens, and ones.

And we can look at how our numbers are structured to help us read it.

And when we do any new learning, it's always good to start the learning by looking at a smaller number.

So let's look at this number.

How would you read this number? The digits are one, nine, three, seven.

We can use a place value chart to help us read numbers.

That's right, Laura.

We need to have an understanding of how the digits are grouped.

And Jacob tells us that he can see that the digits of a number are grouped into threes.

We've got the ones, the thousands, and the millions.

Do you see something that is similar between those groupings? That's right, within each grouping you've got ones, tens, and hundreds.

So you've got one 1, ten 1s, hundred 1s.

1000, 10,000, 100,000s.

1,000,000, 10 millions, 100 millions.

And Laura is telling us that if a number has more than three digits, it means that we need to deal with thousands.

If it's got three digits or fewer, we'll be just be dealing with the ones, won't we? The last three digits of a whole number represent the hundreds, tens, and ones then.

And we group the hundreds, tens, and ones together as ones.

We use separator commas to partition the millions, thousands, and the ones to help us read these numbers.

Once we have grouped the digits, we can then read the number more efficiently.

We can see the digits one, nine, three, seven, while the one then has a separator comma after it, and the separator comma partitions those thousands from the ones.

So we would read the number as 1,937.

Let's revisit this number that Laura and Jacob generated on the calculator, and we can use what we've just learned to help us group the digits in this number.

Two, five, six, comma, nine, two four, comma, one.

And that prepares us to read the number.

So can you see what Jacob's done? He has grouped the digits into groups of three, hasn't he? Oh, Laura's respectfully challenging him.

Why would she do that? He grouped the digits into threes, didn't he? Oh, of course we do, don't we? We need to group the digits in threes from the right not to the left, because the last three digits are the hundreds, tens, and ones.

So we should have grouped the two, four, one together, the five, six, nine together and then the two.

Ah, yes, Jacob.

So Jacob is now aware that we should group the digits as two, comma, five, six, nine, comma, two, four, one.

So we've grouped them in threes from the right hand side, from the lowest value digit.

Ah, and Laura is agreeing now.

She supports him.

He has now grouped this appropriately.

Let's check your understanding with this.

Could you look at the number on the calculator? How should it be written using separator commas to partition the millions, thousands, and ones.

Have a look at A, B, and C and see which you think is the accurate way to write it with the separator commas.

Pause the video while you do that.

And when you are ready to go through the answer, press play.

How did you get on? Did you say it must be A? It can't be B because we haven't grouped in threes from the right hand side.

The six is on its own and we know the six one should be with the tens and the hundreds.

What about C? Well, we did start by grouping in threes from the right hand side, but then we grouped in twos.

We can see the five, eight, six represent the hundreds, tens, and ones.

The five, two, four represent the thousands and the eight represents the millions.

And it's important that we group in threes from right to left, identifying the value of the final three digits first, those hundreds, tens, and ones.

Jacob then performs a calculation, and this is the answer to his calculation.

Can you see the digits there? 6,556,788.

9.

What do you notice? That's right, in this number there is a decimal point.

So how do we group the digits in this number to help us read it? Do you think we still group them in threes from the right hand side? Jacob does, and that's how he's grouped them.

So you can see he's got six, five, comma, five, six, seven, comma eight, eight point nine.

He's grouped them in threes from the right hand side, hasn't he? Would you agree with Jacob? Ah, Laura doesn't, does she? She's challenging him again and suggests we use a place value chart.

So if we represent this number in a place value chart, what do you notice? That's right.

It's got some tenths, hasn't it? But we need to start by identifying the hundreds, tens, and ones.

And these are usually the last three digits on the right unless we have a decimal fraction, then the hundreds, tens, and ones are the three digits to the left of the decimal point.

And once we have identified the hundreds, tens, and ones, we can group the other digits in a number.

And that's now what Jacob has done.

He has grouped the digits in threes from the left of the decimal point.

So he's grouped the seven, eight, eight together because they are the hundreds, tens, and ones.

And the 0.

9, that's nine tenths.

That's the decimal fraction part of the number.

And Laura now supports him.

Did you know? Ooh, what Laura? We do not use separator commas in the fractional part of a number.

Ah, I see.

And that's because we don't read it in the same way that we read the non fractional, the whole part of the number.

Let's check your understanding with that.

Look at this number.

I'll read the digits to you.

One, two, nine, four, six, seven, nine point three.

How should that be written using a separator comma and a decimal point? Pause the video while you have a look at the options A, B, and C.

And when you think you're ready to go through the answer, press play.

How did you get on? Did you say, "Well, it can't be A, because we haven't grouped in threes from the left of the decimal point.

We've got the nine, nine ones on their own." Same with B, we've only got the seven and the nine, the seven tens and the nine ones on their own.

We need to put the hundreds with them.

So it must be C, 679.

Six, seven, nine are the hundreds, tens, and ones.

We can then group the rest of the digits in threes.

It's important that we group in threes from right to left, identifying the hundreds, tens, and ones first.

And remember those, decimal fraction parts of the number we don't group.

We don't use separator commas in that part of the number.

Your turn to practise now.

I'd like you to use a calculator where possible to create some numbers of five, six, or seven digits by multiplying different combinations of numbers that have different numbers of digits, so it's up to you.

You could do something like 8,631 multiplied by 483.

I'd like you to record each calculation using the separator commas correctly.

So remember to group in threes from those hundreds, tens, and ones.

And remember, we cannot type the comma into a calculator.

So if you are going to type in 8,631, eight, comma, six, three, one, you won't be able to type the comma in.

You'll just have to do it without.

It will be fine.

For question two, could you sort these numbers into groups to show whether they have been correctly written or not? For any that you think are incorrectly written, give reasons to support your decision.

And can you make up two examples of your own.

One for each of the groups? Have a go at both of those questions.

Pause the video while you do that.

And when you are ready to go through the answers, press play.

How did you get on? So you might have created calculations like this.

Jacob typed eight, six, three, one multiplied by four, eight, three into a calculator.

And that was his answer.

He had the digits four, one, six, eight, seven, seven, three.

And then he recorded the calculation using those separator commas correctly.

So we identified the hundreds, tens, and ones first.

So in 8,631, he identified the 631 and then there was a comma to separate those ones from the thousands.

And in his answer, he separated the digits in groups of three from the right hand side.

So he identified the hundreds, tens, and ones as 773 and then he could use a separator commas.

For question two, you had to sort these numbers into groups to show whether they have incorrectly written or not.

Six, comma, four, three, nine, point one.

6439.

1.

Well, that's correctly written.

We've identified the hundreds, tens, and ones.

And 763,148.

Again, the hundreds, tens and ones have been identified and separated.

4,826,591.

Again, correctly written.

But then seven, three, six, comma, one, point eight.

Well, we need to identify the hundreds, tens, and ones.

So that's not correct.

We've only identified the ones there, haven't we? And the same with one, eight, five, comma, seven, two.

We haven't identified the hundreds, tens, and ones.

They would be the last three digits, the five, seven, two.

You might have reasoned that it is important that we group in threes from the right to left, identifying the hundreds, tens, and ones first.

The incorrectly written number should have been written as seven, three, six, one, point eight.

So we've identified that three, six, and one are the hundreds, tens, and ones, 361.

and 18, comma, 5, 7, 2, we've identified that the five, seven, two are the hundreds, tens, and ones.

You might have made up two examples of your own.

So I wrote one here, three, comma, four, four, five, comma, six, eight, seven, point two, three.

So I haven't used to separate comma for my decimal part of the number, but I've identified the hundreds, tens, and ones, the 687.

And one that was incorrectly written, three, oh, two, comma four, five, point four.

Well, I've got the four and the five, but I actually needed to identify the hundreds as well, that too, so that was incorrectly written.

How did you get on with those? Well done.

Fantastic learning so far.

I'm really impressed with how hard you are trying and that's the most important thing is that we always try really hard to the best of our ability.

We're going to move on now that we understand the structure of larger numbers.

And we're gonna have a go at reading and writing numbers to 10 million.

So now that we understand the structure of our numbers, we can group the digits accurately.

We can read and we can write numbers efficiently.

So let's revisit this number.

One, nine, three, seven.

We can use a separator comma to help us read it.

We know we need to identify the hundreds, tens, and ones for nine, three, seven, and then we can group those together and partition them from the thousands with our separator comma.

We can use this in a place value table as well.

And we can see we've got 1,937.

Let's place an extra digit shall we, in the 10,000.

So this time, we've got 51,937.

What if we place another digit at the front? Then we would have 451,937.

So can you see here how 937 has been separated from the thousands? And that's how we read it.

We read the number of thousands first and then the number of ones.

451,937.

What if we place another digit? Well now we go into the millions, don't we? And we need another separator comma to part in the millions from the thousands, and the millions and thousands from the ones.

So we would say 5 million, so five comma, 451,000, four, five, one, comma, 937.

Let's look at this number in further detail.

We've got 5,451,937.

What do you notice? That's right, the separator commas in the numeral are where we say the words million.

You see 5 million in the in the digits.

In the numeral we have a five comma, but in the words, it's 5 million with the comma.

And the second comma there, we use for the word thousand, 451,000.

So in the numeral, we don't write the word thousand, we use a comma instead.

Sometimes numbers do not have separator commas, though you might have noticed an example like this.

Sometimes on calculators or in some books, they might be written without the separator comma.

In this number, spaces have been used in place of the comma.

Does that mean that we need to read it or write it differently? No, that's right, we still need to identify the hundreds, tens, and ones digits, and then we can group the other digits.

We read this number as 4,672,135.

Let's check your understanding with this.

True or false? We read, and I'll read the digits out to you, three, comma, four, five, seven, comma, one, two, five as three million four hundred and fifty seven, one hundred and twenty five? Do you think that's true or false? Pause the video, maybe chat to somebody about this.

And when you are ready for the answer, press play.

How did you get on? Did you say that's false? That's not how we read it, is it? But why not? Is it because digits are grouped in threes from the left? It should be three, four, five, comma, seven, one, two, comma five, which is read as 345,712,005.

Or is it B, digits are grouped in threes, millions, thousands, and hundreds, tens, and ones? It should be read as 3,457,125.

Pause the video.

Will you think about which reason it is? And when you are ready to find the answer, press play.

How did you get on? Did you say that three, four, five, seven, one, two, five should be read as 3,457,125 because our digits are grouped into groups of threes, we have to identify the hundreds, tens, and ones and group in threes then from the right, so then we would have 457,000 and then we would have 3 million.

Well done.

It's your turn to practise now.

For question one, could you work out the following, using a calculator? Three comma, five, zero, zero multiplied by seven, eight, two? Could you write your answer as a numeral with separator commas? And could you write it as number words? For question two, could you refer back to your calculations from task A? Could you write the products as number words and, where possible, read them aloud to a friend? Pause the video while you have a go at both of those questions.

And when you are ready to go through the answers, press play.

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

For question one, you are asked to work out the following using a calculator.

If you worked it out using a calculator, you would've got the answer with the digits two, seven, three, seven, zero, zero, zero.

And that can be written using separator commas by identifying the hundreds, tens, and ones first.

They were all zeroes, and then we can group in threes from there.

And it could be written as two, comma, seven, three, seven, zero, zero, zero.

And that helps us read the number because then we can see we've got 2 million, where that first comma is, 737,000 for that second comma.

For question two, you are asked to refer back to the calculations you made from task A and write the products as number words, and, where possible, read them aloud to a friend.

So Jacob recorded a calculation as eight, comma, six, three, one multiplied by four, eight, three is equal to four, comma, one, six, eight, comma, seven, seven, three.

And he said that that could be written and read as 4,168,773.

How did you get on with yours? Well done.

Fantastic learning today.

I can see that you have tried really hard to grasp this understanding of how we read and write numbers up to 10 million.

We know that numbers can be read and written by identifying the number of millions, the number of thousands, and the number of hundreds, tens, and ones.

We know digits are grouped in threes to show the ones thousands and millions.

And we know the groups of three digits are separated with a comma, and we assume that the digit on the right hand side is the ones digit unless we have a decimal fraction.

Really impressed with how hard you have worked today, and you should be really proud of yourselves as well.

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