Lesson video

Hello, welcome to today's math lesson.

My name is Dr.

Shorrock and I'm very much looking forward to guiding you through the learning today.

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

This lesson is called Represent numbers up to 10 million.

As we move through the learning today, we will deepen our understanding of how we can use place value counters to represent numbers and how we can use zero as a placeholder when there is no digit in a particular place value place.

Sometimes new learning can be a little bit challenging.

It is okay, I'm here to guide you.

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

So let's get started, shall we? How can we represent numbers up to 10 million? The key words for our learning today are million and placeholder.

Now, you may have heard those words before, but it's always useful to practise saying them aloud.

My turn million, your turn.

Nice, my turn, placeholder, your turn.

Fantastic.

Now one million is composed of 1,000 thousands and we write it as a one followed by six zeros and ten one millions make 10 million.

A placeholder is a zero and it shows us that there is no digit in that particular place and they are used so we can write numbers properly.

So let's get started with our learning today, thinking about how we can represent numbers up to 10 million.

And we have Laura and Jacob to guide us through the learning today.

Jacob uses some counters to represent a number.

Let's have a look at what he's done, shall we? Hmm.

What number is represented by these counters? What do you think? Have a look.

What have we got? What do you notice? We can start by determining the digits that the counters represent.

So we have two ones, three tens, six one hundreds, five one thousands, one 10 thousand, two 100 thousands, and one one million.

And what can we do then to help us read this number efficiently? We've identified the digits in the number, but how do we read it? That's right, Laura, thank you.

We're going to start by identifying the hundreds, tens, and ones.

Can you see which digits they are? That's right.

They're usually the ones on the far right of a number.

So we've got six, three and two, six hundreds, three tens and two ones.

Once we've grouped the hundreds, tens and ones together, we can then group the thousands together and then the millions, and this helps us to read numbers efficiently.

We can now use place value separator commas to help us read this number.

Remember, the digits are grouped in threes from the right.

So we can write this numbers one comma two, one, five, comma six, three, two.

We've separated the digits into groups of threes from the right and we are using separator commas to separate the millions from the thousands from the ones.

Let's have a look at this number in more detail.

We can see you've got one comma because one comma, two, one, five, comma six, three, two, while it's written and read as one million, two hundred and fifteen thousand, six hundred and thirty two.

So we read the millions first, then the thousands, then the ones.

Let's check your understanding with that.

Which number is represented by these counters? It might be worth trying to find the digits first that the place value counters are representing.

Pause the video while you try and figure out what number is represented and when you're ready to go through the answers, press play.

Did you identify the digits first? We had six ones, one ten and three hundreds, two thousands, four 10 thousands, one 100 thousand, and two one millions.

And then you could group those digits into threes from the right-hand side, identifying the hundreds, tens, and ones first, and we can write this number then as two comma, one, four, two, comma, three, one, six.

We've identified the three, one, six as our hundreds, tens and ones, 316.

We identified the one, four, two as the thousands, 142 thousand and there was two million.

So we can read this number as two million, one hundred and forty-two thousand, three hundred and sixteen.

How did you get on with that? Well done.

Now Jacob wants to represent the number one million, four hundred and thirty-two thousand, one hundred and fifty-four using counters.

What should he do? Ah, good start.

Yes, let's write the numeral.

That will help us know how many counters we need to use.

So we've got one million, a one, then a comma, 432 thousand.

So that's our next group of three digits.

So four, three, two, comma, and then we've identified the hundreds, tens, and ones, 154, one, five, four.

And now Jacob knows the last three digits on the right, are the hundreds, tens and ones so he can represent that part of the number using place value counters.

We've got four ones, five tens and 100.

And the next three digits of a thousands, we've got two one thousands, three 10 thousands and four one 100 thousands.

And then the next digit is the million, so we need one one million place value counter.

So Jacob has now represented that number one million, four hundred and thirty-two thousand, one hundred and fifty-four with counters.

Well done Jacob.

We can also represent numbers on the Gattegno chart.

Which number is represented here? Take a moment, have a look.

What do you think? Let's take a look at this part of the Gattegno chart.

We can determine which number is being represented by recombining the parts.

Two million added to 100 thousand, added to forty thousand, add four thousand, add three hundred, add twenty, add one, and we read that number as two million, one hundred and forty-four thousand, three hundred and twenty-one.

Let's check your understanding with that.

Could you use counters or draw counters if you don't have them available, an accurate representation of two million, three hundred and fourteen thousand, five hundred and twelve? A good place to start might be to identify the numeral first.

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

How did you get on? Did you write the numeral as two, comma three, one, four, comma five, one, two? We've got 512 ones, so two ones, one ten and five hundreds.

Then we've got three hundred and forty thousand, so we've got four one thousands, one 10 thousand and three 100 thousands and then we've got two one millions.

Well done.

Your turn to practise now.

Could you for question one, have a look at this representation of a number.

Then could you write in words numbers that are, A, 100 more than this number, one million more, 20 thousand more, 10 less, and 100 thousand less.

For question two, could you use these clues to determine the number, then represent it using counters or by drawing, and then write the number in words.

The number has seven digits and the millions digit is a three.

The tens is the same as the millions digit.

The ones digit is one more than the tens digit.

The digit sum of the hundreds, tens and ones is nine and there are four hundred and twelve thousands.

Pause the video while you have a go at both those questions and when you are ready to go through the answers, press play.

How did you get on? For question one you were asked to look at this representation of a number and then write in words numbers that are part A, 100 more.

So first of all, we had to start by identifying what this number was and we could see that we have got 543 ones, 252 thousands and three million, so we read it as three million, two hundred and fifty-two thousand, five hundred and forty-three.

We could then work out numbers that are for part A 100 more, 100 more than three million, two hundred and fifty-two thousand, five hundred and forty-three is three million, two hundred and fifty-two thousand, six hundred and forty-three and we write it as three, comma two, five, two, comma, six, four, three.

You can see only the hundreds digit has changed and it is 100 more, was 500 it's now 600.

For part B, one million more than three million, two hundred and fifty-two thousand, five hundred and forty-three.

Well one million more than three million is four million, isn't it? So we must now have four million, two hundred and fifty-two thousand, five hundred and forty-three.

And we would write that as a four, comma, two, five, two, comma, five, four, three.

For part C, 20 thousand more than three million, two hundred and fifty-two thousand, five hundred and forty-three.

That would be three million, two hundred and seventy-two thousand, five hundred and forty-three and we would write that as three, comma, two, seven, two, comma, five, four, three.

And you can see it's only the tens of thousands digit that has changed.

It was a five, we needed to add two more tens of thousands, 20 thousand and it becomes a seven.

For part D, ten less than three million, two hundred and fifty-two thousand, five hundred and forty-three is three million, two hundred and fifty-two thousand, five hundred and thirty-three and we write that as three, comma, two, five, two, comma, five, three, three.

You can see it's only the ten that has changed.

It was four tens, we've taken away one ten, so it's now three tens.

For part D, 100 thousand less than three million, two hundred and fifty-two thousand, five hundred and forty-three is three million, one hundred and fifty-two thousand, five hundred and forty-three.

We write that as three, comma, one, five, two, comma, five, four, three.

You can see that only the 100 thousands digit has changed.

It was a two, but we needed to remove 100 thousand, so it was a one.

For question two you were asked to use these clues to determine the number.

We were told the number has seven digits and the millions digit was a three.

So I've got seven digits and I've put a three in the millions place.

We were told the tens digits the same as the millions digits, so I can pop that in.

The ones digit is one more than the tens digit.

Well, if the tens digit is a three, the ones digit must be a four, one more.

The sum, the digits sum of the hundreds, tens and ones is nine.

Well, I've got three and a four, which is seven.

So the hundreds must be two because the hundreds, tens and ones digit add to nine, seven and two is nine.

There are 412 thousands.

So I can put the digits four, one, two into the remaining boxes.

You were then asked to represent it using counters or by drawing and then write the number in words.

So I've got four ones, three tens, two one hundreds, two one thousands, one 10 thousand, four one 100 thousands, and three one millions.

And we could split those groups into threes to help us read it and we can pop the separate commas in, three, comma four, one, two, comma two, three, four, and that can be written in words as three million, four hundred and twelve thousand, two hundred and thirty-four.

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

Fantastic learning so far.

I'm really impressed with how hard you are trying and that's what's really important that we always try our best.

So we've had to look at how we can represent numbers up to 10 million.

We're going to move on now and think about how we use zero as a placeholder.

Let's look at this representation of a number.

What do you notice? Do you notice anything? What number is it representing? Jacob is saying the number represented here is three, comma, one, three, comma, six, five, two.

Do you agree with Jacob? Oh, Laura doesn't.

"I respectfully challenge you! We need to group the digits in threes from the right." That's what we've been learning, isn't it? Whereas Jacob has has represented the six, five, two, he's grouped those together, but then he hasn't grouped the three and the one and the three together, has he? So Laura is saying the number represented here is three, one, three, comma, six, five, two.

Do you agree with Laura? Jacob doesn't.

He's respectfully challenging her.

He says, he's noticed we've got three one millions counters and Jacob's noticed something.

I wonder if you've noticed this.

There are no counters representing the 10 thousands digit.

Good spot.

So that means we need to use a placeholder to show that there are no 10 thousands.

We can't just leave it blank.

Otherwise we would not be writing that number accurately.

So here you can see we've got two ones, five tens, six one hundreds, three one thousands.

Then we put a zero placeholder to show that there are no 10 thousands, one 100 thousands, and three one millions.

Even though there is a zero placeholder, we still group the digits in threes to read them.

So you can identify we've got 652 ones, 103 thousands and three million.

So we can write the number then with its separator place value comma.

Three, comma, one, zero, three, comma, six, five, two.

So how would we read this number? We would read it as three million, one hundred and three thousand, six hundred and fifty-two, just like we would read any other number, but this time it's got a zero as a placeholder, but we need to include it to make sure we are writing and reading the number accurately.

We can also have a look at numbers on a Gattegno chart.

What do you notice? Ah, Laura has noticed something.

There's no hundred thousands digit in this number.

Look, there's nothing along the hundred thousands row, is there? When writing this number we need to use a placeholder to show that there is no a hundred thousands digit and we can determine which number is being represented by recombining the parts.

So we can add together the six million, the seventy thousand, the seven thousand, the nine hundred, the eighty, and the six.

And we must remember that placeholder zero.

So we've got six million, seventy-seven thousand, nine hundred and eighty-six, but we've got that zero in the a hundred thousands place to show that there is no digit there.

And we can read this as six million, seventy-seven thousand, nine hundred and eighty-six.

Let's check your understanding with this.

True or false.

Four million, two hundred and seven thousand, six hundred and forty-two is written as four, comma, two, seven, comma, six, four, two.

Do you think that's true or do you think that's false? Pause the video while you decide and when you are ready for the answer, press play.

How did you get on? Did you say that was false? But why is it false? Is it because we group digits in threes from the right, the number should be written as four, two, seven, comma, six, four, two? Or did you say, well there is not a 10 thousands digit so we need to use a placeholder zero.

The number should be written as four, comma, two, zero, seven, comma, six, four, two.

Maybe find someone to have a chat about this with, see which one you think it is.

Pause the video while you do that and when you are ready for the answer, press play.

How did you get on? Did you say it's false because there is not a 10 thousands digit, so we need to use a placeholder zero.

The number should be written as four, comma, two, zero, seven, comma, six, four, two.

Four million, two hundred and seven thousand, six hundred and forty-two.

How did you get on with that? Well done.

It's turn to practise now.

For question one, could you represent these numbers using counters or by drawing them and then write them as a numeral? You've got A, five hundred and three thousand and forty-one.

B, one million, thirteen thousand, four hundred and two.

C, two million, three thousand, two hundred and fifty-one.

Part D, three million, one hundred and three thousand, one hundred and six.

Take care to spot if you need to use a placeholder zero.

For question two.

Jacob has written the number three million, forty-two thousand, five hundred and sixty-four as three, comma, four, two, comma, five, six, four.

Jacob is wrong.

How should he write the number? Convince me that you are correct by representing this with counters or drawing them and giving a reason for your answer.

Pause the video while you have a go at both those questions and when you are ready to go through the answers, press play.

How did you get on? For question one, you were asked to represent some numbers using counters and then write them as a numeral.

The first one was five hundred and three thousand and forty-one.

We can identify that we've got tens and ones, 41, but we had no hundreds and we've also got no tens of thousands.

So we need to still identify the groups of three and then we can write the number five, zero, three, for five hundred and three thousand with no tens of thousands digits.

So we used that placeholder zero and 41, zero, four, one.

No hundreds digits, so we needed to use a placeholder zero.

For part B, one million, thirteen thousand, four hundred and two.

Again, we can group the numbers into what should be there, threes and then we can identify the digits.

We've got one million, we've only got thirteen thousand, so we needed a place holder zero in the hundred thousands place.

Four hundred and two, we had no tens digit, so we needed a place holder zero in the tens place.

Two million, three thousand, two hundred and fifty-one.

Again, we can group them into threes.

We can see we've got two million, but we've only got three thousands but we still need to use those placeholders zeros.

This time we needed two of them next to each other because there are no 100 thousands and no 10 thousands.

So it's two, comma, zero, zero, three, comma, two, five, one.

For part D, three million, one hundred and three thousand, one hundred and six were represented with place value counters and then grouped them into their threes.

We can see we've got three million, so it's three comma, we've only got one hundred and three thousand, so it's one, zero, three.

We need a zero in place of the fact that there are no 10 thousands digit, one hundred and six.

We needed a zero in the tens place to show we had no tens digit.

For question two, Jacob wrote the number three million, forty-two thousand, five hundred and sixty-four as three, comma, four, two, comma, five, six, four and he was wrong, I told you that.

How should he write the number though? Jacob should have written the number as three, comma, zero, four, two, comma, five, six, four.

He did not use a placeholder in the hundred thousands place to show that there is no digit in that place.

I represented it with place value counters and you can see there was no hundred thousands digit.

And we can write the number as three million, forty-two thousand, five hundred and sixty-four and it's written in numeral as three, comma, zero, four, two, five, six, four.

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

Fantastic learning today.

You have really made deep progress in representing numbers up to 10 million and you have tried really hard.

We know that numbers can be represented using counters or a Gattegno chart, and we know a zero in a number shows that there is no digit value in that column and it's called the placeholder.

And they're really important to show that we are writing numbers properly and when we read numbers, we group the digits into threes from the right.

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

I've had a great fun working with you and I look forward to working with you again soon.