Lesson video

Hello, my name is Dr.

Shorrock.

And I'm really looking forward to learning with you today.

We are gonna have great fun as we move through the learning together.

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

This lesson is called composition of one million and 10 million.

As we move through the learning today, we will deepen our understanding of how one million and 10 million are made.

We will look at this in the context of reading scales on graphs.

We will also use bar models to make connections between the composition of one million and 1,000 and of 10 million and 10,000.

Sometimes new learning can be a little bit tricky.

But it's okay because I know if we work really hard together, and I'm here to guide you, then we can be successful in our learning.

Let's get started, shall we? The key word in our learning today is composition.

You may have heard of that word before, but it's always good to practise.

My turn.

Composition.

Your turn.

Nice, and when we talk about composition, the composition of a whole is the way in which something is built or the way in which it is made.

For example, if one is the whole, then 0.

3 and 0.

7 are parts of the whole.

We can say that one is composed of 3/10 on 7/10.

In the context of this lesson, we're going to look at equal parts of the whole.

For example, one is composed of two equal parts of 0.

5.

We will start our learning today looking at the composition of one million.

And in this lesson we have Laura and Jacob to guide us.

Laura and Jacob are both researching the populations of some countries and they present their findings in a bar graph.

And Jacob is just reminding us that what we mean by population is the number of people who live in a particular country.

Let's look at Laura's graph.

Take a look.

What do you notice? Do you notice that it's a bar graph and it's showing the populations of some countries? Which countries there? That's right.

The horizontal access shows us.

We've got Slovenia, Bahamas, and Bahrain.

And the vertical axis that is the population.

And have you noticed that the population of Slovenia is two million, but to read the scale, to determine the population of the Bahamas and Bahrain, we would need to know about the composition of one million because the population for Bahamas and Bahrain that's not exactly on a millions number on the scale, is it? The Bahamas is, we can see there are fewer people than one million and in Bahrain there are more people than one million.

Let's look at Jacob's graph.

What do you notice from Jacob's graph? That's right, it's still a graph showing the populations of some countries, but he has looked at Barbados, Malta and Mauritius.

And we can see that to read the scale, to determine the populations of these countries, we would need to know about the composition of one million.

So to support it, let's make connections with prior learning about the multiplicative composition of 1,000.

Take a look at these bar models.

What can you remember about 1,000? If 1,000 is divided into two equal parts, each part is worth 500.

We can say 1,000 is composed of two equal parts of 500.

What about if 1,000 is divided into four equal parts? That's right.

We can say ,1000 is composed of four equal parts of 250.

What about if we divide 1,000 into five equal parts? That's right.

We can say 1,000 is composed of five equal parts of 200.

And what about if we divide 1,000 into 10 equal parts? That's right.

We can say 1,000 is composed of 10 equal parts of 100.

But how does that help us thinking about the composition of one million? Let's relate the composition of 1,000 to that of one million.

What do you notice about the bar models? Have you noticed something that is the same or something that is different? Jacob is reminding us that 1,000,000 is read as one million and that one million is equivalent to 1,000 thousands and we can use that to help us.

The whole has been divided into two equal parts.

So to find the value of each part, the whole can be halved or divided by two.

And we can use unitising to describe the similarities between halving 1,000 and halving one million.

We know that half of 1,000 is 500, so half of 1,000 thousands must be 500,000.

And that means that one half of one million, which is 1,000 thousands, is 500,000.

So let's look at the composition of one million.

We can use the bar model to form an equation.

We can see that one million has been divided into two equal parts and each part must be worth 500,000.

Using this equation, what else do we know? What else could we determine? That's right, we could use our known facts, couldn't we? We could also say that one million divided by 500,000 is equal to two.

We could say that one million multiplied by 1/2 is equal to 500,000, or 1/2 of one million is equal to 500,000.

We could also say that two multiplied by 500,000, two 500 thousands, is equal to one million.

And 500,000 multiplied by two or doubled is equal to one million.

That's a lot of information we can work out from one equation, isn't it? Let's look at the different way to compose one million and we're gonna compare it to the composition of 1,000.

We can see that the whole has been divided into four equal parts, and to find the value of each part the whole can be quartered or divided by four.

And we can use unitising again to describe the similarities.

We know that 1/4 of 1,000 is 250, so 1/4 of 1,000 thousands or one million must be 250,000.

So we can say, 1/4 of one million is 250,000.

And again, we can look at this composition of one million and use the bar model to form an equation.

One million divided by four is equal to 250,000.

And using this equation, what else could we determine? What else do we know? That's right.

We could say one million divided by 250,000 must be equal to four.

One million multiplied by 1/4 is equal to 250,000 or 1/4 multiplied by one million, 1/4 of one million is equal to 250,000.

We could say four multiplied by 250,000 is equal to one million, or 250,000 multiplied by four is equal to one million.

It's a lot of equations again, isn't it? Just by knowing one and using our known facts.

Let's work together with this.

I'd like to complete the sentences using the bar models to compare the composition of one million to that of 1,000.

I'm going to model this for 1,000 divided into five equal parts.

Then I'd like you to have a go when 1,000 is divided into 10 equal parts and compare that to the composition of one million.

We can say that we know that 1/5 of 1,000 is 200.

So 1/5 of 1,000 thousands must be 200,000.

And so I can see there that 1/5 of one million is 200,000.

Could you have a go now at completing the sentences using my structure to help you? Remember, you are comparing the composition of 1,000 when it's divided into 10 equal parts to that of one million being divided into 10 equal parts.

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

How did you get on? Did you say that we know 1/10 of 1,000 is 100? So 1/10 of 1,000 thousands must be 100,000.

And then 1/10 of one million is 100,000.

Well done.

Let's try that again.

This time, I'm going to use the bar models to form equations describing the composition of one million.

I'm going to model this where one million has been divided into five equal parts, and then I'd like you to use my structure to have a go at modelling when one million is divided into 10 equal parts.

So I could say one million divided by five is equal to 200,000.

I could also then say that one million divided by 200,000 is equal to five.

We know when we divide by five, it's the same as finding 1/5.

One million multiplied by 1/5 is equal to 200,000 or 1/5 of one million is equal to 200,000.

I could then say that five multiplied by 200,000 is equal to one million.

Or 200,000 multiplied by five is equal to one million.

I'd like you to have a go now using my structure to complete the equations for having divided one million into 10 equal parts.

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

How did you get on? Did you form an equation to describe the bar model? One million divided by 10 is equal to 100,000.

We could then use known facts to say one million divided by 100,000 must therefore be equal to 10.

And we know if we are dividing by 10, it's the same as finding 1/10.

So we could do one million multiplied by 1/10 equals 100,000 or 1/10 of a million equals 100,000.

And we could then say that 10 multiplied by 100,000 is equal to one million or 100,000 multiplied by 10 is equal to one million.

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

Let's revisit Laura's graph.

We now know about the composition of one million and this can help us to read the scales and interpret the graphs.

And you can see on this graph the vertical scale has been divided into five equal parts.

So each interval must be worth 200,000.

So the population of the Bahamas must be 400,000 because we've got two equal parts.

And the population of Bahrain must be 1,600,000.

It's above the one million and it's three parts, and we know each part is worth 200,000, so it must be 1,600,000.

Let's revisit Jacob's graph.

If we look at the vertical axis, we can see that in between the steps of one million, we have divided into four equal parts.

We know now that one million is composed of four equal parts of 250,000, so each interval must be worth 250,000.

We can now see that the population of Barbados must be 250,000.

And that of Malta, well that's the equivalent to two parts, so that must be 500,000.

Let's check your understanding with this.

Could you work out the population of Mauritius? Pause the video while you have a think about this.

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

How did you get on? Did you notice that one million is composed of four equal parts of 250,000? So each interval must be worth 250,000.

The population of Mauritius must therefore be 1,250,000.

How did you get on? Well done.

It's your turn to practise now.

For question one, could you read the scales? And tell me what numbers are shown by the given letters? Remember, have a look at the scale first, how many equal parts are there and then think about making connections with what that would be for 1,000.

For question two, could you fill in the missing numbers in these equations? For question three, could you look at the bar graph and could you find the difference between the mass of the heaviest and lightest animal? Remember, you'll have to look at that vertical scale and see how many parts there are in between each marked interval of one million to help you.

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

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

So for question one, you had to read the scales and tell me what numbers are shown by the letters.

So in part A, one million has been divided into 10 equal parts.

Each part must be worth 100,000.

So A is 100,000, B has a value of 400,000 and C 900,000.

For part B, one million has been divided into four equal parts.

Each part must have a value of 250,000.

So D 250,000 and E 750,000.

In part C, the whole has been divided into five equal parts.

Each part must be worth 200,000.

So F is 200,000 and G would be 600,000.

For question two, you had to fill in the missing numbers.

One million divided by four is equal to 250,000.

200,000 is equal to one million divided by five.

1/10 of one million is equal to 100,000.

And four multiplied by 250,000 is equal to one million.

1/4 multiplied by one million is equal to 250,000.

That's the same as 1/4 of one million.

For question three, you had to look at the bar graph and find the difference between the mass of the heaviest and lightest animal.

Well, we can see that in between each marked interval of one million there are 10 equal parts.

And we know one million is composed of 10 equal parts of 100,000.

So each interval must be worth 100,000.

We had to find the difference between the mass of the heaviest and lightest animal so we could work out the mass of the hippo is 4 million grammes and the mass of the lion is 200,000 grammes, because it's two equal parts.

To find the difference, we need to subtract 4 million.

Subtract 200,000 is 3,800,000 grammes.

So the difference in their masses is 3,800,000 grammes.

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

Fantastic learning so far.

I can see how hard you are trying and that's what's really important.

I can see that you have deepened your understanding of the composition of one million.

We're going to move on now and have a look at the composition of 10 million.

Let's see if we can see anything that is the same or different.

What can you remember about the multiplicative composition of 10,000? Let's have a look at these bar models.

The first bar model, the whole of 10,000 has been divided into two equal parts.

Can you remember what the value of each part would be? That's right.

If we halve 10,000, we get 5,000.

We can say 10,000 is composed of two equal parts of 5,000.

If we double 5,000, we get 10,000, don't we? What about if we divide 10,000 into four equal parts? Can you remember what the value of each part would be? That's right, it would be 2,500.

10,000 is composed of four equal parts of 2,500.

What if we divide 10,000 into five equal parts? What would the value of each part be? That's right, it would be 2,000.

10,000 is composed of five equal parts of 2,000.

And then, if we look at the composition of 10,000 and divide it into 10 equal parts, what would each part be worth? That's right, 1,000.

10,000 is composed of 10 equal parts of 1,000.

Let's relate that knowledge of the composition of 10,000 to that of the composition of 10 million.

What do you notice about the bar models? Is there something that is the same? Is there something that is different? That's right, we could use unitising to describe similarities.

We know that 1/2 of 10,000 is 5,000.

So what does that mean about 1/2 of 10 million? That's right, 1/2 10,000 thousands must be 500,000.

So we can say 1/2 of 10 million is 500,000 or five million.

1/2 of 10 million is five million.

Let's look at this composition of 10 million.

When 10 million is divided into two equal parts, each part is worth five million.

And we can use this bar model to form an equation.

10 million divided by two is equal to five million.

Half of 10 million is five million.

But we can use that equation and form some other equations.

We could say 10 million divided by five million is equal to two.

We could say that 10 million halved is equal to five million, or half of 10 million is equal to five million.

We could say two multiplied by 5 million is 10 million.

So five million doubled is also equal to 10 million.

Lots of equations we can find out, isn't there? Just from that first equation formed by that bar model.

Let's look at a different way to compose 10 million.

And let's compare it to the composition of 10,000.

If 10,000 is divided into four equal parts, each part is worth 2,500, and we can use unitising to describe the similarities.

We know that 1/4 of 10,000 is 2,500, so 1/4 of 10,000 thousands must be 2,500 thousands.

That is, 1/4 of 10 million is 2,500,000.

And let's look at this composition and form some equations from our bar model.

We know 10 million divided into four equal parts and each part is equal to 2,500,000.

We could also say then that 10 million divided by 2,500,000 is equal to four.

We could also say that if we've got 10 million and we multiply it by 1/4 we get 2,500,000.

Or if we find 1/4 of 10 million, it would be equal to 2,500,000.

We could say four multiplied by 2,500,000 is 10 million.

And 2,500,000 multiplied by four is 10 million.

All those equations just from knowing one equation.

Let's have a go at working together.

I'm going to model completing some sentences using the bar models.

My bar model is 10,000 divided into five equal parts, and I'm going to relate that to 10 million divided into five equal parts.

And then I'd like you to repeat what I do but for a bar model where 10,000 or 10 million have been divided into 10 equal parts.

We know that 1/5 of 10,000 is 2,000.

So 1/5 of 10,000 thousands or 10 million must be 2,000 thousands.

So we can say 1/5 of 10 million is two million.

It's your turn to have a go at completing the sentences.

Use my structure to help you.

But remember, you are looking at when 10,000 and 10 million are divided into 10 equal parts.

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

How did you get on? Did you say that we know that 1/10 of 10,000 is 1,000? So 1/10 of 10,000 thousands must be 1,000 thousand.

And we can say 1/10 of 10 million is one million.

Let's now use the bar models to form equations describing the composition of 10 million.

I will model this showing the composition of 10 million divided into five equal parts, and then I'd like you to have a go at the composition of 10 million divided into 10 equal parts.

So I can say, 10 million divided into five equal parts, each part has a value of two million.

And then I can use that equation to form other equations.

We could say 10 million divided by two million is equal to five.

We could say that 10 million multiplied by 1/5 is equal to two million, or finding 1/5 of 10 million is also equal to two million.

We could say five multiplied by two million is equal to 10 million, and two million multiplied by five is equal to 10 million.

Could you use the structure of my equations to form your own equations related to the composition of 10 million? Pause the video while you have a go.

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

How did you get on? Did you form your first equation by using the bar model? 10 million divided by 10 is equal to one million.

And then we could say that 10 million divided by one million is equal to 10.

And then 10 million multiply by 1/10 is equal to one million.

We could say 1/10 multiplied by 10 million is equal to 1,000,000.

And 10 multiplied by one million is equal to 10 million, and one million multiplied by 10 is equal to 10 million.

How did you get on with those? Well done.

It's your turn to practise now.

For question one, could you read the scales? What numbers are shown by the given letters? For question two, could you fill in the missing numbers in these equations? And for question three, could you solve this problem? "In 2023, the population of Portugal was about 10 million.

At that time, about 1/5 of the population was over 60 years old.

Approximately how many over 60s lived in Portugal in 2023?" Pause the video while you have a go at those three questions.

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

How did you get on? For question one, you are asked to read the scales.

So if we look at part A, the whole, 10 million has been divided into 10 equal parts.

Each part must be worth one million.

So the value of A, at the end of the second part, is 2 million, B 5 million and C 8 million.

For part B, the whole of 10 million has been divided into four equal parts.

Each part must be worth 2,500,000, and E then would be 7,500,000.

For part C, the whole has been divided into five equal parts.

Each part must be worth 2 million.

F would then be 4 million and G would be 8 million.

For question two, you had to fill in the missing numbers in the equations.

10 million divided by four would be 2,500,000.

Two million is equal to 10 million divided by five,.

1/10 of 10 million is equal to one million.

Four multiplied by 2,500,00 would be equal to 10,000,000.

And 1/4 of 10 million is equal to 2,500,000.

For question three, you had a problem to solve.

And I represented this in a bar model.

My whole is 10 million and we know we need to divide the whole into five equal parts, because we want to find 1/5.

10 million divided by five is equal to two million.

So in 2023, we can say there were about 2 million over 60s living in Portugal.

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

Fantastic learning today.

Really impressed with how hard you have tried and that's what's really important.

When we try really hard, we can be successful.

You have really deepened your understanding of the composition of seven or eight digit numbers.

We know we can use unitising to support the composition of seven or eight digit numbers.

We know one million is composed of two equal parts of 500,000, four equal parts of 250,000 and five equal parts of 200,000, or 10 equal parts of 100,000.

We know 10 million is composed of two equal parts of five million, four equal parts of 2,500,000, five equal parts of two million or 10 equal parts of one million.

I have loved my time learning with you today.

I look forward to learning with you again, soon.