Lesson video

Hello.

I trust you're feeling well today.

My name is Dr.

Shorrock, and I'm very much looking forward to taking you through our learning today.

We are gonna have great fun together.

Today's lesson is from our unit, Order Compare and Calculate With Numbers With Up To Eight Digits.

This lesson is called Composition of Seven Digit Numbers.

As we move through the learning today, we are going to deepen our understanding of how larger numbers are composed and the different ways in which we can read the same number.

Now, sometimes new learning can be a little bit difficult, but that's okay, I am here to guide you.

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

So let's get started then, shall we? How are seven digit numbers composed? These are our key words for the learning today.

We have addend, minuend and subtrahend.

It's always good to read new words aloud.

So let's have a go at this together.

My turn, addend.

Your turn.

Nice.

My turn, minuend.

Your turn.

Lovely.

And my turn, subtrahend.

Your turn.

Fantastic.

An addend is a number added to another number to give a sum.

The addends are the parts in an addition equation.

The first number in a subtraction, the whole, well that's known as the minuend.

And the minuend is the number from which another number, the subtrahend or the part, is to be subtracted.

So let's get started with our learning today, shall we? Let's have a look at the composition of seven digit numbers.

And today we have Aisha and Lucas to help us.

Lucas and Aisha are learning about the composition of the number 1 million.

They've represented 1 million on a place value chart.

The digit one is worth 1 million.

1 million has got no thousands or ones, Lucas is saying.

Would you agree with him? Oh, Aisha doesn't.

She's respectfully challenging him.

I wonder why she might be challenging him.

Well let's look at the composition of 1 million, in terms of one hundred thousands.

We know that each power of 10 is composed of 10 of the previous power of 10.

So we can represent 1 million on our place value chart and we know that it must be composed of 10 of the previous power of 10.

So 1 million is composed of 10 one hundred thousands.

So even though the digit in the hundred thousands place of 1 million is a zero, actually 1 million is composed of 10 one hundred thousands.

But because there's 10 of them, it means that we have put a one in the one millions place because we don't put 10 in any of these place value places do we? It's represented there in the place value chart just to show you.

So let's look at the composition of 1 million in terms of ten thousands.

We can represent 1 million on a place value chart.

We know 1 million is equivalent to 10 one hundred thousands.

So how many ten thousands do you think will be equivalent? That's right.

1 million is composed of 100 ten thousands.

So even though the digit in the ten thousands place of 1 million is a zero, 1 million is actually composed of 100 ten thousands.

Let's check your understanding with that.

Could you complete the sentence describing the composition of 1 million? You can see I've represented 1 million in the place value chart for you.

1 million is composed of mm thousands.

So pause the video, maybe find someone to talk to about this and when you are ready to go through the answers, press play.

How did you get on? Did you say 1 million is composed of 1,000 thousands? Even though the digit in the thousands place of 1 million is a zero, 1 million is actually composed of 1,000 thousands.

So, Aisha and Lucas are now comparing two numbers.

Can you read those numbers? Should we read them together? 1,240,056.

916,753.

Well done.

Lucas is saying that 916,753 is composed of more hundred thousands than 1,240,056 is.

Do you agree with him? Aisha doesn't, she's respectfully challenging him.

Why might she be challenging him? So let's represent these on the place value chart.

Good idea.

We've represented both numbers on the place value chart and we can see Lucas is correct.

916,753 is composed of 900 thousands.

But what about 1,240,056? Well, even though 1,240,056 has the digit two in the a hundred thousands column, it's not composed of two hundred thousands is it? It's composed of 12 hundred thousands.

Because if we remember, 1 million is composed of 10 hundred thousands and we have another 200,000.

So that's 12 hundred thousands.

Well, Lucas wants her to prove it, he's not too sure yet, is he? So we know that each power of 10 is composed of 10 of the previous power of 10.

And we can partition 1,240,056 into its parts.

But we also know that 1 million is the same as 10 one hundred thousands.

And 10 one hundred thousands add those two one hundred thousands is 12 one hundred thousands.

We can represent this in an equation.

1 million add 200,000 is equal to 1,200,000.

And it's usually read as 1,200,000.

But we can also read it as 12 hundred thousand.

So if we revisit our original number, 1,240,056, is usually read as one million, two hundred and 40 thousand and 56, but it can be read as 12 hundred and 40 thousand and 56.

1,240,056 has the digit two in the hundred thousands place, which is worth 200,000.

But 1,240,056 is actually composed of 12 hundred thousands.

Aisha shows how to write this composition as an equation.

So you can see 1,240,056 is composed of 1,200,000 or 1,200,000, add 40,000, add 50, add six.

And it's not been fully partitioned has it, by doing it like this? We've partitioned the hundred thousands together.

So the 1 million, that's 10 hundred thousands, and that 200,000, they've been partitioned together.

Let's check your understanding on this.

Could you look at this number and then complete the sentences? The value of the digit six is mm, the number is composed of mm one hundred thousands and then complete the equation.

Pause the video while you do that.

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

How did you get on? Did you say the value of the digit six is 600,000? But how many one hundred thousands is this number composed of? That's right, 16.

Because that 1 million is equivalent to 10 one hundred thousands, then another six one hundred thousands.

So we have 16 one hundred thousands.

And we can represent this partitioning as an equation.

1,605,431 is equal to 1,600,000, plus 5,000 plus 400, plus 30, plus one.

How did you get on with that? Well done.

It's your turn to practise now.

For question one, looking at this number, could you complete the sentences below all talking about its composition, and the equations that go with it? For question two, could you complete the equations using the inequality or equal signs? For question three, could you tell me if this statement is true or false? And then give a reason for your answer.

The statement is, 7,000 thousands is the same as 70 hundred thousands.

Hmm, be interesting to see what you think there.

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

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

How did you get on? So for question one, you had to look at this number and complete the sentences.

The number was 3,719,520.

And it is composed of 37 hundred thousands.

We've got seven, the digit seven, in the a hundred thousands place.

But remember each million is made of 10 one hundred thousands, and there are three millions.

So that must be 30 hundred thousands.

Add the seven that's already there, 37 hundred thousands.

And then we can write an equation to show that.

3,719,520 is equal to 3,700,000, or those 37 hundred thousands, add 10,000, add 9,000, add 500, add 20.

And then we could look at the composition of this number in relation to ten thousands.

So there must be 371 ten thousands.

And again we can write an equation for that.

3,719,520 is equal to 3,710,000, plus 9,000, plus 500, plus 20.

Then we can look at the composition of this number in relation to thousands.

3,719,520 is composed of 3,719 thousands.

And we can write an equation to show that is equal to the parts 3,719,000, add 500, add 20.

For question two, you are asked to complete the equations using the inequalities or the equals sign.

2,000,000, well that must be greater than 20 thousand.

Because 2 million has 20 hundred thousands.

2 million must be greater than 200 thousand, because again we've just said, the 2,000,000 is equivalent to 20 hundred thousands, not 200 thousands.

So then it must be equal to 2000 thousands.

1,300,000 must be greater than 13 thousand, because we've got 1300 thousands.

It must also be greater than 130 thousand, because we've got 13 hundred thousands.

So then it must be equal to 1,300 thousands.

2 million must be greater than 2 hundred thousand, because it would be 20 hundred thousand.

And so 2 million is equal to 20 hundred thousand, because each million is worth 10 hundred thousand, so there's 20 hundred thousands.

2 million must be less than 200 hundred thousand, because 2 million is equal to 20 hundred thousands, And 200 hundred thousands are greater than.

For question three, is this statement true or false? And give reasons for your answer.

7,000 thousands is the same as 70 hundred thousands.

Well it's true and you might have given a reason like, 7,000 thousands is equal to 7 million, and 70 hundred thousands is also equal to 7 million.

Or you might have given a reason like, hundred thousands are 100 times larger than thousands, and 7,000 is 100 times larger than 70.

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

Fantastic learning so far.

You've tried really hard to understand and to deepen your understanding of the composition of seven digit numbers.

We're going to move on now and have a look at the part-whole relationship and unitizing.

Aisha and Lucas are playing a game.

Aisha says that she has collected 3 million pounds and Lucas has collected 200,000 pounds, and we're wondering how much more money Aisha has.

And we can represent this in a bar model.

So you can see, Aisha's is the whole amount and Lucas has a part.

And to find out that missing part, how much more will we need to subtract? And we can form an equation to help us.

3 million subtract 200,000.

But how are we going to calculate this? Aisha has remembered that unitizing supports us to calculate.

We know 3 million is composed of 30 hundred thousands.

We know, using our known facts, 30 subtract two is equal to 28.

So 30 hundred thousand subtract two hundred thousand must be equal to 28 hundred thousand.

And we can write that as an equation.

Let's check your understanding with that.

Could you solve this calculation? 4 million, subtract 400,000.

So have a think about using the language of unitizing and known facts.

What known facts might help you here? Pause the video, maybe talk to somebody else about this.

When you're ready to hear the answer, press play.

How did you get on? Did you realise you could use the known fact, 40 subtract four is equal to 36? Then 40 hundred thousand, 'cause that's the same as 4 million, and we're going to subtract the four hundred thousand, well that must be 36 hundred thousand.

And then we can write that in numerals.

So if we know 3 million subtract 200,000 is 2,800,000, well what else do we know? We could start by representing this in a bar model to help us.

So we know the whole is 3 million, one part is 200,000 and the other part is 2,800,000.

What else do you know from this? That's right, we could also know that 3 million subtract the other part, 2,800,000, will be equal to 200,000.

We could add the parts together.

2,800,000 add 200,000, well that must be equal to 3 million.

And then we could write the add-ins around the other way.

200,000 add 2,800,000 is equal to 3 million.

So we know all these four equations from that one first equation.

So if we know these, what else do we know? That's right.

We must also know these equations, where we can write the sum, or the difference, first.

So, yes, I am really impressed as well.

It really is a wow moment, Aisha.

From knowing one equation, we can determine eight facts just from knowing one fact.

That one bar model, where we had the whole and the part, we can determine all of these eight equations.

And we can use this knowledge to support us when we solve missing number problems. So let's look at this equation.

We've got 5,700,000 add something, is equal to 6 million.

What do we know? Well we know the missing part is an addend.

So we need to subtract the other addend from the sum.

So we know from our previous investigations that if we do this subtraction, that will tell us what the missing part is.

And unitizing supports us to calculate.

60 hundred thousand subtract 57 hundred thousand must be 300,000.

So we know the missing part is 300,000.

Let's look at this equation.

What do you notice here? What's missing? That's right, the missing part is the subtrahend.

So we need to subtract the difference from the minuend.

We need to do 4,000,000 subtract 3,000,000.

700,000.

And again, unitizing supports us to do this calculation.

We can say 40 hundred thousand subtract 37 hundred thousand.

Well that's equal to 300,000.

So the missing part is 300,000.

Let's check your understanding with this.

Could you complete these two equations? So have a think about what's missing and how do we find that missing part? Pause the video while you do that.

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

How did you get on? Did you know that to find the missing addend, you would need to subtract the given addend from the whole? 7,300,000 subtract 6,800,000 is equal to 500,000.

Because 73 subtract 68 is equal to five.

So the missing part is 500,000.

For the second equation, we were missing a part or the subtrahend.

So we know we need to subtract the difference from the whole, which gives us 400,000.

So the missing part, or subtrahend, is 400,000.

How did you get on with those? Well done.

It's your turn to practise now.

For question one, could you complete these equations? Think about what do you notice? What are we missing here? How's that going to help you? For question two, using knowledge of the part-whole relationship and unitizing, could you solve these problems? A, Lucas and Aisha play a game, in total they have scored 4 million points.

1,740,000 points have been scored by Lucas, so how many points did Aisha score? And part B, in his game, Lucas has won 5 million points, he spends some of his points buying new building resources.

He has 4,800,000 points left.

How many points did he spend? Pause the video while you have a go at 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 had to complete some equations.

You had to notice what was missing.

So for A, a part was missing, or the addend.

So to find the missing addend, we subtract the other addend from the whole.

400,000 subtract 360,000.

So we could use our known facts and unitizing there.

40 subtract 36 is four, so it must be 40,000.

For the next equation, again, we were missing a part, an addend.

So we had to subtract the other addend from the whole.

3,000,000 subtract 2,930,000 is equal to 70,000.

And for part C, again we were missing a part.

So we had to subtract the other part from the whole.

5,000,000 subtract 4,995,000 is equal to 5,000.

For question two you had to use knowledge of the part-whole relationship to solve problems. For part A, Lucas and Aisha are playing a game, they'd scored 4 million points in total and we can represent that as a whole in our bar model.

1,740,000 points were scored by Lucas, so that's one of our parts.

So we can form an equation, one of our parts, 1,740,000, added to the other part that we don't know, is equal to 4 million.

And we know if the missing part is an addend, then the other addend needs to be subtracted from the sum.

So we can form our equation, 4,000,000 subtract 1,740,000.

And we can use a unitizing and known facts to help us.

We can say 400,000 subtract 1,740,000 is equal to 2,260,000.

So Aisha must have scored 2,260,000 points.

Part B, in his game, Lucas won 5 million points and spent some money and had 4,800,000 points left.

And we represent that in a bar model.

So we can see we are missing the subtrahend.

We've got the whole and we've got the difference, how many points he had left.

And we know that if the missing part is the subtrahend, then the difference can be subtracted from the minuend, so we can form our equation that will help us solve this calculation.

5,000,000 subtract 4,800,000.

We can unitize to help us.

50 hundred thousand subtract 48 hundred thousand is equal to 200,000.

So Lucas spent 200,000 points.

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

Fantastic learning today everybody.

I am really super impressed with how hard you tried, and how much deeper your understanding of the composition of seven digit numbers is now.

We know that known facts and unitizing can be applied when partitioning seven digit numbers.

We know if the missing part is an addend, then the other addend is subtracted from the sum.

And we know if the missing part is the subtrahend, then the difference is subtracted from the minuend.

So well done today, well done for trying your hardest.

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

Until then, goodbye.