Lesson video

Hello there, my name is Mr. Tilstone.

It's lovely to see you, and it's lovely to work with you today on this lesson, which is all about four digit numbers.

If you're ready, I'm ready, let's begin.

The outcome of today's lesson is, I can use place value and number facts to decompose numbers in different ways.

And we're going to be thinking particularly about four digit numbers.

We've only got one keyword today, my turn, partition, your turn.

Have you heard that word before? Can you remember what it means? Would you describe it, explain it? Well, the act of splitting an object or value down into smaller parts is called partitioning.

For example, 57 could be partitioned into 50 and seven.

It could also be partitioned into 40 and 17, amongst other ways.

Our lesson today is split into two different cycles; place value in four digits, and partitioning four digit numbers in different ways.

So if you're ready, let's start by thinking about the place value in four digit numbers.

In today's lesson, you're going to meet Lucas and Sofia.

Have you met them before? They're here today to give us a helping hand with our maths.

Can you help Sofia to count in thousands? I bet you can do this.

I bet you're going to be good at this.

You've seen thousands before, I'm sure.

1000, what's coming next? 2000.

3000.

This is easy, isn't it? Let's keep going.

4,000.

5,000.

6,000.

7,000.

8,000.

9,000.

And finally, 10,000.

So if you can count from one to 10, you can count from one to 10,000 no problem.

So we've got a number line from zero to 10,000.

The numbers can be represented using Base 10 blocks.

And maybe you've got some of these in your classroom.

Don't worry if you haven't, but if you have, that's even better, and you can be using those alongside this.

So that's 1000, so that big cube represents 1000.

How could we represent 2000 then? Two cubes, 3000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000.

And if you had 10 of those big cubes, you would have 10,000.

You can represent any four digit whole number using Base 10 blocks.

So starting with that big block representing a thousand.

You can use the other ones as well.

So, the 1000 looks like this, as we've already established.

The 100 looks like this.

Have you got one of those in front of you? That's a hundred.

You can count, don't do it, but you can count a hundred little squares in that.

So that's representing a hundred.

The 10 looks like that.

You can count that very easily.

There's 10 of those little squares inside that.

And one looks like this.

So a thousand, a hundred, a 10, and one.

Let's think about some specific four digit numbers then, and how we can represent those with Base 10 blocks.

This four digit number, whole number, has been partitioned into thousands, hundreds, tens and ones.

And it's 1,342.

A four digit number.

It's got four digits, it has some thousands, it has some hundreds, it has some tens, it has some ones.

It's got four parts.

So 1,342.

There's one 1000, and we could represent that with one of those big blocks.

There are three one hundreds, and that's how we could represent that, with three of the big squares.

There are four tens, and that's how we can represent that.

And what about the two? Two ones, and that's how we can represent that.

So that number is worth 1,342.

That is what it is representing.

Blank counters can be used alongside a place value grid to represent the numbers.

Have you got some counters in front of you? So let's have a look at this number, same number as before.

So we've got 1,342.

The one counter represents 1000.

1000.

There are three counters, the three counters that represent three hundreds or 300.

The four counters that represent four tens or 40.

And the two counters represent two ones or two.

1000.

300.

40.

Two.

Add them together, we've got 1,342.

So 1000 plus 300 plus 40 plus two equals 1,342.

Let's have a little check.

What number has been made here? Complete the stem sentences under each set of counters.

Pause the video, welcome back, let's have a look.

There's five counters here, so the five counters represents five thousands or 5,000.

That's how we write that.

The two counters represent two hundreds or 200.

The six counters represent six tens or 60.

And the three counters represent three ones or three.

5,000 plus 200 plus 60 plus three equals 5,263.

And very well done if you got that number.

Let's have another check.

If you've got some place value counts in front of you and you've got the grid, use your place value grid and counters to create 3,572.

And again, can you use those stem sentences? Pause the video.

What did you get? Let's have a look, did you do this? Three, the three counters represents three thousands or 3000.

What have we got here, five.

The five counters represent five hundreds or 500.

What did you put in the next one? Seven, the seven counters represent seven tens or 70.

And then what do you do in the last one? Two, the two counters represent two ones or two.

3000 plus 500 plus 70 plus two equals 3,572.

So well done if you represented that number in that way.

You may or may not have seen one of these before.

This is a Gattegno chart, it's very useful.

By placing translucent, so you can almost see through them, counters on one number from each row, different four digit numbers can be made.

Let's look at an example.

So we've got this translucent counter, we put that over the 3000.

And in our place value grid, we can write three there.

Here we're placing it over the 500.

How many hundreds is that? Five.

Here we're placing it over the 70, how many tens is that? Seven.

And we're placing a counter over the two.

How many ones is that? Two.

So what number have we made here? 3000 plus 500 plus 70 plus two equals 3,572.

And that is how we say it, 3,572.

Okay, what number am I creating here? Follow along on your Gattegno chart if you've got one in front of you.

It has a 30.

Can you place a counter on the 30? Should be there.

What else has it got? Did you notice, by the way, I didn't start with the thousands there.

Will that matter? It has an 8,000.

That's one of its parts.

Can you place a counter on 8,000? It's just there.

Got two other parts, what else has it got? Got seven.

Place it on the seven.

Seven ones.

Just there.

It's got a 200.

Can you place your counter on the 200? Just here.

That's the parts that it's got.

30 plus 8,000 plus seven plus 200.

Does it matter that those numbers weren't in order starting with the thousands? Not really, we've still got the number.

Is it 3,872? No, that's not how many thousands we've got, is it? It's 8,237.

And you can read that very clearly by going from top to bottom.

8,237.

That's how it looks, that's how we would write it, and that's how we say it.

Say it with me, 8,237.

Let's do a little check, over to you.

Create this number on your Gattegno chart, and write and say that number.

So it's got an eight, a 20, a 7,000 and a 500.

Can you make that, can you write it, can you say it? Pause the video.

Let's have a look.

There's your eight, there's your 20, there's your 7,000, there's your 500.

Pop all of those together and you've got 7,528, and that's how we say it.

7,528.

Well done if you got that.

What number is being represented here? We can use those stem sentences to help.

So let's have a look.

And first of all, before you do that, do you notice something? Hmm, something about this number that's a bit different to the other numbers that we've seen before.

Something's missing, or is it? The three counters represent three thousands or 3000.

The five counters represent five hundreds or 500.

The seven counters represent seven tens or 70.

And how can we say the next part? There's nothing there.

So we can say the zero counters represent zero or zero.

Put those parts together, we've got 3000 plus 500 plus 70 plus zero, and that is 3,570.

That's how we write it and that's how we say it.

Oh, what do you notice here about this one? Something similar to the last question, isn't there, but not quite the same.

Something missing again.

Let's use a stem.

The three counters represent three thousands or 3000.

The five counters represent five hundreds or 500.

Hmm, what about this next one, the tens? There's no tens, how can we say it? The zero counters represent zero tens or zero.

And what about the last one? The two counters represent two ones or two.

So let's put those parts together.

That's a 3000, a 500, a zero, and a two.

And that makes 3,502.

That's how we write it, that's how we say it.

What about this one? Hmm, something missing again, isn't there? Let's explore.

The three counters represent three thousands or 3000.

Tricky part, what we're gonna say here? The zero counters represent zero hundreds or zero.

What about the next one? The seven counters represent seven tens or 70.

Last one.

The two counters represent two ones or two.

Let's put those parts together.

That gives us 3000 plus zero plus 70 plus two, and that is 3072.

That is how we write that, and that is how we say that.

3072, that's quite a tricky number to write.

Let's have a check.

There's a part missing on this one.

What number is being represented here, and please use that stem sentence.

Off you go.

Let's see.

The four counters represent four thousands or 4,000.

The three counters represent three hundreds or 300.

The zero counters represent zero tens or zero.

And the five counters represent five ones or five.

That gives us 4,000 plus 300 plus zero plus five.

Put all those parts together and we've got 4,305.

That's how we write it, that's how we say it.

Well done if you've got that.

It's time for some practise.

So you've got some resources hopefully in front of you.

Maybe you've got some Base 10 equipment, maybe you've got counters, maybe you've got a Gattegno chart, maybe you've got a mixture of all of them.

So however you want to do this, represent the numbers using manipulatives.

So have some fun with that.

Number two, complete these questions.

Number three, which four digit numbers can be made using the digit six, zero, two, and four? Explore that using your Gattegno chart.

Can you be systematic about that? Hmm, can you use a system rather than doing it randomly? Number four.

Four number cards make a four digit number by placing seven in the tens column, four so that it has the highest value of all the digits, and the remaining two digits so that three has the highest value.

Lots to think about there.

Have a good think and have a go at that.

And number five, using the digits five, two, nine, and four, make the following largest possible odd number, smallest possible odd number, largest possible even number, smallest possible even number.

Have some fun exploring that, and I'll see you soon for some feedback.

Welcome back, how did you get on? Let's have a look.

So number one, let's say you used a good Gattegno chart.

You might not have done, you might have used Base 10 or counters, but this is a Gattegno chart.

So, that's 2,135.

That is 3082.

Tricky one there 'cause of that part missing, so we used a zero for the placeholder.

That is 3,502.

That is 3,580.

Now, this one where you were given four different parts but in a sort of jumbled order, that is 2,354.

And this one, again they're jumbled.

We could represent it this way.

Easy to see we've got 2054.

And that's quite a tricky one to write.

2054, that's how we write it and that's how we say it.

Number two, put those numbers together, you've got 2,932.

Put those together, you've got one of the parts missing there, so that's 4,083.

For C, they jumbled up, but that's 9,478.

They jumbled for D as well and there's a part missing, so that's 9,078.

5,543 is split into four parts.

They are 5000, 500, 40 and three.

6,427.

What's the missing part there? We've been given 6,000, the 20 and the seven.

What's the four? That's 400.

And then 7,834.

We've got three of the parts, but they're jumbled at this time.

So we've got the four, we've got the 7,000, we've got the 800.

It's that three we haven't got.

What's the three worth? 30.

And then for eight, 6,040.

That's 6000 and 40, that had two parts missing.

And then number three, which four digits can be made using the digit six, zero, two and four? So the example on this Gattegno chart shows 6,420, and that's the largest digit that can be made, and that's the system that I'm using here.

I'm starting with the largest possible one and then working down to the smallest.

That way I can be sure when I've got them all.

So the possibilities are 6,420, that one.

6,402.

6,240.

6,204.

6,042.

6,024.

They're all your 6,000 ones, we've got some 4,000 ones.

They are 4,620.

4,602.

4,260.

4,206.

4,062.

4,026.

And then we've got some 2000 possibilities.

2,640.

2,604.

2,460.

2,406.

2064 and 2046.

Why can't we start with a zero then? Because if we did that, it would create a three digit number, and that's not what the question asked for.

Number four then.

The seven will go there.

That's seven's in the tens column, that's what it's asking for.

Four, so that it's got the highest value of all the digits.

So where do you put it if it's got the highest value? There, in the thousands.

The remaining two digits so that three has the highest value.

So where would you put three? What's the highest place value left? There, and then that just leaves the five.

So 4,375 is the right answer.

And then make the largest possible odd number.

Let's start with that.

Well, it's an odd number, so it must end in five or nine.

They're your two odd numbers.

Using the nine for the thousands will make a much bigger number than using the five was, so that's what we're going to do.

So if nine's there, that must mean five is there.

It's an odd number.

Of the remaining two digits, four is the largest, so it should go in the larger place value, which is the hundreds.

So that's where that's going to go.

And that just leaves the two.

So the largest possible odd number is 9,425.

Well, then if you got that, what about the smallest possible odd number? That's 2,459.

The largest possible even number, 9,542.

The smallest possible even number, 2,594.

Well, then if you got those, little bit of thinking going on there, wasn't there? Okay, let's move on to the next cycle.

Partitioning four digit numbers in different ways.

The partitioning of four digit numbers can be shown by creating part-part-whole models.

So that's got some parts.

One, two, three, four parts.

What do the one represent, what does the three represent, what does the four represent, what does the two represent? I think you'll be good at this.

The one represents 1000.

The three represents, what do you think? 300.

The four represents 40, and the two represents two.

So this is the same thing you've already done in cycle A.

Now, equations can be created by covering up parts of the model.

So using your hand, you can cover up some of those parts to make some subtraction.

So if we covered up that part, that is saying 1,342.

Take away, that's what you're covering up, the thousand.

What does that give us, what's left? 342.

What if you did this, what's that showing? That's showing 1,342.

What we're taken away, what we covered up, the 300.

So 1,342 take away 300, what's left? What number can you read there? That's 1,042.

What if you did that? That's 1,342, and you're covering up the 40, you're taking away the 40.

What number can you see left? 1,302.

And then what if you did that? 1,342, take away the two, what's left? 1,340.

Okay, over to you, let's have a check.

You've got a new four digit number.

Partition it and give some subtraction equations by covering one part at a time.

So use that stem sentence as well, please.

Pause the video and give it a go.

Let's have a look.

So the four represents 4,000.

The six represents 600.

The three represents 30, and the two represents two.

And then you can use your hand to cover up different parts of that.

And that gives us these equations, 4,632, takeaway 4,000 equals 632.

4,632, take away 600 equals, what can you see left? 4,032.

4,632, take away the 30 this time gives us 4,602.

And then 4,632, take away the two this time.

What can you see left? That's 4,630.

A four digit number can be partitioned in lots of different ways by combining or moving parts.

Now, if you've got some of these place value counters, they're going to be really helpful here.

Don't worry if you haven't, you can still do it without them, but they're going to help and support your thinking.

So we've got 1,342, but the part-part-whole model is only showing three parts.

So what could we do here? How could we partition it in different ways? By moving those counters about, let's have a look.

What if we did this? What if we combine the thousand and the hundreds together for one part.

That would give us three parts.

What three parts can you see? I can see 1,300, I can see 40, and I can see two.

So just by moving the counters around a little bit, that's three different parts.

Okay, what about this one? What three parts can you see there? You might have noticed the tens and the ones have been combined to make one part.

What can we see? I can see 1000, I can see 300, and I can see 42.

What about now, what can you see now? Now, this one's been grouped unusually, because we've used one of the hundreds with a thousand, but kept the other two as a part by themselves.

So what three parts can you see here? I can see 1,100, 200, and forty two.

That's our three parts.

What about now? Again, quite an unusual one.

One of the tens has been regrouped with the ones.

And the hundreds and the tens have been grouped together.

There's so many ways you can group these counters, by the way.

That gives us 1,330 and 12.

That's three parts.

Now, a four digit number can be partitioned into two parts in a similar way.

There are a huge number of possible ways to partition.

You could be at this all day.

Let's look at some.

What about if we did that? Combine the thousands, the hundreds and the tens together, and just left the ones as a separate part, what would that give us? That gives us 1,340 for one part and two for the other one.

What about this? Different parts, can you see? So we've taken the 10, two have stayed in one group and two in the other.

What have we got, what two parts have we got? We've got 1,320 in one part and 22 in the other.

Let's have a check.

Which of the following are possible ways to partition 4,672? There is more than one option here, by the way.

You may wish to use place value counters and part-part-whole models if you've got them.

That will make this a lot easier.

Okay, pause the video, give it a go.

Let's see, is it possible to have 4,672? Yes, it is.

Is it possible to have 3000 and then 1,672? Yes, it is.

One of the thousands has been regrouped with the 672.

Is it possible to have 4,100 as one part, 570 as another, and two as another? Yes, it is.

One of the hundreds have been regrouped with the thousands.

Is it possible to have 4000, and 500, and 72? No, that's changed their number.

The number's been partitioned, but then it's been reduced by 100, so that's not the same.

Okay, you've got some problems to solve that are going to use those skills.

So you're going to apply those skills, and they've got a bit of a measures theme.

And you may have had some very recent experience using measures, so read those very carefully.

And then number two, how many ways can you partition 6,952 into two or three parts? And as I said before, there are lots and lots of ways.

So don't stop when you've got a few, just keep going.

And again, if you've got some counters in a part-part-whole model, you can use those too, but you don't have to.

Okay, pause the video.

Have fun with that and I'll see you soon.

So number one, that's 9,570 kilometres.

Take away, subtract that 9,000.

So you could cover that up, couldn't you, with your hand? And that will give you 570 kilometres.

B, 4,850 grammes.

Take away the 800, cover that up, and that leaves you with 4,050 grammes.

1,275 millilitres, take away 70 millilitres.

Cover that part up, that gives you 1,205 millilitres.

And then how many ways can you partition that number? Lots, there are many, many, many ways to partition that.

But for example though.

Number two, how many ways can you partition 6,952 into two or three parts? The answer is lots, lots and lots.

And I hope you've got lots of possibilities, and here are just some.

So into two parts, it could be 6,800 in one part and 152 in another.

And in three parts, it could be 5,800, 1000, and 52.

Hope you had fun finding lots of different ways, and maybe you had a system too.

We've come to the end of the lesson.

Today's lesson has been using place value and number facts to decompose four digit numbers in different ways.

Four digit numbers can be partitioned into thousands, hundreds, tens and ones.

They can also be partitioned in other ways.

Various resources and models, such as Base 10 equipment, place value counters, plain counters, place value grids, Gattegno charts, part-part-whole models, all sorts of ways we can use to represent these parts.

Showing how they can be composed and decomposed.

In this example, we've got a good old Gattegno chart, and it's showing 3,572.

I've really enjoyed today's lesson.

Hope you have too, and I hope you've learned lots.

Enjoy the rest of your day, whatever you've got in store.

Take care and goodbye.