Lesson video

Hello, everyone! Thank you for joining me today.

My name is Ms. Jeremy, and today's math lesson is focused on place value.

For today's lesson, all you will need is a piece of paper and a pencil, and a nice quite area to work in.

So, just spend a bit of time getting yourself ready with no distractions, and once you're ready, we'll begin our lesson.

Okay, so let's start with our agenda for today.

So, we're going to start off with a quick warmup where we will be representing four-digit numbers using means.

We're then going to be looking at counting upwards in hundreds and one thousands, and we'll be using place value counters formats.

I will also be representing five-digit numbers and partitioning five-digit numbers before our independent task and quiz at the end.

I've also thrown in a little challenge at the end to see how you get on with that.

So, lots to pack in today.

Let's get started.

As I said before, if you don't have a pencil and paper today, do get yourself sorted with those first in a nice quiet atmosphere ready to get learning.

Once you're ready, come back and join us and start the video.

So, we're going to start with our warmup.

We're going to be looking at representing four-digit numbers, Numbers with thousands, hundreds, tens, and ones, and we'll be looking at how we can represent those numbers, that means show those numbers using Dienes.

As you can see on my screen here, I've got some Dienes that are representing, that means showing, a four-digit number.

What I would like for you to try and work out is how we can represent this number using a place value chart instead.

So, what numbers would I put inside my place value chart? What number is being represented by these Dienes? I'm going to give you ten seconds to work out what you think the number is.

Are you ready? Off you go.

Did you get it? Okay, let's look at it together.

So, here I can see that I've got thousands, which are these big cubes here, I've got hundreds just here, tens just over here, and my ones are just here.

If you can see my huge thousands here, my thousands are represented by these big blocks, and I know that they're thousands because I can see that one thousand of those small one Diene cubes would fit into one of these big thousand cubes.

So, I need to work out how many thousands I have.

Let's count them.

One, two, three, four.

I've got four thousands.

So, I'm going to need to write the digit '4' in my thousands column.

Now let's look at my hundreds.

How many hundreds do I have? As you can see, I've only actually got one hundred here, so I'm going to write the digit '1' in my hundreds column.

Here, I'm looking at my tens, and I've got four tens, so I'm going to write '4' in the tens column.

And now I'm going to count my one Diene cubes.

I've got one, two, three, four, five, six, seven.

I've got seven ones, so I'm going to write the digit '7' in my ones column.

As you can see here, my number is -let's say it together- 4,147.

And if we look at the digits I've written in, we can see I've written the number four twice, the digit '4' twice, but they have very different values.

The four in my thousands column has a value of -let's say it together- 4,000, whereas the four in my tens column has a value of -let's say it together- 40.

So, even though I've written the same digit twice, they have very different values depending on where they're placed in my place value table.

Okay, let's look at our main task.

The first thing we're going to be doing today is counting up in hundreds, and we're going to be starting with four-digit numbers which we looked at in our warmup.

So, let's have a look at the first problem together.

Let's read it.

It says, these long distance runners have run 9,200 metres.

They have 400 metres left to run.

And the part in purple is our unknown information.

It asks, how far will they have run in total? The first thing that I'm going to do is I'm going to see if I can write down an equation to demonstrate this problem.

So, I'm starting with the information that I know.

I know that the long distance runners have run 9,200 metres so far, and.

Oh, I beg your pardon.

Just rub that out.

And they're going to run an additional 400 metres.

We want to know how much that is in total.

So, as you can see here, I've actually represented 9,200 using place value counters.

I've got nine thousands.

That's equal to 9,000.

And two hundreds, and that's equal to 200.

Overall, that's 9,200.

I'm going to need to add 400 to my place value charts.

Have a think.

Which of the columns will I need to add my 400 to? I'm going to need to add to my hundreds column, so I'm going to add four place value counters, each equal to a hundred.

One, two, three, four.

And that's the great thing about place value counters.

They're so easy to draw.

If you want to, you can even add a hundred at the top here to show that that is equal to a hundred, but actually, because it's in the hundreds column, we know it's value.

Here I've represented 9,200 plus 400.

Let's see what my answer is.

Well, I've still got 9,000, but this time, I've got one, two, three, four, five, six hundreds.

I've got no tens, and I've got no ones.

So, my answer is 9,600.

You can see what we've done there is represent, which means to show, an equation involving four-digit numbers, and our answer is 9,600 metres.

I need to make sure I add in my unit of measure.

Let's have a look at a question that's slightly more challenging now.

Let's read this one together.

These long distance runners have run 9,200 metres.

They have two laps of 400 metres left to run.

And the part in purple is our unknown information.

How far will they have run in total? So, again, I'm starting with exactly the same number, and I'm going to write my equation to begin with.

I'm starting 9,200, but this time, instead of adding 400, I'm adding two lots of 400.

I'm going to use my known number facts to help me here.

So, I know that two times four is equal to 8.

So, two times four hundred must be equal to 800.

I'm adding 800.

And once again, what I'd really like to do is represent this using my place value table and using place value counters.

So, I'm going to begin by representing 9,200 on my place value chart.

Spend five seconds now working out where I'm going to put my place value counters.

Brilliant.

You should have known, or should have seen there, that I'm going to put nine of these place value counters in my thousands.

That's eight and nine.

And then I want two hundreds just here.

I'm going to be adding on 800, so I'm going to need to be focusing on my hundreds column to add my 800.

Let's add our 800.

I'm going to have to add 800 in here.

One hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eight hundred.

So, there.

I've represent using my place value counters on my place value chart, I've represented 9,200 in the blue, adding on 800, which I've represented in red.

Let's see what my answer is.

Well, I haven't changed my thousands, but now I've got one, two, three, four, five, six, seven, eight, nine, ten in my hundreds.

This is a bit tricky because I can't have a two-digit number, the number ten, in one column.

What I'm going to need to redo is regroup all of these hundreds, my ten hundreds, and reground them for one one-thousand.

One thousand there.

So, now you can see I've got ten thousands.

But again, I've got a problem.

Can you work out what my problem is? I'll give you five seconds.

So, my issue here is that I've got ten in my thousands column, and I can't put a two-digit number in one column again.

It's the same problem I had in my hundreds.

So, I'm going to need to take these ten thousands, and I'm going to need to regroup them for one ten-thousand.

So, there you can see I've got my one ten-thousand.

I haven't got anymore thousands left.

I haven't got anymore hundreds left.

I never had any tens and ones.

So, my answer is 10,000, and I want to write it just here.

This is our first five-digit number, and the number is 10,000.

Okay, let's have a look at our next question.

So, this time we're going to be counting up in thousands again, but with a number line.

As you can see here at the top of my screen, I've got a number line, which has some four-digit numbers on and some five-digit numbers on.

I'd like us to say them together.

Let's start with the first number.

The first number is 7,350.

Then, 8,350.

9,350.

10,350.

11,350.

What we're going to try and do is work out what the next number on our number line is likely to be.

You might already have heard a little bit of a pattern coming along as we read those numbers out, and you might already know what the answer is.

What I'd like us to do is to represent this problem using place value counters, digits, and then look at what it might be based on that, just to prove that we're correct.

So, what I'm going to do first of all, is I'm going to have a go at representing 11,350 on my place value chart using place value counters, and using digits.

Let's give that a go.

So, I can see straight away, I've got one ten-thousand.

I've got one thousand.

I've got three hundreds.

I have five tens, and I don't have any ones there.

So, that represents 11,350.

Now what I'm going to do is just add in my digits just below to demonstrate exactly what I've shown you using my place value counters.

11,350.

I'm going to be adding on one one-thousand.

So, the column we need to focus on is our thousands column.

This is the column that is going to be focused on when we add in our one one-thousand.

So, let's have a go at adding in this one one-thousand.

I'm going to add it in just here, and I'm going to change this into a two because I now have two thousands in this column.

So, actually my answer now, the next number on our number line is 12,350 as you can see there.

No other digits have changed.

I've just focused on changing my thousands.

With that in mind, take ten seconds now to work out what the next number will be on our number line.

Did you get it? Hopefully you've seen that here, if we just look at our thousands column, the digit in our thousands column is currently a '2', that means two thousands.

If we add on one extra thousand, our next number will be 13,350.

So, I can rub out or question mark and add in our 13,350 just up here.

Brilliant.

You can do this exact same method for adding on a thousand, use your place value counters to help you out.

So, let's have a practise at this.

What I'd like you to do is have a look at the number line that we've got here.

Instead of having four- and five-digit numbers here, we've just got five-digit numbers.

Let's start by reading them together.

Let's start with the first one.

The first number is 17,249.

The next number is 18,249.

The next number is 19,249.

What I'd like you to have a go at doing is working out what the next three numbers in our number line sequence are.

There are two methods you can use.

The first method is you can draw your place value charts, drawing your place value counters, the 19,249, and then add on a thousand to see what your answer is for the next number in our sequence.

Remember, you might need to do a bit of regrouping for this one.

The second method you might like to use is to do what we did previously, which is look at the number, the digit in the thousands column, and see what that would be if we were to add on an extra thousand.

Whichever one method you'd like to use.

Spend a bit of time working out the next three digits, the next three numbers, in our number line sequence.

Pause the video to complete the task, and resume it once you're finished.

So, hopefully you've had an opportunity now to have a go at working out the next three numbers in our sequence.

Let's have a look at it together.

I'm going to use method number two, where I look at the digit in the thousands place and see if I can add on an extra thousand.

I'm going to start by looking at the number 19,249, and the digit in my thousands place is the digit '9.

' Let's try and add on an extra thousand.

I've got a little bit of a problem, though.

If I try and add an extra thousand onto the nine, the nine becomes ten thousand instead.

And actually, I can't fit two digits, a ten, inside that column, so I'm going to need to regroup, and I'm going to need to change my ten thousand, as well.

So, the next the number in my sequence is actually going to be 20,249.

The next number is going to be a little bit simpler for us to work out.

Again, we're looking at the digit in our thousands place, and currently it's a zero.

We're adding on an extra thousand, so the next number is 21,249.

Finally, again we're looking at the digit in our thousands place.

At the moment, it's a one, which is equivalent to one thousand, and adding on an extra thousand.

The next number is 22,249.

So, hopefully you have had a go at those and seen how you can use both the place value counter method or looking at the digit method to work out which number is next in sequence.

Let's have a go at representing some five-digit numbers now.

So, we've had a look at how to add on thousands.

We've had a look at what five-digit numbers might be on a number line.

Let's have a think about how we represent them using a place value chart.

I've got the number, a five-digit number, here.

Let's say it together after three.

One, two, three.

34,051.

I'd like to represent this five-digit number, that means to show this five-digit number, using place value counters and digits, our numerals, in my place value chart here.

So, I'm going to start with place value counters.

Well, the first thing I can see is that I've got three ten-thousands.

That's equivalent to 30,000.

So, I'm going to need to draw three place value counters in my ten thousands column.

Next thing I'm going to look at is my thousands.

I can see I've got four thousands, so I'm going to see if I can draw four thousand here.

I don't have any hundreds.

Because I don't have any hundreds, I don't need to put any place value counters in.

I do need to put a digit in in a moment as a place holder, but I don't need to use place value counters.

I can see I've got five tens, so I'm going to put in five tens here.

And I only have one one.

So, I'm just going to put my one one in there.

So, what I've done is I've represented 34,051 using place value counters.

Now what I'd like to do is use digits to represent these, as well.

So if I put a three in my ten thousands place, it shows you that that is 30,000.

I've got four in my thousands.

I don't have any hundreds.

I have five tens.

I have one one.

34,051.

I'd like you to have a look at that number and that place value chart.

Can you tell me the value of the digit '4'? The four is in the thousands column.

What value does it have? See if you can think of it in five seconds.

The four has a value of 4,000 because it's in the thousands column.

What about the digit '5'? The digit '5' has a value of 50 because it's in the tens column.

And the digit '1' has a value of one because it's in the ones column.

So, I'd like you to have a go at this yourself now.

I've got three five-digit numbers we need to have a look at.

And what I'd like you to have a think about, if I remove the video there, is to show me and represent these three five-digit numbers on a place value chart.

I'd like you to have a go at representing them using place value counters and also using digits, the same way that we did a moment ago.

We've got the numbers 14,762.

Say the next one with me.

It's 82,478.

And the third one, together.

98,999.

Spend some time now representing those three numbers using place value counters and using digits on a place value chart that you can draw on your piece of paper.

Pause the video to complete your task and resume it once you are finished.

Okay, the next thing that we're going to be looking at and the last thing for today's lesson is partitioning five-digit numbers.

So, we've learned how to represent five-digit numbers using place value counters, using numerals that we put into place value charts, as well.

For the next thing I want us to think about is how I might break up a five-digit number, how we might partition these into different combinations, and how we can represent that using an equation.

So, I've got a five digit number for us just here.

Have a think about what this five digit number would be, and let's say it together after three.

Three.

33,134.

And you can see that we've put this into a part-whole model.

33,134 is our whole, and we filled in one of our parts, this box here shows one of the parts, but we've represented it using place value counters rather than digits.

What I'd like us to think about is what we need to add to this box here.

What is our other part to make 33,134? The first thing I'd like to do is just to represent 33,134 using a place value chart.

So, let me fill this in.

I've got three ten-thousands, three thousands, one hundred, three tens, and four ones.

Lovely.

What I'd like to do is work out what we have in our first part so that we can work out what we need to add to that to make our whole.

So, I can see there that I've got, in our first part there, I've got three ten-thousands.

I've got three thousands, one one-hundred, and three tens.

Spend five seconds now having a think about what that might represent.

So, let's fill in our place value table and see what that part has.

Well, I've got three ten-thousands.

I've got three thousands.

I've got one one-hundred, and I've got three tens, but I don't have any ones represented in that part there.

I have no ones.

So that part shows me 33,130.

I'm going to write that as the first part of our equation.

33,130.

We know we're going to need to add another part before we can equal our whole, which is 33,134.

So, we can see really clearly using our place value table that the part that is missing is the ones.

How many ones do we need to add to our 33,130 to equal 33,134? Work it out in five seconds.

So, you might be able to see that we need to add four ones.

What I can do is rub out our question mark and add in our four ones, and for this one, I will just put the one in there so we can see that each of these is equal to one.

I'm going to add in our four ones just there.

That shows me that one way of partitioning 33,134 is to partition into two parts 33,130 as one part, and four as the other, and when we add that together, we get our whole.

Let's have a go with another example.

Let's have a look at the first example on this side of our screen that's here.

The whole is another five-digit number.

Let's say it after three together.

40,352.

Let's see if we can work out what is in the first part, and then use that to help us determine what our second part will be.

I can see here really clearly that I've got four ten-thousands.

That's equal to 40,000.

I don't have any thousands.

I don't have any hundreds.

Remember, I've got to fill these in with zeroes, otherwise my number will be incorrect.

I have one, two, three, four, five tens and two ones.

So, in this first part, I have 40,052.

I need to work out what I need to add to that to make 40,352.

I'd like you to spend some time working that out.

I'm going to give you ten seconds.

If you need to, pause the video, draw out your place value chart like we did earlier, and see if you can work out the missing part bits.

You might be able to see that actually the part that we're missing is our hundreds here.

I've got my ten-thousands, there were no thousands to begin with anyway.

We've got our tens, and we've got our ones, but we don't have our hundreds.

So, our missing part must be 300, so I'm going to draw 300 in.

Each of these is worth a hundred.

I'm going to add in 300 like this.

That is one way of partitioning 40,352.

I can partition into 40,052 plus 300, and adding those together will give me my whole.

My whole again is -let's say it together- 40,352.

I'm just going to remove my camera there so you can see the next question for you to have a go at.

This time, we've partitioned 40,352 into different parts.

Can you work out what the missing part will be? Pause your video for a moment if you need to.

I'm going to give you ten seconds to work out this final part if not.

Okay, so we should be able to see here that actually, in this part here, I've got no ten-thousands, no thousands, three hundreds.

I've got five tens, and I've got two ones.

This part is equal to 352.

I need to work out what my next part is going to be.

What I can see, if I match it up to my original whole, I've got my hundreds in there, I've got my tens, I've got my ones, but I don't have my ten-thousands.

How many ten-thousands do I need? I need four of them.

I need 40,000.

So, my other part is 40,000.

If I want to, I can represent that here with four place value counters, each equivalent to 10,000.

I'm going to struggle to squeeze that in, but we know that each of those is equivalent to 10,000.

Now, what this shows us is that we can partition numbers in loads of different ways, which is actually really exciting.

We don't just have to partition into two different parts, either.

I could decide to partition 40,352 into 40,000 plus 300 plus 50 plus 2.

You can partition into loads of different ways.

This is just a demonstration of how we might fit them into part-whole models.

So, let's have a look at the independent task.

What I'd like you to do is to draw yourself a place value chart to begin with, and then I'd like you to represent each of these five-digit number on your place value chart using place value counters that you've drawn on, and then I'd like you to find two different ways of partitioning each of those numbers.

You can decide to demonstrate that using an equation or a part-whole model like we saw earlier on.

Let's have a go at the first one together.

For the first number, let's say it together.

It's the example one, and it's written in italics.

The first number is 32,178.

The first task I need to complete is to represent that using place value counters.

So, here I can see I've got three ten-thousands, I've got two thousands, I've got one one-hundred, I've got seven tens, three, four, five, six, seven tens.

That's equivalent to 70.

I've got eight ones.

One, two, three, four, five, six, seven, eight ones there.

Great, so I've done my first task.

I've represented the five digit number using a place value chart.

If I wanted to, I could also write the digits down just below like you learned to do earlier in the lesson.

I'll add those in for us just there.

Now, the second thing I need to do is find two different ways of partitioning this number.

So, I'm going to go with the first method, I'm going to start with partitioning and taking my ten-thousands on one part, and my thousands, hundreds, tens, and ones in the other part.

Let me show you what that means.

So, my ten-thousands.

I've got 30,000 there because I've got 3 in the ten-thousands.

That's equivalent to 30,000.

Then what I'm going to do is, my other part, I'm going to make that 2,178.

I've partitioned there in one of the ways there, and that demonstrates how I partition using my ten-thousands for one part and my thousands, hundreds, tens, and ones for the other part.

Now, let me think of another way of partitioning this.

Well, I could partition with my ten-thousands and thousands together, and my hundreds, tens, and ones in the other part.

Let's see if I can do that.

Let me try and take my ten-thousands and my thousands.

I've got 3 ten-thousands.

I've got two thousands.

Then, I'm going to add on my hundreds, tens, and ones.

So, I've got 178 there.

That's another way of partitioning this number out into 32,000 plus 178.

Still gives me exactly the same answer when I add those together.

So, what I'd like you to do now is to spend some time working through the independent task.

For the next four numbers on your page there, I would like you to work through representing each number on a place value chart, and then finding two different ways of partitioning each number using equations.

Then you can tick off your two tasks like I've done there.

Pause the video now, and restart when you're ready to have a look at some answers.

Brilliant.

Let's have a look at an example together.

One of the numbers you were working on was 21,465.

The first thing we need to do is to represent this using our place value counters, so let me do that first.

I can see I've got two ten-thousands, I've got one thousand, four hundreds, five tens, and five ones.

If I'd like to, I can add in my digits, as well, so I know that the number matches to the place value counters that I've used.

The number is 21,455.

There were a lot of ways you could have partitioned this.

So, actually, the answers you might have given will be different potentially to the answers I've given, but let me show you two ways you might have decided to do it.

The first way I decided to partition it was to partition my ten-thousands and my thousands, hundreds, tens, and ones into two different parts.

I'll represent this using an equation.

My ten-thousands.

I've got two ten-thousands.

That's equivalent to 20,000.

Then my thousands, hundreds, tens, and ones together, that's equivalent to 1,455.

That might have been one method that you used for partitioning 21,455.

Let's try a little bit more of a challenging one.

This time, what I'd like to do, is to take my ten-thousands and thousands and hundreds as one part, and then my tens and my ones as another part.

Let me just show you that.

I'm going to take these all together for one part, and these will be in a separate part.

Let's have a go at that.

I know I've got two ten-thousands, one thousand, four hundreds.

Then I've got five tens, five ones.

That's equivalent to 21,400 plus 55.

That's another way of partitioning out this number, this five-digit number.

So, the very last thing we're going to do before you have a go at your quiz is to have a look at this challenge.

I'd like you to look at the number 72,367.

Which of the following options, A, B, C, or D, is the correct way of partitioning 72,367? Just took my camera away so you can see really clearly there.

There are two different methods that you can use to partition the number 72,367.

Which of those two is correct? I'm going to give you ten seconds to have a look at them all and work out which will be correct.

So, let's have a look together.

Hopefully you've been able to see.

Let's go through them.

My first one says 70,000 plus 2,367.

This one is correct.

The reason is that I can see I've got my 70,000, my ten-thousands partitioned as one of my parts, and my thousands, hundreds, tens, and ones partitioned as another part.

That's correct.

Let's have a look at B.

That says 73,000 plus 267.

Well, this has got an error in it.

First of all, 73,000 is way too high.

It's a much greater number than the one I started with, so it couldn't possibly be one of my parts.

Remember, the parts are always smaller than the whole.

So, I already know this is incorrect.

Let's look at C.

C says 72,300.

So, in this one they've taken the ten-thousands, thousands, and hundreds, and then they've added 67, the tens and the ones together.

I can see that this is potentially correct, so I'm going to leave that off for the moment because I do need to double check D.

D says 70,0007 plus 236.

I know D can't be correct because it's not 236.

This '2' represents 2,000.

So, therefore, my answer must be A and C.

A and C are the correct answers.

So, what we'd love is, just before you move on to your quiz, please do feel free if you'd like to, to ask your parent or carer to share your work that you've done today on twitter, tagging @OakNational and #LearnwithOak if you'd like.

Now, that we've finished our lesson, don't forget to complete the quiz.

Thank you so much for joining me today for our maths lesson on place value.

I look forward to seeing you soon.