# Lesson video

In progress...

Hi everyone.

Thank you for joining me for our math lesson today.

We are going to be focusing on the place value of digits within six digit numbers.

My name is Miss Jeremy.

What I'd like you to do is just get yourself sorted with a nice quiet space before beginning the lesson.

Make sure there's no distractions and then press play to continue your lesson.

Okay, let's begin with looking at our lesson agenda for today.

We're going to be starting with counting up on a number line before we look at a six digit numbers and the place value within six digit numbers.

The final thing we'll look at today is partitioning six digit numbers before your independent task and quiz.

So the things you'll need for today's lesson are a pencil and some paper and a nice quiet space as well.

Get yourself sorted with these resources.

Press pause, and then press play when you're ready to begin your lesson.

So we've got two questions for our warm up.

The first one says, what are the intervals on this number line? So we've got number line here, and we're looking at this word, intervals, and just kind of a reminder of what this means.

On a number line intervals are the spaces on a number line.

These are always equidistant, which means that they're equally spaced apart.

And what we've got to try and determine is for each of the numbers on a number line, what are they increasing by? What are the intervals on this number line? So let's look at the three numbers at the start of our number line.

Let's say them together.

We've got 72,000.

The next number is 82,000.

Saying it together, the next number is, 92,000.

And what I want to know is what these numbers are increasing by each time.

So I can see straight away that there is a little bit of a pattern.

It seems like this is the digits that is changing each time on our number line.

And that is the digit in the ten thousands column.

So I know that each time my intervals are increasing and I'm going to write add to show increasing by 10,000 each time.

So what I've got to do now for question number two, is to work out which number features next on the number line.

If I'm adding on 10,000 to 92,000, what is the next number on my number line? Well, you can see here, I'm going to find this a little bit challenging because I'm adding on 10,000 to 92000.

So it's really difficult to add on a 10,000 to a nine because I can't have a double digit in the 10 thousands column.

I'd like you to think about what you think the next number might be on my number line.

If I'm adding 10,000 to 92,000, what number is going to feature next? I'm going to give you five seconds to calculate this, and then we'll have a look at it together.

So thinking back to our regrouping and understanding that actually we're going to have to regroup our 10 10,000 for 100,000 thousand.

And so actually my answer is now going to be, the next number or my number line is going to be 102,000.

That's the next number on my number line, goes just there.

So you can see that actually we might have to regroup in some cases, but each time my interval is staying the same, we're still increasing by 10,000 each time.

So moving on to our main lesson, we're going to start looking at six digit numbers today.

We just saw an example of a six digit number.

That number was 102,000.

And we're going to be looking at more six digit numbers a little bit later.

But I want us to think about how we would represent six digit numbers as well.

So you can see here that I've got some Dienes blocks.

In this Dienes block here, we have got 1,000.

That is representative of 1,000.

And I know that because each of those tiny little Dienes cubes, if I were to put 1,000 of them together, that would create this larger Dienes cube here.

So that is equivalent to 1,000.

So if that is equivalent to 1,000, then what about this diagram that I have here? This representation of Dienes that I have here.

I've got 10 of those 1,000.

What number is being represented by this column of Dienes? I'm going to give you five seconds to have a think about this.

Okay, so in order to work this out, I need to either count up in my thousands or I can do 1,000 multiplied by 10 to help me out.

I'm going to do both methods.

Let's count up in our one thousands first of all.

I'm going to cross off my Dienes blocks as I go.

So 1,000, 2,000, 3,000, 4,000, 5,000 6,000, 7,000, 8,000, 9,000, 10,000.

So that's equivalent to 10,000.

Let's just double check using our equation down here.

1,000 multiplied by 10 is equal to 10,000.

So that's huge big column of Dienes there is equivalent to 10,000.

So if we know that that is equivalent to 10,000, let's have a look at one of these.

This time, we have got a column of Dienes which we know is equivalent to 10,000, but we've got 10 of those columns.

So reminding ourselves that one of those columns of Dienes represents 10,000, what do ten columns represent? I'm going to give you five seconds to see if you can work it out.

So again, using the same strategy that we used last time, this time we're going to do 10,000.

And because I've got 10 columns of those 10,000 I want to multiply by 10.

And did you get what the answer was? 10 multiply by 10 is equal to 100,000.

And that's our place value counter for 100,000.

So when we have our 100,000 represented with those columns, we've got to remind ourselves that each of those small, small, tiny Dienes is added together, we have 100,000 of those small, tiny Dienes added together to make those 10 columns, as you can see on our screen.

So a lot of small, tiny Dienes, and that is equivalent to 100,000.

100,000 is a six digit number.

I know that because there are six digits in the number.

Let's count them, one, two, three, four, five, six, six digits in the number of 100,000.

So now that we've introduced some six digit numbers, let's talk about how we might represent them.

I've got a six digit number here.

I'm going to just say it, then I'd like you to say it.

The number is 305,421.

One, two, three, 305,421.

Now we've demonstrated how you can represent six digit numbers using Dienes.

But actually if I were to try and draw around 305,421 using Dienes, I would spend a long time doing that and it'd be quite challenging.

So you can also represent them using place value counters.

And I'm going to show you how to do that today.

What I'm going to do is put my place value counters and together in this place value chart to represent the number 305,421.

So, first of all, I've got to look at my different columns.

That's this number here, my 300,000.

So what I'm going to do is I'm going to put three place value counters in my hundred thousands columns.

If I wanted to, I could write 100,000 on those place value counters so I know that they are equivalent to 100,000.

But actually because I've put them in my hundred thousands column, I know that that they're equivalent to 100,000 so I can just leave them as they are.

Now, I'm looking at my ten thousands column.

I actually don't have anything in my 10 thousands columns.

So for the moment, because I'm dealing with place value counters, I'm going to leave that blank.

Looking at my thousands now, I can see that there are five thousands.

So I'm going to put one, two, three, four, five, place value counters in my thousands column, that's equivalent to 5,000.

Then moving on to my hundreds column, I can see that there are 400.

So I'm going to put four place value counters each equivalent to 100 in my hundreds column.

They're now looking at my tens.

There are two tens and there is just one one.

So you can see here, I represented 305,421 using place value counters in my hundreds, ten thousands, thousands, hundreds, tens, and ones place value charts.

So looking back at this number, what I can also do underneath each of the place value counters that I've written for each column, I can write the digit in to remind myself of what that represents.

So I've got three hundreds thousands, I've got no ten thousands, I've got five thousands, I've got four hundreds I've got two tens, I've got one one.

I've got 305,421.

So what I'd like you to think about now is the value of each of those digits.

For example that three that's in the hundred thousands column, that does not have a value of three.

It has a value of 300,000.

What about the five that's in the thousands column? What is the value of that five? The value of the five is 5,000.

And what about this two that's in the tens column? What's the value of the two? 20.

So you can see that even though we're talking about these digits, one, two, four, five, zero, and three dependent on which column or which place they're put in changes the value of that digit.

Let's look at another example.

So this number here, we've got another six digit number.

Let's say it together off three, one, two, three, 271,432.

Let's have a go at representing this number using our place value chart.

First thing I'd like us to think about is how are we going to put our place value counters into represent this number? So again, looking straight to our hundred thousand column first of all, and I've got two in there.

So I'm going to need to put how many places value counters in my hundred thousands? Two place value counters.

I'll put those in there.

What about my ten thousands column? Can you show me on your fingers how many 10,000 we'd need? We would need seven.

So I'm going to put seven 10 thousands in one, two, three, four, five, six, seven.

How many thousands do I need? I need one.

How many hundreds? I need four.

The number of tens, I'm going to need to put in, I'm going to put in three and I'm putting in two ones into my place value chart.

And you can see that I've represented really quickly the number 271,432.

Remember I could do this with Dienes, but it would take me a long time, and it'd be quite a hard job.

The next thing I need to do is to put in my digits to represent those different columns.

So I've got 271,432.

And now finally thinking about the value of each of those digits.

So I'd like you to, first of all, think about the value of these two just here in the hundred thousands column.

What value does that two have? After three, it has a value of 200,000.

What about the seven that's just placed here? What value does that seven have? It has a value of 70,000.

My one that's placed inside my thousands column has a value of? 1,000.

My four is placed inside the hundreds column, has a value of 400.

My three is placed inside the tens column has a value of? 30.

And my two placed inside the ones column has a value of two.

So again, you can see I've represented the six digit number using place value counters and also digits.

And then I've identified the value of each of those digits as well.

I've got two numbers here for you that I'd like you to have a go at representing using place value counters, and then also using digits on a place value table.

You're going to need to draw out your place value table just like I've done.

You'll need six columns on your place value table because we are dealing with six digit numbers.

I'd like you to have a go at representing the number 521,960 using your place value counters and your digits, and then 203,178 using your place value counters and using your digits.

If you'd like a little challenge, I'd also like you to do what I did before, which was to tell me the value of each of those digits in your number.

What is the value of that digit five, for example.

So take a little bit of time now, pause the video to complete your task and resume once you're finished.

Okay, how did you get on with that activity? So let's have a quick peek at the second number.

I want us to focus on this number here at b, 203,178.

Looking at that number, can you tell me what the value of that digit seven is? After three, one, two, three, the value of the digit seven is 70.

What about this digit two? What is the value of the digit two? After three, one, two, three, the value of the digit two is 200,000 because it's in the hundred thousands place.

So then you can see really simply a way of representing the different numbers that we have here, the different six digit numbers, and also determining the value of each of the digits in those numbers.

So let's have a look at partitioning.

This is moving our learning on little bit.

We've got this little explanation here of how partitioning can happen.

It says I can also represent six digit numbers using place value counters.

What number have I represented here? So you can see this is a representation using place value counters.

This time they have actually written the numbers on the place value counters, and that's because they haven't put them inside the place value counters table.

So we don't know what they'd represent otherwise.

So we've got 300,000 plus a 10,000 plus 4,000 plus five.

And what I'd like to know is what these place value counters are representing, which number are they representing? I'm going to give you 10 seconds to see if you can come up with an answer for me.

If you're finding this a bit tricky, draw out a place value table to help you out with this particular activity.

Okay, so let's have a look together.

So I'd like to work out what these different place value counters are representing, and if there are any missing out.

So I'm just going to draw a little place value table just here and you can see how quickly you can draw one, just using this method here.

So I've got my place value table here.

These are my hundred thousands, these are my ten thousands, these are my thousands, hundreds, tens and ones.

So you can see really, really nice and simple, just using the first letter of each of those column names to help you remember.

So let's look how many hundred thousands I have first of all.

Well, I've got 300,000, so I want to put a three just there.

What about my ten thousands? I've only got one.

So I'm going to put it just there.

And how many thousands have I got? I've got 4,000.

So I'm going to put it there.

Have I got any hundreds? No, I don't.

So what do I need to do because I'm working with digits because I need to place a placeholder in the hundreds column to show that there are no hundreds.

Similarly, there are no tens, I'm going to have to place a place holder just there into the tens column to show that there are no tens and I've got five ones, just there.

So you can see if I write my number out a little bit clearer, I've got just these digits over here.

And you can either put a little space here or you can put a little comma to show there's a separation when you're saying the number.

Let's say the number together after three, one, two, three, 314,005.

So because we don't have those hundreds and we don't have any tens, we say the word and to help us get over to the ones.

So we say three hundred and fourteen thousand and five, and that demonstrates the number that has been partitioned here.

Again, it's a six digit number because it has six digits in the overall number.

Let's look at another way of partitioning.

Well, we can use a part whole model to also partition.

And a part whole model is really useful because it demonstrates two parts and then the overall whole.

So my six digit number here is 316,425.

And I've got one of those parts just here.

And what I'm going to try and do is work out what this missing is here.

What is missing? The first thing I need to do is to put my whole number into my place value charts.

I'm just going to add these digits in.

316,425 just like that.

Now, what I'd like to do is to put one of the parts into my place value chart.

So I can see the difference between my parts and my whole.

See what I have to add to my part, to make my whole.

So let's see what's in my parts.

Well, I can see that I've got 300,000.

I've got one 10,000 and then I've got one, two, three, four, five ones, but I haven't got any thousands, any hundreds, any tens.

And straight away here, I can already see how much is this is going to help me because I can straight away see what's missing and what I'll need to add to my other parts.

This top number here is my whole.

The second number is my first part, and I can see straight away that I'm missing my thousands, my hundreds on my tens.

The ones are there, the ten thousands are there, the hundred thousands are there.

So in my missing part, I'm going to need to have 6,420.

My missing parts is worth 6,420, and that's really nicely demonstrated and really clear to see when you draw your whole at the top of your place value chart, then below it you draw your first part.

You work out what is missing from that first part.

And in this case, it's 6,420.

Just bear in mind that that's why this placeholder in, because if I didn't add that zero at the end, it would say 642.

That's not what I want it to say.

I want it to say 6,420.

So I have to add that little place holder zero, just at the end of my number.

Let's have another go at one of these.

So in this case, I want you to have a liquid peak and work out what is the whole if we know what those two parts are.

So try and calculate what part one is equal to, then calculate what part two is equal to, see if you can work out with a whole is equal to.

I'm going to give you just a few minutes or so to do that.

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

Okay, let's have a look at this together.

So let's work out first of all, what our first part is equal to.

In our first part, I can see I've got 100,000.

I don't have any ten thousands, I'll put a zero here.

I have two thousands, those are those two there.

I have three hundreds.

I have four tens.

I don't have any ones.

That complete that part there.

So that shows me that in my first part, I have 102,340.

Let's have a look at my second part.

Oh, interesting, I only have ones in my second part.

Let's have a look at one, two, three, four, five, six, seven, seven ones in that second part, just there.

And I've got to work out what that whole is.

Well, I can see actually really easily how to work out the whole in this case, because all I'm doing is adding my first part to my second part here.

And all I need to do is add on my seven ones.

So my final answer, my whole is 102,340, don't forget the ones, seven, 347.

So in this case, what I've done is just added my two parts together to make my whole.

So moving on to independent task for today.

What I'd like you to do is look at the four numbers I've written in pink just here on your screen.

I would like you to represent each of those numbers on a place value chart.

You can use that nice efficient method that I used earlier on where I just put the different letters to demonstrate what those different columns represented.

I'd like you to represent the numbers using place value counters, and then digits.

And then I'd like you to find two different ways of partitioning each number.

If you want to, you can use a place value or you can use a part whole model, sorry, just like we demonstrated in the previous slide.

So you can use two parts and a whole for each of the numbers in two different ways.

Or if you want to just write out the equation to show your partitioning, you can do that as well.

Pause the video to complete your task, but don't forget to resume once you're finished to have a look at one of the answers together.

Okay, let's have a look at one of the answers together.

So you might have noticed that actually there was lots of ways that you could partition these numbers.

I'm just going to go through one example together.

Let's have a look at the question 109,345.

So the way that you should have demonstrated this using place value counters is as follows.

We have one in the hundred thousands.

We don't have any ten thousands, so no place value counter goes there.

I'm going to draw nine thousands to demonstrate how many thousands I've got.

I've got three hundreds, I've got four tens, and I've got five ones.

I can put my numbers just below.

So I've got 109,345.

That's one way of demonstrating our, or representing our number 109,345 using place value counters.

Now I'd like to think about how to partition this number.

So I'm going to represent two different ways of partitioning this number using an equation to demonstrate this.

The first way I'd like to partition it is I'd like to break it up into my hundred thousands, my ten thousands and thousands as one of the parts.

And then my hundreds, tens and ones as another one of the parts.

So this I'd have to write 109,000.

That's my first part plus 345 is equal to 109,345.

That is one way of partitioning my numbers.

I'm just going to write my numbers slightly closer together here.

So you can see that it says 345 like that.

Now another way of partitioning, I think this time I'm going to partition with my hundred thousands, ten thousands, thousands, and hundreds altogether.

And then my tens and ones at the end.

So this time it will be 109,000 and I'm going to include my hundreds this time, 300, and then my tens and ones at the end plus 45 is equal to 109,345.

So you can see two very different ways of partitioning, both produce exactly the same result.

Both lead back to the number 109,345.

So we've come to the end of our lesson today.