Lesson video

Hello everyone.

Thank you for joining me today.

My name is miss Jeremy.

Today, our Maths lesson is focused on comparing five digit numbers.

So get yourself into a nice area where you're free from distractions and when you're ready, we'll begin the lesson.

So let's begin by looking at our lesson agenda for today.

We're going to begin with a warmup where we count upwards in 100s and in 1000s.

We're then going to be using a number line to compare five digit numbers before exploring how we work out which number has the greatest value.

After that, we'll look at ordering five digit numbers before our independent task and quiz at the end of the lesson.

So in order to get ready for our lesson today, you will need a pencil, some paper, and if you have some dice at home, that will be really helpful.

Don't worry if you don't.

I can tell you how to do the activity without the dice, but do get some if you do.

Pause the video now to get your resources and to get yourself sorted in a nice quiet space, and when you're ready, restart the video to begin the lesson.

So let's begin with our warmup.

On our screen here, we can see we've got a number line with a five digit number.

I'd like us to say that five digit number together after three.

One, two, three.

32 400.

And what we need, the question that we've got to begin with here is how would we count up in 100s? We want to think about how we would count up in 100s.

The first thing I'm going to need to do is to look at the digit that is in my 100s place.

And if you see here, the digit is a four.

That's equivalent to 400 because it's in the 100s column.

And I've got to think about what would come next in my number if I was counting up in 100s.

So the rest of my digits stay exactly the same.

It's that 100s digit that changes.

So I'm still going to have 32 000, but instead of 400, I'm going to have 500.

Now let's look at the next number that would come in our number line.

So starting with 32 500, remember we're counting up in 100s.

I'm focusing on the digit that is in the 100s place.

In this case, it's a five.

The next number would be 32 600.

So I'll write that one in 32 600.

Sometimes people put a comma just between these numbers here, so that it reminds us to say 32 000 and the rest of the number 400 or 500 or 600.

In our case, we sometimes put a space as well, because that helps us with partitioning, with breaking up that number as well.

So we've learnt how to count up in 100s.

Let's think about how we would count up in 1000s, Let's rub out my 100s calculations here.

And I'd like you to have a think, if I've got this number 32 400, what would I do to count up in 1000s? I'm going to give you five seconds to work out my strategy.

So hopefully you've seen that what I could do is I could focus on the digit that is in the 1000s place.

So in this case, the digit is a two.

Remember that digit doesn't have a value of two.

It has a value of 2000 because it's in the 1000s place.

Let's think about which number would come next.

Remember my 1000s digit stays exactly the same, still 30 000 there, but this time instead of 2000, it would be 3000.

So it becomes 33 400.

Let's say the rest of the numbers.

The next one would be 34 400, 35 400, 36 400.

Remember when it comes to regrouping, when I get to 39 400, it's not just the digits in the 1000s place that would change, I would also need to regroup.

So my digit in the 10,000 place would change as well.

But typically, unless you're regrouping the digit in the 1000s places is the one that changes when you're counting up in 1000s.

Let's look at our next activity.

So the first thing that we're going to be doing with comparing numbers today, is using a number line.

A number line is a great way of comparing numbers because it places them in a row so we can see which number has the greatest value towards the right of our screen and which number has the smallest value, the one that's closer to zero.

I've got 2 five digit numbers on screen here.

I'd like us to say them together, this digit over here or this number, sorry, number A and this number over here is number B.

Let's say number A together.

A is 14 862.

And B is 41 682.

I wonder looking at those numbers, do you notice anything interesting about them? I'm going to give you five seconds to see whether you can spot something interesting about the numbers that I've used there.

So you might have seen that I've actually used exactly the same digits.

I've used a one, I've used a four, I've used an eight, I've used a six and I've used a two.

Both of those numbers have all of those digits, but I've placed them in different positions in the number.

And actually what you'll see is that even though I've used exactly the same digits, those numbers have very different values because it's not about the digits that I use, it's about where I place them in the number that counts.

So let's have a look at where I would place these numbers on my number line.

I'm going to start with 14 862.

Now, as you can see on my number line, I've got big intervals here that go up in 10 000s.

I've got 0, 10 000, 20 000, 30 000, 40 000 so on and so forth.

And my smaller intervals, these smaller intervals just here are equal to 1000.

So we've got a number line with bigger intervals and then smaller intervals in between.

So what I'm going to be doing is placing these numbers, approximately, which means roughly on my number line.

I can't place them in exactly the right position because actually my small intervals are so closely spaced together, that actually it'd be really hard with my thick pen to place exactly in the right place.

But approximate position will do just fine because it will still help us to work out which number is greater and which number has a kind of smaller value.

Let me start with 14 862.

I know that 14 000, and I remember I'm focusing really on the 10 000s and 1000s here.

This is somewhere between 10 000 and 20 000.

And I know that the number halfway between 10 000 and 20 000 is 15 000.

14 000 is less than 15 000.

So I'm going to place number A around here.

Just remember it's an approximate placement.

We don't have to be really exact with that placement.

Now let's look at number B what I'd like you to do is spend 10 seconds, exactly the same method as I've done.

Can you work out the larger intervals between which this number is placed and then put your finger on the screen, approximately where you think 41 682 would be placed.

I'll give you 10 seconds.

Okay, time's up.

Let's have a look.

So I know that 41 682 is somewhere between 40 000 and 50 000.

And I know again, I'm looking at my halfway point, the number halfway between 40 000 and 50 000 here is 45 000.

So 41 682 well, it's less than that.

It's going to have to be somewhere around here.

Remember it's an approximate placement.

It's not exactly where it would be, but it's roughly there.

Now using this strategy, we can see really clearly that the number with the greatest value is 41 692.

And that's because it's further along towards my greater numbers on my number line, whereas 14 862 is closer to the 0.

So therefore, the number with the greatest value is 41 682.

Hopefully that's shown you how we can use a number line to compare different numbers, even if they have the same digits.

So now it's your turn to have a practise.

I've got a number line here that goes from 0 to 80 000 and I've got four numbers, A, B, C, and D that I would like you to place approximately on the number line.

And what I'd like you to do is work out, with that approximate placement, which number has the greatest value.

Be warned, I put in a little red herring for you.

For those of you who don't know what a red herring is, a red herring is a question or part of a question that has an intentional mistake in it.

And that's to see whether you can work out what the mistake is.

So there is a red herring in this question.

See if you can work out the intentional trick, the intentional mistake, and well, as you're adding these numbers to your number line.

So pause the video for a moment, place the numbers approximately on the number line and work out which number has the greatest value.

When you're ready to restart, resume the video.

Okay, how did you get on? Let's have a look at this together.

So at first of all, we're going to place at number A on the number line.

Number A is a 71 349.

So using my method again, I'm going to work out which are the kind of larger numbers and that I'm going to have in between 71 000 and 71 349.

So I know that this number is going to go somewhere between 70 000 and 80 000.

The number halfway between 70 000 and 80 000 is 75 000.

71 349 is less than that, it's actually probably a lot closer to 70 000.

So I'm going to place A just about here.

Let's look at B.

So B is 13 794.

We're looking at a number that begins with 13 000.

I know that 13 000 is somewhere between 10 000 and 20 000.

The number halfway between 10 000 and 20 000 is 15 000.

So 13 794 is less than that.

I'm going to place it approximately here.

That's where B's going to go.

So you can see already, we know that A has a much greater value than B.

That's helped us out.

Now, I wonder whether you spotted the red herring, the trick, because it comes up in the number that we have to see.

Did you spot it? You would have see hopefully, that C has 91 000 at the beginning of the number.

And actually you might notice that it's impossible to place this number on our current number line.

Why? Well, our number line only goes up to 80 000.

91 374 is a lot greater than that, so actually our number would have to be somewhere further up the scale.

So I'm going to write C here because I can't fit it onto my number line.

But there was a little red herring there to see whether you could spot what the error was.

That's have it looked for D.

D says 43 179.

And I know that is going to be somewhere between 40 000 and 50 000.

The halfway point between 40 000 and 50 000 is 45 000.

So 43 179, I'm going to place it about here and I'm going to label it D.

And hopefully you've seen really clearly here that this number line has helped us to order our numbers is ascending order.

So that means going from smallest value to greatest value, or if we wanted to, in descending order, going from greatest value to smallest value.

So let me order them.

First we've got B, that's the smaller value, then we've got D, then we've got A, and C is completely off our scale.

We know that one's got the greatest value.

What I've done there is, I've ordered those numbers in ascending order.

That means I've started with the smallest number or the number that has the smallest value and gone all the way up to the number that has the greatest value.

If I wanted to order them in descending order, I'd start with C, then A, then D then B.

So using a number line really helps us to visualise numbers in ascending and descending order.

It helps us to compare numbers.

So the next thing that we're going to have a go at doing is working out how we could use, not just a number line to compare numbers that have five digits, but also a place value chart.

So we've got this question here, which number has the greatest value? How do you know? And we've got three numbers that we're going to be looking at in order to compare them.

I've got number A, B and C.

Let's start by saying number A together.

Number A is 24 710.

Number B is 24 071.

Notice where I said the "and." I said the "and" because there is no digit in my 100s column.

So instead of saying twenty four thousand seventy one, I say twenty four thousand and seventy one to help me say the number.

And number C is 21 704.

So what we're going to do is have a look at how we can use a place value chart to order these numbers, to work out which number has the greatest value.

So the first thing that I'm going to need to do is I'm going to need to places numbers in my place value chart, nicely aligned.

So what that means is that I'm placing all of the digits there in the 10000s column nicely lined up together, all of the digits, they're in the 1000s column nicely lined up together.

And that's why it's really useful to use a place value chart, otherwise sometimes our numbers can switch over, can look like they're in a different column.

When you've got your columns drawn in, that's really helpful for this activity.

So first thing I'm going to do is place the number 24 710 in my place value chart.

I'm going to place it right up here, 24 710.

Whilst we focus on this number, I wonder whether you could tell me what the value of the digit four in my number is.

it's in the 1 000s column, it has a value of 4 000.

It doesn't have a value of four.

It's a four in the 1000s columns, that value is 4 000.

Okay, let's place number B in our place value chart.

We've got 24 071.

Remember I have to say that "and" because I haven't got a digit in the 100s place there.

And last but not least, let's place the last number in our place value chart.

The last number is 21 704.

Wonderful stuff.

Now I'm going to show you how we would work out which of these three numbers has the greatest value, even though we haven't put them on a number line.

The way we do it is we start by looking at the digits that are in the 10 000s column and we compare them.

If they're all the same, we then have to take a peak at the digits that are in the 1000s column.

If they're all the same, we continue to look at the columns all the way down the numbers until we find a difference.

When we find a difference, when we find the digit that is greater than one of the numbers, we know that that number overall has a greater value.

Let me show you an example.

So we're going to start with looking at the 10 000s column.

Well, actually I can see in the 10 000s column, all of these numbers have exactly the same digit.

They all have two in their 10 000s column, they all have 20 000 there.

I can't compare them, they're all exactly the same.

So now let me have a look at the 1000s column.

Ha! I think I might have found a difference.

In numbers A and B, they have exactly the same digits in the 1000s column, but C has a one in the 1000s column.

And I know one is less than four, therefore, straight away I know the C has the smallest value, the whole number C, 21 704, is a lower value and it's smaller than the other two numbers.

So, great.

I already know that, I've worked something out.

I don't need to look at C anymore.

Now let's look at comparing A and B because we haven't found a difference yet between those two numbers.

So let's take a little peak at the 100s column, and I think we might have a difference here.

Let's see.

Well, in A, I've got seven in the 100s column, whereas in B I've got zero.

Straight away, I can tell that A must be the number that has the greatest value, because when I compare them, when I compare A to B and C, I can see that it's got numbers that are in the 10 000s, 1000s and 100s are greater.

So therefore, when I'm comparing these numbers, I know that C is the number that is smallest or has the lowest value, then it's B and then it's A.

A is the number with the greatest value.

So hopefully this has shown you how you can compare numbers using a place value chart, and you don't just need to use a number line.

You can also use a place value chart in this way.

So I'd like you to have a little practise at this.

As you can see here, we have got a group of numbers over here.

I'm going to call them A, B and C, and then a group.

I've got another group of numbers here, I'm going to call them i, ii, iii.

and you can see I've used Roman numerals here to show you the difference between the numbers that are in my kind of question number and the numbers that are actually part of the question.

So these are two different examples here.

What I'd like you to do is on your sheet of paper, draw a lovely place value chart, make sure you've got five columns for your 10 1000s, 1000s, 100s, tens, and ones, make sure it stretches a fair way down your page as well so that you can add in all of these numbers.

Then I'd like you to focus on the numbers A, B and C first of all.

Can you add those numbers into your place value chart and work out which number is greatest? Which number has the greatest value based on our comparison method? Once you've done that, have go for the next question, which one, i, ii, iii, which one has the greatest value? Spend a few minutes doing this now.

Pause the video to complete the task and when you're ready, restart, and we'll have a look at some of the answers.

Okay.

So hopefully you've had a really good go at working out, which number has the greatest value in both of those examples.

The first one was a little bit simpler because actually straight away, you should have noticed that if you compare the 10 000s columns, A clearly has a six in the 10 000s column, whereas B and C have a two and a four, so A is our greatest value.

The next example was a little bit more challenging because actually they were all very similar all the way up until you got to the 100s column.

And then you could see that one and two were really similar there, but actually when you start to look at the tens column, it's clear that one has the greatest value because it's got a seven in the tens column whereas the number two only has a one in the tens column.

So using our comparison method, using our place value chart, we can really easily work out which numbers are greatest or which numbers have the greatest value.

So actually we can use this method to order numbers.

We can put them in ascending order starting with the number with the smallest value and working our way up or descending order, starting with the number with the greatest value and working our way down.

I've got four numbers on our page here and what we're going do is pop them into our place value chart, and work out which numbers are greater and which order we would put these numbers if we were ordering them in ascending order.

So the first thing I need to do as we've done already several times, is to put all the numbers into the place value chart.

That's my first one, I'm going to call that A, B is going to go in just below, 27 541.

I'm going to pop C in 71 245, and then I'll pop D in just below.

I'm going to have to write it just here, 71 524.

As you can see, it's quite useful to have a really long place value chart so you can put all your numbers there.

So I'm going to be ordering these numbers in ascending order, which means that I would like the number with the greatest value to be here.

And I'd like to work my way up.

So that's what I'm going to be filling out.

I'm going to work out which number has greatest value.

Is it A, is it B, is it C or is it D? We'll use the same method I've used all the way along.

I'm going to start with my 10 000s column and compare all the way until I find enough differences to work out which number has the greater value.

Let's start with looking at the 10 000s.

Straight away I spotted a difference.

I can see that I've got a seven here, seven here, and a seven here, but here I have a two.

So the number, my number that is B, 27 541 must be the number that has the lowest value, the smallest value.

So already I worked out, I'm going to give myself a tick for that, already I've worked out that B is my starting point.

It has the smallest value, the lowest value Now let's look at our 1000s, to make a comparison with our 1000s.

Huh, let's have a look.

I'm looking, remember I'm not looking at B anymore 'cause I've already worked out where that's going to go.

Ah, A, B, C, and D all have exactly the same digit in the 1000s.

The 1000s column isn't going to help me here.

Let's have a look at the 100s.

Huh, interesting.

I've got a two, a two and a five.

So already, here I've worked out that actually number D, 71 524, must be my greatest number because it's got a five in the 100s whereas the other two numbers have a two in the 100s.

So I already know that D is going to be my number, which has the greatest value.

Now I've just got to compare A and C.

Let's have a look at the tens.

Well, for A I've got five in the tens, whereas for C, I've got four.

Huh, now that means that this number here A must be greater than C because it's got five compared with the four.

So A is going go here and C is going to go here.

Now you might actually think to yourself that we've ordered them in ascending order, but you could do that just by looking at these numbers on the side here.

And you absolutely could.

You've just got to make sure, and this is where the place value chart helps, you need to make sure that your digits are aligned because if you've got a number with only four digits that you're comparing with a number that has five digits, if all of those digits have been filled in, if all of those columns have been filled in, the number with the five digits is greater, just purely from the fact that it has a digit in the 10 000s column.

So just be careful if you're comparing without a place value chart, but you can very easily do that just by looking at the numbers and working your way from left to right.

So I'd like you to have a think about this question.

It says, let's arrange these digits to make the number with the greatest possible value.

I've got the digit two, I've got digit nine, the digit six, the digit three and the digit seven.

I would like to place these digits in order in my place value chart, so that I have made the number with the greatest possible value.

How am I going to do that? I'd like you to spend 10 seconds working that out now.

Okay.

What did you think? So what you might have noticed is that when we're working with placing digits in a place value chart, the space, the column that has the most, the kind of greatest value is our 10 000s column here.

So what we really want to do to maximise that 10 000s column is to place the digit that has the greatest value in that column.

If I place a two in that column, that would be equal to 20,000.

If I placed a nine in that column, it would be equal to 90 000.

You can see the difference there, and you can see the value of placing a higher, a greater digit in that column.

So that's where I'm going to place my nine, because that's the number that is greatest out of the digit cards that I've got.

So I'd like to place a nine just here.

Let's move to our 1000s.

Well, actually here, we need to think about the next digit that has the next greatest value and in our case between two, three, six, and seven, it's seven.

So I want to place a seven just here.

Now let's think about 100s.

Out of two, six and three, which of those numbers has the greatest value? It's going to be a six.

So I'm going to place my six just here.

Out two and three when I'm looking at my tens, I can see my three should go here and my two should go here.

Automatically, what I've done there is I've placed my digits in descending order.

I've started with the number that has the greatest value and gone all the way down to the number with the smallest value.

Let's say the number that I've made together, the number is 97 632.

That's right.

So you can see here when we're placing our digits, we need to be really careful with the placement to make sure we maximise those columns that have the greater value and that the digits that have the smaller value, lower values, we place towards the group ones end of our place value chart.

So I'd like you to have a go.

What I'd like you to do is look at the digits that we have on the screen there, we've got four, we've got a one, a zero, an eight and a seven.

I would like you to place and arrange these digits to make the number with the greatest possible value.

And then to make a number that has the smallest possible value.

How would you arrange those digits in order to do that? How did you get on? So hopefully you might have seen that in order to make a number that has the greatest possible value, you would have needed to use digits that have the greater value in the 10 000s column of your number.

So my great, my number would be 87 410.

And you can see that I've used the eight first in my 10 000s column because that provides it with the greatest possible value.

If I want to create a number with the smallest possible value, well, if I was using my zero at the beginning, I'd place zero in my 10 000s, that means that the 10000s has no value there, and then I'd use my one, my four, my seven and my eight.

That would mean that my number was 1 478.

However, that is cheating slightly because I'm using my zero, but I'm not really using it for a purpose there.

So the other number I could create would be 10 478 and that means my zero has a value.

So if you've got any of those numbers really well done, really well done for positioning them in positions that allow you to have numbers that have a greater value and a smaller value.

So the final thing that we're going to do today is to use our dice if we've got one.

If you don't, you can place number cards.

So write the numbers one to six on some cards, place them face down and select them at random for this activity.

You're going to start by drawing a place value table, and then you're going to roll the dice five times.

You're going to have five digits that you have rolled.

And what I'd like you to do is each time you roll decide where you're going place your number on the place value table, so that you achieve the number with the greatest value.

Now, you might decide that you're going to roll all the digits first of all and get your five digits and place them accordingly so you get the number with the greatest value, or if you want to make this a bit more tricky, a bit more challenging for yourself, each time you roll place that digit in the place value table.

You won't know what's coming next.

It will make it a little bit more challenging to try and make sure your number has the greatest possible value.

And then I'd like you to explain why you've placed the digits in those positions at the end.

How about you do this five times.

Once you've done that select one of the numbers that you have on your place value chart and see whether you can rearrange your digits to make a number that is greater than 30 000 and then rearrange the digits to make a number that is less than 12 000.

Pause the activity now and complete your independent task and then restart when you're ready.

So hopefully you've got on okay with your independent task today.

We were learning about ordering and comparing five digit numbers, understanding place value tables and number lines.

If you'd like to share any of your work with Oak National, please ask your parent or carer to share this via Twitter, tagging @OakNational and #LearningwithOak.

Now it's time to complete your quiz.

Thank you so much for joining me for our Math lesson today, it's been really great to have a go at ordering, comparing five digit numbers.

Hopefully you'll join me again soon.

Have a lovely rest of your day.