Lesson video

Hi there.

My name is Mr. Tilstone.

I'm a teacher and my favourite subject just has to be maths.

So it's a real pleasure and a real delight to be working with you today on this lesson, which is all about comparing and ordering four digit numbers.

So if you are ready, I'm ready, let's begin.

The outcome of today's lesson is I can compare and order four digit numbers and we've got some keywords.

So my turn order, your turn.

My turn, compare your turn.

My turn, greater than, your turn.

My turn, less than, your turn.

What do those words mean? Are they familiar to you already? Let's have a check.

When we order a set of numbers, we put them into their correct place following a rule.

For example, from lowest to highest.

When we compare numbers, we note the similarity or difference between them, for example, which is greater and I'm sure that you've ordered and compared numbers before, maybe three digit ones.

If a number is greater than another number, it is bigger or worth more.

This can be shown using that symbol, that's the greater than symbol.

If a number is less than another number, it is smaller or worth less and that can be shown using that symbol, that's the less than symbol.

And again, I bet you've used those before.

Our lesson today is split into two cycles.

The first will be comparing four digit numbers and the second, ordering four digit numbers.

So if you're ready, let's compare some four digit numbers.

In this lesson, you're going to meet Lucas and Andeep.

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

Andeep is recalling his previous experiences of comparing three digit whole numbers.

And he says, "You can use these symbols to compare numbers." That symbol means less than.

And that's how you remember that.

So for example, 496 is less than 499 in the same way.

Look that one is less than three.

So those blocks are helpful and that symbol means greater than, and you can remember it this way.

So three is greater than one look.

And in the same way, 933 is greater than 930.

Lucas is comparing the amount of liquid in two different containers.

Container A has 3,270 millilitres of liquid and he's represented that using place value grids and counters.

You might have had some recent experience doing that yourself and container B has 2,750 mils of liquid.

And again that's been represented with counters.

What do you notice though about those two numbers? Have a little look.

Anything that you notice, anything at all, the thousands digits are different.

Can you see? Look at the thousands.

How many in the first value? Three.

How many in the second one? Two.

So they're different.

The hundreds digits, are they different? Yes they are the tens digits.

Are they different? Yes they are, the ones digits are the same.

They've both got no counters in in when comparing four digit whole numbers start with the thousands start with the highest value.

So container A has more thousands so it contains more liquid.

There's no need to look at the other digits.

We've already decided that that's got more liquid in the thousands.

Tell us that the number of thousands, so if there are thousands are different, that's all you got to look at.

This can be expressed using greater than and less than symbols.

3,270 is greater than 2,750 millilitres.

We could look at that the other way, couldn't we? We could say 2,750 millilitres is less than 3,270 millilitres.

Now Lucas is comparing the lengths of the walls in his classroom.

And again, he's represented that with counters.

So he is measured it.

Maybe you've done something similar recently.

He's used a metre stick and he's found out that wall A has a length of 4,250 millimetres and wall B has a length of 4,520 millimetres.

What do you notice this time, anything? Have a look, look at the numbers.

Are they different in each column? Are they the same? What do you think? This time the thousands have the same value.

Did you notice that both got four? So the hundreds must be compared.

So we cannot use the thousands to say which is bigger, but we can use the hundreds.

That's the next biggest value.

Look at the hundreds, how many of each one got? So there we go.

So that first wall that's got two hundreds or 200 and the second one's got five hundreds or 500.

Wall A has a smaller number of hundreds.

So the number has a smaller value, simple as that.

The wall is slightly shorter.

There is no need to look at the other digits.

We've already decided it will be a waste of time.

That tells you which one's shorter.

So let's use our symbols.

We can say 4,250 millimetres is less than 4,520 millimetres.

And we can switch that round and say 4,520 millimetres is greater than 4,250 millimetres.

But the important point here is that the hundreds were helpful this time.

Now Lucas is comparing the masses of different objects in his classroom and again is represented the numbers with counters and object A, has a mass of 1,250 grammes and object B, has mass of 1,205 grammes.

Have a look at those two values, what do you notice? What's the same? What's different? Start with the thousands.

Same or different? Well, they're the same.

So we can't compare them with the thousands.

What about the hundreds? Oh, they're the same.

They've both got two in the hundreds, so we can't compare them that way.

But we can look at the tens.

The thousands are the same value and so do the hundreds.

So compare the next highest place value, which is the tens.

And that top one has got five and the bottom one has got none.

So the first one must have a greater mass.

Again, there's no need to look at the ones we've already decided.

So 1,250 grammes is greater than 1,205 grammes or 1,205 grammes is less than 1,250 grammes.

Let's do a check.

There are two oak trees near Oak Academy.

That's how it got its name.

Lucas is using a trundle wheel to see which one is closer to the school entrance.

Compare those distances.

So tree A is 1,123 metres away and three B is 1,129 metres away.

Can you use those greater than and less than symbols? Pause the video.

What do you think, which one's greater, which one's less? Well this time the thousands have got the same value.

The hundreds have got the same value, the tens have got the same value.

So we have to compare the ones.

So there's not much in that at all.

They're very close together, those values, but one of them is slightly greater, which one is it? Well, the first one's got fewer ones, it's got three, the second one's got more ones, it's nine.

So tree A is ever so slightly closer to the score since the ones have a smaller value and we can use symbols to represent that.

So 1,123 metres is less than 1,129 metres or 1,129 metres is greater than 1,123 metres.

Let's have another check.

Which of these statements are true? Explain your choices, pause the video.

You'll notice I didn't read those out because you have to figure out what the symbols are saying.

That is true.

4,593 is greater because it's got more thousands.

We didn't need to look at the other digits to work that one out, it's greater.

Let's look at the next one.

No, that's not true, it's actually greater.

They've got the same number of thousands, but 5,206 has got more hundreds.

So we need to choose the other inequality symbol.

What about the next one, is that true or not? No, that's not true.

6,725 is less than 6,752.

They've got the same number of thousands, they've got the same number of hundreds, but 6,725 has got fewer tens, three fewer to be exact.

So again, this symbol needed to be the other symbol.

And this one, is that true or not? Yes, it is.

4,403 is less than 4,405.

They have the same number of thousands.

They've got the same number of hundreds, they've got the same number of tens, but 4,403 has got fewer ones.

So that is correct, well done, if you've got those.

Lucas and Andeep are playing a game to help them practise comparing four digit whole numbers.

You're gonna play this soon as well.

They draw boxes on their whiteboard like so, just like you will.

They've got set of number cards from zero to nine jumbled up just like you've got.

They take it in terms to turn over a card and decide where to put it.

And the winner is the player with the greater number.

So follow along then see who's going to win this one.

It's Lucas versus Andeep.

Good luck fellas, here we go.

So Lucas says, "If I put three, 'cause he just turned over a three in the thousands place, it will mean I end up with a number greater than 3000 and less than 4,000." So he is gonna have 3000 and something.

"I don't think that will win." He says, "I don't think it will either.

I think I will use it to represent three tens." So that's where he is going to put his three.

He's gotta put it somewhere.

He's putting it in the three tens.

Andeep says, "I think I'll use that seven.

He's just turned over a seven in the thousands to make 7,000 and something." Seven's pretty high, isn't it? I think that's a good choice Andeep, you might pick eight or nine, but there we go.

And that's why he hopes, "I hope Lucas doesn't turn over eight or nine or I have lost!" 'Cause that's where Lucas will put his, isn't it? He'll put his in the thousands, but that's what he is done for now.

And then Lucas has turned over the five.

What would you do if you were him? Where would you put it? Where wouldn't you put it? If I put five in the thousands, I've lost straight away.

Yeah, I'll put it in the hundreds.

So he's banking on getting that eight on nine I think.

Right, Andeep's got zero.

What would you do with that? You've gotta put it somewhere.

Where would you put it? Trying to get the highest number possible.

"That's an easy choice," he says.

"It's the lowest value.

So I'll put it in the lowest place value." That's a good idea, Andeep, pop it there.

Lucas has got six.

What would you do? Where would you put that? If he puts it in that thousand, it's lost as in his, so I wouldn't recommend that.

Hmm, yeah, he says, "If I put six in the thousands, Andeep's number is automatically greater.

It will have to go in the ones." It will, right? How can Lucas still win? 'Cause it's not game over yet.

What does he need to turn over do you think? Well, Andeep's turned over the nine.

So that's unfortunate for Lucas, isn't it? But I'll bet Andeep now wishes he'd left that thousands blank, but nevermind, he could still win.

So what would you do with that nine? He says, "Yes, now the only way Lucas can win is by turning over the eight.

So Lucas's gotta keep all his fingers crossed that he gets the eight and he's right.

I'll make this worth 900.

That's the next highest value that it could be.

So nine for 900.

'Cause it can't be 9,000, right, okay.

It's gonna come to this, isn't it? Whatever Lucas turns over next will decide whether he wins or loses.

Who do you think is going to win? Let's have a look.

Please be eight, please be eight.

Please be eight is what he's saying.

Let's have a look.

Oh he is, got it.

He's got the eight.

Yes, I win, my number is 8,536.

One point to me, hard look Andeep.

Oh that's nice of him is today he's saying hard.

"Well done Lucas." That's nice of Andeep too, I like that.

Let's finish this off then.

Yeah, he is gotta finish the game.

He's got to make his own number.

He knows he's lost but he's turned over one.

And there we go.

My number is 7,910 and he says do the honours Lucas, because Lucas can only win when he compares the numbers and he is done that he's put the symbol in the right place in between them.

There we go.

8,536 is greater than 7,910.

Rematch, Andeep.

Yes, having a rematch.

The boys decide to add a twist to the game though.

And you can do this if you like later.

This time, they can either place a chord in their own box or in their partner's box.

That makes it more interesting, doesn't it? They can sabotage each other if they want.

The winner is still the play with a greater number.

So same rules.

"I'll keep this five," he says, that's the first one.

Lucas has turned over, "But I won't use it for my thousands.

I can do better." It's a little gamble, isn't it? That's halfway.

It could be lower, it could be higher.

So let's see, let's see if that pays off.

He's going to use it for his tenths three for Andy.

"Ooo! Choices, choices." He says, "I think I'll place is three into Lucas's thousands box, so he ends up with a low number." Oh, okay, wow, poor Lucas.

What's he gonna do now? "Wow, thanks Andeep!" He says, "You better hope I don't get zero, one or two now.

'cause you'll know where I will be putting it." Where do you think he's gonna put that? In the thousands.

Oh, he's got six.

So Lucas has got six.

"I'll put this into Andeep's ones.

At least he can't use it to make 6,000.

Yeah, it's limited his chance, isn't it? So there we go.

Hmm, ooh, wonder what's going to happen next.

Exciting, isn't it.

One for Andeep, what would you do with that one? How would you put it? Remember I can put in Lucas's box or his own box.

"Hmm, might as well keep this and use it for my lowest remaining value, the tens." Okay, the nine for Lucas.

"Oh the nine, that means Andeep can't make 9,000." That's good, so what would you do? Put it in one of your own boxes or put it in Andeep's box.

Put it in his own box.

So he is got a high value of hundreds, right? How can Andeep win, what numbers are left? What do you think he's got two.

What'd you do? "I'll keep this two," he says, "If I put it in the thousands I've lost." So there's only one real sensible place to put it.

The two there.

And he say, "Please be zero, please be zero.

Please be zero." It's eight.

Oh no, he says, "I can't put that into Andeep thousands box or he wins." So he's got to keep it.

He's gotta put it somewhere and he's put it there.

So that's Lucas's number.

And then Andeep is turned over four.

"Oooo! it was a close one," he says, "But I win." He has only just then he is gotta finish it off by using the inequality symbol.

That's what he's done, he's used the less than symbol.

3,958 is less than 4,216, which means, and Andeep wins.

"Well done, Andeep!" Says Lucas, "That was tense.

We're still friends, right?" And Andeep says, "Of course." Let's do a check, explain who's won, Lucas or Andeep and why, which symbol can be used to compare the numbers, pause the video.

What do you think? Who's won here outta those two? Lucas has got 7,830 and Andeep's got 6,954.

How can you compare them? Well you start with the thousands, are the thousands the same? No, they're different.

So which one's got more, Lucas? Lucas wins, his number has more thousands, Andeep may have more hundreds, tens and ones, but the thousands is the highest digit value to compare.

You can stop there when you've compare the thousands.

If one's different, you can stop there.

This time the boys decide to fix the thousands digits so that they can focus on comparing the other digits.

So they're both going, going to end up with a number that's 5,000 and something.

Let's see what happens, so Luke's got two and that's where he is put it.

Andeep is got seven and put it there.

Lucas' got six, put it there.

Andeep got nine, put it there.

What do you notice? Lucas says, "Oh no! I can't win now I can't beat nine hundreds.

Well done Andeep, let's finish the round." So he put his remaining card there and Andeep put his remaining card there.

So all that needs to happen now is Andeep needs to put the inequality symbol in.

So why has Andeep won, can you explain that? Andeep's won because the thousands have the same value, but he has more hundreds got nine hundreds, Lucas only got three hundreds.

So we can use this inequality symbol.

This time, the boys decide to fix the thousands and hundreds digits so that they can focus on comparing the other digits, the tens and the ones.

So Lucas's got zero, put it there Andeep's got one and he put it there.

Lucas's got five and put it there and Andeep got four and put it there.

So I check, who's one and can you explain why? Well let's have a look.

Of course the thousands are the same and the hundreds are the same.

So we have to look at the tens now.

One, somebody's got more tens and that's Lucas.

So Lucas is one.

The thousands have the same value than the hundreds do, but he has more tens just slightly, only one more.

So we can use this symbol.

So that says 5,750 is greater than 5,741.

Not by much.

It's time for some practise.

Task number one, use those symbols, the inequality symbols to compare the values.

Number two, use the digits 4, 5, 6, and seven.

How many ways can you complete that statement? And there are quite a few ways, so explore them.

Maybe you could be systematic.

And number three, play the same game that Lucas and Andeep played.

So remember you can choose whether to play the version where you only put numbers in your own boxes or you can do that second one where you can put it in your opponent's box, if you like.

So draw box on your whiteboard, shuffle a set of zero to nine cards and then take it in turns to turn over a card just like the boys did and decide where to put it.

The winner is the player with a greater number.

But you can only claim your point by writing in the correct symbol and say that sentence.

So A, start by having all the boxes, blank.

B, fix the thousands digit.

Now it says eight here, you can use eight or you can fix the different digit.

That's up to you.

And then C, fix the thousands and hundreds digits.

And that's an example of what you could do there.

You can use that one or a different one.

But whatever you do, have fun.

And I'll see you soon for some feedback.

Welcome back, let's have a look, how'd you get on? So number one, 4,029 is greater than 2094.

It's got more thousands.

2049 is less than 2,409.

It's got fewer hundreds.

2049 is less than 2094.

It's got fewer tens.

3,824 is greater than 3000 plus 800 plus 10 plus four.

So you notice the tens were different.

The first number got more tens.

And then 3,824 is greater than 900 plus 3000 plus four plus 10.

'Cause if you put those numbers together in the right order, you've got 3,914, which is a little bit more.

And using those digits, how many ways can you complete it? There are 11 possibilities for the first number, which are presented here systematically from lowest to highest.

So tick off any of these that you've got.

And in this example player A wins because there's more thousands in 5,236.

So we just needed to compare the thousands.

And in this example play a B wins because there's more hundreds in 8,764.

So we can use that symbol.

And in this example play A wins because there's more tens in that number.

Are you ready for cycle B? I think you are, let's go.

Andeep and Lucas are ordering these giraffes according to their masses.

So we've got Jack, Jenny, Jill, and Jim, and they've all got different masses.

Have a look at them.

We need to start with the lowest mass and we're going to use the inequality symbol.

The less than symbol specifically to explain this.

So ordering from lowest to greatest, who's got the lowest mass? "And it must be either Jenny or Jill as both have a one for the thousands digit," says Lucas.

He's right.

We need to look at the hundreds digits.

So yeah, Jenny's got 1000.

Jill's got 1000, but Jenny's got four hundreds and Jill's got 100.

One of those is lower.

It is four for Jenny and one for Jill.

Jill's is lower, yes.

So Jill's mass goes first, 1,150 kilogrammes.

And let's tick her off so that we don't include her mass again, right? What's it got to be next then? It's gotta be Jenny's mass.

That's the other one that had one in the thousands column.

So let's tick her off.

Jack and Jim have the same digit for the thousands.

Yeah, they do, look, they've both got two.

So we need to look at something else.

That means we need to look at the hundreds as Lucas.

Yes, but the hundreds are the same two.

Yes they are, aren't they? What is it? Zero.

They've both got zero.

, so what do we do now? We look at the tens.

Jack has a smaller number of tens.

Yes he has, Luc.

So his mass comes next.

Jack's got no tens in fact, so there we go.

We can put Jack in next.

And that only leaves Jim.

He's got the greatest mass of all the giraffes.

So now that says 1,150 kilogrammes is less than 1,475 kilogrammes, which is less than 2008 kilogrammes, which is less than 2080 kilogrammes.

We've ordered them.

Let's do a check order these mammals from greatest mass to lowest mass.

Pause the video.

You might notice this time that we're using a different inequality symbol, we're using the greater than symbol.

So let's start.

The African elephant has the greatest mass and we can find that out by just looking at the thousands column.

It's got the highest number, hmm.

So looking at the thousands column, what's next? 3,988, right? And now we've got a little issue because the other two have got the same number of thousands, which is one 1,430 kilogrammes comes next 'cause it's got more tens, three more in fact.

And that leaves the lowest as 1,400 kilogrammes.

And that's a southern elephant seal.

So that's the order that it went in.

Well and if you got that, you are on track.

It's time for some more practise.

So number one, complete the following.

Order the mammal masses from lowest to greatest.

And then B, order the mammal masses from greatest to lowest.

And here's the rainfall in the United Kingdom from 2020 to 2023.

Order the rainfall from the most to the least.

Number three, Andy's monitoring the amount of food eaten each week by his dog to ensure he is getting enough food.

Order the massive food eaten each week from lowest to highest time to pause the video.

Good luck with that and I will see you soon for some feedback.

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

So number one then the order went like this.

1,206 is less than 1,260, which is less than 1,600, which is less than 1,602.

And for B 6,500 is greater than 3,988, which is greater than 3,750, which is greater than 3,178.

So that's the order.

Number two, 1,334 is greater than 1,190, which is greater than 1,104, which is greater than 1090.

Number three, 1,100 is less than 1,250, which is less than 1,320, which is less than 1,350.

We've come to the end of the lesson.

Today, we've been comparing and ordering four digit numbers.

When comparing and ordering four digit whole numbers start with a thousands.

If the thousands are the same, compare the hundreds.

If the thousands and hundreds are the same, compare the tens.

If the thousands, hundreds and tens are the same, compare the ones greater than and less than symbols can be used to compare an order.

So in this example, hey look, we've got 3,958 is less than 4,216.

And in this example, we only needed to look at the thousands to determine that.

Well done on your achievements today, give yourself a well deserved pat on the back.

You've been amazing.

I hope I get the chance to work with you again in the future on some more maths.

But until then, enjoy the rest of your day.

Take care and goodbye.