Lesson video

Hello, everybody.

I'm Mrs. Crane and welcome to today's lesson.

Today, we're going to be learning how to order and compare numbers beyond 1,000.

In a moment, I'll run through all of the equipment that you will need for today's lesson.

But first, if you can, make sure you turn all of the other notifications off on any of your devices so that you're not going to be distracted.

Then, try and find somewhere in your home that's also going to be a distraction-free area where you can get on and do our lesson together today.

Once you've done that, then let's begin.

Okay then, let's have a look at today's agenda.

So, we're going to start off by looking at greater than or less than.

Then we're going to go on to exploring by completing some inequalities.

Don't worry, if you've seen this word and thought, I don't know what that means, that's okay.

We're going to find out what that word means before we do that part.

Then we're going to be writing our own inequalities.

Then it will be time for your independent task, and we're going to be comparing numbers and then we're going to go through the answers together.

So, let us get started.

To get started today, we're going to need a pencil and some paper.

So please pause the video now if you haven't got those things already.

Okay, welcome back.

Let's get started then.

So, first thing we're going to do today is have a look at what's the same and what is different.

We've got two different place value, two of the same--sorry--place value groups here.

We're going to look at two different numbers in a moment and compare them with knowing what's the same and what's different.

So let's have a look at our numbers.

Our numbers have been represented by Dienes.

What I'd like you to do is look really closely at those two numbers and have a think about that question.

What's the same and what's different? Okay, I can see from looking at my screen that the thousands column shows three thousands in this number, and it also shows three thousands in this number.

So that's something that's the same.

Now, I can also see that there's numbers in my tens column in both of my two numbers.

There's digits in my tens column.

Those are the only things that are the same here.

I can see quite a few differences.

So I can see here there's no hundreds here, whereas we've got hundreds in this column.

We've got one, two, three, four, five, six hundreds in this column.

Although, there's both numbers in both of the tens columns, I can see they're clearly not the same number.

I can see there's six tens in this number, and I can see there's four tens in this number.

And then finally, if I look at my ones column I can see there's four ones in this number and there's no ones in this number.

So there's quite a few differences.

The main similarity being our thousands.

Let's have a look then at these numbers where we can see them in numbers rather than Dienes.

Now, have a think.

What's the same and what's different about these two numbers? Well, as we discussed a minute ago I can see that my three in my thousands column is the same.

And I can actually also see, when I can see it written down a little bit more clearly, that we've actually used the same digits in both numbers but they're used in different places.

Because I can see a zero, a six, and a four here.

And I can see a six, and a four, and a zero here.

So I know that their numbers, the digits, are the same.

But they're representing different numbers because those digits are in different columns.

And while they're in different columns, that means that that six here represents six hundreds here, whereas the six here represents six tens here.

So it means that those two numbers are very different even though they use the same digits.

That brings us on really nicely to thinking about the greater than or the less than.

Which is a part of our learning today.

So, you can see here two blank equations.

Now, you can see here two symbols.

This symbol here is the greater than symbol.

This symbol here is the less than symbol.

Now I'm sure lots of you will always remember it, because I do from when I was in school, as the crocodile always snaps the highest number.

So the number that's always in the more open part of our symbol, here for this one or here for this one, is always the larger number.

Because the crocodile is always really hungry for those large numbers.

So, I'm going to use that to help you today.

And these two numbers, we're going to use to compare them in our inequality signs here.

So these are what we call inequalities.

All inequalities means is just that these two numbers aren't equal to each other.

So, if this number was the same as this number, it would have an equal sign.

But because it's not, because this number has to be greater than this number here, we use the greater than sign.

And because this number here has to be less than this number here, we use the less than sign.

Okay? So, let's have a go then at putting our two numbers, 3,064, or 3,640, into our inequalities.

So, I know that 3,640 is greater than 3,064.

How do I know that, you might say? Well, I know that because my thousands have the same value but six hundreds is greater than zero hundreds.

So this number has to go here.

Less than.

So I'm going to use the same two numbers.

So if I know that this number is greater than this number, then I must know that 3,064 is less than 3,640.

Now I know that because if I, again, look at my thousands columns, they're the same.

But my hundreds columns, zero is definitely less than six, so 3,064 is less than 3,640.

Now, this time we're going to look at some new numbers.

How can I complete this inequality? I've got 8,272 here.

I've got a blank space here to put in either my greater than or my less than symbol.

And I've got 4,763 here.

What is the first thing that I could do to help myself solve this inequality? What do you think? Well done if you said, Mrs. Crane, why don't you represent them with Dienes to have a look at it like that? So, let's represent our numbers with Dienes.

Let's just double check that our deans are correct and look at these numbers a bit more closely.

So, 8,000.

Yup, I've got eight thousands here.

Two hundreds here.

Four, five, six, seven tens here.

And two ones here.

So that makes my number, 8,220.

272.

Don't know where I got 22 from then, there's definitely seven tens.

And my second number.

4,000.

700.

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

If you would count along with me.

Three tens here, yep.

And six ones.

One, two, three, four, five, six ones.

Now, I'm going to start at the number in the column with the greatest value.

Now that column here, is the thousands column because we're look at four-digit numbers.

So if I start off here, I can quite clearly see that eight thousands are greater than four thousands here.

Do I need to look and compare all of the other columns? Or can I just stop there if they're different and one's clearly greater than the other.

What do you think? Absolutely! I can stop there if my thousands are different values and I can clearly see which one is the greater value.

I know that 8,000 is greater than 4,000 so I can put in 8,272 is greater than 4,736.

Let's have a look then at the next equation.

So, first thing that I'm going to do again is I'm going to put in my Dienes to compare the numbers.

Let's put them both in.

Okay.

So, 3,000.

Yep, I've got three thousands.

800.

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

40.

One, two, three, four.

And 47.

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

Yup.

That's 3,847.

Let's check this number then.

3,000.

One, two, three.

One, two, three, four, five, six, seven, eight, nine hundreds, yup.

Two tens, yup.

And seven ones.

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

Absolutely.

So, like we did last time we're going to start off in the column with the greatest value.

Three thousands here, three thousands here.

Can I stop there? No, I can't.

Just because the column with the greatest value is the same, doesn't mean that my numbers are equal to each other.

The next thing I must do is look at the hundreds column.

Now here, I know there's eight hundreds because I've just counted them with you.

And here I know there's nine hundreds because I counted them with you, as well.

Now, I know that nine is greater than eight.

So I can stop there.

I don't need to double check my tens and my ones because that's not going to help me.

So this time, I need to say that 3,847 is less than 3,927.

Because this is the greater number because nine is greater than eight.

Or you could say eight is less than nine.

And that eight and nine represent hundreds not just eight and nine.

We know that because they are in the hundreds column.

Now, if you want to and you're feeling confident, you can pause the video and have a go at either drawing out the Dienes to help you or completing this inequality on your own.

If you're not feeling so confident that's absolutely fine, we're going to go through the example again together now.

Okay? So, again we're going to make our numbers using our Dienes.

So, let's look at the numbers really carefully and then decide which symbol goes here to complete my inequality.

First number, 1,000, yep.

700.

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

Yep.

And 20.

Two tens.

Six.

One, two, three, four, five, six.

Second number then.

1,000.

700.

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

20.

Three! Okay, let's start off in our column with the greatest value.

Now, I can see clearly here they've both got one thousand.

If I look here as well at my numbers.

Next column then, hundreds.

I can see here that there's seven.

I can see here that there's also seven.

If I look here and here, again, there's seven in both.

Now, going to carry on and I'm going to go to my tens column.

Two here and two here.

Oh! That means I must really look closely at my ones column.

There's six ones here, there's three ones here.

I know that six is greater than three, so I know that 1,726 is greater than 1,723 Because six is greater than three.

Okay, time for our Let's Explore today, in completing some inequalities.

So, for your Let's Explore today, I would like you to complete the following inequalities by using the correct greater than, here, or less than symbols.

Remember, you can use a place value grid like we were just using and draw on the Dienes if if will help you.

You've got three questions here and we're going to go through it together in a moment.

So, pause the video now to have a go at today's Let's Explore.

Okay, welcome back.

Let's have a look then at our answers.

So, 5,096 is greater than 4,370.

If I look at my thousands column, 5,000 is greater than 4,000.

Next, then.

3,433 is less than 3,789.

If I look at my thousands, they're the same.

But if I look at my hundreds I know four is less than seven.

The four and the seven represent hundreds this time.

Three.

5,036 is less than 5,096.

The five thousands are both the same, the zero hundreds are both the same.

But, three tens is less than nine tens.

So that makes 5,096 greater than 5,036.

Or you can say 5,036 less than 5,096.

Okay then, we're going to move on now and think about the real world.

Now, what I want you to do is have a look through these different mountains.

The name of the mountains first, then it has where the mountain is, and then it has the height of the mountain.

I want you to think about what you can notice about the different heights of these mountains.

Have a really close look at them.

Don't worry if you can't pronounce them very well, I've had a go and you'll have to bear with my pronunciation, because some of them are a bit tricky to say.

Okay, when I first looked at this I noticed that some of the mountains seemed quite a lot taller, the numbers seemed a lot bigger.

So for example Mount Elbrus seems quite a lot taller than somewhere like Zugspitze, which seems quite a lot smaller.

So I noticed there were different numbers in the thousands column of most of my mountains.

Now, we're going to use these to help us complete some of our own inequalities.

So, here we've got an empty inequality.

But we do have our symbol.

I know that this number here has to be greater than this number here.

I know that, I remember my crocodile is eating that number and I also remember because I am looking here and saying, something is taller than something else.

So, this number here has to represent a mountain that's taller than the mountain here.

So I'm going to use this table here to help me to complete this inequality and this sentence.

So, let's have a look.

Which of these mountains can we use to complete that inequality? So, I'm going to see firstly that I could use the mountain Mount Elbrus, its in Russia, and its height is 5,642 metres tall.

So I'm going to put that in here.

Now this number has to be greater than this number.

So when I look back over here I'm looking for a mountain which has a smaller height than this number here.

So I'm going to choose the mountain Zugspitze, it's in Germany and its height is 2,962 metres.

So I can put that in here.

Now I know that Mount Elbrus is taller than Zugspitze, so this number is greater, because if I look at the thousands column there's five in this thousands column and there's a two in this thousands column.

Now, I need to put that into my answer here so I need to say Mount Elbrus is taller than Zugspitze.

This time, my inequality here, the symbol here is showing me something different.

It's showing me that this number here has to be less than this number here.

Because if I think about my pneumonic, my way of remembering it, is that my crocodile eats the tallest number, which has to go here.

I know that this number here, this mountain here, has to be shorter than this mountain here.

I also can see that by looking at my sentence, somewhere is shorter than somewhere else.

So, which of the mountains am I going to use to complete this inequality? Let's have a look.

I'm going to go for Mulhacén, I believe that's how you pronounce it, is in Spain and its height is 3,479 metres.

So I'm going to put that in here.

Now this has to be shorter than the next mountain that I choose.

So I have to pick a mountain that is taller next.

I've picked Shkhara next that's in a country called Georgia and its height is 5,201 metres.

Now I know that 3,479 metres is shorter than 5,201 metres because if I look at the column with the greatest value, which is the thousands, I can see here that three is less than five.

So I know that 3,479 is less than 5,201.

So I can say here Shkhara is shorter than Mulhacén in my sentence.

Now, if you're feeling really confident you can have a go at this question.

This question, we're going to need three different mountains and three different numbers.

Don't worry if you're not feeling so confident, we're going to go through it together, just now.

So, I can see here that this number here has to be the smallest because this number here has to be bigger than that number and this number here has to be bigger than that number.

Because I need to find a mountain that's shorter than another mountain which is also shorter than another mountain here.

Okay? So, I'm going to start off by picking the mountain called Coma Pedrosa.

It's in a country called Andorra and its height is 2,943 metres.

My next mountain has to be bigger than this mountain here.

So the next mountain that I've chosen is Grossglockner, its in Austria, and its height is 3,798 metres.

I know 3,798 is greater than 2,943 because if I look at my thousands column, two is less than three.

Three is greater than two.

So I know my symbol, my less than symbol, shows me that 2,943 is less than 3,798.

I'm not finished there though.

This time I have another box that I need to complete.

So I need to find another mountain, this time this mountain has to be greater than the height of Grossglockner.

So I've chosen Mont Blanc.

Its in France and partly in Italy.

So, it's height is 4,810 metres.

So I'm going to put that in there.

Now, how do I know that this mountain is greater than this mountain? Well I look at my thousands column.

Here, I've got three thousands, here I got four thousands.

That shows me that my 3,798 is less than 4,810.

So, to complete my sentence I then need to put in the names of the mountains.

So it starts with Coma Pedrosa is shorter than Grossglockner which is shorter than Mont Blanc.

Okay, so now it's time for your independent task.

You're going to be comparing four-digit numbers.

So, using the mountain names and the heights, answer the following questions.

You've got all of the names and the heights here for you.

Decide whether each statement is true or false.

So firstly, you need to decide true or false.

Then, you need to write in the numbers into these square boxes.

And then you need to write in the correct greater than or less than symbol here in the circles to complete the inequalities.

You've got questions one to three on this sheet, and questions four to six on this one.

Look carefully at question six because you've got three different mountains to compare.

Okay? Please pause the video now to complete your task.

Don't forget to resume it once you've finished so we can go through the answers together.

Okay! Welcome back.

We're going to go through the answers together now.

So, my first question said Mont Blanc is taller than Mulhacén.

It is true, it is taller than Mulhacén because 4,810 is greater than 3,479.

I can tell that by if I look in my thousands column, 4,000 is greater than 3,000.

Question two.

Mount Elbrus is taller than Shkhara.

It's true, because 5,642 is greater than 5,201.

Now my thousands column is the same this time so I must look at my hundreds column and I can see here 600 is greater than 200.

So I know that I can put in that symbol here to complete my inequality.

The greater than symbol.

Question three.

Grossglockner is shorter than Zugspitze.

It's false.

3,798 is greater than 2,962.

So it's not right because Grossglockner is actually taller than Zugspitze.

I know that because if I look at my thousands column, 3,000 is greater than 2,000.

Question four then.

Shkhara is taller than Coma Pedrosa.

Let's see.

It's true, because 5,201 is greater than 2,943.

I know 5,000 is greater than 2,000.

Zugspitze is shorter than Grossglockner.

It's true because 2,962 is less than 3,798.

I know that because if I look at my thousands column, two is less than three.

And question six, we had to compare three different mountains here.

Mont Blanc is taller than Mulhacén which is taller than Coma Pedrosa.

It's true.

Let's have a look then.

So, Mont Blanc is 4,810 metres tall which is greater than Mulhacén which is 3,479 metres.

I know that because 4,000 is greater than 3,000.

Which is also greater than Coma Pedrosa, which is 2,943 metres.

I know that because I can see that three is greater than two in my thousands column.

If you'd like to, please ask you parent or carer to share your work today on Twitter by tagging @OakNational and #LearnWithOak.

You've worked really, really hard today.

Well done at trying to pronounce those different mountains, they we're quite tricky.

And well done at looking really carefully at that place value.

Now, what I'd like you to do is complete the following, the final quiz, and the hopefully we'll see you again soon for some more math.

Thank you and bye-bye.