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Welcome to your math lesson.

My name is Mrs. Harris, and we're going to be comparing and ordering numbers up to 10 million.

Why I recommend this lesson is a lot of it has real life context.

It's always quite nice to know what you're going to be doing in a lesson and this is what we're going to be doing.

First of all, we'll have a look at greater than, and less than just to refresh ourselves.

Then we'll compare numbers, following that we'll order numbers and we'll finish with an independent task.

You'll need a couple of things, a pencil, maybe a rubber.

A ruler is always good and some paper or a book that you can write in.

If you don't have those things, pause the video, go find them, and then come back to me.

All set? let's get on then.

So like I said, the first thing we're going to look at is greater than and less than.

When we think about greater than less than, we can say it, but we don't really want to spend the time writing that, especially when we're doing mathematical expressions.

So we have the symbols that you can see on the screen, which one's which, which one's greater than, which one's less than and which one's equal to.

I hope you know that one.

Okay.

So this is what they are.

We have greater than, equal to and less than.

Though sometimes that's a little tricky to remember.

So I like to think of them like this.

Like I've put some cubes in them and when I have the greater than, I can have more cubes in the open side of the symbol than in the closed side.

When I have equal to, I have two sets of cubes that are the same as each other, that's why my lines are straight.

They're parallel.

And then when I have less than I have my smallest number, my least number of cubes, my fewest cubes, and then my greater number of cubes.

I can say it with the numbers, I can say, four is greater than one.

One is less than four or two is equal to two.

And this is how I would write them.

You see why we want to write the expressions rather than the sentences.

Takes much less time.

I said we were working with larger numbers today.

Numbers up to 10 million.

Well, what if my cubes didn't have a value of one.

They had a value of a million each.

Now I can say 4 million is greater than 1 million.

2 million is equal to 2 million and 1 million is less than 4 million.

And then I can write the expressions as you see underneath as well.

Look at all the zeros.

So, now we know about the greater than, less than, and equal to symbols, we can start applying them.

I have two numbers here represented on a place value chart with place value counters.

We can quite clearly see how many hundred thousands we've got.

How many 10 thousands we've got.

How many thousands we've got.

How many hundreds we've got, how many tens we've got, and how many ones we've got in each number.

Which number is greater than and which number is less because ideally I'd have them side by side, but it'd be too small for you to see.

I would like for you to work out whether I need to put the greater than symbol in between them, the less than symbol or the equals to.

Let's take a second to look at the counters.

Okay, my top number is greater than my bottom number.

I can work the number out, but you know what I don't need to.

I can just see, see that I've got more counters in my ten thousands column in the top number than the bottom number.

They therefore is definitely greater than the bottom number.

Let's have a look at another one.

This time, instead of counters, I've put numbers in my place value chart.

I've got my first number one million, three hundred and fifty-seven thousand, eight hundred and eight-one.

And my second number, the one at the bottom is one million, three hundred and eighty-one thousand, four hundred and ninety-one.

I don't think I need to look at all the digits.

I don't need to look at the ones column.

I don't need to look at the tens column.

I don't even need to look at the hundreds column and I don't need to look at the thousands column.

I know that the top number is less than the bottom number.

When I start to compare the ten thousand column, Look, the top number has five ten thousands, and the bottom number has eight, ten thousands.

Therefore, whatever came after that, it just doesn't matter.

So my top number is less than my bottom number.

I could say one million, three hundred and fifty-seven thousand, eight hundred and eight-one is less than one million, eight hundred and one thousand- Oh, I got that wrong.

So, let me do it again.

One million, three hundred and fifty-seven thousand, eight hundred and eighty-one is less than one million, three hundred and eighty-one thousand, four hundred and ninety-one.

I got that number out at that time.

Now I have done the number and a number as words.

Sometimes we might see them as words, not very often, look how long it is, Am I going to put a greater than, less than or equal to in my circle? We thinking? I'm going to put an equal to.

The number that I write in words is simply the number that's represented in numerals in digits.

So, the number 1,562,844 is equal to, the same as, one million five hundred and sixty two thousand, eight hundred and forty four.

So, we've used greater than, less than and equal to.

We'll have a bit of a word problem now.

The population in Brussels, Belgium, is, bet you can say it? One million, one hundred and eighty-seven thousand, eight hundred and ninety.

The population of Birmingham, in the UK, is one million, one hundred and eleven thousand, three hundred and seven.

Which city has the largest population? Now you might be able to work this out quite quickly.

If you remember what I said about place value, we're going to spend a little bit of time just unpicking it and making sure that we all know how to solve this problem.

If I had a place value chart and counters, I would start to solve this problem by representing the population of Brussels and Birmingham, with the place value counters.

Now we can see that both cities in both countries have 1 million equal.

They have more than that, but the 1 million is the same.

Both of them have 100,000 people in that population, but the difference then comes when we look at the 10,000 column, we can see that in Brussels, there is 80,000, but in Birmingham is 10,000.

We don't even need to look at the columns of the thousands, the hundreds and the tens we just had because I'm covering it up.

So we can see quite clearly from this representation.

That its Brussels in Belgium, that has the greatest population.

And now we can say the population of Brussels in Belgium is one million, one hundred and eight-seven thousand, eight hundred and ninety.

The population of Birmingham in the UK is one million, one hundred and eleven thousand, three hundred and seven.

Belgium has the larger population, but I'd like you to tell me which statement, which expression is correct and how do you know? Pause the video now.

Okay, so the rest of the numbers, right? That wasn't the difference you were looking for? The one that is correct, the expression, the statement that's correct is the blue one, the top one, because that has a greater than symbol.

If we wanted to read that out, we would say 1,187,890 is greater than 1,111,307.

Whereas the other one we'd have to say less than, and that wouldn't be right.

Now that we've compared numbers, we're ready to do some ordering numbers and actually ordering numbers, it's just like comparing them, but with more so we're going to work with populations again.

And my table here shows a population of five cities across the world and we want to order them from smallest to largest.

From less than to greater than.

I think we should start by having a look in the millions column.

We've got a clear winner there, our greatest.

And we need to start looking at the hundred thousand column.

And then the 10,000 column is how I order them.

So, I've gone Paris, Rome, Madrid, Berlin, London that doesn't really help us does it in terms of the numbers.

So, first, as my smallest population, I put Paris.

It has 2,244,000.

But that is less in the hundred thousand column than Italy, than Rome in Italy.

And you see the two and then the eight, for the Rome in Italy.

And then I need to put one of my countries that has a population starting with 3 million.

I went with Madrid in Spain because in the hundred thousand column that has a one, whereas Berlin in Germany has a six in the hundred thousand column.

On my next number, I didn't need to look at anything other than the millions.

Look at the eight, that is much greater than the three.

So 3 million is less than 8 million and London, UK is the largest city in my table so it comes last.

I'd like you to do some ordering now.

I've got some numbers for you.

I want you to order them from smallest, least the most smallest to greatest just before I set you off.

Should I read them to you? We've got one million, five hundred and forty three thousand two hundred and ninety.

Then we have one million, three hundred and forty five thousand, three hundred and eight.

One million, one hundred and seventy-nine thousand and ninety-eight.

One million, and ninety-nine thousand, four hundred and fifty-two.

So did you put them in the right order for me, smallest to greatest? Have a think what column you're looking at.

Okay, so, well, I always say from smallest to greatest, I actually put the greatest one first and I'll write them going up and I'll read them going down.

So, look, my first number, you didn't have any numbers, any digits in the hundred thousand column.

So I put that one as my smallest number.

Then my next number, I had a one in a hundred thousand column.

It had one, one hundred thousand.

So I'll put that one next because the next one and a three in that column and the final one out of five in that column.

I did not need to look at all the digits.

Have a go at this one now, greatest to smallest.

Okay, this is how I ordered them.

How that how you ordered them? Which columns did you need to look at? Which ones did you not need to look at? Well done.

You're getting good.

We could also show greater than, or less than, the order numbers on a number line.

I've got some more populations here and I'd like you to represent the populations of these three cities on the number line and what comparisons can you make.

So, pause the video now and pop these on the number line.

Okay, welcome back.

How did you guys on? What did you notice? First of all, I noticed that these were quite big populations, bigger than we'd been working with already.

The first one I put on was Tehran.

I found I had to work out what the scale was on my number line.

I popped it just there.

The next one, I put on, was Nagoya.

Yes, nine million four hundred thousand.

So, I popped it there just short of nine million, five hundred thousand, and then my greatest population I popped on the end, just there with an arrow, pointing to it, rather than writing them.

I decided to use the flags.

Now it's time for your independent learning.

You need to bring together everything we've done in this lesson.

We're going to work on populations again.

I'd like you to do this bit of research.

It's a bit like a geography lesson, isn't it? I bet you'd find the population of these cities, Munich, Barcelona, Cologne, Copenhagen, and Glasgow, and then five more that lie between them.

And what you need to do with that data is put it in a table and order the cities from the largest population to the smallest.

So, pause the video now.

Do your independent learning and press play when you're finished.

Welcome back.

Now I'm thinking we might all have slightly different results depending on what website we went to or what year we looked at, but I had Barcelona as my greatest population.

It had 5 million in the millions column, so I didn't need to look at anything else.

Nothing was even close.

Munich came second.

It had 1 million.

And so did Cologne.

So I had to look at a hundred thousands column and Munich had four hundred thousand in its column.

So I put that next.

Followed by Cologne and then with no millions, I had Copenhagen, which was just greater than Denmark, then Glasgow, sorry, because it had a six in its hundred thousand column.

They were very close though.

Now, if you did the extra bit where you had to find five other countries that sit between them, you would have had to have something that had less than 5 million, 575,000 and more greater than 590,500,000- oh, what a number, 598,830.

Well, I don't know which one you chose.

Well, I can find out which ones you chose though, is if you asked your parents or carer to share your work on social media, I'll be looking at it on Twitter.

And if you tag Oak National, hopefully I'll see the city and your ordering of their population.

So all that's left for you to do is to do the quiz.

And for me, to say goodbye, bye!.