Lesson video

Hi everyone, thank you for joining me for a Maths lesson today.

My name is Ms Jeremy, and today's maths lesson is going to be focused on comparing 6-digit numbers.

So get yourselves sorted with a nice, quiet space to learn, free from any distractions.

And when you're ready, press play to get started with the lesson.

Let's start by looking at our Lesson agenda for today.

So we're going to start with a little warm up which is going to be all about rounding.

We're then going to look at place value in 6-digit numbers.

And then think about inequalities, looking at numbers that are greater than or less than other numbers.

We're going finish off our learning with an independent task and quiz.

For today's lesson, you will need a pencil and some paper, and a nice quiet space for your learning.

Pause the video now to get these resources ready.

And restart when you're ready, for the lesson to begin.

Okay, so let's look at our warm up for today.

The question asks us how could we round this number to the nearest 10,000.

So we want to round the number 83,671 to the nearest multiple of 10,000.

We've got a number line to help us today.

What I'd like you to do before we get started and before I demonstrate how we complete this, I'd like you to see whether you can work out a strategy.

What would you do to round this number to the nearest multiple of 10,000? I'm going to give you five seconds to have a think about your strategy.

If you need a little bit longer, pause the video and restart when you're ready.

Okay, so because we're focusing on rounding to the nearest 10,000, we are looking at that digit that's in the 10,000th place, which is an eight.

That 8 has a value of.

80,000 We need to work out whether this number is going to round up or down.

The first thing I need to do is to work out what the smaller multiple of 10,000 is that's closest to this number.

So in this case, the smaller multiple of 10,000 is 80,000, and I'm going to need to write it just here at the end of my number line.

Then I'm going to count 10,000 up to find the larger multiple of 10,000, and that large multiple of 10,000 is 90,000.

I'm going to write it just here at the other end of the number line.

I need to find a halfway point, because remember any numbers that are greater than my halfway point, they round up.

Any numbers that are less than my halfway point, they round down.

So my halfway point, what number is halfway between 80,000 and 90,000? Three seconds to work it out.

Did you get it? It's 85,000.

So I'm going to write 85,000 just here, so I know what my halfway point is.

The next step I need to do is to place my 83,671 on my number line, so I can work out whether it's greater than my halfway point or less than my halfway point.

So looking at my number line here, I can see that 81,000 would be here.

82,000 would be here 83,000 is here.

So 83,671 is going to go around here.

And you can see that even though it's close to my halfway point, it is not greater than my halfway point, so therefore the number rounds down.

I know that 83,671 when rounded to the nearest multiple of 10,000 rounds to 80,000.

We're going to be using some of those strategies a little bit later on so keep an eye on those number lines and keep thinking about how we use those number lines to help us with place value and with rounding.

Okay, so let's have a look at our main task for today.

So we're looking at six-digit numbers today, and I've got six digit cards here, with different digits on them and what I want to know is which six digit numbers could I make with these digits? And then, how does the value of the digits change depending on the placement on my place value chart that I've got on my screen here.

So what I'm going to have a go at doing is putting these six digits in one order at the top of my place value charts, and then in another order at the bottom of my place value chart and looking at how the value of the digits change.

So let me start off, all I'm going to do is literally put my digits in just as they appear on the screen.

I'm going to put a 3 in my 100,000s place.

A five in my 10,000s.

I'll put zero in my 1,000s.

Four in my 100s.

One in my Tens.

And two in my ones.

That's one potential way of arranging these six digits.

What number have I made here? Let's say this six digit number after three.

One, Two, Three.

350,412 So now thinking about how I could maybe reorganise these digits.

This time, I'd quite like to make a number that is greater than the one I've already made.

So this time instead of putting a 3 in the 100,000s column, what could I put in there instead to make a number that's greater? I'm going to give you three seconds to work out which of those digits I should put in my 100,000s place this time.

Three Two One Okay, so you should have seen that there are two options.

If I want to make a greater number than the one I've already made, I either need to use my four or my five in the 100,000s place.

I'm going to use my five because I want to make a really big number now.

So I'm going to put my five there.

I'm going to use my next greatest number which is the four, and I'm going to put that in the 10,000s place.

My next greatest number is the three, I'll put that here.

My next greatest number is my two, I'll put that here.

My one goes next, and my zero goes there.

You can see my numbers have been placed in descending order, they're going down.

So it starts with five, four, three, two one and then zero.

That is the greatest number that I could possibly make.

Can we say what that number is after three together? One Two Three 543,210 And now thinking about the value of those digits.

Can you see the five that I've placed here, and how I moved it to put it there? Can you see the difference between the value of the five in my first number and the value of the five in my second number? Spend a bit of time thinking about that now.

What is the value of the five in both of those numbers? I'll give you five seconds.

Okay, so you should have seen that the value of the five in the fist number, because it's in the 10,000s column, it has a value of 50,000, whereas the value of the five in the second number has a value of 500,000, because it's in the 100,000s column.

So what this demonstrates is that if you put the same digit on different positions on your place value chart, you will find that they have different values.

And you can re-organize digits to make a number that is greater than or less than a different number, depending on where you put those digits on your place value chart.

So let's have a look at this question here.

I've got three numbers, I'm going to call them: Number A, B and C, just to make it easier to refer to.

And the question says how has the value of the digit '5' changed in each of these numbers? I'd like you to have a think now.

What is the value of the five in number A? What is the value of the five in B? What is the value of the five in C? I'm going to give you ten seconds this time.

If you'd like a little bit longer, pause the video and resume when you're ready.

Okay, so hopefully you've seen that the value of the five has changed in numbers a, b and c.

For A, the five is located in the hundred thousands place.

That means it has a value of? 500,000.

In B, the five is located in the 1,000s place.

That means it has a value of? 5,000.

And in C, the value of the five is located in the tens place That means it has a value of? 50.

So here just by moving that digit five, to different positions in our place value chart, we have changed it's value each time, and in this case, it's value has decreased because we moved it across our place value chart like this.

Okay, let's move on to a little independent task for you to complete now.

What I'd like you to do is look at the three numbers we've got on the screen.

Let's say those numbers together first of all.

The first number is? 672,391.

The second number is? 120,479.

And the third number is? 108,722.

And what I'd like you to do is to use the sentence starters that we have there on the screen to tell me what the value of the digit that's underlined in each of those numbers is.

So you can see I've underlined the digit two in those numbers, but they have different values depending on where they've been placed.

You can either write down your sentences and you should have three sentences written down on your piece of paper, or if you prefer you can just say these sentences out loud.

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

Okay, so hopefully you've had a bit of an opportunity to work out the value of those digits.

I'd like us to look at this together.

So let's look at the first number.

What is the value of that digit two? Well I can see that that two, currently, is in the 1,000s column.

The value of the digit two in the number 672,391 is 2,000.

Now let's look at the second one.

The value of the digit two in the number 120,479 is 20,000, because it's in the 10,000s column.

And the last one, the value of the digit two in the number 108,722 is 20, because it's in the 10s column.

How did you get on with those? So moving on, let's have a look at some inequalities.

One way of comparing two six-digit numbers, or actually any two numbers that you'd like to compare, is by using these inequality symbols.

The inequality symbols demonstrate which of the numbers is greater than the other, and I'm going to show you how to use those in a minute.

So what we're going to do is try and compare the two numbers that we have on the screen.

Let's say what those two numbers are.

The first number is? 305,421.

The second number is? 305,241.

So you can see we've only got a very small change, a swap around of two digits in that number.

But we're going to compare them to work out which one is greater.

One of the ways that you can compare numbers is to put them into a place value chart, and compare from left to right.

Let me show you what I mean.

So I'm going to put the first number in my place value chart initially.

So I've got 305,421.

Now just below it I'm going to put the other number in.

I've got 305,000 this time 241.

And what I'm going to do is compare from left to right, I'll be looking at each of the columns in turn, and working out if there are any differences.

As soon as I get to a difference, I need to make a comparison and work out which number is greater.

So let's have a look.

So I'm starting with my 100,000s column.

At the moment, both of these numbers are exactly the same.

That means that, in both numbers, we have a three in the 100,000s place.

That's 300,000.

My 10,000s, really similarly, both those digits are the same, so I'm going to move on again to the next column.

In my 1000s place, in my 1000s column, those digits are exactly the same.

Still haven't found any differences.

Let's look at my 100s.

Ah, in my 100s, I've found a difference.

I can see that I've got 400 here, and 200 here.

What's greater? 400 or 200? It's 400.

So therefore, I know that this number here is my greater number, it has the greater value.

So what I need to do is put an inequality sign between these two numbers at the top of my screen to demonstrate that.

I need to show that 305,421 is greater than 305,241.

I'm going to be using this inequality here, and I'll draw it in for you like that.

And what that shows is that actually, the first number, my number on my left is greater than the number on my right.

I have a sneaky way of remembering it if you would like to, I like to remember this as a crocodile mouth.

I'm going to draw some teeth in so you can see what I mean.

So my crocodile mouth looks like that.

And the crocodile mouth is always open towards the number that is greater, because he's quite a greedy crocodile.

So, always face your open crocodile mouth towards the greater number, or the number with the greater value.

So let's have a little practise with this.

What I'd like you to do is do exactly the same thing I just did, but with these two numbers instead.

I'd like you to write both these numbers in a place value chart, one above the other.

Use the comparison method that I demonstrated to show which number is greater.

And then choose the inequality sign that fits in between both of those numbers.

Don't forget my top tip of remembering the inequality sign looks a little bit like a crocodile mouth.

The crocodile is a bit greedy and wants to eat the number that has the greatest value.

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

Okay, how did you get on? So you might have been able to see that when you were comparing these numbers, the digits in the 100,000s, 10,000s and 1,000s and even in the 100s columns, all of those digits were exactly the same.

It was only when you got to the tens column that there was a difference.

We had three tens in our first number, and two tens in our second number.

And that means that this number here is the greater number.

And I'm going to put my inequality sign facing this way to demonstrate that that is the greater number.

How did you get on with that? Let's move on to our independent task.

We're going to be using inequality signs just like we've learned to do with these examples on your screen here.

What I'd like you to do is write out the equations with both sets of numbers for each equation, and then I'd like you to work out which way the inequality sign should face.

Let's do the first one together.

We need to work out is 561,782 greater, or is 821,901 greater? Well in this case, I don't actually need to draw a place value chart.

I can see straight away, looking at the digits that are in my 100,000s place, that 821,901 is greater, therefore my inequality symbol is facing this way here.

I'd like you to complete this for all of the questions: A to F, and then I'd like you to complete the challenge question, where you'll need to draw an inequality symbol here, and an inequality symbol just here.

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

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

So what I'd like you to do is take your pen or pencil, and just tick off as you go.

Tick to show whether you got the answer correct or incorrect.

I'd also like us to have a little look at the challenge, so have a little look these numbers that we've got here.

Let's say the three numbers together.

The first number is 101,234.

The next number is 726,421.

The last number is 891,014.

Notice how because there are no hundreds, I say the word and instead of saying a digit for the 100s column, just to help me say the rest of the number correctly.

What we're going to try and work out is which inequality symbol should be placed in those gaps.

So I can see here that for the first gap, this number is greater than this number, therefore my inequality symbol faces this way.

When I'm comparing these two numbers here, I can see that this number is greater than this number, so my inequality symbol faces this way as well.

And by default, if I know that this number is greater than this number, then this number is greater than this number along here.

So you can see we've got a nice equation there, with three different numbers, with the inequality symbols to demonstrate how they relate to one another.

So I've got a final challenge for you for the end of the lesson.

Have a look at these new place value charts.

I'd like you to work out which is the number with the greatest value.

So without even needing to work out what the place value charts represent, what numbers they represent, I think you can probably tell this fairly immediately.

I'm going to give you 5 seconds to work out which is the number with the greatest value.

Five.

Four.

Three.

Two.

One.

So you might have seen, that actually in this case, because we're starting with our 100,000s and we're making comparisons with that column first, all we need to do is look at which of these numbers has more place value counters in the 100,000s column.

And in this case, it's my second number here.

I don't actually need to compare any of the rest of the number, I can see straight away which one is greater, because I've looked at my first column and there is a difference there.

Hopefully you've managed to get that too.

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

Only thing left to do for the rest of the lesson today is to complete the quiz! Thank you for joining me for our Maths lesson today.

It's been fantastic learning with you.

Do join me again soon.

Bye-bye.