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Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson.

The lesson comes from our unit on multiples of 1000.

So we're gonna be looking at those bigger numbers.

How are they put together, how are they composed? Where do we find them in real life, and how can we learn about them so that we can work with them when we're solving problems? So if you're ready to make a start, let's get going.

So in this lesson, we're going to be positioning six digit multiples of 1000 on a marked but unlabeled number line.

So six digit multiples of 1,000, six digit numbers.

Well, that's got 100 1000s in it, hasn't it? So we're gonna be thinking about numbers with 100, 1000 and more and positioning them on a number line.

So if you're ready, let's make a start.

So we've got two keywords in our lesson today.

They are scaling and multiple, so I'll take my turn and then you can say it.

My turn, scaling, your turn, my turn.

Multiple, your turn, well done.

You might be familiar with those words, but they are gonna be useful in our lesson.

So let's just check that we know what they mean.

Scaling is when a given quantity is made times the size.

And in this lesson, scaling will involve making values 1000 times the size.

A multiple is the result of multiplying a number by an integer, so a whole number not multiplying by fractions.

There are two parts to our lesson today.

In the first part, we're going to be finding midpoints on number lines, and in the second part we're going to be positioning multiples of 1000 on number lines.

So let's make a start with part one and we've got Aisha and Sam helping us in the lesson today.

So what's the midpoint of this number line? Aisha says there are 10 equal parts between the start and the end of the number line.

There they are, and the whole distance from one end to the other is 1000.

It's a zero to 1000 number line.

And Sam says if we divide the whole by the number of parts, we can find the size of each part.

So we're going to divide the whole length of the number line by the number of parts.

1000 divided by 10 is equal to 100.

So each of those jumps is 100.

Each of those points marks 100 on the number line.

That means that the midpoint will be five lots of 100, which is 500.

So that's our midpoint, 500, halfway between zero and 1000.

So let's look at these number lines and think about their midpoints.

We can use our knowledge of scaling.

Aisha says, she says, I know the midpoint between zero and 10 is five.

There we go, so the midpoint of zero and 1000 is 500.

Each number on the number line has been scaled up so it is 100 times the size.

Five times 100 is equal to 500, 10 times 100 is equal to 1000.

So the midpoint between zero and 1000 is 500.

And this is a stem sentence you're going to use quite a lot in this lesson.

So what's the same and what's different here? Aisha says there are the same number of intervals, Sam says, but each number has been scaled, so it is 1000 times the size.

So at the end of the top number line, we have 1000.

At the end of the bottom number line, we have 1000 1000s.

So it's 1000 times bigger.

So if our midpoint on the top number line is 500, the midpoint on the bottom number line will be a 1000 times bigger.

So 500,000.

So the midpoint between zero, 1000 and 1000 1000s is 500,000.

And Aisha says you can change the words to numerals to represent the 1000s.

So 500,000 can be written in digits 500,000 with the comma there to separate the 1000s from the 100s, 10s and ones.

So we've got our midpoint.

Let's count up in multiples of 100,000, zero, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, one million.

So we've counted all the way up to one million.

What if we tried to find the mid points between the multiples of 100,000? Says Sam, let's look at these points.

A, B, and C.

What do they represent? Ah, we brought back our zero to a 1000 number line, haven't we? Aisha says, we can use our knowledge of a zero to 1000 number line to help us find the values.

So let's start with A, so for A, the midpoint between 100 and 200 is 150.

So if we then look at the underneath number line where we've scaled everything up by a factor of 1000, we can say that the midpoint between 100,000 and 200,000 is 150,000, and that's how we write that with digits.

What about B? Can we use the stem sentences to help us? Let's look at the top number line first.

The midpoint between 400 and 500 is 450.

So if we think about that scaled up by a factor of 1000, the midpoint between 400,000 and 500,000 is 450,000.

And we write that as a six digit number like that with a comma separating the 1000s from the 100s, 10s, and ones, over to you to find the value of C, pause the video and use the stem sentences to help you work out what the value of C is.

How did you get on? Did you spot that on the top number line, the midpoint between 600 and 700 is 650, and then we've got to scale everything up by a factor of 1000.

So the midpoint between 600,000 and 700,000 is 650,000, and that's how we write it in numerals with the comma separating our 1000s from our 100s, 10s and ones.

What about the value of D? Pause the video, use the stem sentences and work out the value of D.

How did you get on? This time we took away the zero to 1000 number line, so we had to think about that one in our heads first.

So the midpoint between zero and 100 is 50.

So the midpoint between zero and 100,000 must be 50,000.

And there it is written in numerals, time for you to do some practise.

You're going to complete the stem sentences and write down the midpoints and they're labelled A, B, C, and D.

So use those stem sentences, use your knowledge of the zero to 1000 number line to help you and think about that scaling that we've been talking about.

Pause the video, have a go and we'll go through the answers together.

How did you get on? So for A, we were looking at that idea of between 100 and 200 or 100,000 and 200,000.

So the midpoint between 100 and 200 is 150.

So the midpoint between 100,000 and 200,000 is 150,000.

For B, we were looking between 300 and 400 if we imagined the zero to 1000 number line.

So the midpoint between 300 and 400 is 350.

So the midpoint between 300,000 and 400,000 must be 350,000.

What about C? Well, we know we're just beyond the midpoint of the whole number line.

So just beyond 500,000.

So between 500 and 600,000.

So we can think about that 500 and 600.

So the midpoint between 500 and 600 is 550.

So the midpoint between 500,000 and 600,000 will be 550,000.

And what about D? We're right at the far end of the number line now, aren't we? So we're between 900,000 and 1,000,1000, which is a million.

So we're between 900 and 1,000.

So the midpoint between 900 and 1,000 is 950.

So the midpoint between 900,000 and on 1000 1000 or a million is 950,000 and that's how we write it.

Well done if you've got those right.

On into the second part of our lesson and we're going to be positioning multiples of 1000.

So what do you think the value of each letter is here? we've got our number line back from zero to 1000.

What would you think those values are? You might want to pause and have a think before Sam gives you the answer.

Sam says, I estimate that A is 220, B is 480 and C is 990.

So you can use your knowledge of numbers positioned between zero and 1000 to help you find numbers between zero and a million or 1000 1000s.

So we've put those A, B, and C on the sort of matching points on the number line from zero to a million.

So Aisha says if A is 220 on the zero to 1000 number line, then A is 220,000 on the zero to a million number line and Sam's showing us how we write 220,000 in digits with her comma in the correct place.

So we can label point A 220,000.

What about B? Well, Sam says if B is 480 on the zero to 1000 number line, then B is 480,000 on the zero to a million number line, everything has been scaled up by 1000, multiplied by 1000.

And there it is on the number line, just before we get to 500,000.

And if C is 990 on the zero to 1000 number line, then C is 990,000 on the zero to a million number line and Aisha's showing us how we write it really close to our million, we're only 10,000 away.

So there's 990,000 and again, she's used the comma correctly to separate the 1000s, the 900,000 and the 90,000 and the no 10,000s from our 100s, 10s and ones where again, we've got no extra values to record there, but we need the zeros there to show us that those nines are 990,000.

Okay, Sam says, I've got a challenge for you.

If I point to a number on the gattegno chart, can you place it on the number line? You might want to join in with this.

Maybe you could sketch yourself a number line and join in with Sam and Aisha as they play this challenge.

Okay says Aisha, you're on.

So there's our gattegno chart, it's a gattegno chart just showing us 1000s, 10 1000s and 100,000s.

So those are the numbers that Sam has circled.

And Aisha says 20,000 plus 900,000 is 920,000, 920,000 is between 900,000 and one million, but it's closer to 900,000.

I think she's remembered that work we did with mid points, the midpoint would be 950,000.

So 920,000 is less than that.

So that's where Aisha's placing 920,000.

What about this one? We've still got a nine and a two floating around here, haven't we? But I'm not sure they're the same values.

Let's see what Aisha thinks.

Oh, Aisha's spotted it, this time we've got 90,000 and 2000, which is 92,000, only a five digit number, so it's got to be less than 100,000.

And there it is, 92,000 is less than a 100,000, but it's not far away.

It's only 8,000 away.

We've got 100,000 in between there.

So 92,000, that's about the right place for it.

Oh, now what have we got? Sam's sticking with those nines and twos, isn't she? What have we got this time? Well, Aisha's spotted it.

We've got 900,000 and then we've got 2000.

So we've got 902,000.

We've got no 10,000s this time, but we need that zero to show us that the nine represents 900,000 and the two represents 2,000.

902,000 is very close to 900,000 on our number line.

Our number line goes all the way up to a million.

So we've got 100,000 to fit in that gap.

So 902,000, very close to 900,000 and you might want to continue playing this game.

Perhaps you could challenge each other by pointing at numbers on the Gattegno chart and writing them in on your number lines.

Time to check your understanding though.

Can you mark the given number from the Gattegno chart onto the number line? So a bit like the practise I just suggested you might like to do.

So let's have a look at this one together after you've paused the video.

What did you see this time? Well, we had 700,000 and 40,000, so we had 740,000.

That's quite close to the midpoint between 700 and 800,000, isn't it? 700 and 800, the midpoint would be 750.

So between 700,000 and 800,000, the midpoint would be 750,000 and 740,000 is just before we get to that point.

So well done if you positioned that correctly.

And another check, can you mark 360,000 on the number line? Pause the video, have a go and then we'll look at it together.

How did you get on? 360,000 will be between 300 and 400,000 and it'll be just over halfway.

360 is just a bit bigger than 350, which would be the halfway point 350,000.

So 360,000 close to halfway, but just beyond it on our number line, between 300 and 400,000, well done if you got that right.

Time for you to do some practise.

You're going to mark the numbers onto the number line.

We've got a lot of eights there.

I think the zeros are going to be very important.

So think carefully about the place value, what the zeros represent and what that means for the position of these numbers on your number line.

And a challenge for question two, you can use the digits one to six only once, so no repeated digits, to complete the missing values on the number line.

So we know that there are three digits before we get to the 100s, 10s, and ones.

So we've got to fill in the 100,000s, the 10,000s on the 1000s to give a reasonable estimate of the value of those points on the number line.

So pause the video, have a go, and then we'll look at the answers together.

How did you get on? So let's start by looking at one where we were marking these numbers on the number line.

Did you sort out all those eights and zeros? So let's look at 8,000.

Well, we're on a number line from zero to a million.

So our first division is 100,000.

So 8,000 is very close to zero on this number line.

There it is.

What about 80,000? Again, 80,000 is less than 100 1000.

So it's still sitting in that first division on our number line, but much closer to the 100,000 this time.

So there's 80,000, 800,000 is a multiple of 100,000.

So it's going to sit exactly at one of our points, isn't it? We can see where 500,000 is 600,000, 700,000, 800,000.

So we know exactly where 800,000 goes.

What about 88,000? Well, we've got another one there that's less than 100 1000, haven't we? We know where 80,000 is, so it's going to be quite close to but just beyond 80,000.

There it is, and then we're left with 808,000.

Well, we can see where 800,000 is and 808,000 is just a little bit further along the number line than 800,000.

So there's 808,000.

I hope you positioned those correctly on the number line.

And I hope you really thought about the zeros, especially in the 808,000 and interesting that three of those numbers sat in the first division.

They were less than 100,000.

And what about question two? You were asked to use the digits one to six only once each to complete the missing values on the number line.

So this was our solution.

Could there have been another one? So we knew that this first number had to be between 200 and 300,000 on the number line, and it couldn't be beyond the midpoint.

So we knew it had to have a two in the 100,000s, and we knew it couldn't have a five or a six because it wasn't exactly halfway and it wasn't beyond halfway and it couldn't have had a one in the 10,000s because 210,000 something would've been much closer to 200,000.

So it had to have a four in the 10,000s.

Now the five or the six, I wonder, I wonder if that depends on the other number.

So I think we've got to have the two in the 100,000s and the four in the 10,000s of that first number.

Let's look at the second number now.

Well, we know it's between 300,000 and 400,000, so it's to have the three in the 100,000s.

We are left with five, six, and one.

Well, it's definitely beyond the halfway and I think it's far enough beyond the halfway that maybe we need the six in the 10,000s there to show that it's definitely beyond halfway.

So we know that that's got to be 360 something 1000.

And we know that the first number's got to be 240 something 1000.

I think the one and the five could probably have gone in either place.

Each of those divisions is worth 100,000.

So 1000 and 5,000 are very small distances along that number line.

So you might have had 241,000 and 365,000.

I don't think that makes too much of a difference.

Were there any other solutions you could have come up with? Do you think you could have had 350 something 1000, maybe 356,000? But then how would we have made the other one definitely just below 250,000? I think there were some variations, but not that many for this question.

But I hope you've had fun experimenting with it.

I wonder if you could find another two positions on the number line that you could label using those six digits as well, that might be interesting to explore.

And we've come to the end of the lesson.

Thank you for all your hard work and especially all your thinking in that last task.

We've been positioning six digit multiples of 1000 on a marked but unlabeled number line.

So what have we been learning about today? You can identify unlabeled marks on a number line by finding the size of each interval and counting on or back.

We divided the whole value of the number line by the number of divisions to find out what each division was worth.

And we also thought carefully about midpoints along the number line as well.

The midpoints were really useful for positioning numbers on the number line or identifying unlabeled positions.

We've also learned that you can use your understanding of numbers positioned between zero and 1000 to help you identify the position of multiples of 1000, 10,000 and 100,000 between zero and one million.

And we thought about scaling there.

Everything had been made 1000 times bigger, and that helped us when we were identifying those positions.

Again, thank you for your hard work.

I hope you've enjoyed the lesson as much as I have, and I hope I get to work with you again soon.

Bye-bye.