Lesson video

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 a thousand.

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 five digit multiples of a thousand on a marked but unlabeled number line.

So the number lines will have marks on them, but not all the divisions will be labelled.

So we'll have to do some thinking about where these five digit multiples of a thousand sit on the number line.

So you ready to make a start? Let's get going.

We've got two key words in our lesson today, scaling and multiple.

I'll take my turn and then you can repeat them back.

So my turn, scaling, your turn.

My turn, multiple, your turn.

They're probably words you are familiar with, but let's remind ourselves what they mean because they're going to be useful to help us with our thinking today as we go through the lesson.

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

And in this lesson, scaling will involve making values 1,000 times the size.

And a multiple is the result of multiplying a number by an integer.

So that's a whole number, not a fraction.

There are two parts in our lesson today.

In the first part, we're going to be finding mid points, and in the second part, we're going to be positioning multiples of a thousand.

And all of this is centred around number lines.

So let's make a start on part one, and we've got Jacob and Izzy in this lesson helping us with our learning.

So what is the midpoint of this number line? The midpoint is what it says, the point in the middle.

What do you think? Izzy says "There are 10 equal parts between the start and the end of our number line." And there they are.

And the whole distance from one end to the other is 100.

So our line goes from zero to 100.

There it is.

Jacob says, "If we divide the whole by the number of parts, we can find the size of each part." So we know there are 10 parts.

100 divided by 10 is equal to 10.

We know that 10 tens are a hundred.

So each of our gaps must be worth 10 on the number line.

That means the midpoint will be five lots of 10, which is 50.

So there we can put our midpoint of 50 onto the number line.

When your number line is unmarked, it's really useful to be able to put the midpoint in.

It helps you to locate at the numbers.

What's the midpoint of this number line? And Izzy says, "Well, we can also use our knowledge of scaling." Can you see we've got a zero to 10 number line and a zero to a hundred number line.

I know the midpoint between zero and 10 is five.

So the midpoint of zero to a hundred is 50.

Each number on the zero to 10 number line has been scaled, so it is 10 times the size.

So the midpoint between zero and a hundred is 50.

And if we look at those two number lines, we can see that 10 times 10 is equal to 100 and 5 times 10 is equal to 50.

What do you notice this time? So we've got our zero to a hundred number line and our midpoint of 50.

This time we've got zero thousands to 100 thousands.

Izzy says, "Each number in the zero to 100 number line has now been scaled so that it is 1,000 times the size." 100 has become 100,000, a thousand times bigger.

So the midpoint would be 50,000, a thousand times bigger than 50.

The midpoint between zero thousand and a hundred thousand is 50,000.

There it is.

What do you notice this time? You can change the words to new rules to represent the thousands.

So 50,000 can be written as 50,000, 50,000, with the comma separating the number of thousands from the hundreds, tens, and ones.

Let's count up in multiples of 10,000.

0, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000.

"What if we tried to find the mid points between the multiples of 10,000?" says Jacob.

Let's have a look.

So what would these midpoints be? And we've put our zero to a hundred number line back on here.

Izzy says, "We can use our knowledge of a zero to 100 number line to help us find the value of A." So thinking about A, the midpoint between 10 and 20 is 15.

So the midpoint between 10,000 and 20,000 is 15,000.

And we can represent that in digits to put on our second number line.

Now let's find B.

So B is between 40 and 50.

The midpoint between 40 and 50 is 45.

So the midpoint between 40,000 and 50,000 is 45,000.

Time to check your understanding.

Can you find the value of C and complete the stem sentence underneath? Pause the video, have a go, and we'll look at the answer together.

What did you work out? Well, the midpoint between 60 and 70 is 65, looking at our top number line.

So the midpoint between 60,000 and 70,000 must be 65,000.

So there's our point C on our zero to 100,000 number line.

What about the value of D? Again, fill in the stem sentence, pause the video, and we'll have a look at the answer together.

How did you get on? This time, we haven't got the zero to a hundred number line to help us, but let's think about what it would be.

So the midpoint between zero and 10 is five.

So the midpoint between zero thousand and 10,000 is 5,000.

So point D marks 5,000.

Time for you to do some practise.

So you are going to complete the stem sentences and write down the mid points A, B, C, and D marked on that number line.

Remember to use your knowledge of the zero to a hundred number line to help you with the zero to 100,000 number line.

Pause the video, have a go, and we'll come back for some feedback.

How did you get on? Let's look at A.

If this was on the zero to 100 number line, we'd be looking at the midpoint between 10 and 20, and that would be 15.

So the midpoint between 10,000 and 20,000 is 15,000.

Let's look at B.

If it was on a zero to 100 number line, we'd be looking at the midpoint between 30 and 40.

So we need to think about that scaled up a thousand times.

So the midpoint between 30 and 40 is 35, so the midpoint between 30,000 and 40,000 is 35,000.

What about C? Well, we can see the midpoint of the line is that 50,000.

So we'd be looking to see that idea of the midpoint between 50 and 60 and then scaling it up.

The midpoint between 50 and 60 is 55.

So the midpoint between 50,000 and 60,000 is 55,000.

And then for D, we're right at the top end of the number line, aren't we? Between 90 and a hundred.

So the midpoint between 90 and a hundred is 95.

So the midpoint between 90,000 and 100,000 is 95,000.

And on to the second part of our lesson.

This time we're going to be positioning multiples of a thousand.

So without midpoints anymore, we've still got our midpoint there in green of 50 on our zero to a hundred number line.

But what do you think the value of each letter is here? Lucas has had an estimate.

He says, I estimate that A is 22, B is 48, and C is 99.

Ah, we've brought back our zero to 100,000 number line this time.

Izzy says if A is 22 on the zero to a hundred number line, then A is 22,000 on the zero to 100,000 number line.

It's a thousand times bigger on the number line underneath.

"And we write 22 as this," says Lucas, with the comma to separate our thousands from our hundreds, tens, and ones.

And there's 22,000 on our number line.

Lucas says, "If B is 48 on the zero to a hundred number line, then B is 48,000 on the zero to 100,000 number line, a thousand times bigger." And it's Izzy's turn to write down 48,000 this time.

And again, she's used the comma to separate the thousands from the hundreds, tens, and ones.

It makes our numbers easier to read.

And there's 48,000 on the number line.

What about C then? Well, Lucas estimated C to be 99 on the zero to 100 number line.

So he says, "C must then be 99,000 on the zero to 100,000 number line." And Izzy's written down 99,000 using the comma correctly to make it easy to read for thousands, and then the hundreds, tens, and ones.

99,000.

Lucas 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?" Now if you've got a number line in front of you, or maybe you could sketch one, you could join in with Izzy in the game.

Okay, so this Izzy, you're on.

So here's the Gatenno chart showing us our multiples of a thousand, 10,000, and 100,000.

And there's a number line from zero to 100,000.

So there are our first pair of numbers.

And Izzy says 2,000 plus 90,000 is equal to 92,000.

92,000 is between 90,000 and 100,000, but closer to 90,000.

So that's where she's positioning 92,000.

Well done, Izzy, I think you're about right.

Lucas has given us another one this time.

Oh, I can see two and nine again, but things are not in the same place, are they? Izzy says 20,000 plus 9,000 is equal to 29,000.

Ah, and she's reasoned that 29,000 is just less than 30,000.

So she's placed it just before 30,000 on the number line.

Oh, just one this time.

Izzy says 9,000.

That's just less than 10,000.

So it sits between zero and 10,000 on the number line, but very close to 10,000.

Time for you to have a go.

Can you mark the given number on the number line? Pause the video, have a go, and we'll get together to look at the answer.

Where did you think it went? What did we have? Well, we had 70,000 and 4,000, which is 74,000.

So it's between 70,000 and 80,000.

It's very close to the midpoint, but just before the midpoint.

So there's 74,000 just before 75,000, which would be halfway.

Another check.

Can you mark 36,000 on this number line? Think about what those missing divisions represent and use your knowledge of a zero to a hundred number line to think about where the number will go.

Pause the video and have a go, and then we'll look at it together.

How did you get on? Did you use your knowledge of a zero to 100 number line? So we can see here that 36,000 goes between 30,000 and 40,000 and this time it's just beyond the midpoint.

36,000 is bigger than 35,000.

Well done if you've got that right.

Time for you to have some practise now.

Can you mark the numbers on the number line? So we've got some numbers there for you and a number line from zero to 100,000.

Can you mark those numbers on? And question two says, can you mark the value of these expressions on the number line? So you've got to evaluate the expressions, work out there, total value, and then mark it onto the number line.

Again, zero to 100,000 number line.

So pause the video, have a go at your tasks, and we'll get together for some feedback.

How did you get on? So we had 3,000 to mark on first, and that is between zero and 10,000.

And it's below the midpoint, isn't it? 37,000 is between 30,000 and 40,000, just beyond the midpoint.

41,000, quite close to 37,000, just beyond 40,000.

72,000, again, we can see our midpoint of 50,000.

So we know the next mark is 60,000.

The next is 70,000, and 72,000 is just beyond that.

And then 91,000 is just after 90,000 on the way up to 100,000.

I hope you estimated the position of those accurately.

And in part two, we had to work out the value of these expressions.

So 45 times 1,000 is 45,000.

So where's that going to be on the number line? Well, it's the midpoint between 40,000 and 50,000, isn't it? So we can be fairly accurate with that one.

This time we had to do an addition.

So 20,000 plus 7,000 is 27,000.

We can use our place value to think about that.

So that's going to be between 20,000 and 30,000, just beyond the midpoint, closer to 30,000.

Now we had to do some multiplication and addition.

So we had six lots of 10,000, and four lots of 1,000.

So 60,000 and 4,000, 64,000.

So just before the midpoint between 60,000 and 70,000.

And then we had seven times 10,000, 70,000 plus nine times 1,000, which is 79,000.

So that's going to be just before 80,000 on our number line.

And then finally, gosh, lots of things to look at there.

Well, we need to be careful as well.

We've got some 10,000 and some 1,000.

So let's have a look at the 10,000.

So I can see one, two, three, four, five, lots of 10,000, and two lots of 1,000, so 52,000.

So that's just beyond the midpoint of the number line as a whole, just beyond 50,000.

I hope you enjoyed out the value of those expressions and then reasoning where they sat on the number line.

So we've come to the end of our lesson.

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

We thought carefully about the mid points, what's halfway between those points.

They're often really useful to help us when we're estimating the position of numbers on a number line or the value of a mark on the number line.

We've learned that you can identify unlabeled marks on a number line by finding the size of each interval and counting on or back.

We also saw that you can divide up the total value of your number line by the number of divisions to work out how big each division is as well.

And you can use your understanding of numbers positioned between zero and a hundred to help you identify the position of multiples of a thousand between zero and 100,000.

Thank you for all your hard work and your mathematical thinking today, and I hope I get to work with you again soon.

Bye-bye.