Lesson video

Hello there, my name is Mr. Goldie and welcome to today's maths lesson.

I'm sure you're going to enjoy it.

And here is the lesson outcome for today's lesson.

I can position three-digit numbers on number lines.

And here are our keywords.

So our first keyword is represent.

Can you say represent? Our next keywords are three-digit number.

Can you say three-digit number? Excellent.

And our last word is position.

Can you say the word position? Brilliant.

Let's look at what those keywords mean.

So represent means showing something or standing for something.

The number 10 can be represented as 10 in digits or as a full 10s frame, or is a base 10 block.

A three-digit number represents a number of 100s, 10s, and ones.

127 is a three-digit number.

Position means where something is located.

The number 15 is positioned between 14 and 16.

And here's our lesson outline.

So the first part of the lesson is positioning ten's numbers, and the second part of the lesson is positioning one's numbers.

Let's get started.

And in this lesson you will meet Sofia and Andeep who will be helping you today and asking you some questions as well.

Sofia represents three-digit numbers on a number line.

"Every number has its own position on the number line," says Sofia.

"You can use the multiples of 100 to help you position each number," says Andeep.

So any 200s number appears here.

So if it has a two as the 100s digit, it would appear somewhere between 200 and 300.

Any 500s number appears here.

So any number with a five as the hundred's digit would appear there.

So 560 would be somewhere on there.

So would 561, so would 589.

Any 800s number appears here.

So the 100s number is really important for positioning three-digit numbers on a number line.

"The 50s numbers are halfway between the 100s numbers," says Sofia.

You can use these to help you position other numbers.

It's not only the 100s numbers really important, the numbers halfway between the 100s numbers are really helpful as well.

So for example, 150 is halfway between 100 and 200.

350 is halfway between 300 and 400.

550 is halfway between 500 and 600, and 850 is halfway between 800 and 900.

And sometimes on number lines, there's a slightly thicker interval mark to help you as well.

So you can see where the halfway point is.

So Sofia is representing three-digit numbers on a number line.

"Where would 230 and 270 be shown," asks Sofia.

And Andeep is saying, "They are both in between 200 and 300." So somewhere between 200 and 300.

Now to help us work out where 230 and 270 are on a number line, let's position 30 and 70 on a number line first.

So Sofia is going to work out where 30 and 70 will be on a zero to 100 number line.

There are 10 steps from zero to 100.

The steps count up in 10s.

"I'll start by positioning 50 on the number line," says Sofia.

Which is very, very sensible.

So you can see there's a slightly darker interval mark right in the middle between zero and 100.

So 50 will go here.

Sofia can count forwards or backwards in 10s.

So she could start from 50 and count back to get to 30 or she could start from zero and count forwards to get to 30.

So 30 will be there.

So Sofia counts back two steps from 50 to find 30, 50, 40, 30.

70 would be there on the number line.

Sofia counts forwards two steps from 50 to find 70.

So 50, 60, 70.

So 70 would be the position there on the number line.

Can we use that to help us work out where 230 and 270 are? Then Sofia positions 230 and 270 on a number line.

So it's a number line going from 200 to 300.

So I'll start by positioning 250 on the number line.

So 250 would be halfway between 200 and 300, be on a slightly darker interval mark in the middle.

Sofia can count forwards or backwards in 10s to find 230 and 270.

So she can count backwards from 250, 240, 230 and that will give her the position of 230.

She can count forwards from 250 to find 270.

So 250, 260, 270.

270 would be positioned here.

What do you notice? 30 and 230 are positioned at the same step before the 50s number.

70 and 270 are also positioned at the same step after the 50s number.

So once you can position numbers between zero and 100, it's much easier to position any number on a number line.

Sofia represents three-digit numbers on a number line.

"Where would 540 and 580 be shown?" And Andeep's saying, "They are both between 500 and 600." Let's look at the part of the number line in between 500 and 600.

So let's make that slightly bigger.

Let's enlarge that.

So Sofia is going to position 540 and 580 on a number line.

And there we have our number line, this time going from 500 to 600.

And again Sofia is going to start by positioning 550 on the number line.

It goes on the slightly darker, the slightly thicker interval mark in the middle.

Sofia can count forwards or backwards in 10s.

How would she position 540, I wonder? 540 is the 10s number before 550.

What about 580, where would that go? 580 would be here.

580 is two steps before 600.

So between 580 and 600 would be 590.

Sofia represents three-digit numbers on a number line.

Again, we're going back to our zero to 1,000 number line.

"Where would 820 and 890 be shown?" asks Sofia.

"They are both between 800 and 900," says Andeep.

So we're going to look at the parts of the number line between 800 and 900.

So position 820 and 890 on a number line.

There's our number line there starting at 800, and ending at 900.

Where would 820 and 890 be? Start by positioning 850 on the number line.

Count forwards or backwards in 10s.

Pause the video and see if you can work out where 820 would be on the number line and where 890 would be.

And welcome back.

Now Sofia gave you the advice of starting off by positioning 850 first.

So hopefully you put 850 right in the middle of 800 and 900 on that slightly darker interval mark and that can help you work out what the other numbers are.

So 820 would here.

820 is two interval marks away from 800.

890 is the 10s number before 900.

Very, very well done if you managed to position those numbers correctly.

Sofia positions numbers on a number line.

There are a hundred steps from zero to 100.

The steps count up in ones.

"I'll use the multiples of 10 to help me position each number." So what number would go between 10 and 20? The number would be 15.

What number will go straight after 40? What number is one more than 40? 41 is one more than 40.

So 41 will go here.

59 is one less than 60.

So 59 will be positioned here.

And finally, what number is one more than 90? 91.

Andeep positions multiples of 10 on a number line.

So Andeep's going to be looking at the numbers from zero to 1,000 and he's going to be positioning multiples of 10 on a number line.

There are 10 steps from zero to 100.

The steps count up in 10s.

So each interval mark on the number line is a 10.

"I'll use the multiples of 100 to help you position each number." So Andeep is going to look very carefully at the three-digit numbers.

Look at the 100s number and that is going to help him position the numbers.

So this first number here is halfway between 100 and 200.

What number would that be there? That would be 150.

This number is one interval mark greater than 400.

So it's 10 more than 400.

So the number must be 410.

410 is 10 more than 400.

What about this number here? This number is the interval mark before 600.

So it must be a 500 number, 500 and something and it's 10 less than 600.

The number must be 590.

590 is 10 less than 600.

And lastly, this number here, this number is the interval mark after 900.

So it's 900 and something and it's 10 more than 900.

The number must be 910.

What do you notice? So you can see there the number line that Sofia did with the one's numbers and the number line that Andeep used for the 10s numbers.

What can you spot? "The top number line counts in ones and the other number line counts in 10s," says Andeep.

"Although the number lines are different, the numbers are positioned at the same steps," says Sofia.

150 is equal to 15 10s.

"410 is equal to 41 10s," says Sofia 590 is equal to 59 10s.

910 is equal to 91 10s.

Andeep positions numbers on a number line.

Where would you position these numbers? 330, 490, 770, 980, and 610.

"I'll use the 100s and 50s numbers to help me position them," says Andeep.

The first number is going to be positioned is 330.

So we could count from 300 to work out where the number would be.

So we're counting up in 10s, remember.

Or we could position 350, work out where 350 is and count back from 350.

So 330 would be positioned here.

330 is three steps after 300.

Next number, 490, where would you position 490? 490 is the interval mark before 500.

490 is 10 less than 500.

So 490 would be positioned here.

Next, let's look at 610.

So 610 is 10 more than 600.

So 610 would be positioned here.

10 more than 600.

770, where would you position 770? Well, halfway between 700 and 800 is 750.

So you count on two interval marks from 750 to get 770.

750, 760, 770.

So 770 would be positioned here.

770 is two steps after 750.

Our last number is 980.

So 980 would go here.

980 is actually two interval marks before 1,000.

Represent the three-digit numbers on a number line.

Where would you position these numbers? 290, 440, 930.

"Use the 100s and 50s numbers to help you," says Andeep.

Very, very good advice, Andeep.

So pause the video, see if you can work out where you would position those three numbers.

And welcome back.

Let's see how you got on.

So the first number we're going to try to position is 290.

290 is a 200s number.

So it's somewhere between 200 and 300.

And in fact it's 10 less than 300.

So it would be the interval mark before 300.

So 290 would go here.

Let's look at the next number, 440.

So 440 is actually 10 less than 450.

450 is halfway between 400 and 500.

So 440 would be positioned at the interval mark before 450.

So 440 would go here.

And our last number is 930 and we can count up from 900 or count back from 950.

So 930 would be positioned here.

So very, very well done if you positioned those numbers correctly.

And let's move on to task A.

So task A, the first part of task A, you're going to label the numbers, you're going to work out what numbers the arrows are pointing at.

That very, very first number line, we've got the numbers between 200 and 300.

And the second number line underneath starts at 700 and ends at 800.

So we're looking at 700s numbers.

So think very, very carefully about what the numbers would be.

So have a go trying to label those numbers.

The second part of task A, this time we're using a number line from zero to 1,000.

You're going to label the numbers.

These are all 10s numbers, but use the 100s and 50s numbers to help you.

So think very, very carefully about which 100s number they are and you can count up or back from the 50s numbers as well to help you.

And here's the third part of task A.

So the third part of task A Andeep is thinking of a 10s number.

"The digits of the number add up to equal 12," says Andeep.

So Andeep's number could be 390.

Three add nine, add zero equals 12.

390 Would be positioned here on the number line.

What other numbers could Andeep be thinking of? Can you position those numbers on the number line as well? Pause the video and have a go at task A.

And welcome back.

And let's look at those answers.

So here are the answers for part one of task A.

So that number line, starting at 200 and going all the way to 300, you should have labelled numbers 210, 240, and 280.

And I hope you make good use of those 100s and 50s numbers as well to help you work out the positions of the numbers.

Here's part two of task A.

So you have to label the numbers.

Our first number was 60, it was 10 more than 50.

The next number was 240.

That was 10 less than 250.

So remember, make good use of those 100s numbers and 50s numbers to help you work out the answers.

And finally, here are all the possible answers for Andeep's challenge.

So remember the digits of the number had to add up to equal 12 and it had to be a 10s number as well.

So those are the possible answers and that is where the numbers would be positioned on a number line.

So very well done if you got onto to part three and managed to get some of those answers as well.

Excellent work.

And let's move on to part two of the lesson.

And part two of the lesson is positioning one's numbers.

Sofia represents three-digit numbers on a number line.

So again, she's looking at number line from zero to 1,000 to start off with.

"Where would 335 and 375 be shown?" asks Sofia.

"They are both in between 300 and 400," says Andeep.

So first Sofia is going to use a zero to 100 number line and I'm going to position 35 and 75 on the number line.

Sofia can count forwards or backwards from the 10s numbers.

Well 35 would actually be quite easy to find, wouldn't it? 'Cause this time the number's halfway between the 10s numbers must be a number with a five as the ones digit.

So 35 will be halfway between 30 and 40.

35 is halfway between 30 and 40.

Where would 75 be? 75 is halfway between 70 and 80.

And again you can see those slightly darker interval marks halfway between the 10s numbers.

Next Sofia uses a 300 to a 400 number line.

So this time the number line's labelled from 300 to 400.

"I'm going to position 335 and 375 on the number line," says Sofia.

Sofia can count forwards or backwards from the 10s numbers.

So again, to find 335, Sofia could look at 330.

335 must be halfway between 330 and 340.

375 must be here.

375 is halfway between 370 and 380.

What do you notice? "35 and 335 are positioned at the same interval mark after the 30s number," says Sofia.

"75 and 375 are positioned at the same interval mark after the 70s number." So if you get a little bit stuck trying to position a three-digit number, think of numbers between zero and 100 and use that to help you.

Sofia represents three-digit numbers on a number line.

"I want to position these numbers on the number line," says Sofia.

545, 563, 506, 589.

"They're all in between 500 and 600," says Andeep.

So lets take the part of the number line between 500 and 600.

Sofia used the 10s numbers to help her.

"So 545 is halfway between 540 and 550," says Sofia.

So 545 would be positioned here.

"563 is three more than 560," says Sofia.

So 563 would be positioned here.

506 is one more than 505, 505 is halfway between 500 and 510.

So 506 would be positioned here.

506 is much nearer 500 than 600.

589 is one less than 590.

589 is much nearer 600 than 500.

And here's a task for you to try on your own.

Got to label the numbers and again, you've got a number line going from 500 to 600.

Can you work out what numbers are represented by the arrows? And here's Andeep with a bit of useful advice.

"Use the 10s numbers to help you." So look carefully at those 10s numbers.

Think about which 10s number is nearer and use that to help you work out the answers.

Pause the video and see if you can work out those three numbers.

And welcome back.

Let's see if you've got them right.

So that very, very first one is the number that comes before 510.

And the number is 509.

Our next number is one less than 550.

So it must be 540 something.

So the answer is 549.

And our last number is one more than 575.

575 is halfway between 570 and 580.

And this number is one more than 575.

So the number is 576.

Very well done if you've got all three of those correct.

Excellent work.

Sofia represents three-digit numbers on a number line.

"I want to position these numbers on a number line," says Sofia.

784, 756, 801, 838.

Andeep is saying, "They are all in between 750 and 850." So let's use a number line going from 750 to 850.

So Sofia is going to use a number line going from 750 to 850 to help her position the numbers and she's going to use the 10s numbers to help her.

The first number is 784.

So we need to find on the number line 780 and perhaps we could find 785.

784 is one less than 785.

So 784 would be positioned here.

Our next number is 756.

Sofia is saying, "756 is one more than 755." So where would 755 be on the number line? Well, it would be between 750 and 760.

So 756 would be positioned here, one more than 755.

What about 801? Where would that be positioned? Well we can see 800, and 801 is one more than 800.

So 801 would be positioned here.

And our final number is 838.

"838," says Sofia, "is two less than 840." So we can find 840 and count back two.

838 would be positioned here.

And here's a problem for you to look at on your own.

Andeep has labelled some of the steps on this number line.

So you see that he's labelled four of the numbers.

"Have I labelled them all correctly?" says Andeep.

Have I got all the numbers in the right positions? What do you think? Pause the video and see if you can work out whether Andeep is correct with all four of those numbers.

Welcome back.

Let's see how you got on.

Did you spot any that Andeep's got wrong? Let's have a look.

So 752 is in the right position.

789 is not in the right position.

789 is one less than 790.

This step is actually 784.

Oh Andeep, 817 isn't in the right place either.

So this step is 807 not 817.

But Andeep, you got the last one, right.

847 is in the right place.

So very, very well done if you spotted both of Andeep's mistakes there.

And let's get started on task B.

So for the first part of task B, you've got to label the numbers.

So you've got there a number line starting on 600 and ending on 700.

What numbers are indicated by the arrows? For part two, you've got to position the numbers on the number lines.

So you've got there a number line starting on 800 and going to 900, you've got to position all those 800 numbers.

And the second number line starts at 670 and ends at 770.

So can you position all those numbers on that number line? And finally, part three, Andeep is thinking of a number between 560 and 660.

"The digits of my number add up to equal 14," says Andeep.

"So Andeep's number could be 563," says Sofia, because five adds six and three equals 14.

Sofia has very helpfully positioned 563 on the number line.

What other the numbers could Andeep be thinking of? Position them on the number line as well.

So pause the video and have a go at task B.

And welcome back.

And let's have a look at those answers.

So the first part of task B, here are the answers.

So you had to position the numbers on the 600 to 700 number line.

So the first number indicated by the arrow was 605 and the second number was 635.

And I hope you made good use of those 10s numbers and those five numbers to help you label the numbers.

And here are the answers for part two of task B.

And again, if you need to pause the video at any time to help you mark your work, you can do.

So that very, very first one on the 800 to 900 number line was 808 and the second one was 832.

And again, make good use of those 10s and fives numbers to help you position the numbers.

And finally, here are all the possible answers for Andeep's challenge.

So remember, the digits of his number had to add up to make 14.

So all the numbers there, the digits add up to make 14.

So you could have had 608, you could have had 635, you could have had 653 and very well done if you managed to get onto part three of task B and managed to find lots of different answers.

And hopefully you are feeling lots more confident at positioning 10s and ones numbers on number lines all the way up to 1,000.

Excellent work today.

Very, very well done.

And let's look at our lesson summary.

So use the multiples of 10 and 100 to help you position each number.

Use the halfway steps to help you find the five or 50s numbers.

You can count forwards or backwards to find the positions of numbers.