Lesson video

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

I'm sure you're going to have lots of fun.

And here is our lesson outcome.

I can estimate the position of three digit numbers on an unmarked number line.

And here are our key words.

I'm going to say the words.

Can you repeat the word back to me? So the first word is estimate.

The next word is position, and the last word is unmarked.

Excellent.

And let's look at what those words mean.

So estimate means finding a value that is close to the answer.

The unmarked step on the number line could be estimated as being 40.

Position means where something is located.

The number 15 is positioned between 14 and 16.

And unmarked means that many of the steps on a number line are not given.

Sometimes only the start and end steps are labelled.

It can also be when your teacher's been really, really busy and hasn't had a chance to look at your work.

And here is our lesson outline.

So the first part of today's lesson is estimating positions between 100's numbers.

And the second part of the lesson is estimating numbers on a zero to a thousand number line.

Let's get started.

In this lesson, you will meet Sofia and Andeep and they're going to be asking you lots of questions and helping you with your work today.

Andeep and Sofia want to measure James's height and mass.

Here's James, he's a giraffe and here's James on some scales.

So you can measure height by finding out how tall he is, and you can measure mass by finding out how heavy he is.

Sofia is saying "It's going to be really difficult "because the scales are unmarked".

It's gonna be really difficult to work out how tall James is and how heavy James is.

We need to find out how to estimate the position of numbers says Andeep and that's what today's lesson is about.

It's all about estimation.

Sofia estimates the position of numbers between zero and 100 on an unmarked number line.

So on the number line, the only positions that are marked are zero and 100.

And none of the numbers in between are marked.

Sofia is saying "What number is halfway "between zero and 100?" Oh, thank you Andeep.

Andeep is saying "50 is halfway between zero and a 100".

So if we can work out where the halfway point is, that's where 50 should be.

What number is halfway between zero and 50? Bit of a trickier question this one.

And here's Andeep very, very helpfully to tell us.

25 is halfway between zero and 50.

And that's one to remember.

Try and remember 25.

And then Sofia is asking "What number is halfway between 50 and 100?" And here's Andeep.

And Andeep is telling us that 75 is halfway between 50 and 100.

And again, that's a number to remember 75, see if you can remember that one for later.

Sofia estimates the position of numbers between 100 and 200 and Sofia is asking straight away "What number is halfway between 100 and 200?" Andeep says "150 is halfway between 100 and 200".

So 50 is halfway between zero and 100.

150 is halfway between 100 and 200.

What number is halfway between 100 and 150? See if you can remember back to what we just did when we looked at the zero to 100 number line.

The answer would be 125.

125 is halfway between 100 and 150.

What number is halfway between 150 and 200? And again, try to think back.

Can you work out what the number would be? The number would be 175.

175 is halfway between 150 and 200.

And those numbers 25 and 75, are going to be really important today.

See if you can remember them.

Sofia estimates the position of numbers between 500 and 600.

What number is halfway between 500 and 600? 550 is halfway between 500 and 600.

What number is halfway between 500 and 550? And again, see if you can remember back.

What do you think it would be? The answer would be 525.

525 is halfway between 500 and 550.

What number is halfway between 550 and 600? The answer would be 575.

575 is halfway between 550 and 600.

Sofia estimates the positions of numbers between 300 and 400.

Let's start off by putting 350 in the middle, right in the middle of 300 and 400.

What number is halfway between 300 and 350? What number is halfway between 350 and 400? You got two questions to answer there.

Pause the video and see if you can answer both questions and see if you can work out where both numbers would go.

And welcome back.

Let's have a look to see whether you got them right or not? So the first number, what number is halfway between 300 and 350? You should have said 325 and that's where 325 would be positioned on the number line.

What number is halfway between 350 and 400? The answer would be 375 and that's where 375 would be positioned on the number line.

Sofia estimates the position of numbers between 400 and 500.

"I'm going to estimate the position of 410 and 480" says Sofia.

First, let's mark the positions of 450, 425 and 475 and by marking those halfway points between numbers, it's really, really helpful to try and work out where the other numbers would be.

So, let's first of all work out where 450 is.

That's halfway between 400 and 500.

And then we can mark on 425.

That's halfway between 400 and 450.

And then we can mark 475 and that is halfway between 450 and 500.

Now Sofia wants to estimate the position of 410 and 480.

"I know 410 is halfway between 400 and 420" says Sofia.

So, Sofia marks 420 on the number line and uses that to help her estimate the position of 410.

So 420 would be roughly positioned there and 410 would be positioned there.

420 isn't very far away from 425, it's only five away.

Sofia also knows that 480 is five more than 475.

So, when she positions 480 on the number line, she knows it's not going to be much more than 475.

Sofia also marks 490 to help her estimate the position of 480.

490 would be positioned there, slightly nearer to 500 than 475 and 480 would be positioned there.

Sofia estimates the position of numbers between zero and 200.

This time the number line starts on zero and ends on 200.

What number is halfway between zero and 200? So we've marked the halfway point already.

What number is halfway? It's not going to be a 50 number this time is it? It can't be 50 or 150, what number would it be? 100.

100 is halfway between zero and 200.

What number is halfway between zero and 100? Nice easy one that one.

The answer would be 50.

And then our last mark we're going to put on this number line is what number is halfway between 100 and 200? We should know the answer to that one.

It would be 150 and those benchmarks are really, really helpful for helping us to position other numbers on the number line.

Sofia estimates the position of numbers between 200 and 400.

"What number is halfway between 200 and 400?" asks Sofia.

Have a little think.

What number do you think it would be? It would be 300.

So 300 is halfway between 200 and 400.

What number is halfway between 200 and 300? What number is halfway between 300 and 400? Pause the video, see if you can work out the answers to both of Andeep's questions and think carefully about where you would position those numbers on the number line.

And welcome back.

Let's see how you got on.

So what number is halfway between 200 and 300? You should have said 250 and it's halfway between 200 and 300 and that's where it will go on the number line.

What number is halfway between 300 and 400? The answer is 350 and that's where 350 will be positioned on the number line.

Very well done if you got those two correct.

Sofia estimates the position of numbers between 600 and 800.

"I'm going to estimate the position of 630 "and 770" says Sofia.

First, let's mark the positions of 700, 650 and 750.

And those benchmarks are going to have Sophia position 630 and 770 later on.

So, we can mark 700 in the middle of 600 and 800.

We can mark 650 in the middle of 600 and 700 and then in the middle of 700 and 800 we can mark the number 750.

So where would 630 and 770 go in the number line? "I know 630 is between 600 and 650" says Sofia.

It is nearer 650.

So Sofia marks the 10s numbers between 600 and 650.

So, 610, 620, 630, 640.

And then she labels 630.

So, 630 would be positioned roughly there.

That's a very very good estimation that Sofia has done.

Sofia knows that 770 is between 750 and 800.

Sofia marks the 10's numbers and labels 770.

So we've got 760, 770, 780, 790 and we then end with 800 and they're roughly the same distance apart.

So Sofia labels 770's position there.

That's where 770 would be positioned.

Sofia uses some number cards.

So she's got the number cards one, five and six.

I'm going to use them to make the numbers represented by the arrows.

So we've got a number line starting at 500 and ending on 700.

And Sofia is going to make three digit numbers and position those on the number line.

"I'm going to help Sofia by estimating the positions "of some numbers" says Andeep.

So, let's put 600 on the number line.

That's halfway between 500 and 700.

550 would go there, 650 would go there.

The first arrow shows a number between 500 and 550.

The 100's digit must be a five and the 10s digit must be a one, 'cause the number is less than 550.

So it can't be 560 something.

So the number must be 516.

The second arrow shows a number between 550 and 600.

The 100's digit must be a five, 'cause it's still 500 and something and the 10s digit must be a six.

We can't use the one as a 10s digit because we know the number is bigger than 550.

So, the number must be 561.

The last arrow shows a number very close to 650.

The 100's digit must be a six.

It's a 600 and something number and the 10's digit must be a five.

It can't be a one the 10's digit because this number is bigger than 650.

So, the answer must be 651.

Use these number cards, three, nine and two.

Rearrange the cards to complete the numbers represented by the arrows.

Andeep says "I'm going to help you "by estimating the positions of some numbers".

Andeep is going to help you by positioning 300 on the number line.

That's halfway between 200 and 400.

He's positioned 250 as well and he's positioned 350.

Can you work out what those two numbers are? Pause a video and have a think and see if you can work out what those two numbers are.

And welcome back.

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

So remember you've got to use those number cards.

That first number.

We've used the two already.

The first arrow shows a number less than 250.

It cannot be 293, so it must be 239.

The second arrow shows a number between 350 and 400.

The number must be 392.

It can't be 329, because that would be less than 350.

The number there must be 392.

Very well done if you managed to get those two numbers correct.

And here's another problem to try on your own.

So use these number cards, two, seven and eight.

Rearrange the cards to make the numbers represented by the arrows.

I'm going to help you by estimating the positions of some numbers.

So 800, Andeep says will be there.

750, will go there and 850 would go there.

Can you work out what numbers are represented by the arrows? Don't forget to use the number cards to make the numbers.

Pause the video and see if you can work out the answers.

And again, welcome back.

Let's see how you got on.

Let's see if you've got the right numbers.

So, the first arrow shows a number less than 800, but greater than 750.

The 100's digit must be a seven and the 10's digit must be an eight.

So, our first number must be 782.

It can't be 728 because that would be less than 750.

The second arrow shows a number greater than 850.

The 100's digit must be an eight and the 10's digit must be a seven.

So, that number there must be 872.

And again, very, very well done if you've got both those numbers correct.

And let's look at task A.

Part one of task A, you've got to estimate the position of the numbers on the number lines.

So for question A, you've got to position 325, 350 and 375.

That should be a fairly nice easy one.

And a halfway step is marked on the number lines for them to help you.

Part two of task A, estimate the position of the numbers on the number lines.

So part A, you've got to estimate 450, 500, 550, and then part B, you've got to estimate 825, 875 and 975.

And then part three, use the number cards to make three digit numbers.

Estimate their positions on the number line.

So.

pause the video and have a go at task A.

And welcome back and let's look at those answers and see how you got on.

So part one of task A, that's the positions of 325, 350 and 375 on the number line, and the number line underneath, hopefully you remembered to mark the positions of 450, 425, 475 and then use those to work out the positions of 440 and 480.

Here's the answers for part two.

So for B, you had to position 825, 875 and 975 and in fact, 875 is half way between 850 and 900.

So if you've marked those benchmarks on the number line, those would be incredibly helpful.

And then here's the answers for part three.

And again, hopefully you put those benchmarks on the number line.

So 700, 650 and 750 to help you.

And then you should have marked the other numbers on there.

So, marked on the number line are the positions of, 679, 697, 769, and 796.

And don't worry if your numbers aren't in exactly the same places, remember it's an estimate.

It only has to be roughly correct, but they shouldn't be too far off.

So, very well done on completing task A.

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

So, the second part of the lesson is estimating numbers on zero to 1000 number lines.

Andeep and Sofia think about how to estimate the position of numbers between zero and 1000.

"What number is halfway between zero and 100?" asks Andeep.

500 is halfway between zero and 1000.

The 500 should be positioned there.

"What number is halfway between zero and 500?" asks Sandeep.

250 is halfway between zero and 500.

So 250 would be marked there on the number line.

25 is halfway between zero and 50.

250 is halfway between zero and 500.

"What number is halfway between 500 and 1000?" asks Andeep.

"750 is halfway between 500 and 1000" says Sofia.

So 750 would be positioned there on the number line.

75 is halfway between 50 and 100.

750 is halfway between 500 and 1000.

Andeep thinks about using 100's numbers.

I'm going to use a number line marked with 100's to help me.

So, we've got number line from zero to 1000 and each of those intervals there is a 100's number.

Thinking about the 100's numbers, can really help position numbers accurately.

So 500 goes right in the middle.

250 is between 200 and 300.

750 is between 700 and 800.

That's the position of 100.

100 is closer to zero than 250.

There's 400.

400 is closer to 500 than 250.

There's 800.

800 is much closer to 750 than 1000.

Andeep estimates the positions of numbers between zero and 1000.

"I'm going to estimate the position of 200, "450 and 900" says Andeep.

I'll mark the positions of 250, 500 and 750 to make it easier.

Now it's always easiest to find the halfway down first.

So, let's go for 500 in the middle.

500 would be positioned there.

250 is halfway between zero and 500.

750 is halfway between 500 and 1000.

And those can help us estimate the positions of 200, 450 and 900.

So, 200 would be positioned roughly there.

200 is much closer to 250 than zero.

450 would be positioned there.

450 is much closer to 500 than 250.

900 will be positioned there.

900 is slightly closer to 1000 than 750.

900 is halfway between 800 and 1000, so it's slightly nearer 1000.

Arrange these number cards into three digit numbers.

So there we've got the cards, one, five and nine.

Match them to the numbers shown by the arrows.

So, are three arrows on that zero to 1000 number line.

Can you work out what numbers are represented by the arrows? "I'll mark the positions of 250, "500 and 750 to help Andeep" says Sofia.

Very helpful Sofia, thank you very much indeed.

So 500 will be positioned there.

That's about halfway between zero and 1000.

250 will be positioned there.

That's halfway between zero and 500.

750 will be positioned there.

That's roughly halfway between 500 and 1000.

So what's that first number going to be? It's less than 250, isn't it? Let's have a look.

It must be a 100's number because it's less than 250 and there's no two, so it must be 100 and something.

So the number cannot be 159, because that is position much closer to zero.

159 would be roughly halfway between zero and 250.

So, the answer should be 195.

Number here should be 519.

It's not much more than 500 is it? The number is positioned close to 500.

So it is 519, not 591.

And that last number, it's got to be 900 and something isn't it? 'Cause it's bigger than 750.

So it must be 900 and something.

What do you think it could be? 951.

The number cannot be 915 because that is positioned further away from 1000.

Arrange these number cards into three digit numbers.

So, this time you've got the number cards, zero, three and seven.

"Match them to the numbers shown by the arrows" says Andeep.

"I'll mark the positions of 250, 500 "and 750 to help you" says Sofia.

So, 500 will be there.

250, it's roughly there.

750 is roughly there.

Can you work out what numbers are represented by the arrows? Pause the video and see if you can work them out.

And welcome back.

Let's see whether you got them right.

So that first arrow, it's bigger than 250, this number, but smaller than 500.

What do you think the number would be? You should have said 307.

It cannot be 370, because 370 is about halfway between 250 and 500.

So, the number must be 307.

This number here must be 730.

703 would also be a good estimate.

So if you decided if a 703, think you'd get away with that one as well.

So do you remember James the giraffe from the beginning of the lesson? Well, Sofia and Andeep are now ready to estimate James' height.

"How tall is James?" asks Sofia I'm going to mark the positions of 250 centimetres, 500 centimetres and 750 centimetres on the number line.

So again, Andeep is going to mark the 500 first, 250 would be marked there.

750 would be marked there.

So how tall do you think James is? He's taller than 500 centimetres, isn't he? He's not as tall as 750.

Is he closer to 500? Is he closer to 750? James's height is slightly closer to 500 centimetres than 750 centimetres.

So a good estimate for James's height would be 600 centimetres.

Sofia and Andeep are all ready to estimate James's mass as well.

"So how heavy is James?" asks Sofia "So, I'm going to mark the positions of 250 kilogrammes, "500 kilogrammes and 750 kilogrammes" says Andeep.

500 would be there, 250 would be there, 750 would be there.

How heavy do you think James is? He's heavier than 750 kilogrammes, but he is not as heavy as 1000 kilogrammes.

James's mass is closer to 1000 kilogrammes than 750 kilogrammes.

A good estimate for James's mass would be 900 kilogrammes.

Sofia and Andeep estimate Jack's height.

"How tall is Jack?" asks Sofia.

"I'm going to mark the positions "of 250 centimetres, 500 centimetres and 750 centimetres" says Andeep.

There's 500, 250 and 750.

How tall is Jack? Jack's height is closer to 500 centimetres than 250 centimetres.

A good estimate for Jack's height would be 450 centimetres.

Sofia and Andeep estimate Jack's mass.

"How heavy is Jack?" asks Sofia.

And again, Andeep is going to mark the positions of, 250 kilogrammes, 500 kilogrammes and 750 kilogrammes.

There's 500.

There's 250.

There's 750.

So Jack's mass is much closer to 500 kilogrammes than 750 kilogrammes.

A good estimate for Jack's mass would be 550 kilogrammes.

Estimate Jenny's height.

I'm going to mark the positions of 250 centimetres, 500 centimetres and 750 centimetres to help you.

So let's mark the halfway mark, first of all, so we always do 500 first, then 250, then 750.

What would be a good estimate for Jenny's height? Pause the video and see if you can work it out.

And welcome back.

I wonder how close your estimate was to Andeep's answer? So Andeep says Jenny's height is closer to 250 centimetres than 500 centimetres.

A good estimate for Jenny's height would be 300 centimetres.

If you said 350, or anywhere in between 300 and 350, that's also a pretty good estimate as well.

Estimate Jenny's mass.

I'm going to mark the positions of 250 kilogrammes, 500 kilogrammes and 750 kilogrammes to help you.

500, 250, 750.

How heavy do you think Jenny is? Can you estimate Jenny's mass? Pause the video and see if you can work out an answer.

And again, welcome back.

Let's see how close you were to Andeep's answer.

So Andeep says "Jenny's mass is about halfway "between 250 kilogrammes and 500 kilogrammes".

A good estimate for Jenny's mass would be 380 kilogrammes.

So, very, very well done if you got close to Andeep's answer.

And we're now ready for task B.

So part one of task B, can you position each of the numbers on the number line? There are five arrows marked on the number line as well.

Mark the positions of some numbers to help you.

Two of these numbers are not represented by arrows.

Can you estimate their positions? So the number line goes from zero to 1000.

Be sensible to mark 500 first of all, wouldn't it? And then see if you can work out where those numbers would be.

And two of them are not marked by arrows on the number line.

Can you work out where those numbers would be as well? Here's question two.

Can you estimate Jake's height and mass? And don't forget to use those benchmarks to help you as well.

So, mark 500, 250 and 750 on each of the number lines.

And in part three of task B, Andeep thinks of a number.

"The digits of my number add up to equal 15" says Andeep.

So, Andeep's number could be 771.

Seven plus seven, plus one equals 15.

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

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

And welcome back.

And let's look at those answers.

So part one of task B, position each of the numbers on the number line.

So you should have marked those seven numbers on the number line.

And the two numbers that weren't marked by arrows were 17 and 660.

And that's roughly where those two numbers would be as well.

So very well done if you competed part one of task B.

Part two of task B.

So a good estimate for Jake's height would be 550 centimetres.

And a good estimate for Jake's mass would be 800 kilogrammes.

So, very well done if your answers were close to those two estimates.

And part three of task B, here are some possible answers and that's their estimated positions on the number line.

Excellent work today.

I hope you're feeling much more confident about placing numbers on unmarked number lines.

Fantastic work.

Very, very well done.

And let's finish by looking at our lesson summary.

So look carefully at the start and end numbers of the number lines.

Mark the halfway steps to help you estimate the positions of numbers.

And finally think carefully about which number is nearer.

Add the 10's, or 100 steps to help you estimate accurately.