Lesson video

Hi there, my name is Mr. Tilstone.

I'm a teacher and I'm really excited to be with you today for this lesson which is all about mixed numbers.

Now I'll bet you've heard about mixed numbers before.

I'll bet you know quite a bit about mixed numbers already.

Well, let's see if we can take that knowledge even further.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can identify numbers on marked but unlabeled number lines.

And our key words, my turn, mixed number, your turn.

And, my turn, integer, your turn.

I think you probably know what a mixed number is, but we'll have a little recap anyway.

But what about integer? A mixed number is a whole number and a fraction combined.

So here's an example, that's one and a half, that's a mixed number.

An integer is a number that has no fractional part, they're whole numbers.

So this includes the counting numbers like one, two, three, and zero.

Our lesson today is split into two cycles or two parts.

The first will be positioning numbers on a number line and the second, identifying numbers on a number line.

So if you're ready, let's begin by thinking about positioning numbers on a number line.

And in today's lesson, you're going to meet Aisha and Andeep.

Have you met them before? They're here today to give us a helping hand with the maths.

Look at these two number lines.

What do you notice? Because that's what good mathematicians do, they notice things.

What do you notice about these number lines here? Have a good look.

Can you see anything that's the same about them? Can you see anything that's different about them? Well, both whole line segments are the same length.

Did you notice that? The two lines are the same length.

But they have been divided into different numbers of equal parts and they have different fractional parts.

Did you notice that? So one was dealing with quarters and one was dealing with fifths.

All these numbers could have been presented on one number line, but that would've been confusing and hard to read.

So they've been presented on two different ones.

Let's use the number lines to answer some questions.

Are you ready? First one is this.

And remember, there's more than one possible answer to this.

The first one is this.

Can you find a number between two and three? And can you do that on both of those number lines? So a number between two and three.

I've got one.

Have you got one? Let's see if it's the same or different.

Well, these are the numbers in between two and three.

What about this one? Can you find a number that's very close to three? Hmm.

Can you do that on both number lines? I've got one.

It's a mixed number that's very close to three on the top number line.

And I've got a mixed number that's very close to three on the bottom number line, let's see.

Did you have the same as me? Two and three-quarters is really close to three.

It's the closest mixed number to three on that top one and two and four-fifths is the closest mixed number to three on the bottom number line.

What about this question? Can you find a number that is greater than two but very close to two? Hmm, can you do that on both of those number lines? I'm going to do that.

Okay, I've got one for the top number line and I've got one for the bottom number line.

Okay, I wonder if I've got the same as you.

Shall we find out? Did you have the same as me? So two and one-quarter, two and a quarter is greater than two, but close to two and two and one-fifth is greater than two, but close to two.

Let's have a check.

Can you find a number this time that is smaller than two, but very close to two? Can you do that on both number lines? Pause the video and have a go.

Okay, I've got one for each.

I wonder if you've got the same as me or different.

Let's have a look.

So here on the top one, the one in quarters, one and three-quarters is smaller than two, but it's very close to two.

You couldn't get any closer on that number line and the same on the bottom line.

So one and four-fifths, that's smaller than two, but it's close to two.

Aisha and Andeep are taking it in turns to position numbers on this number line.

See if you can help them.

Aisha picks a card with a number on it.

She's picked three-fifths.

Where do you think she should position this number? Where would three-fifths go? Hmm.

Would it go after the three? No, it wouldn't go after the three, would it? Hmm.

Three-fifths has no whole part.

So it's smaller than one.

Yes, of course.

It's just got a fractional part.

Each interval between the integers is divided into five equal parts.

So if you look between zero and one, there are five equal parts, between one and two, five equal parts, between two and three, five equal parts.

And between three and four there are five equal parts.

So that's why we're counting in fifths.

Three-fifths will be located at the end of the third part because it's three-fifths.

And that's where it would be.

That's three-fifths.

Well done if you spotted that.

Andeep now picks a card with a number on it.

Let's see what he's got.

He's got this number.

Can you say that number? Can you read that number? What does that say? That's one and two-fifths.

Hmm.

Where shall we put that number? What do you think? It's a mixed number this time, it's got more than just a fractional part.

It's got a whole number and a fractional part.

One and two-fifths has one whole part, so it's greater than one, but smaller than two.

So because it's one and something, it's greater than one and smaller than two.

That's a part-part-whole model.

So we can see that one and two-fifths has got the one, that's the integer part, and the two-fifths.

So it's somewhere after one, specifically it's two-fifths after one.

We're working in units of one-fifth.

So one and two-fifths will be located at the end of the second part after one.

It will be just there.

Well done if you got that one.

And let's have a check to see how confident you're feeling.

Where would you position this number on the number line? Two and four-fifths.

Where would it go? The other examples have been left on as a little reminder that might help.

Where would you position two and four-fifths? Pause the video and have a go.

Let's have a think.

Well, it's got a whole number part, that integer is two, and it's got a fractional part, four-fifths.

So we know it's going to be after two, but before three.

And it's going to be four-fifths along from the two.

So it's just here, it's C.

Well done if you said C.

Two and four-fifths has two as its whole part so it's greater than two but smaller than three.

We're working in units of one-fifth so two and four-fifths will be located at the end of the fourth part after two.

I think you're ready for some practise.

Let's have a go.

Number one, position these numbers on the number line.

So what have we got here? Let's have a look.

We've got three-sixths.

What do you notice about that number? We've got one and four-sixths.

It's a different kind of number, isn't it? Two and one-sixth and two and five-sixths.

So where would you put those numbers? Number two, position these numbers on the number line.

Let's see what we've got this time.

We've got two and three-eighths, one and seven-eighths, six-eighths and one and two-eighths.

Where would they go? Think about the integer if it's got one.

And then think about the fractional part.

I have got a good feeling that you are going to do very well on these tasks, but let's find out.

Pause the video and off you go.

Welcome back.

Was I right? Did you well on that? Let's find out.

So number one, let's position these numbers on the number line.

Well, three-sixths has just got the fractional part, so it must be less than one.

And we're dealing with sixths here, so it's three along.

So that's three-sixths.

One and four-sixths.

Well, that's a mixed number.

It's after one, but before two.

It's four-sixths along from one because that's how the number's composed, it's got a one and a four-sixths.

So there we go.

Two and one-sixth is just here.

Again, it's a mixed number, it's got a two, that's the integer.

It's got a one-sixth, it's two and one-sixth, that's where it goes.

And then two and five-sixths is just here.

So just before the three.

It's five along, five-sixths along from the two.

And it's one-sixth before the three.

And then position these numbers on the number line.

Two and three-eighths goes here.

It's a mixed number.

It's got a two, it's got a three-eighths.

It's three-eighths along from two.

One and seven-eighths is just here.

That's either seven-eighths along from the one or one-eighth before the two, either way.

Six-eighths has just got a fractional part, it's not a mixed number.

We're counting in eights, it's six along, that's where it goes.

And then one and two-eights is another mixed number.

It's got a one part, it's got the two-eights part, so it's two-eights along from the one and that's where it is.

Well, you are doing really, really well.

And I think you're ready for the next part of the lesson, which is identifying numbers on a number line.

So look at this number line here.

Let's see if we can work out the value of each of these letters, hmm.

How would you identify the numbers represented by the letters on this number line? What would you do? What would be your first strategy? Well, for starters, I don't know what the fractions are yet.

So we need to work that out, don't we? We need to determine that.

How could you do that? What could you count? We need to determine the unit that we're working with.

And what about that number line? What do you notice? Let's use a stem sentence to help us out.

Each interval between the integers on the line is divided into mm equal parts.

This allows us to count in mm.

So between zero and one, how many equal parts are there? It's the same number as between one and two and the same number as between two and three.

What is that number? That will determine the fraction.

Well, it's seven.

There are seven equal parts between zero and one or one and two or two and three.

So we're counting in sevenths.

That should help us with A.

So let's look at A, what do you notice? A is before one which means the number that it represents is smaller than one.

It's not a mixed number, so it will not have a whole number part.

The unit we're working with is one-seventh and A is at the end of the first part.

So the value of A must be one-seventh.

Well done if you got that.

What about B, do you know what B is? B is after one but before two, which means the number that it represents will have one as its whole number part, it's going to be one and something.

So we've determined what the whole number part is.

What about the fractional part? How far along is it? The unit we're working with is one-seventh and B is at the end of the first part.

So the value of B must be one and one-seventh.

Did you get that? We can represent this mixed number as a part-part-whole model.

So I'm sure you've got lots of experience using these are very useful I think, in seeing how that mixed number is composed.

So one and one-seventh is composed of a one and a one-seventh.

And we can write an addition equation based on that.

So we can think of it as one, that's one of the parts, plus one-seventh, that's the other part, equals one and one-seventh, that's a mixed number, that's the total.

One and one-seventh is located between one and two on a number line.

What about C? What can we say about C? What's the same and what's different? Hmm.

C, just like B, is after one but before two.

So they've got that in common.

They're both one and something.

So the number that it represents will have one as its whole number part, just like before.

The unit we're working with is still one-seventh and C is at the end of the fifth part, so the value of C must be one and five-sevenths.

Did you say that? One and five-sevenths? And then just like before, we can represent that mixed number as a part-part-whole model.

The whole is one and five-seventh, a part is one and the other part is five-seventh.

That will help us to create an equation, an addition equation specifically.

So you can see that's composed of one plus five-seventh equals one and five-sevenths.

One and five-sevenths is located between one and two on a number line.

Looking at the position of C, did you notice that you could have counted on five parts from the one? You might have done that like this.

But there was a quicker away, there was a more efficient way.

I wonder if you did something else.

You could have counted back two parts from the two.

So that's one and six-sevenths and that's one and five-sevenths.

And one of those methods was definitely more efficient, wasn't it? That second one was definitely quicker.

Let's have a little check for understanding.

What is the number represented by D? Pause the video.

Well, it's going to be a mixed number, isn't it, because it's greater than one.

And it's got a fractional part, it's in between the integers.

So it's going to be two and something, isn't it? Because it's greater than two and less than three.

And we know we're dealing with sevenths.

So how many sevenths along is it from the two? And the answer is four, it's four-sevenths along from the two.

So that's two and four-sevenths.

Very well done if you've got that.

And here is the final practise.

Number one, by determining the unit that we are working with, identify the numbers represented by letters on this number line.

So what's A, what's B, what's C, and what's D? Now there's something that I notice about A that's different from B, C, and D.

I wonder if you do too.

We haven't established what the fraction is that we're counting yet, have we? So you're going to have to do that.

What strategies have you got for that? Let's see.

And then number two, Andeep says that the number represented by the letter A is two and two-thirds, but that's incorrect.

Can you explain why? Try and be as clear and simple as possible and help Andeep out.

Number three, what volume of water is in each of these jugs? Give your answer as a mixed number amount of litres.

So it's just like before.

We've been looking at horizontal number lines, these are vertical number lines, but they work in the same way.

Pause the video, good luck with that and I will see you shortly for some feedback.

Welcome back.

How did you get on, how are you feeling? Confident? Well, let's see.

So what was the fraction? We needed to determine that first, didn't we? By counting the parts in between the intervals, the marked intervals.

So each interval between the integers on the line is divided into 10 equal parts.

So we were counting in tenths, so that should help now.

We've done the hard work, I think now.

So that's two-tenths.

And that, it just had a fractional part, that wasn't a mixed number.

The others are mixed numbers.

They're all greater than one and less than two.

So it's going to be one and something.

Still tenths, remember? So how many tenths along is each one? So B is one and one-tenth, C is one and four-tenths, and D is one and nine-tenths.

And I wonder if you were efficient and rather than counting nine along from one, did you count one back from two? Hmm.

Number two, Andeep says that the number represented by the letter A is two and two-thirds.

Andeep is not correct.

Explain why.

Can you see where he's gone wrong and why he might have said that? You might have used a stem sentence to prove why he's incorrect.

Each interval between the integers on the line is divided into four equal parts.

So it couldn't be something and a third, could it? This allows us to count in quarters, not thirds.

The A is positioned on the second part after the two so the number that A is representing is actually two and two-quarters.

Did you recognise that? Well done if you did.

And number three, what volume of water is in each of these jugs? Give your answer as a mixed number amount of litres.

Well, let's have a look at this one.

So it's a vertical number line, but it works the same.

It's greater than one litre, it's less than two litres.

There are integers.

Now let's think how many equal parts there are in between those integers.

Let's count one, two, three, four.

So we're dealing with quarters.

So it's going to be one and something-quarters.

How many quarters? Three.

So that's one and three-quarters.

And that's how we write one and three-quarters.

The next one wasn't quarters.

So we need to determine what we're counting in.

We need to establish that fraction by counting how many parts there are between each integer.

I think it doesn't really matter which pair of integers you choose, as long as they're consecutive.

So each interval this time is divided into five equal parts.

This allows us to count in fifths.

The water-level is positioned on the second part after the two litres.

So the volume of water in the jug is two and two-fifths of a litre.

And that's how we write two and two-fifths of a litre.

We've come to the end of the lesson.

Today's lesson has been identifying numbers on marked but unlabeled number lines.

So our number lines today had the whole numbers on, the integers if you like, but we didn't know what the fractions were, so we had to work that one out.

So within a mixed number, the whole number is the most significant part.

Within a mixed number, the whole number part can be used to decide which integers it will be placed between on a number line.

The fractional part of the mixed number can then be used to establish exactly where it will be placed between these numbers.

You've been fantastic today.

You've made so much progress.

You're doing really, really well.

So well done.

Give yourself a pat on the back.

You've earned it.

I do hope I get the chance to spend another math lesson with you in the near future.

But until then, take care.

Have a great day.

Whatever you've got in store, succeed at it.

And goodbye.