Lesson video

Hello there, how are you? My name is Mr. Tilston and I'm a teacher.

If I'm meeting you for the first time, it's really nice to meet you, and if I've met you before, it's nice to see you again.

Today's lesson is going to be about mixed numbers.

You've probably got some familiarity with mixed numbers already.

Today we're going to be developing what we call fraction sense.

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

Let's begin.

The outcome of today's lesson is this.

I can estimate the position of a number on a number line using fraction sense.

And our key words, my turn, integer.

Your turn.

my turn, estimate.

Your turn.

What do those words mean, do you know? Let's have a little reminder.

An integer is a number that has no fractional part.

They are whole numbers, so not mixed numbers.

This includes counting numbers, e.

g.

one, two, three, and even zero.

When we estimate, we find a value that is close enough to the right answer, usually with some thought or calculation involved.

So you're going to be doing some estimating today.

Our lesson is split into two cycles or two parts.

The first will be estimate the position of numbers on a number line, and the second will be problem solving.

So if you are ready, let's focus on estimating the position of 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.

Aisha and Andeep are taking it in turns to choose a number card and then to estimate its position on the number line.

So what do you notice about that number line? Well, you can see that it's split into different intervals.

The intervals are marked.

They're integers, zero, one, two, three, and four.

What can't you see that you might have expected to have seen? You can't see any parts in between those intervals.

So we're going to use what's called fraction sense.

So here we've got half, where would you put half? Where would you estimate half to be? Well Andeep using some reasoning skills.

He's saying this number has no whole part.

So it sits between zero and one.

Did you notice that? So it's not a mixed number, it's just got the fractional part.

So it's got to be less than one.

It's got to be between zero and one, but where? Just here, exactly halfway between zero and one, that's where we would put half.

Aisha takes a turn to choose a card and then estimate its position on the number line.

Let's see what she's got.

She's got this number.

It is a mixed number this time, it's one and one third.

Where would you put one on one third? What do you think? Hmm, can you use fraction sense? What two intervals or integers would it be in between? Aisha says one and one third sits between the integers one and two.

Yeah, so it's gotta be somewhere between those two integers.

Let's imagine that the one to two interval is split into three equal parts.

Let's see if you can do that with your visualisation skills.

Can you picture splitting that into three equal parts? So you'd need two marks on there.

And we want one of those parts because it's one third, so that is where we can estimate that one and one third would go just there.

Aisha takes another turn to choose a card and then estimate its position on the number line.

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

Let's see if you can use your fraction sense to see where it would go.

We've got this one, two and four fifths.

Hmm, between which two integers would you place that two and four fifths? Well, I Aisha say the previous integer before two and four fifths is two.

Yes.

And the integer after two and four-fifths is three.

So it's got to be in between those two integers.

Let's imagine this time that the two to three interval is split into five equal parts.

Can you do that with a power of your mind? Can you picture that being split into five equal parts? We want four of them.

So that is where we can estimate two and four fifths will go.

That would be a good estimate.

Andeep says, wait, there is an easier way, we can use our fraction sense superpower.

Hmm, what has Andeep notice? Did you notice anything? Two and four fifths, is there anything about that four fifths fractional part that stuck out to you? Five fifths make one hole.

So two and four fifths is only one fifth away from three.

Yeah, it's really close to three, isn't it? I estimate that two and four fifths is close to three, yeah, that's what's called using our fraction sense.

So let's do a check.

Which of these is an accurate estimation for the position of three and one fifth? Is it A, B, C, or D? So think three and one fifth.

Pause the video and give that a go.

Which letter is three and one fifth? It's this one, it's C.

Three and one fifth sits between three and four.

C and D both sit between three and four, don't they? Imagine the interval between three and four is divided into five equal parts, so you can see if you can picture that with your mind and we want one of those parts.

We could also use our fraction sense knowing that one fifth is very close to the previous integer.

So because it's three and one fifth, it's got to be close to the three.

The children look at a different number line and mixed number.

And the mixed number this time it's got a very big denominator.

This is one and 18 20ths.

Okay, what sticks out about that fraction, 18 20th? Hmm, what would you say about that? What would you estimate the position of this mixed number on the number line? Andeep says, I will imagine the interval between one and two is divided into 20 equal parts.

Very good.

And we want 18 of those parts.

Yes we do.

Is there a more efficient way? Did you need to do that? Did you need to think about it divided into 20 parts? 'Cause that's quite hard to picture, isn't it? That's not like picturing it being split into three or four parts, that's hard.

Aisha says we can use our fraction sense superpower, hmm.

And what do you notice about that fractional part? This mixed number is close, in fact very, very close to two.

We can tell that because there are 20 equal parts and we have 18 of them, it's almost all the way there isn't it? To the next hole number.

This is only two away from the next hole.

So we would put or could put one in 18 20ths just about there, that would be a good estimate, I think, very, very close to the two.

Let's have a check.

Which letter represents where you would estimate the position of this mixed number on the number line? So we've got one and 98 100s.

Where do you think that would go? Use your fraction sense, pause video.

Well that 98, that numerator is really close to 100.

So it's really close to a whole number.

It is one and 98, 100.

So it's somewhere between one and two, but they all are.

But it's close to two, isn't it? Because it's close to the next whole number.

So D would be the best estimate there.

We could use our fraction sense knowing that 98 1 hundreds are close, very close to the next integer, in this case only two away, so really close.

It is time for some practise and I think you are ready but you're doing really well.

Number one, estimate the position of these numbers on the number line.

Where would you put them? Use your fraction sense.

Think are they close to one integer? Are they close to a different integer? Is it about halfway between the integer, all that kind of thing? That's called using your fraction sense.

And then number two, estimate the position of these numbers on this number line.

Number three, estimate the position of this number on the number line.

Good luck at using your fraction sense and I will see you soon for some answers.

Welcome back.

How did you get on? Are you feeling confident? Let's have a look.

So number one, let's have a look where we would position these mixed numbers, they're all mixed numbers.

Five and a half is here.

It's halfway between five and six.

Six and one third, well it's going to be in between six and seven, isn't it? 'Cause it's six and something.

And if we picture it being split into three equal parts, we could put it about there, that's a good estimate.

Seven and three quarters is going to be in between which two integers? Seven and eight, so it's seven and something.

I could picture that being split into four equal parts and we've got three of them.

I could also picture the fact that it's quite close to the next whole number.

It's quite close to eight, so we could put it just about there, that's a good estimate.

And then eight and one 10th, that's in between eight and nine, isn't it? It's more than eight, less than nine.

It is only a little bit more than eight though, so it's going to be very close to eight.

It would go about here, that's a good estimate.

Number two, estimate the position of these numbers on this number line.

Two and nine tenths would be about here, it's a good estimate, it's very close to three.

One and one fifth is very close to one.

Two thirds is not a mixed number, so it's got to be less than one.

So I'm going to picture the space between zero and one, those intervals being split into three equal parts and we want two of them so we could go about there, that's a good estimate.

And then three and three seven, that's in between three and four, it's close to half, why isn't it three sevens? So just a little bit before halfway, that will be a good estimate for that.

And number three, estimate the position of this number on the number line.

We've got three and two 20 fifths.

What could we say about the fractional part there, two 20 fifths? Two's only a very small part of 25, isn't it? So it must be really close to three.

We can use our fraction sense knowing that the two 20 fifths are close to the previous integer, in this case three.

You may have positioned yours in a slightly different position, but it should be close to three, so a good estimate.

Well, so far so good.

I think you are ready for the next cycle and that's problem solving.

Aisha and Andeep are trying to solve a problem.

They need to determine which number from the given numbers is represented by A.

So have a look at A.

Is it four fifths, two and a half, two and nine tenths, three and three quarters, two and four fifths? I think looking at those, we can discount some of those.

We can get rid of some of those.

We can eliminate some possibilities.

Which ones could it not be? What do you think? Well let's think about four fifths to start with.

It couldn't be four fifths because four fifths is smaller than two, and in fact it's smaller than one, it's not even a mixed number.

So it couldn't exist between two and three.

Let's see if we can discount any more possibilities.

What about three and three quarters? No, it couldn't be that because that is greater than three.

This line goes between two and three, so that wouldn't fit anywhere there.

But the rest of the numbers, the rest of the numbers could all fit somewhere between two and three, 'cause they've all got two and a fractional part.

Can we discount any of them though? Is there any that it couldn't possibly be? Well it couldn't be two and a half because you can see quite clearly that A is not positioned halfway along that number line, it's nearer to three.

So it's definitely not two and a half, I'm very confident about that.

Let's narrow it down to two possibilities.

Two and nine tenths and two and four fifths.

Hmm, I think we're getting close now.

What do you think? Can we get rid of any of those? It must be representing two and four fifths, here's why.

A cannot represent two and nine tenths, 'cause nine 10th is only one 10th away from the hole and nine more parts of the same size will not fit between two and three.

So if you could possibly picture that being split into 10 equal parts, that's not nine of them, it's more like eight of them, but close.

But two and four-fifths it is.

If we split the space in between those two intervals into five equal parts with our mind, if we visualise that, that would be four of them.

So two and four fifths is a good estimate.

Let's have a quick check.

Look at this number line, then determine which of these numbers is represented by the letter A.

What do you think? Is it four fifths, two and a half, two and nine tenths, three and three quarters, two and four fifths? Just like before, can you discount any possibilities? If you've got a partner to chat this through with, I always recommend that.

Pause the video and give that a go.

What do you think, which of these is A? Is there, it is two and a half.

It's in between two and three.

The integer part is two, so it's going to be after two, but between four three and it's halfway in between.

So two and a half, well done if you've got that.

And it is time for some final practise.

Which of the following numbers is represented by the letter A? Give reasons for your choice.

And just like before, you might want to discount some possibilities before you arrive at your final answer.

Number two, Andeep says that the number represented by the letter A is nine and four fifths.

Andeep is incorrect.

Why? Can you explain that? Could you suggest a number that could be being represented by the letter A? So see if you can explain that in its clear and simple way as you possibly can.

Pause the video, give that a go and I'll see you soon for some feedback.

Welcome back.

How are you getting on? Are you feeling confident? Let's give you some answers.

So number one, it can't be three and two fifths because three and two fifths is not in between five and six.

It can't be seven and three eight for that very reason, that will be past the six on the number line.

It could be the other three.

They're all possibilities because they all light in between five and six.

It couldn't be five and a half because it's not halfway and it couldn't be five and six sevenths, because five and six sevenths is really close to six.

So that leaves the most likely possibility.

We can estimate that that is five and three sevenths.

Well done if you gave a good explanation for that.

And number two, Andeep says that the number represented by the letter A is nine and four fifths, but that's not correct.

Why? Could you suggest a number that could be being represented by the letter A? Well, first of all, I think we've got to give Andeep a little bit of credit because he did say it was going to be nine and something and it is, it's in between nine and 10.

So the integer pot is nine, but not four fifths, a fractional part's wrong.

It must be incorrect, because nine and four fifths will be very close to the next integer, in this case 10.

A is just after halfway, so a number that it could represent is nine and three fifths, or you may have given a different number with nine as its whole and a fractional part that's just over halfway.

We've come to the end of the lesson.

In today's lesson, you've been using fraction sense.

The lesson has been estimating the position of a number on a number line using fraction sense.

In previous lessons you might have explored number lines that had unlabeled marks on this time.

You didn't have those at all, you had to use your fraction sense and your estimation skills and your reasoning.

So to estimate the position of mixed numbers on a number line, first identify which integers it sits in between.

Which whole numbers does it sit in between.

Then when you've done that, use the fractional part of the number and fraction sense to decide where within the known interval the mix number sits.

So maybe you could think to yourself, is it halfway? Is it close to halfway? Is it close to a particular integer, or closer to the other integer that it lies in between? So that's called using fraction sense, and I think you've done really well today developing your fraction sense.

I've had so much fun working with you today on this lesson, and I do hope I get the chance to spend another maths lesson with you in the near future.

But until then, have a great day.

Whatever it is you've got in store, I hope you succeed at whatever it is you've got in store.

Take care and goodbye.