Lesson video

Hi there.

My name is Mr. Tilston.

I'm a teacher, and I'm feeling very happy, and very lucky today, because I love maths, and I get to spend this math lesson with you.

We're going to be talking about mixed numbers.

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

So let's see if we can take you even further along that journey.

If you're ready, I'm ready.

Let's begin the lesson.

The outcome of today's lesson is this.

"I can compare and order mixed numbers using fraction sense." So have you got any experience of comparing and ordering other kinds of of numbers? Have you used inequality symbols, for example? You're going to be using those today.

Our keywords, just the one phrase.

We've got, my turn, "Mixed number," your turn? So mixed numbers.

What are they? Let's have a reminder.

A mixed number is a whole number and a fraction combined.

So for example, here is one and a half.

It's got an integer, the one, and it's got a fractional part, the half.

Our lesson today is going to be split into two parts or two cycles.

The first will be using a number line, and the second comparing and ordering mixed numbers.

Let's start by thinking about using a number line.

In this 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, and very good they are too.

Andeep is identifying the numbers that are represented by letters.

See if you can do this before Andeep has a go.

So, look at the number line.

See if you can work out what the fraction unit is, and then can we say what each of those numbers are? What would you do first, then? He says, "We need to know the unit that we are working with." Yes, we need to know the fraction.

Can you identify the unit that we're working with? Andeep says, "Each interval between integers," so between zero and one, or between one and two, or between two and three, is divided into seven equal parts.

And you can count that for yourself if you like.

You can check that.

Seven equal parts.

This allows us to count in sevenths, so we've established our unit.

Sevenths are the unit that we are working with.

Let's identify the number represented by A.

Well, what do you notice about A? Anything sticking out? Well, it's less than one, isn't it? So it's not going to be a mixed number.

A must be greater than zero, but smaller than one.

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

It exists on this number line, but it's not a mixed number.

A is at the end of the first part, so the value of A must be one seventh.

There we go.

So that's one seventh.

So now we know we're working with sevenths, that should help us with our mixed numbers.

What do you say about B? It's a mixed number.

It's going to have a whole number part and a fractional part.

What will they be? What do you notice about the position of B? Andeep says, "B must be greater than one, but smaller than two." Absolutely, it's in between one and two.

We can see that.

So it's going to be one and something.

B is at the end of the first part after one.

So the value of B must be one and one seventh, and it is.

That's one and one seventh.

What about C? What could we say about C? I think we've already got the whole number part established.

What about the fraction part? And is there an efficient way to do it, I wonder? What do you notice? "C must be greater than one, but smaller than two." Yep, just like B was.

"C is at the end of the fifth part after one.

So the value of C must be one and five sevenths." Yes it is.

I thought of it slightly differently.

It was quite close to two.

It was two one sevenths away from two.

Identify the number represented by D.

Pause the video and give that a go.

How did you get on with that? You managed to come up with an agreement.

Let's have a look.

D must be greater than two, but smaller than three.

So it's two and something.

Two is the whole number part of this mixed number.

We know we're working with sevenths.

So it's two and something sevenths.

How far along is it? Just after halfway, isn't it? D is at the end of the fourth part after two.

So the value of D must be two and four sevenths.

And it is.

So, well done if you said that.

If you said that you're on track for the next part of the lesson.

Now that we have identified the numbers, we can compare and order them.

Which number is the smallest? What do you think? One seventh is the smallest, because it's the nearest to zero.

That's one good way of looking at it.

"Which number's the greatest?" Hmm.

Well, using that logic, which one's the furthest from zero? Two and four sevenths is the greatest, because it's the furthest from zero.

"We can say that one seventh is smaller than two and four sevenths.

One seventh is smaller than or less than two and four sevenths." So we're using an inequality symbol there.

"Or we can say that two and four sevenths is greater than one seventh." How could we write that? Which inequality symbol could we use? How about this one? Two and four sevenths is greater than one seventh.

That's in words.

And as a mixed number and a fraction, we could compare it like this.

So two and four sevenths is greater than one seventh.

Let's compare one and one seventh and one and five sevenths.

Hmm.

What could we say about those fractions? Those mixed numbers? Hmm.

"Which is greater?" Let's think about which is furthest from zero.

That would help.

One and five sevenths is greater than one and one seventh.

And that's how we can write that, using our inequality symbol.

"One and five sevenths is greater, because it's further from zero." Simple as that.

Let's do a quick check.

Use the symbols, the inequality symbols, to compare two and four sevenths and one and five sevenths.

So you're going to fill in this stem sentence: "Two and four sevenths is hmm than one and five sevenths." And then the same with the actual mixed numbers.

Can you use the symbol this time? All right, pause the video.

Let's see what you came up with, and if it was correct or not.

So, two and four sevenths is greater than one and five sevenths.

So that's the word.

What's the symbol? This one.

That's the greater than symbol.

Well done if you said greater than.

Let's put these numbers in order, smallest to greatest.

And we're going to use symbols.

So let's start with one seventh.

That's the smallest.

And then after that, it's one and one seventh.

So that's bigger, that's greater.

And then one and five sevenths is greater still.

And then two and four sevenths is greater still.

And we can represent that using the inequality symbols.

We can read that sentence as follows: "One seventh is less than one and one sevenths, which is less than one and five sevenths, which is less than two and four sevenths." What did you notice? Anything? The numbers are in the same order as they are on the number line.

This is because the greater the number, the further away from zero it is.

Let's do another little check.

Put these numbers in order from smallest to greatest.

Pause the video, and off you go.

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

So the smallest there was two sevenths, and then we're going up in order.

Then we've got one and six sevenths and we've got two and two sevenths.

And the greatest of them all, the furthest from zero, is two and six sevenths.

Let's do another quick check.

Compare the numbers using that inequality symbol.

Pause the video and have a go.

Here we go.

So we've got two sevenths is less than one and six sevenths, which is less than two and two sevenths, which is less than two and six sevenths.

I think you're ready for some independent practise.

Number one, "Use this number line to support you to compare these numbers." Two: "A, determine the unit that we are working with." So what are we working with? How could you find that out? What is the fraction? "B, determine the numbers that the letters represent." And, "C, starting with the smallest, put the numbers in order?" And you can use those inequality symbols please.

I feel very confident that you're going to do very well on this, so let's find out.

Good luck and pause the video.

Let's see how you got on there, shall we? Okay, so number one.

We can say four sixths is less than two and three sixths.

One and four sixths is greater than one and two sixths.

One and four sixths is less than two and three sixths.

And then we've got three mixed numbers here.

One and two sixths is less than one and four sixths, which is less than two and three sixths.

Well done if you got those.

And then let's determine the unit that we are working with.

Well, each interval between integers is divided into eight equal parts.

So whether it's zero to one, or one to two, or two to three doesn't really matter.

But you can see they're divided into eight equal parts, and that allows us to count up in eighths.

The unit that we are working with here is eighths.

That's helpful.

So now we're going to determine the numbers that the letters represent.

So A must be three eighths.

It's not a mixed number, 'cause it's less than one.

The rest are mixed numbers.

They're in between whole numbers.

So B, that's one and three eighths.

C, that's very close to two, isn't it? So it's one and seven eighths, it's just one eighth before that.

And then D is pretty close to two.

On the other side, that's two and two eighths.

And then, "Starting with the smallest, put the numbers in order." Well, they are in order already.

And with inequality symbols, it goes like this.

Three eighths is less than one and three eighths, which is less than one and seven eighths, which is less than two and two eighths.

You are doing really, really well, and you're definitely ready for the next cycle.

That's comparing and ordering mixed numbers.

"Andeep and Aisha pick two cards." So we've got one and a half, and two.

Do you need a number line to compare those or can you use your fraction sense? Hmm? "How would you compare the numbers? Which is smaller and which is greater?" Andeep wants to draw a number line, but Aisha says, "Wait, I think we can use our fraction sense superpower," and that would certainly be a lot quicker wouldn't it? And a lot more efficient.

So she's going to use some reasoning.

She's going to do a bit of thinking.

She says, "One and a half sits between one and two on a number line." And I can picture that.

It does, doesn't it? Andeep says, "That means it must be smaller than two." Yes.

So we can say one and a half is less than two.

Aisha chooses another two cards.

This time, she's got three, and three and two thirds.

Hmm.

Do we need a number line? No, I don't think we do.

I think we can use our fraction sense.

So what would you say? Which is smaller, which is greater? Aisha says, "Three and two thirds sits between three and four." Yeah, it's in between those.

It's a mixed number in between those two integers.

Andeep says, "That means three must be smaller than it." Yeah, three and two thirds is three and then a bit more.

So we can say three is less than three and two thirds.

No need for a number line.

Let's see if you can do this without a number line too.

"Use your fraction sense to compare these numbers." We've got four, and three and two thirds.

Can you use an inequality symbol to compare them? Pause the video and off you go.

Well, did you need a number line? No.

Did you use fraction sense? Hopefully, yes.

Aisha is good at her fraction sense.

She says, "Three and two thirds sits between three and four." It does.

I can picture that.

And Andeep says, "That means four must be greater than it." Yeah, three and two thirds isn't yet four.

So we can say four is greater than three and two thirds.

You might also say three and two thirds is less than four.

Aisha chooses another two cards.

This time she's got two and three eighths, and one and five sevenths.

What do you notice this time? Hmm? Anything at all? Anything that might make this one a little bit trickier? She says, "Both numbers are mixed numbers.

How can we compare them? Let's use our fraction sense superpower." Are you as good as Aisha is at that? Let's find out.

Two and three eighths sits between two and three.

Yeah? "One and five sevenths sits between one and two.

Two and three eighths must be greater." Yeah, because two's greater than one.

We can say two and three eighths is greater than one and five sevenths.

Aisha chooses another two cards.

How do we compare these? So we've got five and 99 100ths, and eight and one 100th.

How could you compare them? Is there an easy way? Have you got a little hack? Let's see what Aisha's got to say.

"Both of them are mixed numbers." Yes they are.

"Let's use our fraction sense superpower.

She says five and 99 one 100ths sits between five and six." Yeah.

So we're just thinking here, aren't we, about the whole numbers, about the integers.

"Eight and one 100th sits between eight and nine." Yes it does.

"Five and 99 100ths must therefore be smaller," because it's in between five and six.

The other one's in between eight and nine, so it must be smaller.

Five and 99 one 100ths is less than eight and one 100th.

Andeep's noticed something.

I wonder if you have two.

He says, "Have you noticed that if the whole number parts of the mixed numbers are different," So in this case, look, the whole number parts are five and eight, they're different, "It can be used to compare and order them.

Here, five is smaller than eight." So we don't even need to think about the fractional part.

We can compare those numbers just using the whole number part.

Let's do a check.

"Complete the sentence to compare these fractions." 10 and two thirds sits between hmm and hmm.

Nine and five sixths sits between hmm and hmm.

10 and two thirds is hmm than nine and five sixths.

And then can you use an inequality symbol to compare them? Pause the video and give that a go.

Let's have a look at some answers here.

So, 10 and two thirds sits between 10 and 11.

Nine and five sixths sits between nine and 10.

That's all we've got to think about.

10 and two thirds is therefore greater than nine and five sixths.

And we can show that with our inequality symbol: 10 and two thirds is greater than nine and five sixths.

Well then if you've got those.

You are on track and ready for the next part of the learning.

And the next part of the learning is some practise.

Number one, "Compare these numbers using those inequality symbols." Number two, "Put these numbers in order from smallest to greatest.

Which number is the greatest? Explain how you know." I think you're going to ace this.

See if you can prove me right.

Pause the video.

Well, before you paused the video, I said I thought you were going to ace this.

Was I right? Shall we find out? Number one, "Compare these numbers using the less than or greater than symbols." Those inequality symbols.

And it goes like this.

So four is greater than three and four sevenths.

And we just needed to look at the whole number part for that.

Five is less than six and two eighths, the same logic: five is less than six.

Now, five and two fifths and five, they've got the same whole number part.

So, we need to look at the fractional part.

Five and two fifths has got a fractional part, but five hasn't.

So five and two fifths is five and a little bit more.

So we can say five and two fifths is greater than five.

What about 11 and one third, and 12? Well again, the whole number parts are different.

So we can just compare based on that.

And we can say 11 and one third is less than 12.

Two and two thirds, and one and two thirds.

So they've got the same fractional part, but different whole number parts.

And it's the whole number parts that we're interested in.

We could say two and two thirds is greater than one and two thirds.

And then nine and two eighths, and eight and two ninths.

Same whole number or different? Different.

So we can compare just based on those, the whole numbers.

We know that nine's greater than eight.

So nine and two eighths is greater than eight and two ninths.

And then what about this one? 98 and 36 37ths.

That's an unusual one, isn't it? And then 102 37ths.

Although that fraction was quite a complicated, unusual one, we didn't even need to think about it, did we? We can just think about the whole number part.

98 is less than 100, so therefore 98 and 36 37ths is less than 102 37ths.

And what about this one with the three mixed numbers? So, one's two and two fifth, another is three and two fifths and another is four and one fifth.

Are the whole number parts the same or different? They're different, so we can just stick to those when comparing.

So we can say two and two fifths is less than three and two fifths, which is less than four and one fifth.

Number two, "Put these numbers in order from the smallest to greatest." So, what was the smallest one? I would've ticked them off as I was going along, just to make sure that I knew which ones I'd used.

Maybe you did that.

So four and five sevenths is the smallest number there.

That's the one that's the closest to zero.

It was the only one that had a four for its whole number part.

Two numbers had five for their whole number part, so which is next? Well, next it's five.

That's just a whole number.

Five and seven eighths is a whole number plus a fractional part.

So that's a little bit further along.

That's greater.

Relatively easy to see what's coming next, because seven is less than eight.

So that's what goes next on the number line, smallest to greatest.

Now we've got two numbers that have got eight for their whole number.

One is just eight, and then one's a mixed number, eight and four sevenths.

So eight's going to be next.

And then eight and four sevenths is eight plus a fractional part.

So that is the greatest.

Well done if you've got those in that order.

And well done if you gave a really nice clear explanation of that.

It might be something a bit like this.

"Eight and four sevenths is the greatest.

I know this because this mixed number sits after eight, but before nine.

Except for eight, all the other numbers sit before eight, so they must be smaller.

Eight and four sevenths is greater than eight.

It is four sevenths greater than eight." Is the extra fractional part.

We've come to the end of the lesson.

You've been incredible today.

In today's lesson, we've been comparing and ordering mixed numbers using fraction sense.

"Mixed numbers can be positioned on a number line to help compare and order them," but we don't always need to do that.

We can use our fraction sense.

"When comparing or ordering mixed numbers, identify the integers that the mixed numbers sit between.

Mixed numbers where the whole number part is different can be compared or ordered just based on their whole number part." So it's just like comparing and ordering whole numbers.

Well done on your achievements and accomplishments today.

I've really enjoyed spending this maths lesson with you, and I really do hope that I get the chance to spend another maths lesson with you in the near future.

But until then, have a great day, whatever you've got in store, take care and goodbye.