Lesson video

Hello there.

How are you? My name is Mr. Tilston, I'm a teacher.

My favourite subject is maths, so it's a real pleasure to be here with you today to teach you this lesson, which is all about improper fractions and mixed numbers.

If you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is as follows, I can convert an amount of quarters from an improper fraction to a mixed number.

So the fraction we're focusing on today is just quarters.

And we've got some keywords.

My turn, mixed number.

Your turn.

My turn, improper fraction.

Your turn.

Have you heard of those words before? Do you know what they mean? Let's have a look.

Let's have a recap.

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

So here's an example, one and a half, and that's how we write that.

Could you think of a different example of a mixed number? And an improper fraction is a fraction with a numerator, that's the top number is greater than or equal to the denominator, that's the bottom number.

So for example, five thirds and nine eighths are improper fractions.

Could you think of a different improper fraction? Could you think of a situation in real life where we would have a mixed number or an improper fraction? Our lesson today is split into two parts or two cycles.

The first will be improper fractions and mixed numbers, and the second converting improper fractions into mixed numbers.

And again, we're just focusing today on quarters.

Let's start by looking at improper fractions and mixed numbers.

In this lesson, you're going to meet Aisha and Jun.

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

Aisha eats four quarters of an orange.

Hmm.

What do you notice about that? There's something significant about that number.

How would you express that as a fraction? The unit that we are working with is quarters, so that's our denominator.

The denominator is four.

We have four of those parts.

This means that the numerator is also four.

So the numerator and denominator are the same.

Hmm.

What does that tell you? Here we go.

That's our fraction.

We've got four quarters.

Is there another way to think of this? The whole has been divided into four equal parts and we have four of them.

Aisha says, "I notice something" and I'll bet you've noticed something too.

What do you think she's noticed? Four quarters is equivalent to one whole.

Did you know that? Because four equal parts make one whole.

Four quarters equals one.

Jun eats five quarters of orange.

Hmm.

What's different this time? What's the same this time? How would you express that as a fraction? The unit that we are working with is still quarters, so the denominator is still four.

That hasn't changed.

This time though what has changed is we have five of those parts.

So we've got a different numerator.

The numerator this time is five.

How could we write that? The whole has been divided into four equal parts and we have five of them.

So that is how we write that.

We've got five quarters and just like four quarters, this is an improper fraction is one or greater.

Jun says, "I notice something." What do you think Jun's noticed? Five quarters is an improper fraction.

Yes it is.

So it could also be expressed as a mixed number.

Yes, it can.

And I'm sure you've had experiences of doing this before.

Let's use a part to part whole model.

They're always very useful to support us to convert from the improper fraction to the mixed number.

Are you ready? Mixed numbers are composed of a whole part and a fractional part.

So two parts.

We can partition the improper fraction into a part that is equivalent to a whole number and the remaining fractional part.

Let's do some examples.

So this is five quarters.

We can partition five quarters into two parts, four quarters and one quarter.

Four quarters is equivalent to one whole.

We've already established that.

So instead of saying four quarters, let's say one, one whole, they're the same.

Now can you start to see a mixed number forming? We also have one more quarter.

So this is one and a quarter and that's a mixed number.

So we can say five quarters.

That's an improper fraction is equivalent to one and one quarter.

That's a mixed number.

Jun says "Five quarters are equivalent to one whole and one more quarter." So in this case he's got one hole orange and one extra quarter, and that's what that looks like.

So we can see five quarters or we can see one and one quarter they are equivalent.

Now we have six quarters of orange.

What's changed? What stayed the same? How would you express this as a fraction? What about an improper fraction? What about a mixed number? The unit that we are working with is still quarters, so the denominator is still four.

This time we have six of those parts.

That's part that's changed.

This means that the numerator is six.

So the fraction's going to look slightly different.

The whole has been divided into four equal parts and we have six of them.

Do you think you could write that as a fraction? It looks like this.

This is six quarters.

What else could we say? Six quarters is an improper fraction.

It's a fraction that's one or greater.

So it could also be expressed as a mixed number.

What could the mixed number be? Hmm.

How many whole oranges have we got? How many extra quarters have we got? Let's use a part-part-whole model to show this.

So we've got six quarters.

What could the parts be this time? Think about the whole number part, what that would be as a fraction and then the extra fraction.

We've still got one whole orange or four quarters we're going to think of it.

So that's six quarters could be partitioned into four quarters plus an extra two quarters.

Four quarters is equivalent to one whole.

So let's not say four quarters, let's say one.

And can you see that mix number for me? And we have two more quarters.

This is one and two quarters.

So six quarters is the improper fraction, one and two quarters is the equivalent mixed number.

Six quarters are equivalent to one whole and two more quarters.

Those two fractions are exactly the same, even though they look different, they're worth the same.

They're equivalent.

Let's have a little check.

Use the part-part-whole model to write the mixed number as an improper fraction.

So this time we've got seven quarters, so maybe we've got seven quarters of an orange and it's been partitioned for you already into the four quarters and the extra three quarters.

So what could we say that seven quarters, the improper fraction is as a mixed number? Pause the video.

What did you come up with there? So let's think about partitioning that into two parts as we have.

So the four quarters, what could we say about those four quarters? That's one whole.

So therefore seven quarters equals one and three quarters.

That's the mixed number.

Let's look at this sequence of improper fractions and their equivalent mixed numbers.

So four quarters is equal to one.

Five quarters is equal to one and one quarter, six quarters is equal to one and two quarters, seven quarters is equal to one and three quarters, eight quarters is equal to two, nine quarters is equal to two and one quarter, 10 quarters is equal to two and two quarters, 11 quarters is equal to two and three quarters and 12 quarters is equal to three.

Lots of things to notice there.

What kinds of things have you noticed? What's the same? What's different? You might want to take some time to think about that.

Jun says, "I notice that the fractional part of the mixed numbers and the denominator of the improper fractions are the same." It was quarters all the way through.

Did you notice that? We'd established the unit, the denominator and that denominator appears in both the improper fraction and in the mixed number all the way through.

Let's have a little check for understanding.

True or false.

21 quarters is expressed as a mixed number as five and one fifth.

Is that true or is that false? And why? Pause the video.

Did you spot it straight away? Did you spot the fact that we were talking about quarters, 21 quarters and then suddenly talking about fifths five and one fifth, the denominator did not match up.

So that's false.

The denominator of the fractional part of the mix number and that of the denominator of the improper fraction should be the same.

What do you notice this time? What's the same and what's different? Let's have a look.

So we've got four quarters is equal to one.

Eight quarters is equal to two, and 12 quarters is equal to three.

Hmm.

Aisha says, "I notice that when the numerator is a multiple of the denominator, the quantity is equivalent to a whole number." So four is a multiple of four, eight is a multiple of four, and 12 is a multiple of four, and that gave us the whole numbers, one, two and three.

Four quarters is one full group of four quarters.

Eight quarters is two full groups of four quarters.

12 quarters is three full groups of four quarters.

I wonder what would come next in that sequence.

Well, let's think about that now.

Which of these improper fractions are equivalent to a whole number? And the next one in that sequence is there and they may be more too.

So pause a video, which of these are equivalent to whole numbers? So we're looking for multiples of four in this case for the numerator.

Is 18 a multiple of four? No.

Is 16 a multiple of four? Yes.

Is 40 a multiple of four? Yes.

Is 38 a multiple of four? No.

So therefore 16 quarters and 40 quarters are whole numbers.

16 and 40 are multiples of four.

So these improper fractions will be equivalent to a whole number.

So any multiple of four that you care to think of will give a whole number when we think about quarters.

Let's do some practise.

Match these improper fractions to their whole number equivalent.

Number two, Aisha says that 11 quarters expressed as a mixed number would be two and three sixths.

Aisha is incorrect.

Explain why she's incorrect.

See if you can give a nice clear explanation about that using all the wonderful mathematical vocabulary that you can.

Okay, let's go, pause the video.

Welcome back.

Are you starting to feel confident? Do you think you're getting the hang of converting between mixed numbers and improper fractions? Let's see.

Number one, match these improper fractions to their whole number equivalent.

So these are all multiples of four.

The numerator are all multiples of four, so they're going to give whole numbers.

Well, 16 is four lots of four.

So that's equivalent to four.

20 is five lots of four.

So that's equivalent to five.

24 is equivalent to six lots of four.

So 24 quarters is equivalent to six.

28 is seven lots of four.

So 28 quarters is equivalent to seven and 32 is eight lots of four.

So 32 quarters is equivalent to eight.

And number two, Aisha says that 11 quarters expressed as a mixed number would be two and three sixths.

Aisha's incorrect.

Explain why she's incorrect.

You might have heard it when I said that 11 quarters and then two and three sixths.

Did you spot that we haven't got the same denominator there? The denominator of the fractional part of the mixed number and that of the denominator of the improper fraction should be the same.

In this example, the denominator of the improper fraction is a four, a quarters, but the denominator of the fractional part of the mixed number is six.

So six, they don't match, do they? The denominator of the fractional part of the mixed number should be a four.

So quarters.

So well done if you said anything like that.

You're doing very, very well.

I think you're ready for the next part of the lesson and that's converting improper fractions into mixed numbers.

Andeep has 10 quarters of an orange, 10 quarters.

Let's think about that.

Could you think about that in two different ways? Hmm.

How do we write this as an improper fraction? The unit that we are working with is still quarters.

That hasn't changed.

So the denominator is still four.

We have 10 of those parts this time.

This means that the numerator is 10.

So that's what's changed.

The whole has been divided.

That's how we write our fraction bar into four equal parts.

That's what we write for our denominator.

And we have 10 of those parts.

That's our numerator.

And that's 10 quarters.

That's what that looks like.

Now let's convert 10 quarters into a mixed number.

Hmm, how many wholes do you think we've got and how many extra quarters? How would you do that? Aisha says, "Let's start by identifying the unit that we are working with." What is a unit? What is a denominator? The denominator is a four.

So each whole has been divided into four equal parts and four parts make one whole.

The numerator is 10.

This means that we have 10 of those equal parts.

So let's use that part-part-whole model that served us so well in the first cycle to represent that.

So that's 10 quarters.

Let's think about that as two different parts, a whole number part and the extra fraction part.

We need to determine how many wholes we have.

We know we are working with quarters and four quarters make one whole.

I think this time though there's more than one whole, don't you? More than one orange.

It's possible to make two full groups of four quarters, which is eight quarters.

Yes.

So the multiple of four that's closest to that, the one just before 10 quarters is eight quarters.

So that's two wholes.

So eight quarters.

And then how many quarters are left over? Two more quarters.

So we've got eight quarters and two quarters.

Eight's a multiple of four, and it's equivalent to two wholes because two lots of four are equal to eight.

So instead of saying eight quarters, let's say two wholes.

Can you see that mixed number for me? The two quarters form the fractional part of the mixed number, the extra bit on top of the whole number.

So 10 quarters is equal to two and two quarters.

10 quarters of orange is the same as two and two quarter oranges is one, there's two and there's your two extra quarters.

10 quarters is equal to or equivalent to two and two quarters.

Do you think you're getting the hang of this? Let's have a check.

Let's see.

Write this improper fraction as a mixed number.

So we've got 13 quarters.

So sketch out that part-part-Whole model.

Write 13 quarters for the whole.

What are the two parts? And remember to convert the whole number part.

Remember to start by determining how many wholes there are.

So 13 quarters, what is it as a mixed number? Pause that video.

Let's see.

It's possible to make three full groups of four quarters.

Four, eight, 12.

That's three groups.

So that's 12 quarters.

So that can be our first part.

That's what will be the whole number part.

And then what's left over? Not more, it's just one extra quarter.

That's what's the extra part, the fractional part.

So that's one quarter, that's 12 quarters plus one quarter.

Let's turn that 12 quarters it into a whole number.

12 is a multiple of four and is equivalent to three wholes.

So instead of saying 12 quarters, we're going to say three.

So therefore 13 quarters is equal to three and one quarter.

I think that part-part-whole model is really useful.

Hope you agree.

Let's look at this improper fraction.

This time we've got 26 quarters.

That's a lot of orange.

Let's use stem sentences to support us to convert it to a mixed number.

The denominator is, hmm.

So what do you think the denominator is? This means that each whole has been split into hmm equal parts.

Hmm, equal parts make each whole.

The numerator is hmm, this means there are hmm equal parts.

It is possible to make hmm full groups of quarters.

This is hmm quarters and there are hmm more quarters.

Let's break that down.

Let's start thinking about our denominator.

The denominator is four.

This means that each whole has been split into four equal parts.

Four equal parts make each whole.

The numerator is 26.

This means there are 26 equal parts.

It is possible to make six full groups of four quarters because six lots of four are 24, and that's as close as we can get.

So this is 24 quarters and there are also two more quarters.

So 26 quarters looks like this when partitioned, we can partition it into 24 quarters and two extra quarters.

And the 24 quarters we can then think of as six.

So we've got six and two quarters and that is our mixed number.

I think that stem sentence was very helpful there.

We'll get to a point where you don't need it, but for now, very helpful.

Okay, let's have a check.

Use the stem sentences to convert the improper fraction to a mixed number.

So 31 quarters is equal to what? Okay, pause the video, give that a go.

Practise that stem sentence.

Say to a partner.

Good luck.

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

So this time the denominator as before is four.

This means that each whole has been split into four equal parts and four equal parts make each whole.

In a future lesson, we can and will look at different denominators, but for today we're focusing on those quarters.

The numerator is 31.

This means there are 31 equal parts.

It is possible to make how many full groups of quarters? Four times something.

Well, how close can you get? Seven full groups of four quarters.

This is 28 quarters and there are three more quarters.

So that 28 quarters we can say is seven and the extra three quarters.

So that makes seven and three quarters.

Very well done if you've got seven and three quarters, you're on track and you are ready for some practise.

Let's do that.

Number one, match these improper fractions to their mixed number equivalent, and you may notice they're all quarters.

And number two, convert these improper fractions to mixed numbers.

Okay, good luck with that.

Pause the video and I'll see you shortly for some feedback.

Welcome back.

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

So 21 quarters is five and one quarter because it's like 20 quarters plus one extra quarter or five and another quarter.

Six quarters is equal to one and two quarters.

22 quarters is equal to five and two quarters, 50 quarters is equal to 12 and two quarters, 41 quarters is equal to 10 and one quarter and 15 quarters is equal to three and three quarters.

Knowing your four times table is really helpful there isn't it? And convert these improper fractions to mixed numbers.

13 quarters equals three and one quarter because we've got three wholes, that 12 quarters and then one extra quarter.

14 quarters is equal to three and two quarters, 15 quarters is equal to three and three quarters, 17 quarters is equal to four and one quarter, 27 quarters is equal to six and three quarters, 37 quarters is equal to nine and one quarter, 29 quarters is equal to seven and one quarter, 33 quarters is equal to eight and one quarter, and 45 quarters it's equal to 11 and one quarter.

Well done if you got those right.

We've come to the end of the lesson.

I think you've done ever so well today.

You've made lots of progress.

Today, we've been converting an amount of quarters from an improper fraction to a mixed number.

Improper fractions can be converted to mixed numbers.

And you've done that lots of times today.

The denominator of the improper fraction will be the same as the denominator of the fractional part of the mixed number.

If the numerator is a multiple of the denominator, the improper fraction will be equivalent to a whole number.

Well done on your accomplishments and your achievements today, you have been simply fantastic.

Give yourself a very well deserved pat on the back.

I hope you have a fantastic day and that whatever you do, you're the best version of you and as successful as you can possibly be.

I look forward to seeing you again in the future, hopefully.

Until then, take care and goodbye.