Lesson video

Hello, there.

My name is Mr. Tilstone.

I'm a teacher.

My favourite subject to teach is Maths.

And my favourite part of maths to teach is fractions.

I find it really interesting.

So I'm very excited to teach you this lesson today, which is all about mixed numbers and improper fractions.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is this.

I can express an amount of quarters as a mixed number and an improper fraction.

So today, we're just focusing on the fraction quarter.

And our keywords today, my turn, improper fraction.

Your turn.

Have you heard of that before? What is an improper fraction? You'll be very confident about this by the end of the lesson, but let's give you a little sneak preview now.

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, we've got here 5/3 and another example, 9/8.

They're improper fractions.

Our lesson today is split into two cycles.

The first will be whole numbers as improper fractions.

Just quarters remember.

And the second will be mixed numbers as improper fractions.

And again, just quarters.

So let's start by thinking about whole numbers as improper fractions.

And in today's lesson you're going to meet Sophia and Jacob.

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

Sophia has an orange, she cuts it into quarters.

So remember that's our fraction for today, quarters.

Let's represent that as a diagram.

That will make it easier to see the quarters, I think.

Here we go.

So we've got quarters.

How many quarters? How many can you see? How many can you count? There are four quarters.

The whole orange is divided into four equal parts.

It's our denominator.

And we have four of those parts.

So we have all of them.

So that fraction reads four quarters.

This is one group of four quarters.

Let's represent that on a number line.

So you can see a number line here.

Look, it's got whole numbers across the bottom.

Each whole orange is divided into four equal parts.

And we have four of those parts.

So here we go.

So one orange could also be expressed as four quarters.

One whole is equivalent to four quarters.

Jacob also has an orange.

He also cuts his orange into quarters.

So the denominator is the same.

How many quarters does Jacob have? And how many quarters are there altogether? Well, there are two groups of four quarters, which is eight quarters.

Can you see eight quarters there? Can you see two groups of four quarters? There are eight quarters.

Each whole orange is divided, we use our fraction bar to show that, into four equal parts as our denominator.

Now then what's our numerator this time? We have this time eight of those parts.

So that is our fraction, eight quarters.

Let's represent this on a number line.

Where can we put that? Each whole orange is divided into four equal parts, and we have eight of those parts.

So we've got eight quarters.

We've got two oranges, which is eight quarters.

So two wholes are equivalent to eight quarters, whether it's oranges or whatever.

Two wholes are equivalent to eight quarters.

What have we got now? What can you see here? How many hole oranges can you see? How many quarters can you see? How many groups of four quarters can you see? There are three groups of four quarters, which is 12 quarters.

That's a times tables fact.

Let's represent this on a number line.

So where can we put this? What can we write and where can we put it? What fraction can we add to our number line? One orange was four quarters, two oranges was eight quarters, what can we say now? Each whole orange is divided into 4 equal parts, and we this time have 12 of those parts.

So three oranges is 12 quarters.

Three wholes are equivalent to 12 quarters.

What have we got now? How many quarters are there? There are four groups of four quarters, which is 16 quarters.

4 times 4 is 16.

Let's represent this on a number line.

What fraction can we write and where can we write it? One orange is four quarters, two oranges is eight quarters, three oranges is 12 quarters.

Each orange is divided into 4 equal parts, and this time we have 16 of those parts.

So four oranges is the same as 16 quarters, Four wholes are equivalent to 16 quarters.

Let's have a check look at the oranges and then complete the sentence and the number line to describe how many quarters there are.

And for this task, you can use this stem sentence, each hole orange is divided into hmm equal parts and we have hmm of those parts.

Okay.

Pause the video.

Did you get it? Each whole orange is divided into four equal parts, and we have 20 of those parts.

So therefore, our fraction is 20 quarters.

So five oranges is 20 quarters.

Let's have a go at counting the oranges in different ways as Jacob.

How would you count them? How could you count 'em? Can you think of different ways to count them? We can count the whole oranges, yeah.

One orange, two oranges, three oranges, four oranges, five oranges.

That's nice and straightforward.

How else can we count them? Well, we can count the groups of four quarters.

One group of four quarters, join in with me, two groups of four quarters, three groups of four quarters, four groups of four quarters, five groups of four quarters.

How else could you count them? We can count the quarters.

Four quarters, join in with me, eight quarters, 12 quarters, 16 quarters, 20 quarters.

Let's look at the number line in more detail.

So have a good look at that.

Is there anything that you notice? That's what good mathematicians do.

They notice things.

The denominators are all four because the oranges were each cut into four equal pieces.

So the denominator has not changed.

Whole numbers can be written as fractions.

So you can see lots of examples of that.

We can have fractions where the numerator is equal to or greater than the denominator.

So you've had lots of experience in the past with proper fractions.

These are called improper fractions.

Which of these are improper fractions? Eight quarters, one quarter, two quarters, 24 quarters.

There may be more than one answer.

Pause a video and have a go.

Eight quarters is an improper fraction and 24 quarters is an improper fraction.

The other two are proper fractions.

Improper fractions are fractions where the numerator is equal to or greater than the denominator.

So 8 is greater than 4, and 24 is greater than 4.

Did you also notice that the numerators are all multiples of four? Look at the numerator there.

Four quarters, eight quarters, 12 quarters, 16 quarters, 20 quarters.

One 4 is 4, two 4s are 8, three 4s are 12, four 4s are 16 and five 4s are 20.

I can use this learning to write an improper fraction for any whole number in quarters.

Six 4s are 24.

So if six apples were cut into quarters, this will be 24 quarters.

So this is all about times tables, isn't it? So 6 equals 24 quarters.

If seven apples were each cut into quarters, how many quarters would there be? Would there be 7 quarters 21 quarters, 27 quarters or 28 quarters? Pause a video and have a go.

So if seven apples were each cut into quarters, there would be 28 quarters.

Seven 4 are 28.

So if seven apples were cut into quarters, there would be 28 quarters.

It is time for some practise.

I think you're ready for this.

Number one, using a 12 sided dice or some digit cards, generate a number.

Write that whole number as an improper fraction with a denominator of four.

So let's have a look at an example then.

So Sophia's got dice, she threw a six.

So she says, "I will work out how many quarters are equivalent to six." Hmm, what do you think? Turn it into six oranges if that helps, how many quarters would that be? She says, "I can draw something to help or use my four times table." So whatever method you need to use, go for it.

Number two, complete these counting sequences.

5, 6, 7, hmm? Five groups of four quarters, six groups of four quarters, seven groups of four quarters, hmm groups of four quarters, and then 20 quarters, 24 quarters, 28 quarters, hmm quarters.

Number three, solve these problems. A, if 10 apples were cut into quarters, how many quarters would that be? B, at a party, 12 pizzas this time are cut into quarters.

each child eats one slice and all the pizzas are eaten.

How many children are at the party? Hmm, have a good think about that one.

And see, at the same party, some cakes were cut into quarters.

There were 12 quarters.

How many whole cakes were there? And they don't have to be circular cakes, they could be square cakes, rectangular cakes, doesn't matter, but how many whole cakes were there? Hope you get on well with that.

If you can work with somebody else, I always recommend that so that you can share ideas.

Pause the video and away you go.

Welcome back.

How did you get on? Do you think you're getting the hang of these improper fractions? Well, number one, there's all sorts of possibilities that you could come with for this.

You might have rolled a six and then drawn six circles that you could then divide into quarters.

That's a nice quick, easy way to do that.

And it would look a little something like this.

And you might have used your times tables facts to determine that there are six groups of four quarters, which is 24 quarters.

So 6 equals 24 quarters.

You might have had lots of different examples of that.

For example, 5 equals 20 quarters.

Number two, complete these counting sequences.

Really easy one to start with.

Probably the easiest question you'll do all year, I bet.

5, 6, 7, 8, five groups of four quarters, six groups of four quarters, seven groups of four quarters, eight groups of four quarters, and then 20 quarters, 24 quarters, 28 quarters, 32 quarters.

They're going up in fours, aren't they? So the 20 quarters was five wholes, 24 quarters was six wholes, 28 quarters was seven wholes, and 32 quarters was eight wholes.

And then if 10 apples were cut into quarters, how many quarters would there be? You might have used your times tables facts to determine that there are 10 groups of four quarters, which is 40 quarters.

And at a party, 12 pizzas are cut into quarters, each child eats one slice and all the pizzas are eaten.

How many children are at the party where you might have used your times tables facts to determine that there are 12 groups of four quarters, which is 48 quarters.

So there are 48 children at the party.

Knowing those times tables really pays off, doesn't it? And at the same party, some cakes were cut into quarters, there were 12 quarters.

How many whole cakes were there? You might have used your times tables facts to determine that 12 quarters is three groups of four quarters, so there must be three whole cakes.

You're doing very, very well.

And I think you are ready for the next cycle.

In fact, I know you are.

That's mixed numbers as improper fractions.

And we're still focusing today on quarters.

Sophia has some more oranges.

What's she got this time? How would you describe this? What can you see? Sophia says, "I can see two whole oranges," can you see that? "And then one quarter of an orange." It's quite difficult to tell from that picture that that's a quarter, but it's 2 1/4 oranges.

And that's how we write that.

That's the mixed number.

Let's cut the whole oranges into quarters.

It will be more efficient to represent this as a diagram.

We'll see it more clearly that it's in quarters.

So let's do that.

Looks very similar, doesn't it? So this time we've got those oranges represented in quarters.

What can you see? Is there another way that we can describe these oranges now? Jacob says, "I can see four quarters, eight quarters and then an extra one." So he counted four, eight and an extra one.

So that's nine quarters." Did you see nine quarters? Is that how you counted it? Nine quarters.

That's our improper fraction.

Jacob says, "I can also see two groups of four quarters, which is eight quarters, and one more quarter.

So that's nine quarters." Maybe that's how you counted it.

Nine quarters, that's our improper fraction.

A stem sentence can help us to express a mixed number as an improper fraction.

So we can see 2 1/4 there.

There are hmm groups of four quarters, which is hmm quarters and hmm more quarters.

So that is hmm quarters.

Let's fill that in.

So there are hmm groups of four quarters.

How many groups of four quarters can you see there? Two, which is eight quarters.

And then one more quarter makes nine quarters.

So therefore 2 1/4.

can you see that, equals nine quarters, can you see that? They're exactly at the same amount.

Let's add another one quarter piece of orange so that we have 2 2/4 pieces.

So this time we've got 2 2/4.

The stem sentence can help us express a mixed number as an improper fraction.

So let's do that again.

So there are two groups of four quarters, which is eight quarters, and two more quarters, so that's 10 quarters.

So 2 2/4 equals 10 quarters.

We can represent mixed numbers and their equivalent improper fractions on a number line.

So let's examine that number line from left to right.

So one quarter equals one quarter, two quarters equals two quarters, three quarters equals three quarters, and then four quarters, Our first improper fraction, equals one, one whole.

Five quarters equals 1 1/4.

So we've got an improper fraction and a mixed number.

Six quarters, improper fraction, equals 1 2/4, mixed number.

Seven quarters, improper fraction, equals 1 3/4 mixed number.

Eight quarters,, improper fraction, equals 2, a whole number.

Nine quarters, an improper fraction, equals 2 1/4, a mixed number.

And then 10 quarters, an improper fraction, equals 2 2/4, a mixed number.

Let's look at a different mixed number still involving quarters.

We've got three and two quarters.

Jacob says, "I can write this as an improper fraction using the stem sentence to help." So there are hmm groups of four quarters, which is hmm quarters and hmm more quarters, so that's hmm quarters.

So let's think about how many groups of four quarters there are.

There are three groups of four quarters this time, which is 12 quarters, and then two more quarters for that fractional part, so that's 14 quarters.

3 2/4 equals 14 quarters.

That stem sentence is very helpful, I think.

True or false, 2 3/4 equals eight quarters.

Is that true? Is that false? And can you explain why? Pause the video and have a go.

Did you have a go at explaining that to a partner? Did you come up with a nice clear explanation? It is false.

2 3/4 is not equal to eight quarters.

Why? There are two groups of four quarters, which is eight quarters already, and then three more quarters.

So that's 11 quarters.

So we'd write that as 11 quarters.

So that mixed number, 2 3/4, is equal to the improper fraction 11 quarters.

Time for some final practise.

Number one, write these mixed numbers as improper fractions.

So all of these are mixed numbers.

Can you write them as improper fractions? Remember to use this stem centres to help.

There are hmm groups of four quarters, which is hmm quarters and hmm more quarters.

So that is hmm quarters.

So all of these are about quarters today.

Number two, Jacob writes the mixed number, 3 2/4 as an improper fraction.

Can you see it, 3 2/4.

And he says that's equal to five quarters.

Hmm.

What mistake has Jacob made? How should 3 2/4 be written as an improper fraction because that's not correct.

See if you can help Jacob out.

Rightio.

Pause the video.

Off you go.

Welcome back.

How did you get on? Did you work with a partner? Did you manage to come up with some good strategies together? So number one, write these mixed numbers as improper fractions.

So 1 1/4 equals five quarters because it's got four quarters for the one, and then an extra quarter.

1 2/4 is six quarters.

It's got two extra quarters in addition to the four quarters.

And then, 1 3/4 is seven quarters.

2 3/4, well, that's got two groups of four quarters plus three extra quarters.

So that's 11 quarters.

3 11/4 got three groups of four quarters plus one extra quarter, so that's 13 quarters.

And then, 5 1/4 got five groups of four quarters, which is 20 quarters plus the extra one quarter makes 21 quarters.

10 2/4 is 10 groups of four quarters plus an extra two quarters, and that makes 42 quarters.

And number two, he made a mistake, he said 3 2/4 equals five quarters.

Good try Jacob, but not right.

What mistake has he made? Jacob added the whole number and the denominator to get five.

That's not what you do.

He should have used stem sentence to support him to do this.

There are in fact three groups of four quarters, which is 12 quarters and then two more quarters.

So that's 14 quarters.

So it could have written that as 14 quarters just like this.

That's the improper fraction.

We've come to the end of the lesson.

I thoroughly enjoyed today's lesson.

I hope you have too.

Today we've been expressing an amount of quarters as a mixed number and an improper fraction.

A fraction with a numerator that is equal to or greater than the denominator is called an improper fraction.

And you've explored lots and lots of different improper fractions today.

Improper fractions have values that are equal to or greater than 1.

A mixed number can be written as an improper fraction of equal value.

You've done lots of examples of that today.

So I hope you're starting to feel more confident.

We will get the opportunity to do more practise at this.

You've been amazing today.

Hope you have a great day, whatever you've got in store.

Take care and goodbye.