Lesson video

Hello there, my name is Mr. Tilstone.

I'm a teacher.

It's a great pleasure to be here with you today to teach you this maths lesson, which is all about fractions, and that's one of my favourite types of maths.

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 fifths as a mixed number and an improper fraction.

And you might have had some very recent experience of doing that with quarters.

Our keywords today, my turn, improper fraction, your turn.

Hopefully you've heard of improper fractions before.

Can you explain what they are? An improper fraction is a fraction where the 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 five-thirds and nine-eighths.

Could you give a different example I wonder.

Our lesson is split into two cycles, the first will be whole numbers as improper fractions, just fifths.

And the second will be mixed numbers as improper fractions.

Again, just fifths.

But let's begin by thinking about whole numbers as improper fractions.

And in this lesson, you're going to meet Sofia and Jacob.

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

Sofia has a length of string.

She cuts it into five equal pieces, so what fraction could we say she's got? Let's represent it as a diagram.

She's got fifths.

She's got five equal pieces, so she's got fifths.

How many fifths are there? There are five-fifths.

So what could we say about that? The whole piece of string is divided.

We can use our fraction bar, into five equal parts.

We can express that as a denominator.

And we have five of those parts.

That's our numerator.

This is one group of five-fifths.

It's one whole.

Let's represent this on a number line.

So we've got a number line here, it's got whole numbers on the bottom, going from zero to five.

Each whole piece of string is divided into five equal parts, and we have five of those parts.

So one piece of string has got five equal parts.

One whole is equivalent to five-fifths.

Jacob also has a piece of string, he also cuts his string into fifths.

What could we say now? What can you see now? How many fifths are there now? There are two groups of five-fifths, which is 10-fifths.

There are 10-fifths.

Each whole piece of string is divided into how many equal parts? Into five equal parts.

Our denominator.

We have this time 10 of those parts.

Let's represent this on a number line.

So what fraction can we write, and where can we write it? Each whole piece of string is divided into five equal parts, and we have 10 of those parts.

So the improper fraction is 10-fifths.

Two wholes are equivalent to 10-fifths.

How many fifths are there now? Well, there are three groups of five-fifths, which is 15-fifths.

Can you see 15-fifths there? And we can represent that on a number line.

Three wholes is 15-fifths.

Each whole piece of string is divided into five equal parts, and we have 15 of those parts, 15-fifths.

Three wholes are equivalent to 15-fifths.

Three pieces of string are equivalent to 15-fifths in this case.

What have we got now? What can you see now? How many wholes? How many fifths? How many groups of five-fifths? There are four groups of five-fifths, which is 20-fifths.

Let's represent that on a number line.

So we've got four wholes, 20-fifths.

Each whole is divided into five equal parts, and we have 20 of those parts.

Four wholes are equivalent to 20-fifths.

Let's have a check.

Look at the bars and then complete the sentence to describe how many fifths there are.

Each bar is divided into, equal parts, and we have, of those parts, this is, fifths.

Okay, pause the video and give that a go.

Each bar is divided into five equal parts, so that's our denominator.

And we have 25 of those parts, so that's our numerator.

And this is 25-fifths.

So five wholes equals 25-fifths.

Jacob says, "Let's have a go at counting the bars in different ways." How many ways can you think of to count those bars? How would you count them? "We can count the whole bars," says Sofia.

Yes, we can.

One bar, two bars, three bars, four bars, five bars.

Very straightforward.

We can count the groups of five-fifths.

One group of five-fifths, two groups of five-fifths, three groups of five-fifths, four groups of five-fifths, five groups of five-fifths.

We can count in fifths.

Do this with me.

We've got five-fifths, 10-fifths, 15-fifths, 20-fifths, 25-fifths, and we could go on and on.

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

What do you notice? What kind of things can you see? Good mathematicians notice things, what can you notice? The denominators are all five, because the pieces of string were each cut into five equal pieces, so the denominator has not changed.

Whole numbers can be written as fractions.

So we can see we've got one, two, three, four and five, and they can all be written as fractions.

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

So in the case of one, it's equal, five-fifths.

And in the case of two, three, four and five, it's greater than the denominator.

So 10 is greater than five, 15 is greater than five, 20 is greater than five, and 25 is greater than five.

And all of these are known as improper fractions.

Five-fifths, 10-fifths, 15-fifths, 20-fifths, and 25-fifths are all examples of improper fractions.

And there are many others.

So let's have a check.

Which of these are improper fractions? Two-fifths, four-fifths, 10-fifths, 25-fifths.

There may be more than one answer there.

Pause the video and have a go.

Well, I can see two proper fractions, and they are two-fifths and four-fifths.

And I can see two improper fractions, and that's 10-fifths and 25-fifths.

And both of those would represent values greater than one.

10-fifths is the same as two, and 25-fifths is the same as five.

Improper fractions are fractions where the numerator is equal to, or greater than the denominator, and those are both greater.

Did you also notice that the numerator are all multiples of five? One five is five.

Do this with me.

Two fives are 10, three fives are 15, four fives are 20, fives are 25.

Sofia says, "I can use this learning to write an improper fraction for any whole number in fifths." That's confident.

Do you think you could do that as well? So she's starting with six, six-fives are 30.

So if six pieces of string were cut into fifths, that would be 30 fifths.

So this is just times tables facts.

Six equals 30-fifths.

And that's how we can write that.

30-fifths is an improper fraction.

If seven pizzas were each cut into fifths, how many fifths would there be? Would there be 30-fifths, 35-fifths, 40-fifths, or 42-fifths? Pause the video.

Well, the times tables fact that we need to use here is seven lots of fives.

So seven lots of five are 35, so that will be 35-fifths.

Seven pizzas would be 35-fifths.

It's time for some practise.

I think you're ready for this.

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

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

And you might have had recent experience of doing the same thing, but with a denominator of four.

So it's the same thing.

Repeat until you have written at least five improper fractions.

You might even do more, that would be good.

Would you like to see an example? Okay, so here's Sofia.

She threw a six, so she will work out how many fifths are equivalent to six wholes.

"I can draw something to help," she says, "or use my five times table." Remember, five is the denominator.

Number two, complete these counting sequences.

Five, six, seven.

I'm sure you're gonna get that one.

Five groups of five-fifths, six groups of five-fifths, seven groups of five-fifths, groups of five-fifths.

Easy.

And what about this one? 25-fifths, 30-fifths, 35-fifths, fifths.

Number three, solve these problems. If 10 pizzas were cut into fifths, how many fifths would there be? At a party, 12 pizzas are cut into fifths, every child eats one slice and all of the pizzas are eaten.

How many children are at the party? And C, at the same party, some cakes were cut into five equal slices.

There were 25-fifths.

How many whole cakes were there? Okay, good luck with that.

I think you're going to smash it, and I'll see you soon for some feedback.

Welcome back.

How did you get on? Are you feeling confident? Are you getting good with these improper fractions? Let's have a look.

So number one you were using a 12 sided dice, or cards, and you might have rolled a six, and then drawn six bars that you then divided into fifths.

So that would look a little something like this.

You might have used your times tables facts to determine that there are six groups of five-fifths, which is 30-fifths.

So maybe you didn't draw anything at all, maybe you just went straight to the times tables facts.

And then complete the counting sequences, five, six, seven, eight.

Five groups of five-fifths, six groups of five-fifths, seven groups of five-fifths, eight groups of five-fifths.

And then 25 fifths, which is the same as five wholes, 30-fifths, which is the same as six wholes, 35-fifths is the same as seven wholes, and 40-fifths is the same as eight wholes.

And solve these problems. If 10 pizzas were cut into fifths, how many fifths would there be? You might have used your times tables facts to determine that there are 10 groups of five-fifths, which is 50-fifths.

And at to party 12 pizzas are cut into fifths, every child eats one slice, and all of the pizzas are eaten, how many children are at the party? You might have seen the times tables factor there.

You might have used 12 groups of five.

12 lots of five, that's 60, so that's 60-fifths.

So there are 60 children at the party.

And C, at the same party some cakes were cut into five equal slices, and there were 25-fifths.

How many whole cakes were there? Well, you might have used your known times tables facts to determine that 25-fifths is five groups of five-fifths, so there must have been five whole cakes.

You're doing really, really well.

I think you are ready for the next cycle, in fact, you definitely are.

That's mixed numbers as improper fractions.

Sofia has two and one-fifth metres of string.

Can you see that? Can you see the two? Can you see the one-fifth? That's two and one-fifth.

That's our a mixed number.

It's got a whole number part, two, it's got a fractional part, one-fifth.

Let's cut the whole one metre lengths of string into fifths.

There we go.

Now can you see everything is in fifths? How many fifths can you see? It will be more efficient to represent this as a diagram.

So that's all of those fifths.

Jacob says, "I can see five-fifths, 10-fifths, and then an extra one.

So that's 11-fifths." We can see 11-fifths, that's our improper fraction.

Jacob says, "I could also say that there are two groups of five-fifths, which is 10-fifths, and one more fifth, so that's 11-fifths.

I like that method.

That's efficient.

Jacob says, "A stem sentence can help us express a mixed number as an improper fraction." And this is the stem sentence.

There are, groups of five-fifths, which is, fifths, and, more fifths.

So that is, fifths.

Let's do that.

There are two groups of five-fifths, which is 10-fifths, and one more fifth, so that's 11-fifths.

Two and one-fifth equals 11-fifths.

Two and a fifth is the mixed number, and 11-fifths is the improper fraction.

Let's add another one-fifth of a metre piece of string so that we have two and two-fifth pieces.

So two and two-fifths.

That stem sentence can help us to express that mixed number as an improper fraction.

So this time, there are two groups of five-fifths, like before, which is 10-fifths, like before, and two more fifths this time.

So that's 12-fifths.

Two and two-fifths equals 12-fifths.

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

And let's have a look at this number line.

Okay, so we've got one-fifth equals one-fifth, two-fifths equals two-fifths, three-fifths equals three-fifths, four-fifths equals four-fifths.

They're all proper fractions so far.

And then we get to five-fifths, our first improper fraction, which is equal to one, one whole.

And then we've got six-fifths, which is an improper fraction, is equal to one and one-fifth, which is a mixed number.

Seven-fifths, improper fraction, one and two-fifths, mixed number.

Eight fifths, improper fraction, one and three-fifths, mixed number.

Nine-fifths, improper fraction, one and four-fifths, mixed number.

10-fifths, improper fraction, and that's the same as two wholes.

11-fifths, improper fraction, two and a fifth, mixed number.

And then finally on this number line, 12-fifths, which is our improper fraction is equal to two and two-fifths, which is a mixed number.

You might like to practise counting along that number line.

Let's look at a different mixed number.

So we've got three and two-fifths.

Got a whole number part which is three, and it's got a fractional part which is two-fifths.

It's a mixed number.

Jacob says, "I can write this as an improper fraction using that stem sentence to help." There are, groups of five-fifths, which is, fifths, and, more fifths, so that is, fifths.

Okay, let's see if we can do this without a bar model.

There are three groups of five-fifths, that's the whole number part, which is 15-fifths.

And then there are two more fifths, that's the fractional part.

So that's 17-fifths.

So three and two-fifths equals 17-fifths.

True or false? Two and three-fifths equals five-fifths.

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

What did you think, did you have the chance to chat that through with a partner and explain your thinking and improve your thinking? It's false.

There are two groups of five-fifths, so that's 10-fifths, and then three more fifths, so that's 13-fifths.

We write that as 13-fifths, just like that.

That's the improper fraction.

Can you see where the mistake might have been made here? The whole number was added to the numerator.

That's not how we do it.

It is time for some final practise.

Write these mixed numbers as improper fractions.

You might notice some little sequences within that.

Remember to use the stem sentence to help.

There are, groups of five-fifths, which is, fifths, and, more fifths, so that is, fifths.

That stem sentence really helps me to think about mixed numbers and improper fractions.

Jacob writes the mixed number 10 and two-fifths as an improper fraction.

So he is got the 10 and two-fifths right, but he's written that as 12-fifths as an improper fraction, and that's not right.

What mistake has Jacob made? How should 10 and two-fifths be written as an improper fraction? So see if you can come up with a really nice clear way to explain that to Jacob where he's gone wrong.

Pause the video and away you go.

How did you get on with that final round of practise questions? Are you starting to feel super confident? I do hope so.

So number one, write these mixed numbers as improper fractions.

So one and one-fifth is equal to six-fifths, so therefore one and two-fifths is equal to seven-fifths.

One and three-fifths is equal to eight-fifths, and one and four-fifths is equal to nine-fifths.

Now two and one-fifths, well, the two must be 10-fifths plus an extra one-fifth is 11-fifths.

And again, the two is 10-fifths, and the extra three makes 13-fifths.

Three and one-fifth, well the three is 15-fifths, plus an extra one-fifth is 16-fifths.

And six and four-fifths, the six is 30 fifths, plus an extra four is 34-fifths.

And that stem sentence was very helpful there I thought.

And then Jacob's written 10 and two-fifths as 12-fifths.

That's not true.

What mistake has he made? Jacob added the whole number and the denominator to get 12.

That's not how we do it.

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

There are in fact 10 groups of five-fifths, which is 50-fifths, and two more-fifths, so that makes 52-fifths.

Well done if you said 52-fifths for your improper fraction.

We've come to the end of the lesson, you have been amazing.

Today we've been expressing an amount of fifths 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 and lots of different examples of improper fractions today.

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

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

And you've done lots of examples of that too.

So I hope you're feeling really good about improper fractions.

Hope you're starting to feel like you're getting some knowledge and expertise about it.

I think you're doing really well.

So give yourself a pat on the back.

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

Hope you try really hard, and find lots of success just as you have in this math lesson today.

I hope I get the chance to spend another math lesson with you in the very near future, but until then, take care and goodbye.