Lesson video

Hello there, my name is Mr. Tilstone and I'm a teacher.

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

I just love maths, so it's a really great pleasure to be here with your today to teach you this lesson all about fractions.

I'm really excited, so if you're ready, we'll begin.

The outcome of today's lesson is, I can express quantities that are made up of both whole numbers and a fractional part.

And our keywords, we've just got one, it's a phrase really.

So my turn, mixed number.

Your turn.

Now you're going to be learning about this and probably you've never heard of this before, so let's give you a little sneak preview.

A mixed number is a whole number and a fraction combined, for example, this is one and a half and that is a mixed number.

So we'll explore that today.

Our lesson today is split into two parts, so we could think of our lesson as a whole and we could think of each cycle as a part and the first cycle, the first part, we'll be describing quantities composed of wholes and parts and the second, we'll be writing mixed numbers.

So if you're ready, let's begin by thinking about describing quantities composed of wholes and parts.

In this lesson you will meet Jacob and Sofia.

They're here today to give us a helping hand with the maths.

Have you met them before? They're really helpful.

Sofia has two oranges.

Jacob has half an orange.

Can you visualise that? Can you picture that? Can you see that in your mind? Sofia's got two oranges, Jacob's got half an orange.

What does that look like? Here's Sofia with the two oranges and here's Jacob with his half an orange.

How many oranges do Sofia and Jacob have altogether? Mm.

Sofia says, "I have two whole oranges." And Jacob says, "I have one half an orange." Sofia and Jacob have two and a half oranges altogether.

Now let's look at a different example.

How would you describe the height of this sunflower? What can you see? So I can see that it's taller than one metre.

It's one metre and a little bit.

It's not as tall as two metres.

Mm.

Sofia says, "The height of the sunflower is more than one metre." Yep, we can see that.

Jacob says, "We can be more precise and use the divisions.

The height is one and three tenths of a metre." So at that metre mark, that metre is divided into 10 equal parts and there are three more of those equal parts after that.

So we can say it's one metre and three tenths of a metre.

Sofia says, "We could also say the height is three tenths and one metre." What do you think about that, does that sound right? Jacob says, "I respectfully challenge you." I like that, that's very polite, isn't it? I respectfully challenge you.

We could say it like that, but the number of wholes should be said first.

They are more significant.

So people wouldn't say three tenths and one metre, they would say one metre and three tenths or one and three tenths of a metre.

Look at this example.

How long was spent reading? So let's have a look at the table.

We've got Monday, one hour, Tuesday, one hour and Wednesday, quarter of an hour.

Now, we've got a stem sentence here.

Whole hours and one of an hour were spent reading.

This is and a hours spent reading.

Pause the video and see if you can fill in those blanks.

How did you get on, did you manage to fill those blanks in? Let's have a look.

Well, two whole hours and one quarter of an hour were spent reading.

This is two and a quarter hours spent reading.

It's time for some practise.

Look at the image.

Describe how many pizzas there are in total.

So you can see some whole pizzas and then a part of a pizza.

Number two, look at the three sets of images.

Look carefully, do what a good mathematician does and notice things.

What's the same and what's different? Number three, Sofia and Jacob are discussing their ages.

Can you describe your age using whole and parts? So Sofia says, "I am eight and a half." And Jacob says, "I am eight and 10 twelfths." And that's both correct, that's just two different ways that they're each using to describe their age.

So can you have a go? How many different ways can you think of to describe your age using wholes and parts? Righty-oh, pause the video, off you go.

Welcome back, how did you get on describing quantities composed of wholes and parts? Let's have a look.

So here, how many whole pizzas do we have? We have three.

And then what else do we have? We have a half of pizza.

So this is three and a half pizzas.

This is three whole pizzas and one half of a pizza.

And what was the same and what was different here? You might have noticed that each of these has a quantity that was the same.

Did you spot that? Each one was four and two thirds.

You might've noticed that the fractional part was in different positions.

So on the top row, it was on the far right.

On the middle row, it was on the far left and on the bottom row, it was in the middle, but it was the same quantity in each.

Four and two thirds.

It doesn't matter where the fractional part is, we always say the number of wholes first.

So in each of those cases, even though the fractional part's in a different position, we would still say four and two thirds or four and two one thirds.

That's also acceptable.

And Sofia and Jacob are discussing their ages.

Can you describe your age using wholes and parts? Well, there are 12 months in a year, so we can describe our age in whole years and parts of a year.

That's twelfths.

You might've said that you were eight and 10 twelfths.

This means that you are eight whole years old and another 10 months.

So that's one possible way of saying it.

You might've said that you were nine and one twelfth.

This means that you are nine whole years old and another one month.

You might've noticed that Sofia said that she was eight and a half.

This means she's eight whole years and half of the another year, or six months old.

And I'm 21 and a half.

(clears throat) Moving on.

Okay, I think you're ready for the next cycle and that's writing mixed numbers.

Let's revisit this example.

Can you remember this from the start? This is Sofia and Jacob with their oranges.

Sofia's got two oranges.

Jacob's got half an orange.

And we've described that already, but now we can represent it as a part-part-whole model to support us to combine the parts.

Here we go.

Here's a part-part-whole model.

Sofia's got two oranges.

Jacob's got half an orange.

So on the right-hand side, you can see the two that represent Sofia's two oranges and the half that is Jacob's half an orange, and we can combine them to write the number two and a half, and that's how we write it.

Quantities made up of both whole numbers and a fractional part can be written as mixed numbers.

And that is our keyword for today.

So two and a half is a mixed number.

Now, you might notice that when you write two and a half, you don't write and.

So two and a half is written like that.

So this is an example of a mixed number.

Two and a half.

It is composed of a part made of whole numbers and a part made of a fraction.

So what's the whole number part? Two.

And what's the fraction? Half, so it's mixed.

It's got two different parts.

Here's your whole number part and here's your fractional part.

Whole number part plus fractional part equals mixed number.

So what you are seeing there on your screen is a mixed number.

The height of the sunflower is one and three tenths of a metre.

So we described that earlier.

Let's see if we can write that as a mixed number.

We can represent it in a part-part-whole model to help us form that mixed number.

Here we go.

So we've got one, that one whole metre part of it, and then the three tenths, the three tenths of a metre part of it.

And combine those together and we've got one and three tenths.

So that's how we write one and three tenths as a mixed number.

There's your whole part, there's your fractional part and there is your mixed number.

Are you getting this? Well, let's have a check and let's find out.

Two and a quarter hours was spent reading.

Represent this as a part-part-whole and then write two and a quarter hours as a mixed number.

So we've said it, can you write it? So two and a quarter hours as a mixed number is written as.

Pause the video and have a go.

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

So here's our part-part-whole model.

So there's your two hours and there's your quarter of an hour and combine them together and we've got two and a quarter and that is how we write it.

That's how we write that mixed number.

Well done if you got that.

Let's have a different mixed number.

Look at that.

What does that say, could you read that? How would you say it? Sofia says, "This is three and two eights." Mm.

And Jacob says, "I respectfully challenge you." So polite.

Why do you think he's done that? Why has he challenged Sofia? Was he right to do that? Was she right? He says, "You need to say the fraction part accurately." So it's not three and two eights like she said, it's three and two eighths like Jacob's saying.

And Sofia says, "We can also say this is three and two one eighths." That's acceptable too.

It's more common for people to say three and two eighths, but three and two one eighths is acceptable.

Time for some more practise.

Write these words as mixed numbers.

So we've got two and one third.

Could you write that as a mixed number? One and two fifths as a mixed number please.

10 and wo ninths as a mixed numbers please.

You can hear both parts, can't you, when I say it.

And three and four sevenths as a mixed number please.

And then number two, write these mixed numbers as words.

So I won't read these out, because that will give too much of a clue, but have a look at those and write them as words please.

And number three, true or false? A mixed number must always have a value of greater than one.

Mm, what do you think about that? Can you explain that? Have a good think, have a chat about it and then see if you can explain that really clearly.

Give some reasons for your answers, justify it.

Okay, well best of luck with that and I'll see you soon for some answers.

Welcome back, how did you get on? Let's find out.

So write these words as mixed numbers, so two and one third.

Remember, we don't write the and in the mixed number.

We write the two parts.

So two, one third, that's how we write that.

One and two fifths.

One, two fifths, you don't write the and.

That's how you write it.

10 and two ninths, you can hear both parts, so you write both parts.

You write the 10, you write the two ninths.

You write it like that.

And then three and four sevenths.

That's got two parts, you can hear them both when I say that, three and four sevenths.

You write your three, write your four sevenths, and that's how to write that mixed number.

Simple as that really.

And then write these mixed numbers as words.

Now, this is where you will write the and.

So that's how it looks, but you would read that as three and a quarter or you might've written it three and one one quarter.

This is one and a sixth or one and one one sixth.

Both acceptable.

Here we've got four and two eighths.

So we need to write the and when we write it or you could write it as four and two one eighths, and that's how you could say that.

And finally, that mixed number there we could read as this and we could write it as this.

That's two and three twelfths or two and three one twelfths.

And true or false, a mixed number must always have a value greater than one.

What do you think about that? Well, you might have aid that a mixed number is made of a whole number part and a fractional part.

So yes, they must always have a value greater than one, because the smallest whole number is one.

So it's always got to have a whole number part.

It might be one, it might be two, it might be 10, it might be 20, it might be 500 but it's got to have a whole number part and then it's got to have a fraction whether it might be one third, it might be one half, it might be two sevenths.

All sorts of possibilities.

We've come to the end of the lesson.

It's gone by really quickly.

I hope you've enjoyed it, I've really enjoyed teaching it to you.

Today's lesson has been quantities that are made up of both whole numbers and a fractional part.

So hopefully you know the special name for that now.

Quantities can be made of a whole number and a fractional part.

Quantities made of a whole number and a fractional part are greater than one.

So always greater than one.

And a quantity that's made up of a whole number and a fractional part is called a mixed number.

So I wonder if, just as a little check, you might be able to write down a mixed number.

Any mixed number that you can think of, write it down and then show it to your partner and see if they can read it out.

You've been amazing today, so I think you need to give yourself a very well-deserved pat on the back.

I hope I get the chance to spend another maths lesson with you in the near future, but until then, take care, enjoy the rest of your day and goodbye.