Lesson video

Hello there, how are you? Are you having a great day? My name's Mr. Tilston and I'm having a great day because I'm very excited I get to spend this math lesson with you and we get to talk about mixed numbers.

Now, mixed numbers is something that you might already have some familiarity with.

Well, let's see if we can make you into a mixed numbers expert today.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is, I can explain how a mixed number is composed.

And our key words, I'll say it first, you say it back.

So my turn, mixed number, your turn.

And my turn, composition, your turn.

As I said, you might already have a bit of an inkling about what mixed numbers are.

You might have done that very recently.

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

So for example, this is one and a half.

That's a mixed number.

And the composition of a whole number is the way in which the whole number is made up.

So for example, 10 is composed of seven and three.

That's one of the ways that it's composed.

Our lesson today could be thought of as a whole that's divided into two parts, two cycles.

The first part will be the composition of mixed numbers and the second the representation of mixed numbers.

But for now, let's focus on that first part, the composition of mixed numbers.

In today's lesson, you're going to meet Jacob and Sofia.

You might have met them before, they're here today to give us a helping hand with the maths.

Sofia has a sister who is two and a half years old.

Do you have a sister, I wonder? How would you write two and a half as a number? Hmm? Can you think back to your knowledge of mixed numbers? Two and a half.

Well, Sofia says, "Two and a half is a mixed number: it has a whole part and a fractional part." So what's the whole part and what's the fractional part? The two is the whole number part and the half in this case is the fractional part.

And that's what a mixed number is.

A whole number part and a fractional part.

Every single time.

We write a two, that's a whole number followed by half.

And we say two and a half, but we don't write the and when we write the mixed number, we write it like that.

The composition of this mixed number can be represented as an addition equation.

Let me show you what I mean.

So here the whole equals a part plus a part.

So what's the whole there? The whole is a mixed number.

What's one part? The whole number.

And what's the other part? The fractional part.

So the whole is comprised or composed of two parts.

Here we go.

So that's your mixed number whole two and a half.

That's your whole number part two.

And that's your fractional part half.

So we can see two and a half equals two plus half.

That's that mixed number as an addition equation.

Let's have a look at a different example.

Jacob has a piece of string that is three and two-fifths of a metre in length.

Let's think about that as an addition equation.

How would you write three and two-fifths first of all? As a number, as a mixed number? Think about the two different parts it's got.

Three and two-fifths is a mixed number.

It has a whole part and a fractional part.

The three is the whole number part and the two-fifths is the fractional part.

So that again, that's a mixed number.

A whole number part and a fractional part.

We write a three followed by two-fifths and we say three and two-fifths.

We don't write the and, but we do say it.

The composition of this mix number can be represented as an addition equation.

Can you think how we might do that? So the whole equals a part plus a part.

Mixed number whole, plus whole number part plus fractional part.

So what's the mix number whole? That's three and two-fifths.

The whole number part is three.

And the fractional part is two-fifths.

So we can say three and two-fifths equals three plus two-fifths.

That's now an addition equation.

Well let's do a little check for understanding, shall we? Look at this mixed number and complete the addition equation describing its composition.

So I won't say it 'cause that will give you a little clue.

But can you think about the two parts that you can see there? Pause the video and see if you can fill in those blanks.

Let's have a look.

So we've got an addition equation but with blank parts in.

Let's see if we can fill in those blanks.

So seven and three-eights equals seven plus three-eights.

They're the two parts and when you add them together, you get seven and three-eights and we can write it just like that.

It is time for some practise.

Number one, complete the part-part-whole models to show the composition of these mixed numbers.

Then represent as an addition equation.

Now you might notice that some of those part-part-whole models are in different orientations.

Don't be fool by that.

They're still part-part-whole models.

So fill in the part-part-whole models and then write the addition equation for each.

I don't think that's going to take you too long.

So good luck and I'll see you very shortly.

Welcome back, how did you get on? Let's have a look.

So three and four-sevenths.

You can hear it when I say it, can't you? Three and four-sevenths.

Two and one-ninth.

That is two and one-ninth, and five and three-twelfths.

That's five and three-twelfths.

Remember, your parts may have been the other way round.

So in that first example, you might have written the four-seventh first and the three afterwards.

That doesn't matter because addition is commutative.

You can swap those numbers around.

Now let's look at the addition equation for each.

So three and four-sevens equals three plus four-sevenths.

Two and one-ninth equals two plus one-ninth, and five and three-twelfths equals five plus three-twelfths.

Well done if you got those.

And if you did get those, you are ready for the next part of the lesson.

That's the representation of mixed numbers.

Let's go.

So Jacob has a two metre length of ribbon.

Sofia has half a metre length of ribbon.

Can you visualise that? Can you picture that? What would that look like? Picture Jacob with his two metre length.

Picture Sofia with a half metre length.

Have you got a picture in your mind yet? Might look a bit something like this.

That's Jacob with his two metre length.

And that's Sofia with her half metre length.

What length of ribbon do they have in total? Hmm.

Well we can start by representing this as a part-part-whole model, just like you did before.

So we've got two, that was one part, that was Jacob's part.

We got half, that was the other part, that was Sofia's part.

When we combine them, what do we get? To find a missing whole, we need to add the known parts.

We can use the part-part-whole model to form an equation.

Two plus half equals? Together the children have two and a half metre length of ribbon and we can write that as a mixed number, just like that.

So two and a half could be written like that.

That's a mixed and number.

Let's look at the part-part-whole model in more detail.

So here we've got two plus half equals two and a half.

We already formed one equation.

Are there any more addition or subtraction equations that can describe the composition of two and a half? So look at that part-part-whole model.

Are there any other ways you could read that? Anything else that you could see? Any more addition facts, any subtraction facts that you can get from that model using those exact numbers? Well, Jacob says, "Let's start by looking at a simpler case." So we'll come back to that.

We're looking at 21 and 13 and eight.

So 21 is the whole 13 and eight of the parts.

And there are eight different equations that we form.

Eight, let's see if we can get them all.

So 21 equals 13 plus eight.

Okay, I think there's another addition one there.

21 equals eight plus 13.

Yes, we can swap those numbers around, it's commutative.

What's about this? What about we start with the addends? 13 plus eight equals 21.

If we started with the addend and swap those numbers over, we'd have eight plus 13 equals 21.

That's our four addition facts.

Now let's see if we can think of four subtraction facts.

Can you think of one? What about this? 21 take away 13 equals eight.

And you could literally cover up that 13.

You could take it away with your hand and you would be left with the eight.

So 21, subtract 13 equals eight.

And you could rephrase that slightly and say eight equals 21, take away 13.

Any other ways you could say it? We've got two to find.

Can you find any more? What's about this? 13 equals 21 take away eight.

Right now what about if we were to rearrange that slightly? We could have 21 subtract eight equals 13.

So there we go.

Four addition facts and four subtraction facts from that part-part-whole model.

So let's see if you can apply that to mixed numbers.

Okay, let's go back to this part-part-whole model with the mixed number.

That's two and a half equals two plus one half.

Let's see if we can write some equations that show the additive relationships between the whole and its part.

So we're looking for four additions and four subtractions.

Let's go.

Remember there's eight, Jacob says.

Right, let's start with this.

Two and a half equals two plus half.

Two and a half equals half plus two.

Two plus one half equals two and a half, and half plus two equals two and a half.

So that's four different ways that we can use addition equations.

What about those subtraction ones? Two and a half take away, subtract two equals half.

Half equals two and a half subtract two.

Two equals two and a half, subtract half.

And finally two and a half, subtract half equals two.

And that is all eight of the equations.

Well done if you've got all eight.

Each of these equations describe the composition of the mixed number two and a half.

And that's how we write that.

Two and one half is composed of a whole number part, that's two and a fractional part, that's half.

Do you think you got that? Well, let's put that to the test.

Let's have a quick check.

Look at this part-part-whole model.

Can you write equations that show the additive relationships between the whole and its parts? And Jacob says, "Remember there are eight of them!" So see if you can find all eight.

Four addition and four subtraction.

Pause the video and good luck.

Did you manage to find all eight? Let's have a look.

We've got three and two-fifths equals three plus two-fifths.

Three and two-fifths equals two-fifths plus three.

Three plus two-fifths equals three and two-fifths.

Two-fifths plus three equals three and two-fifths.

That's our four addition ones.

Well done if you've got all four of those.

And what about our four subtraction ones? Three and two-fifths take away three equals two-fifths.

Two-fifths equals three and two-fifths take away three.

Three equals three and two-fifths take away two-fifths, and then three and two-fifths take away two-fifths equals three.

And if you've got all eight of those, you are as superstar, well done.

It is time for some final practise.

So number one, use the part-part-whole model to complete these equations.

So we've got four and three-fifths and then we've got the two parts of that, which are four and three-fifths.

So can you complete those equations? Number two, make up your own example using this part-part-whole model, writing the equations to show all the different ways in which you describe the additive composition of your mixed number.

So you are creating a mixed number.

The whole number part has been given.

It's nine.

You've got to think of a fractional part and then write all of the different equations that you can think of.

See if you can find all eight.

And when you've done that, if you've found all eight, why don't you try a different mixed number and then after that, maybe a different one again.

All right, very best of luck and I'll see you soon.

Welcome back, how did you get on with that? Let's have a look.

So use the part-part-whole model to complete these equations.

So four and three-fifths equals four plus three-fifths.

Four and three-fifths equals three-fifths plus four.

Four plus three-fifths equals four and three-fifths.

Something plus four equals four and three-fifths.

And that is three-fifths.

Four and three-fifths, take away four, subtract four equals three-fifths.

Something equals four and three-fifths take away four, that's three-fifths.

And then four equals something take away three-fifths, that's four and three-fifths.

And then finally four and three-fifths, take away three-fifths equals four.

So very well done if you've got all of those.

And then for the second one, there's all sorts of different mixed numbers you could have created.

So in this case we've gone for, nine and one-tenth, but it could have been different fractional parts.

So we've got our nine and one-tenth as the whole and nine is apart and one-tenth as a part.

The written equations for this one would look like this.

We've got eight of them.

Nine and one-tenth equals nine plus one-tenth.

Nine and one-tenth equals one-tenth plus nine.

So commutative, swap them round.

Nine plus one-tenth equals nine and one-tenth.

One-tenth plus nine equals nine and one-tenth.

Nine and one-tenth subtract nine equals one-tenth.

One-tenth equals nine and one-tenth subtract nine.

Nine equals nine and one-tenth subtract one-tenth, and the final one nine and one-tenth subtract one-tenth equals nine.

So well done to you if whatever mix number you chose, you managed to find eight different equations, four addition and four subtraction.

We've come to the end of the lesson.

You have been incredible.

Today's lesson's been explaining how a mixed number is composed.

So we've been thinking of it additively.

We've been looking at addition equations and subtraction equations.

So mixed numbers are composed of a whole number part and a fractional part.

And we've looked at lots and lots of examples of that.

And I'm sure you are getting very confident now about what a mixed number is.

The composition of a mixed number, so how it's put together, can be written as an addition equation, adding the whole part and the fractional part.

And remember we can also swap those parts over because addition is commutative.

Mixed numbers can be represented on a part-part-whole model.

This can then be used to form addition and subtraction equations.

And remember, although there are plenty of different equations that we can write, in fact there are eight different ones.

We only ever say the mixed number and write the mixed number in one way, which is the whole number first, followed by the fractional part.

Very well done on your achievements and your accomplishments today, you've been amazing.

Why don't you do a big sigh of relief? (sighs loudly) Why don't you give yourself a big pat on the shoulder? (pats shoulder) Well done, it's been a great pleasure working with you today and I really hope I get the chance to spend another math lesson with you in the near future.

But until then, have a great day, whatever it is you've got in store.

Take care and goodbye.