Lesson video

Hi there.

Nice to see you.

My name is Mr. Tilstone, I'm a teacher and my favourite subject is definitely maths.

So you can imagine how excited I am to be here with you today teaching you this lesson, which is all about parts and wholes.

Now you might have had some recent experience working with parts and wholes, and you might be becoming quite the expert.

So let's see if we can get you even further on that journey and learn lots of new skills and knowledge all about parts and wholes.

So if you're ready, I'm certainly ready.

Let's begin.

The outcome of today's lesson is I can explain the size of the part in relation to the whole, and we've got some key words.

I'll say them first.

You say them back.

My turn, part.

Your turn.

My turn, whole.

Your turn.

I'll bet you are getting quite familiar with those words, but they're very important today.

So let's have a little recap, a little reminder.

The whole is all of the parts or everything, the total amount, lots of different ways to think about the whole.

And a part is some, but not all of the whole.

And it might be a small part, a larger part, et cetera, et cetera.

And that bar model shows part and a part and a whole.

Our lesson today is split into two cycles, or two parts, if you like, and the first one comparing different parts of same size wholes and the second comparing same size parts of different sized wholes.

So let's start by concentrating on comparing different parts of same sized wholes.

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

Have you met them before? They're here today to give us a helping hand with our maths, and very helpful they are too.

Let's look at some squirrels.

There's a special word for a group of squirrels.

I don't if you know it all can remember it.

You'll find out in a second.

It's scurry.

If the whole is the scurry of squirrels, then the red squirrels and the grey squirrels are parts of the whole.

Can you compare the different parts of this whole? So all of those squirrels together, that scurry of squirrels is a whole, but what do you notice about the parts? Hmm? How many different parts are there? Are they equal or unequal? Hmm.

Jun says the red squirrels are a smaller part of the whole than the grey squirrels.

So they're definitely unequal parts, aren't they? There are more grey squirrels than there are red squirrels.

So he says this is because there are fewer of them.

Yeah, we can see that.

So you could say the number of red squirrels is less than the number of grey squirrels.

Izzy says we could also say that the grey squirrels are a greater part of the whole because? Because what do you think? There are more of them.

Yes, of course.

How could we say that using inequality symbols? We could say this.

The number of grey squirrels is greater than the number of red squirrels.

Let's forget about squirrels for a second.

Let's think about rectangles.

Look at these rectangles.

What do you notice? What's the same about them and what's different? Hmm.

Have a good think.

See what you can notice.

Good mathematicians are good at noticing things.

Let's see if you can.

What can we notice here? What's the same? Well, each whole rectangle is the same size.

So we can say it's the same sized whole and each of them has been divided into two parts.

Can you see that? Each one's divided into two parts? One part is shaded and the other part is not shaded.

And that's true of all of them.

So that's what's the same about them.

What about what's different? The purple part is a greater part of the whole rectangle than the green or blue part is because more of the rectangle is shaded.

So can you see that? The green and blue parts are equal to each other because the same amount of the rectangle has been shaded.

So even though they're in different parts of the rectangle, they're the same as each other.

You can see that.

Different parts of same sized wholes can be directly compared based on their size.

The purple part is a greater part of the whole than the green part is.

Would you agree? There's more purple there than there is green? So we can say purple part is greater than green part.

Agreed.

The green part is an equal sized part of the whole as the blue part.

So those two are the same as each other.

They take up the same amount of space in their rectangles, which are the same size as each other.

So we can say that the green part equals the blue part.

Let's look at a different example where the whole is defined as a distance from Jun's house to school.

So that whole is the whole journey.

Let's think about the parts.

So we're going to compare the distance from the tennis court to the school, that's going be one part of the journey with a distance from the church to the school.

That's a different part of the journey.

And let's compare them.

Here we go.

That's a distance from the tennis court to the school.

And this is a distance from the church to the school.

So are those two parts the same as each other? No.

The distance from the tennis courts to the school is greater than the distance from the church to the score.

Let's have a little check.

Let's see how much you've understood so far.

So look at the two groups of penguins and then complete the sentences.

So look at group A and look at group B.

See what you can notice.

So in group, hmm, the white penguins are a hmm, part of the whole than in group hmm.

The wholes are the hmm.

So we can directly compare the parts and there are hmm white penguins in group hmm.

Quite a bit to think about there.

Have a good think.

Don't rush into it and then have a chat.

Compare answers with a partner.

See if you can work together.

And let's see if you can fill in those blanks.

Pause the video and have a go.

Let's see what you came up with and let's see if it matches what we've got here.

So, in group A, the white penguins are a greater part of the whole than in group B.

So there's more white penguins in group A.

The wholes are the same because each group's got five penguins.

Yeah? So we can directly compare the parts.

And there are more white penguins in group A.

So because the number of penguins in each group was the same, we could say they were the same sized wholes.

Let's do some practise.

Number one, compare the blue, red, and green felt tip parts in this whole pack.

So the felt tips are the parts this time.

And you might like to use this stem sentence to support you.

The mm felt tips make up the mm part of the whole.

I know this because mm.

Number two, look at these sets of counters and you might have some counters in front of you to help you with this.

In which set do the yellow counters make up the smallest part of the whole? In which set do the yellow counters make up the greatest part of the whole? Give reasons for your answer.

Number three, compare the parts of water in each of these jugs.

You might like to use this stem sentence to support you.

The water in jug mm makes up the mm part of the whole.

I know this because mm.

So can you fill in those blanks? Good luck with that.

I'll see you soon for some answers.

Welcome back.

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

So number one, compare the blue, red, and green felt tip parts in this whole pack.

Or we can say the number of red felt tips is less than the number of blue felt tips, which is less than the number of green felt tips.

And you might have written that in words or use the inequality symbols like that.

The red felt tips make up the smallest part of the whole.

I know this because there are fewer red felt tips than blue or green felt tips.

You might have said something like that.

The green felt tips make up the greatest part of the whole.

I know this because there are more green felt tips than blue or red felt tips.

So you might have said it like that too.

Lots and lots of different ways that you can compare those felt tips.

And number two, look at the sets of counters in which set the yellow counters make up the smallest part of the whole.

Well in set C, and look at set C.

The yellow counters make up the smallest part of the whole.

This is because the wholes are the same.

So each whole comprised of seven counters, but there are fewer yellow counters in set C.

So you can see set A had three yellow counters.

Set B had five yellow counters and set C just one yellow counter.

So that made up the smallest part of the whole.

In set B, the yellow counters make up the greatest part of the whole.

This is because the wholes are the same as before, but there are more yellow counters in set B.

So that was the one that had the most yellow counters, even though the wholes were the same.

And number three, compare the parts of water in each of these jugs.

Well, first of all, the jugs were the same size, weren't they? So we can say the wholes were the same size, the same sized wholes.

So we can compare directly.

And we can say that in jug A, the water makes up a smaller part of the whole than in jugs B or C.

Likewise, we can say in jug B, the water makes up a greater part of the whole than in jugs A or C.

You're doing really, really well and I think you are ready for the next cycle, which is comparing same size parts of different sized wholes.

So so far we've looked at same size wholes.

Let's look at different ones.

So Jun and Izzy are playing with some marbles.

So they're different coloured marbles.

Here we go.

What do you notice? What can you see? What could you say? Well, Izzy says, I notice that our whole amounts of marbles are different.

Yes.

They're not the same size, are they? I also noticed that we each have one yellow marble.

Did you spot that too? Well done if you did.

My yellow marble is my whole amount.

Yeah, that's all of her marble collection, isn't it, at this point? But Jun says my whole amount of marbles is greater than Izzy's whole.

Yeah, he's got two marbles in his whole hasn't he? The whole has increased whilst the yellow marble part stays the same.

So this part becomes a smaller part of the whole.

And now Izzy and Jun's friend has joined in and says, my whole is greater than Izzy and Jun's whole.

Yeah, because there's more marbles in that collection.

But what else do you notice? The whole has increased whilst the yellow marble part stays the same.

So this part becomes an even smaller part of the whole.

So the whole is changing size.

In this case it's getting bigger, but that part is remaining the same, becoming a smaller part of the whole each time.

And here comes Alex, my whole is greater than Izzy, Jun and Sam's whole.

Hmm.

Do you agree? Yes.

He's got four marbles that makes his whole, but he's still got one yellow one.

If the whole increases in size, but the size of the known part remains the same.

And in this case that's a yellow marble, that part becomes a smaller part of the whole.

So as we go along each time the yellow marble becomes a smaller part of the whole.

Izzy makes a pattern with shapes.

What do you notice? What's the same? What's different? So be a good mathematician.

See what you can notice.

Have a look.

Can you spot anything that's the same? Can you spot anything that's different? Let's have a look.

Well, each group has two parts that are red.

Did you spot that? So there's three different patterns, but in each of them, two of the parts are red.

The whole increases in size, but the size of the red part remains the same.

So there's not more, or there's not fewer red parts each time.

There's the same amount of red parts each time.

So each time the red part becomes a smaller part of the whole.

In the first instance, there were two red parts out of four.

In the second one there were two red parts out of five.

And in the third pattern there were two red parts out of eight.

That was the whole, that was the size of the whole.

So the red part has become a smaller part as the size of the whole has increased.

Jun pours 250 millilitres of water into two different size jugs.

So those two jugs have got the same amount of water in.

How would you describe them again? What do you notice? What do you see? Remember, each of them has got the same amount of water.

Well, they're different size jugs, aren't they? So jug say the large jug is nearly empty 'cause it's so big.

So 250 millilitres hasn't taken up much space there.

A smaller part of the jug has water in it.

The small jug is nearly full.

A greater part of the jug has water in it.

The whole decreased in size, but the part remained the same.

So the jug got smaller, but the amount of water remained the same.

So the part became a greater part of the whole.

So in that smaller jug, the water is a greater part of the whole.

In the larger jug, the water's a smaller part of the whole.

Let's have a little check for understanding.

Let's see how you are getting on.

So true or false, one part is shaded in each image.

This means that the same amount of each whole is shaded.

Is that true or is that false, and can you justify your answer? Hmm.

Have a go.

Have a think and see if you can explain that really clearly.

Pause the video.

Well, no, that's not true.

That's actually false.

Let's see if we can come up with a justification then.

What did you say? Which of these could we say? If the whole increases in size, but the size of the known part remains the same, that part becomes a smaller part of the whole.

Or if the whole increases in size, but the size of the known part remains the same, that part becomes a greater part of the whole.

Which of those is true? Have another few seconds thinking about that.

Which one is true? It's this one.

So if the whole increases in size and it does each time, doesn't it? It gets one bigger each time and but the size of the known part remains the same, which it does, it is one each time that part becomes a smaller part of the whole.

So in that final example at the bottom, the pink part was a smaller part of the whole than in the top example.

It's time for some more practise.

So make a pattern of shapes like this one of Izzy.

So you could use counters, you could use little sticky notes, all sorts of things you could do.

Explain how your pattern demonstrates your understanding of this concept, that if one part remains the same as the whole increases, then that part becomes a smaller part of the whole.

So that image there proves that.

Can you think of some different ways to prove that? Can you explore that? Number two, these jugs all contain 200 millilitres of water, starting with a jug of water that represents a smallest part of the whole.

Put these jugs of water in order and give reasons for your ordering.

So good luck with that.

See if you can explain yourself nice and clearly.

Have a good think about what you want to say before you write it.

And then check to see if it makes sense.

Be nice and clear and good luck and I'll see you soon for some feedback.

How did you get on? Would you like some answers? Let's check.

So you might have used counters, you might not.

You might have done something different.

And if you use counters, you might have designed a pattern, something like this.

There's all sorts of ways you could prove it.

But let's see what you notice in each case here.

In each of these, we've got the same part.

That's the pink part in these cases.

So the parts remain the same, but the whole is increasing in size, isn't it? So in the first one, the whole is three counters.

In the second one, the whole is five counters.

And in the third one, the whole is seven counters.

So the whole's increasing in size, but the part is remaining the same.

And in that final example, the part was a smaller part of the whole in the first example.

And for number two, you might have ordered the jugs a bit like this.

So this is jug A, jug C, and jug B.

Why might we have ordered them like that? You might have done it differently, by the way as well.

This is just one way to do it.

Well, you might have given reasons like this.

Although each jug contains 200 millilitres of water, the wholes were different sizes.

The part remains the same as the whole decreases.

So the part was the 200 mils of water, but the whole was decreasing in size in this example, the the size of the jug was decreasing.

So that part becomes a greater part of the whole as the jug size decreases.

We've come to the end of the lesson today.

We've been reviewing, explaining the size of the part in relation to the whole.

If the whole is the same, then two parts can be compared directly.

If the whole increases while the part stays the same, the part becomes a smaller part of the whole.

If the whole decreases while the part stays the same, the part becomes a bigger part of the whole and you prove that lots of time, for example, with the water or with the counters, both the part and the whole need to be considered when making judgements about whether a relatively large or small part of the whole is identified.

Well, there's been lots to take on board today and you've done really, really well.

So I suggest you give yourself a very well deserved pat on the back.

Go for it.

You've earned it.

I've really enjoyed spending this math lesson with you, and I hope I get the chance to spend another math lesson with you in the near future.

But until then, enjoy the rest of your day.

I hope it's a good one.

Take care and goodbye.