Lesson video

Hi guys.

MR. Easter here again.

We're going to start off today's lesson by talking about the activity at the end of the previous lesson.

I asked you to find a small glass or container, fill it up to the top with liquid if you had someone's permission at home and then pour that smaller glass into larger glasses and see if it filled the container.

See if it filled a small part of the whole or if it filled a large part of the whole.

If you didn't have a chance to do it, I'm going to do some here.

So again, I've got some kind of liquid.

I'm going to fill the small container and I'm going to pull my small container into a larger glass.

I wonder if you can predict, will this fill the whole of this glass? Will this fill a large part of the glass or will it fill a small part of the glass? Let's see.

Okay.

It's all poured out.

So the whole of that glass has been poured into here.

Now, have a look.

Is that the whole of my glass, is that a part of my glass? Is it a large part, a small part.

It's quite a large part of the glass.

Isn't it? It's about almost the same size.

The part that is liquid, that the part is not, but it's definitely not the whole of the container.

Now you may have found some even larger glasses here.

I found a larger container.

I wonder what happened again if I fill the same glass with liquid and I pour all of this whole into this larger container, can you make another prediction? Will it fill the whole of the large container? Will it fill a large part? Will it fill a small part? Have a think.

Tell someone that's there with you what you think is going to happen.

Let's see, shall we? I've poured it all in again.

It's empty.

And now, before, it was quite a long way out.

My other glass have a look.

Let's compare them here.

Different size glasses.

It's quite hard, the different width, the different heights.

But in this one, the first one in my left hand for me, it's quite a large part of the whole.

And then this one, the part that stayed the same is still all of this glass, but when we put it into a larger whole, it now is a smaller part.

Now this is quite a tricky concept to understand.

In today's lesson, we're going to look at some different examples and some different pictures to help us try and understand what is happening.

In the previous lesson, I showed you this image and in this image there are three glasses, glass A, glass B and glass C.

We said that the whole in each of these images is the glass and they are exactly the same size in each image.

Now I asked you to write some sentences about those three glasses.

Now I've written three sentences of my own.

I want you to see if you agree with the sentences or if you disagree with them and why.

Let me read the sentences to you.

The first sentence says, the water in glass B is the largest part of the whole.

The second sentence says, the water in glass C is a larger part of the whole than the water in glass A.

The third sentence says, the water in glass A is a larger part of the whole than the water in glass B.

So I want you to pause the video and see, do you agree, or do you disagree with each of those statements and why? Let's go through them.

The first one, the water in glass B is the largest part of the whole, because it says largest.

That means we're comparing the size of this part to both of the other parts.

To part C and the part of water here in glass A.

Now largest means biggest.

It's another word for biggest or greatest, is the part that is water here larger than C? Yeah.

Is the part in B larger than the part that is water in glass A? Yes.

'Cause it's bigger than both of those.

We can say the water in glass B is the largest part of the whole.

Let's look at the second sentence.

The water in glass C is a larger part of the whole than the water in glass A.

This time, we're just comparing C and A.

So let's think, is the water in glass C a larger part of the whole than the water in glass A? Do you agree or disagree? I agree.

This part is larger in size than this part.

Let's think about the third sentence.

The water in glass A is a larger part of the whole than the water in glass B.

This time we're comparing A and B.

Let's see, is the part that is water in glass A larger than the part that is water in glass B? No.

Glass A is nearly empty.

Glass B is nearly full.

The part that is water in glass A is smaller, not larger, is a smaller part of the whole than the water in glass B.

Well done if you've got those correct.

In today's lesson, we're going to be exploring the relationship between the parts and the whole further, similar to the examples I used before with my liquid in different size wholes.

We're going look at that, like I said before, using some different examples.

Okay.

So this first example.

I want you to think what is the same and what is different in each of these images? There's four images there, just like in the previous lesson, I want you to use the word whole and then what part when you're describing the similarities and differences.

So pause the video and either say them out loud or write them down or tell someone that's there with you, what's the same and what's different.

Okay.

Let's go through those four images.

Now, some of you might've noticed in each image, that is a red square.

That is the same in each of the four images, but this image there's one red square, in this image is one, in this is one, and then the final one there has one.

So the thing that is the same is one part is red in each image.

Does the whole stay the same in each image? No.

In the first image, the whole is only one square and that one square is red.

In the second image, does our whole get larger or smaller? Our whole has got larger, hasn't it? Now there are two squares which make up our whole.

One of them is red and one of the parts is white.

In our third image, has the whole got larger again or has it got smaller? It's got larger, hasn't it? How many parts are there that make up our whole now? Could you say three? That's right.

If you did, there's one, two, three squares, which make up our whole, but this time, one of them is red.

That's what we said, they're the same.

And now there are two white parts as well that make up our whole.

The final image.

Hopefully you can see again, it's got larger.

This time, our whole is made up of four of these equally sized parts.

Again, one of them is red.

And this time there are three white parts as well.

Okay.

Now I want to look further into this image.

I want us to read two statements and work out which statement we agree with, or do we disagree with both? Or do we agree with both? Let me read the statements.

So Basil states that, "One part is shaded in each image.

This means the same amount of each whole is shaded." Jess says, "Each whole is one part larger than the previous whole.

Only one part of each whole is shaded.

This means that each time a smaller part out of the whole is shaded." So pause the video, have a think, maybe read both of those statements again and see who do you agree with and why do you agree that they are right? So pause the video, say out loud or write it down, or if there's someone there, have a discussion with them, what do you think? Okay.

So let's think about it.

Let's start with Basil.

Let me read his first sentence.

Basil says, "One part is shaded in each image." Let's go back to the images.

In the first image, is there one part shaded red? Yes.

In the second image, is there one part shaded red? Yeah.

Third image is the same, fourth image is the same, in all of the four images, one part shaded.

Let's read his second part of the sentence.

"This means the same amounts of each whole is shaded." So let's think about that part.

In the first image, the whole of the shape is shaded.

Is that the same in the second image? Is the whole of the second image shaded? No, there's one part that is shaded and one part that is not.

So that is not the same.

Let's look at the next one down.

Again, is all of the shapes shaded red? No.

Is one part shaded red and one part not shaded red? No, this time there are two parts that are not shaded.

So the second part of Basil's statement is not correct.

Let's look at Jess's statement.

She says, "Each whole is one part larger than the previous whole." Let's go back to our image.

This whole is made of one part.

This whole is made of one and two parts.

That's one part larger.

We can see that here, this square is here in this image is not there.

So it's increased by one.

Let's look at the next image.

There's one, two, there's three parts.

Again, I can see this is what's grown.

It's now down here.

So it's now three parts and the same for the bottom one.

How many parts is the whole, yeah.

It's four parts each time the number has increased by one.

Let's look at the rest of Jess statement.

"Only one part of each whole is shaded." Yeah, we said that already.

That's the same as one of the things that Basil said.

This means that each time a smaller part out of the whole is shaded.

That's the really important part that we need to try and get our heads around.

I'll re-read it one more time.

This means, each time a smaller part out of the whole is shaded.

So I agree with that, but we're going to see a few more examples to see if you can understand, because even though the same number of parts is shaded each time because the whole is getting larger, that means a smaller part out of the whole is shaded.

Okay.

Same example.

I just want to be really clear about the key things that we need to pay attention to.

In the first image, the part shaded is one square and the whole is one square.

Can you say that with me? The part shaded is one square and the whole is one square.

So they are both the same.

In the second image, the part shaded is one square and the whole is now two squares.

Say that with me, the part shaded is one square and the whole is two squares.

in the third image, the part shaded is one square and the whole is three squares.

Final one, say it with me again.

The part shaded is one square and the whole is four squares.

Each time we're seeing what part is shaded and what the whole is made up of.

This example looks similar but there's a subtle difference.

Now, rather than having squares that are connected, we have counters.

We've got some yellow and some red counters.

Again, I want you to think what is the same and what is different in each image? Did you have a go at that? Did you see the similarities? Now, again, there are some similarities and some differences.

I have circled in each image what the whole is just like we did in the last page.

The last idea together, let's start off by working out what the whole is in each image.

In the first image, the whole is one counter, in the second image, the whole is two counters.

The third image, the whole is three counters.

And in the fourth image, the whole is four counters.

Let's think about the parts.

In the first image, there's just one part, isn't there? And that one part is yellow.

In the second image, how many parts are there? There's two parts.

One part is yellow and one part is red.

In the third image, one of our parts is yellow.

And this time there are two red counters.

So if we're thinking about what is the same in these three images, each time there is one yellow counter, but what's different is the size of the whole.

Let's look at the next image.

Again, can you tell me this time? What is the whole and what are the parts? Hopefully you said the whole it's four counters.

What's the same? There's still one yellow counter.

What's different this time there's one more red counter.

There were two counters.

Now there are three red counters.

We can say the part that is yellow is the same.

The whole gets one part larger each time.

Say that with me.

The part that is yellow is the same.

The whole gets one part larger each time.

Now, this is a challenging question.

I'm going to read it to you.

What do you notice about the size of the part that is yellow in relation to the whole as the whole increases in size? Let me read that one more time.

What do you notice about the size of the part that is yellow in relation to the whole as the whole increases in size? So let's go back to our image.

In the first image, the whole is yellow.

So all of the image, all of the whole is yellow.

In the second image, as the whole increases in size, there's still only one yellow part but now there's also a red part.

The parts are equal in size.

In the third image, the parts are all equal in size.

There's still one yellow counter but now the other part, the red part has become larger.

There's now one more red counter.

So in relation to the whole, this is now one of three counters and before it was one of two counters.

Let's look at the fourth image.

Again, our whole has increased in size.

There's still one yellow counter but now the part that is red has become larger which then means in relation to the whole, the size of this yellow counter, even though it's still the same size in relation to the whole, it is a smaller part of the whole.

Let's look at that written in a more condensed sentence.

As the whole increases in size and the size of the selected parts remains the same, each part becomes smaller in relation to the whole.

That means again, because the size of this yellow part stays the same, because the whole increases in size, then that means each part becomes smaller in relation to the whole.

It's a really tricky concept to understand.

So don't worry.

I haven't got it yet.

Let's look at some more examples.

Okay.

So I really want to focus just on those last two images of the previous example.

We have the example where the whole is three counters and the example where the whole is four counters.

Let's look at that in some more detail.

The first one we said, the whole is three circles.

The yellow part is one part of the whole.

What do you think our sentence would be for the second image? See if you can say it out loud before I show you.

The whole is, the yellow circle is, let's do that together.

The whole is four circles.

The yellow circle is one part of the whole.

In diagram one, the yellow part is a larger part of the whole compared to the part in diagram two, that's the same sentence written in a slightly different way as we did before.

So time for a new concept.

Let's see that in a different way.

It says the same sentence that we've said before there, is it still true, as the whole increases in size and the size of the parts there is the same.

In this example, is the part smaller compared to the whole? What do you think? Same as before, our red bar here is the whole of the first image.

In the second image, is that still true? Is the red part still the whole? No, the red part is only one of the two equally sized parts.

So it is a smaller part of the whole.

In the third image, again, there's one part that's red, but it's an even smaller part of the whole, because now there are three parts in the whole and only one is red.

In the final example, the same thing.

There's still one part that's red but it's an even smaller again, part of the whole, because now there are four parts that make up our whole.

Again, as the whole increases in size and the size of the selected part remains the same, that's the red part in this example, each part becomes smaller in relation to the whole.

So an example that may be you might've experienced at home.

Have you ever made some squash, some orange squash, blackcurrant squash? Have you ever made it? Here, I've made some myself.

Now, this is the same liquid that I used earlier but I've mixed some of the squash with some water.

Then I can try and make it a nice taste.

So three friends are discussing how much orange cordial to put into a glass to top up with water.

Who do you agree with? The first person that's this top left box says, all of the drinks will taste the same when I add water as they all have the same amounts of cordial in.

The second person says, in the first drink, this drink down here, there will be no water as all of the whole is made up of cordial.

The third child says, I would want to drink the last drink as the amount of cordial compared to the whole is less when I add water.

So here are four images.

In this one I should have said before, this part, the part that's coloured in, that is the part that is cordial and the part above it is the part that is water.

Now, if I go back to my example, that's not actually what it looks like 'cause when we mix them together, they all mixed together.

So it wouldn't look like that image on the screen but that's just so you can understand what part is water or what parts are water and what part is cordial.

So pause the video, have a think.

Who do you agree with? Let's go through those three children's statements.

So the first child says, "All of the drinks will taste the same when I add water as they all have the same amounts of cordial." Do you agree with that child? I'm not sure.

If I go back to the example I used before, if I fill all of this glass with cordial do I have enough? Not quite, but if I filled that all with cordial and drank it, that would be very sweet.

That would not taste the same as if I had a part that is cordial and then if I added water, I think they would taste different.

So the first child is not correct because they would all taste different because this one is all cordial, this one is some cordial.

One part is cordial and one part is water.

This one is a smaller relation to the whole because one part is cordial and now there are two parts that are water and this one is smaller.

Still, this would be weaker if it was a drink because there is one part that is cordial, and this time there are three parts that are water.

Let's look at the second child.

In the first drink, there will be no water as the whole is made up of cordial, do you agree with that child? I do.

Again, on my example, I'll make it exactly accurate as I pour in some more, all of this drink, all of this glass is cordial.

The all means the whole.

So the whole of this drink is cordial.

There is no water.

So I agree with that child.

Let's look at the third child.

I would want to drink the last drink as the amounts of cordial compared to the whole is less when I add water.

Now you might agree or disagree, whether you'd like to drink that one but let's see if the mathematical part is true.

The amount of cordial compared to the whole is less when I add water.

So Let's look at it.

Here is the amount of cordial compared to the amount of water, less or the smallest in this example.

Yeah.

I agree with them.

There is one part that is cordial but there are three parts that are water.

So it is smaller in relation to the whole, or for my drink.

It is weaker and much nicer.

Okay.

So something for you to do, a practise activity.

I want you to look for examples of parts and wholes at home where the part might stay the same and the whole may increase in size.

I'm sure.

Now, after the last few lessons you're getting good at spotting parts and wholes.

Here's some ideas for you.

Maybe similar to me, you'd have a go at pouring some water into different containers.

Maybe you could predict again, if you didn't get a chance off the last lesson, if you're using a smaller glass, if you pour it into a larger glass, you might guess where on that larger container it comes up to, let me see if I pour that in here.

Okay.

I think I can see where it would go.

Well, actually it's a little bit lower than I thought.

And here there is a small part that is cordial and there's a larger part that in this example, isn't filled, maybe you can do that with some different containers with somebody at home.

Maybe you could do similar to the other example of making some squash, thinking about if you use a little bit of squash or if you increase the size of the part, or if you use the same size part and you have more water, what happens to your drink? Maybe there's other examples.

Maybe you can play some items of food, like some peas on a spoon, then make the part larger and put it onto maybe a saucer, maybe a plate, maybe a larger plate.

Think about the proportion.

Think about the relationship of the part to the whole all the way through, really important to use that key language of wholes and parts Have a go.