Lesson video

Hi everyone, Mr. Aster, hopefully recognise me from the previous lesson.

If you don't and you didn't have a chance to see that, I strongly recommend having a look at the previous lesson before this lesson, as the ideas we talked about yesterday will be progressed in this lesson.

So here's an image we saw in the previous lesson.

I want us to think about if this sentence is true or false.

If the United Kingdom is the whole, then Europe is a part of the whole.

Pause the video, have a think, explain to yourself, explain to some in the room.

Think about if that sentence is true or false.

So what do we think? Is it true or is it false? You should have said it is false.

The correct sentence should have been.

If Europe is the whole, then United Kingdom is a part of the whole.

We know that Europe should be the whole, because that is what the map is of.

And the United Kingdom is within the whole, which is why it's a part of the whole.

Another one we looked at same image before.

Let's think this time, which statement is correct.

If the United Kingdom is the whole, then England is a part of the whole.

Or if England is the whole, then the United Kingdom is part of the whole.

Which one do you think is correct? The top one or the bottom one? Hopefully you said the top one is correct.

If the United Kingdom is the whole, that's what this map is of.

This is the United Kingdom.

That is what we define as the whole and England, this country here, is a part of the whole.

Another familiar example.

I've got the same image that we saw in the previous lesson.

Remember, we're thinking about journeys.

And I've added some of this information into our stem sentence.

I want you to see if you can work out how we complete the stem sentence.

So let me read it.

If the journey from Sunny's house to Kofi's house is the, then the journey from Sunny's house to Alfie's house is- I wonder if you can work out what was going in the missing gaps.

Have a think.

If you're not sure, maybe think about is a part of the whole and think about the whole.

I wonder if you can work out, which goes where.

How'd it go? Let's have a think about that together.

So the journey from Sunny's house to Kofi's house is the, then the journey from Sunny's house to Alfie's house is- So this is a part of this larger one that must mean that Sunny's house, to Kofi's house is the whole, that must then mean like I said, if this is the whole, then this journey would be a part of the whole.

So another familiar example from the previous lesson, we have a group of sheep.

Am I right if the black sheep are the whole then the white sheep are a part of the whole? Have a think.

Do you think it's correct? Do you think it is incorrect? I think this sentence is incorrect.

If the black sheep are the whole, I'll circle the black sheep this side and the black sheep here, then my part has to be one of those three sheep.

It cannot be the white sheep.

The white sheep would be a different whole so this sentence is incorrect.

So sticking with this image, I want to ask a question, which I ask in almost every math lesson that I teach.

What is the same? What is different? I want you to have a think about and see how many similarities you can find and how many differences you can find just in this one image.

Pause the video, have a go.

Some similarities you might have said, they are all sheep, therefore they all have four legs, they all have two ears, they all have wool.

Can probably go on for quite a while with those examples.

Differences, the size of the sheep is different.

Here, these three sheep are large, these three shape are small.

They may even be lambs.

Other differences, the obvious one, these three sheep are black, whereas these two sheep are white.

So if we have identified some differences, then we can think of parts within a whole, like in the previous lesson.

So here, if all of the sheep are the whole, then the white sheep could be a part of the whole.

So we're going to look at some different ways that we can find different parts of the same whole.

And as I show you these examples, I want you to think about what you notice about the parts compared to the whole.

So my first example in red I've shown the whole is the group of sheep and I've shown the parts, and this one in blue is one of the white sheep.

In my second example, again in red, I've shown the whole is the group of sheep and in blue this time I've chosen both of the blue sheep.

In my third example, again in red, I have shown the whole and in blue, I have shown that the black sheep are a part of the whole.

So I want you to think about what do you notice about all of those parts compared to the whole? Have a think.

Now, unfortunately, I can't take your suggestions like we would if you were in my class, but hopefully you noticed that in all of these examples, the whole is larger than the parts.

We can say that the whole is bigger than the parts.

Your turn.

Hopefully you said that sentence.

If that is true, then this is also true.

The parts are smaller than the whole.

Can you say that? The parts are smaller than the whole? I wonder if that's always true.

Here, I've again shown the whole in red and the parts in blue.

Is it still true that the whole is larger than the part? Or the parts are smaller than the whole? What do you think? Hopefully you can spot that actually they are both the same size.

Because we've circled all of the parts, We've also circled the whole.

So a way that we can say that is by this generalisation.

In this example, the whole is the sum of all of the parts.

Back to this example.

Which is the largest, a part or the whole? Talked about this already today.

We've got the whole, this time in blue, from Sonny's house to Kofi's house.

And we've got a part Sunny's house to Alfie's house.

which is larger, the part or the whole? Again, a part is smaller than the whole.

This is always the case.

Are the parts always smaller than the whole for this example of the map of Europe? Previous lesson, we said there are lots of different parts.

I can see Spain, I can see France, I can see Italy.

Are they all smaller than the whole which is Europe? The example we spoke about earlier was Europe and the United Kingdom.

We've got Europe as a whole and we've got the United Kingdom, shown in orange, as a part of the whole.

Is it true? Is the whole larger than the parts? Yup, a part is always smaller than a whole.

That's the opposite way round to how I said it, but both are true.

So what do you think, which of these statements are true? The United Kingdom can only be the whole, it cannot be a part of the whole.

The United Kingdom cannot only be the whole, but also be a part of the whole.

Let me read this one more time.

The United Kingdom can only be the whole, it cannot be a part of the whole.

Is that what we said? No.

In the lessons today and previously we said that we can define anything as a whole or anything as a part, and then we can find parts of it or find what it is a part of.

The second sentence, the United Kingdom cannot only be the whole, but also be a part of the whole.

Yep, that's what we just said.

Two more examples.

Part or whole? If Europe is the whole, the United Kingdom is a part of the whole.

This is similar to the previous lessons challenge.

In the topics on whole, I have used the United Kingdom as a part of the whole.

In the second example, I've changed the situation, I've changed my definition of the whole and now the United Kingdom is the whole and I can say that England is a part of the whole.

I wonder if you can think about a statement when France is the whole.

If we look back at our map of Europe, you can see in yellow, France is here on the map.

From what you know about France or from the information on the map, can you think of a statement where France is the whole? Pause the video, have ago.

Say it out loud or write it down? A sentence you could say, some of you might have said from the video, from the picture sorry, is if France is the whole, then Paris is a part of the whole.

Maybe you know more about France in the image.

Maybe you could have said something along the lines of if France is the whole, the Eiffel Tower is a part of the whole, because I know the Eiffel tower is in Paris, which is in France.

So my friend thinks that the journey from Sunny's house to Ellie's house could be the whole.

What do you think? A bit confusing? On my picture, it says Sunny's house and I can see it goes all the way to Kofi's house.

So could this be the whole? Let me try and convince you.

I've joined a whole map that includes those four pictures of houses.

But if I just draw a smaller amount, if I cover up Kofi's house, now I can say that in this example, Sunny's house to Ellie's house could be the whole.

Another example for you.

If the white sheep are the whole, what could a part of the whole be? In this example, I can see there's one, two, three white sheep, one, two, three, four black sheep, but there's also a fence around some of the sheep.

We have to be really clear about what the question is asking us.

If the white sheep are the whole, that means we have to focus just on the white sheep.

As I said, there are three white sheep.

What sentences could you say? If the white sheep are the whole then could be a part of the whole.

Two options that I think.

If the white sheep are the whole, then the large white sheep are part of the whole.

Or if the white sheep are the whole, the baby lamb is a part of the whole.

Could have been other examples we could have talked about, if the white sheep are the whole, then the two sheet inside the pen, the two white sheep inside the pen are a part of the whole, or we could have said if the white sheep are the whole, then the white sheep outside of the pen is a part of the whole.

Got to be really specific with the language that we use.

Found an example for you.

I want you to think about, are these statements true or false? I'll read them to you, then I'll give you some thinking time.

So the first statement, if all of the sheep are the whole, the sheep in the pen, are a part of the whole.

Second statement, bottom left.

If the white sheep are the whole, the black sheep are a part of the whole.

Third statement, if the black sheep are the whole, the little black sheep is a part of the whole.

And the final one, if all of the sheep in the pen are the whole, all of the white sheep are a part of the whole.

Pause the video, say what think.

Okay, first one top left.

If all of the shape are the whole, the sheep in the pen are a part of the whole.

That statement is correct.

It's correct because all of the sheep includes all seven of the sheep.

So the sheep in the pen, these five sheep therefore, are a part of the whole.

The second example, if all of the white sheep are the whole, the black sheep are a part of the whole.

That is incorrect.

The white sheep are the whole, one, two, three white sheep, so we can't have the black sheep 'cause that wasn't within the whole that we defined.

The third one, if the black sheep are the whole, the little black sheep is a part of the whole.

What'd you think, true or false? It is true.

Four black sheep is our whole, so the little white sheep, sorry, the little black sheep is a part of the whole.

Final one, if all of the sheep in the pen are the whole, all of the white sheep are part of the whole.

Challenging, what do you think, true or false? That is false because the sheep in the pen, that contains three black sheep and two white sheep, all of the white sheep would include this sheep as well that is not inside the pen was not included in the whole so we cannot say that that is a true statement.

So I've got some practise activities for you.

I want you to do all of these, some of these, depends how much time you've got depends on the resources you've got at home.

So option one, think of a walk that you love to do.

It could be to the shops, it could be to school, it could be a walk to your friend's house, your grandparent's house up to you.

Draw a picture of all of this journey and then think about what the parts of this journey could be.

The second option.

If you have an Atlas, or if you want to flip back to a previous part of the video and use one of the images we have of a map, or if you have access to a computer, why don't you look on Google Earth.

From the map that you find, from the pitch that you find, think about different parts that make up the whole, think about their relative size to the whole that you identified.

Option three, think about this.

If your arm is a part of the whole, what is the whole? What could the hole be? Or the different options that could be? If you've done that, think about what the other parts of the whole, therefore are tricky.

Final option, think of a whole.

Challenge someone to work out the parts of the whole.

I might say to my friend, the sofa is the whole, what could the parts of the whole be? Can you come up with your ideas? Good luck, have a go.