Lesson video

Hi everyone, Mr. East here.

I'm going to take you through today's lesson, and we're going to start off today's lesson by thinking about what Mrs. Soya said to you at the end of the previous lesson.

Your task was to find 16 objects or to imagine those 16 objects or draw them and think about how they can be grouped in different ways so that we can find fractions of those 16 objects.

Now this is a sentence that you'll say time and time again through this lesson, and you also used it in the previous lesson.

It says the whole has been divided into mh equal parts.

One of these parts is one mh of the whole, so if you didn't have a chance to do this, do this now, find 16 objects at home or draw some different representations of these 16 objects divided into different numbers of equal groups, and then think about what fraction one of these parts is off the whole.

So if you haven't done that, do that now, but if you have, let's go through that together.

So the first way that we could divide these 16 counters is like this.

Here I can see how many groups I've got.

I've got one group on top one group below, so there are two groups, two parts.

We need to check that they are equal in size, this group has got eight objects in, this part has got eight objects in, so we can say they are equal, now let's say our sentence then together.

The whole has been divided into two, that's what we just said, two equal parts.

One of these parts is one half of the whole.

We write that like this, one is our numerator, our denominator is two, it's two because like we said there are two equal parts.

You might've arranged them in this way, I can see that there are one, two, three, four equal parts.

The whole has been divided into four equal parts.

One of these parts is one fourth of the whole.

Is there another way we can say one fourth? This is how it's written.

One is our numerator because we've selected one of these parts, four is our denominator because like we said there are four equal parts.

Another way to say this fraction is one quarter.

Let's say both those sentences again with this information.

The whole has been divided into four equal parts, you saying this with me? I hope so.

One of these parts is one quarter of the whole.

Are there any more to divide these 16 counters? I think so, here is another way these 16 counters could be divided.

There are four groups on top, another four groups below, four plus four is eight, so there must be eight groups.

Just check them quickly, yep they are all equal in size.

So let's say those sentences together, the whole has been divided into eight equal parts.

One of these parts is one eighth of the whole.

I write one eighth as one as my numerator, eight as my denominator.

Any more ways? I think there's one more, here I take in my 16 counters, I can see there is one counter in each group, that must mean there's 16 groups.

Four times four is 16, so you get those 16 parts in total, let's say our centres together.

The whole has been divided into 16 equal parts.

One of these parts is one 16th of the whole, that's written as one is our numerator and 16 as our denominator.

In today's lesson, we're going to continue to think about unit fractions, and a unit fraction is when our numerator is one, because we're thinking about one group or one part, and our denominator will change based on how many parts there are.

So in this first context, I can see there are some children, maybe they are friends, maybe they're children from your class.

Now the slight difference from before is, not both of the parts are circled.

This first part is circled, but the second part isn't circled, but I can still see they're equal in size because I can see there is the same number of children in each part.

And I can still see the number of parts because of how they're laid out on my screen.

So I'm going to say these sentences for this first example, the whole has been divided into two equal parts.

One of these parts is one half of the whole.

Now just like in the example before, we can write one half as one as our numerator and two as our denominator, because one of those parts has been circled and there are two of those equal parts.

Now I'm going to change the picture.

I've changed the number of parts, haven't I? But there are still an equal number of children in each part.

So we can still say what fraction of the whole has been circled.

So do this one with me this time, you ready? The whole been divided into three equal parts.

One of these parts is one third of the whole.

Now we write one third like this, one is our numerator, and three is our denominator.

Now why is three our denominator? Is it because there are three children in this group? There's three children in this group, there's three children in that group, is that why it's one third? No, if we go back to our sentence scaffold, it's one third because the whole has been divided into three equal parts.

It's the number of parts that's important, not the number of children in each part, is just so happens that in this example, there's three children in each part, as well as there being three parts, hopefully that wasn't confusing.

Let's look at another example and make sure we're all happy with the fraction that has been selected.

I've changed my picture again, I've changed my image.

If you spotted this and another one of these parts, they're still equal, but there's an extra one.

This time there are four parts let's say the sentences together again, the whole has been divided into four equal parts.

One of these parts is one quarter of the whole.

That's how we write a quarter, same as before.

One is my numerator, this time four is my denominator because there are four equal parts.

Have you spotted the pattern? Can you guess what image is going to come next? Here you go, well done if you guessed that, this time there again has been another one of these equal parts add is to our whole.

So now the whole has been divided into five equal parts.

One of these parts is one fifth of the whole, one is still our numerator because one of these parts has been circled, five is our denominator because there are five equal parts.

Now here I put all of those images above each other, and now I want us to think about what is the same and what is different about each of these images.

So pause the video and see how many similarities and differences you can find.

Okay, let's talk about some of those similarities and differences.

I'm going to start off with the first thing that I noticed, I noticed in each row, there is one red group, and in each of those red parts, there are three children in that part.

So that is the same.

Is there anything else the same? Oh, every group there is the same number of children.

I can see lots of groups of children, that's the same all the way through so we can start to compare the fractions.

Now another thing that's the same is the numerator of each of the fractions is always one, that's because one part has been circled in each of the rows.

So what's different in these images? There's a different number of parts isn't there? In the first image has only one part and that part has been circled, so the whole of that image has been circled.

In the second row there's another part, the number of parts is increased by one, one of those is still circled so now rather than the whole, now half of the group has been circled.

The next image down, we said the new ratio is still one, that's because one part has been circled, but there is another group that's been added, so now we've gone from being two parts to three parts, and that is why our denominator has gone from being two to three.

Now that pattern continues in the fourth row and the fifth row.

Can you see each time one extra group of children, one extra part has been added to our image.

Now if you'd done the previous lessons, this image might be familiar.

This image is something we've looked at and talked about before.

And these two images on the left with the children and on the right where the squares are showing a very similar thing.

We were talking before about the fraction that is shaded each time.

We might not have used the word fraction the last time we talked of this, we might've just talked about the part in relation to the whole, but we said a generalised statement before, even though for our children, even though the number of children that is circled each time is the same, the fraction that is of the whole becomes smaller and smaller for each row, because our whole is getting larger.

Now that's quite a confusing sentence.

Here, I've tried to summarise that a bit more concisely.

I'm going to read the sentence to you.

Each time, the part selected is a smaller part of the whole, because the size of the part has stayed the same and the whole has increased in size.

Let's go back to our image.

We said this thing that stayed the same is the size of the part, there's three children in each part, just like for our squares, there's one red square and each image that is shaded.

Then the next bit says the whole has increased in size, that's also true each time for our people, an extra group has been added, and that group is the same size as the other parts, and that is the same with our squares.

A tricky concept, but hopefully we can see those two patterns.

Okay this time I've still got children as my context, but I've got two different images.

Again, same question though.

What's the same and what is different? I can see some similarities in both images, the image on the left and the image on the right, I can see like I said they're children, I can also see that there is one part that's been selected here, and there's one part selected here.

I can also see that in both of my images, there is an equal number of children in each part.

Would the fraction be the same for both images? I don't think it would.

Here's two fractions, we have one third and we have one fifth.

One of those describes one of the images and one of them describes the other, which ones you think matches with each picture? Now I can see these three children in this part, does that mean a third goes to this image? Do we talk about the number of children in each part, or do we talk about the number of equal parts? We used this sentence, don't we? Let's go back to that sentence and see if that helps us.

The whole has been divided into mh equal parts.

That's what we need to focus on.

So let's look at our first image on the left here.

How many equal parts has the whole been divided into? One part, two parts, three parts, four parts, five parts.

There are five equal parts.

One of these parts is one fifth of the whole.

So we think one fifth would go with this image, let's check is the image on the right then, is that going to be one third? Let's say our sentences again.

The whole has been divided into three equal parts.

One of these parts is one third of the whole, that is one fifth and this is one third.

Well done if you said that to yourself.

We're going to go through some more examples now.

We've looked at groups of objects, this time I have got a shape, lets see if my sentence works.

The whole has been divided into mh equal parts, are the parts equal? Yeah, equal in size, different orientations, but they're all triangles and they are all the same size.

How many parts are there? Let's count these parts carefully.

One, two, three, and four, there are four equal parts.

Lets say the sentence.

The whole has been divided into four parts.

One of these parts is one quarter of the whole.

Our numerator is one, one of those parts is red, our denominator is four because there are four equal parts.

Back with the children.

I haven't seen these groups before though.

How many equal parts are there? There's lots of children in each group, but do I need to count the number of children in each group? I need to see that they're the same, and I can see luckily from how they're laid out, that they are all the parts that are equal in size.

Let's think though about the fraction.

Is any fraction selected at the moment? No, ah, there you go.

There's one part now has been selected.

Now let's see if we can say these sentences together, the whole has been divided into four equal parts.

One of these parts is one quarter of the whole.

That's how we write a quarter, same as before.

One is my numerator, four as my denominator, I just remembered this image, saw this in a previous lesson.

Here, I've got to use my visualisation, I've got to think about inside of this shape.

There's some dotted lines to help me and some little lines on the side to help me think about how many of the green parts would there be in the whole.

I can do some picture, I can think about there's a green box here, another green box to go in front of it, a green box next to it, and another green box.

Do you agree with me? There would be four equal parts in the whole.

Let's say these sentences together, the whole has been divided into four equal parts.

One of these parts is one quarter of the whole, same as before, that's how we write one quarter.

You've spotted the pattern? Keep thinking.

Final image, we've got a number line.

How many parts has my number line been spitting to? Now remember we're not counting a lines on the number line, 'cause there's actually five lines, we're counting the parts.

Here is the first part, that one part, here is the second part, that's two parts, here is the third part, that's three parts.

Here is the fourth heart.

Ah again there's four equal parts.

Have any of the parts been highlighted? Not yet.

Now I can see one of those four parts has been highlighted.

So I know that is one quarter.

Let's just say our sentences one more time so that makes sense.

The whole has been divided into four equal parts.

One of these parts is one quarter of the whole.

Well done for saying that sentence with me.

Now the same as before I put all of those images together, and again my favourite question, what's the same and what's different? Pause the video again, think about similarities and differences.

This time we're going to start with the differences.

Each one is a different context, isn't it? The first image in the top left, that is children as different objects, in the bottom left we've got volume, that's how much space is taken up inside of a shape, the top right we've got a shape, this time a 2D shape.

We've got some triangles we're thinking about area, how much space inside a shape has been selected.

And then we've got a number line, the idea of a linear journey.

So four different contexts.

Can you remember what fraction we said for each of these contexts? Is it the same or is it different? It was the same, wasn't it? For each of them, we said that one quarter was so that's it.

Written in words is one quarter.

So what's the same then for each of these images? For all of them, the one, the numerator, that means that one equal part has been selected each time.

Let's see if that's right, for our people, yeah I can see that one group circled.

one part circled.

In our volume, I can see that I can see one of the four equal parts and I have to imagine the other three of those four equal parts, in our shape again I can see that there is one red triangle, the other three triangles that make up our four equal parts they're not shaded in and from my number line, I've got one part that's in red, and that's one out of the one, two, three, four equal parts.

So what is the same is an each image, one quarter has been shown.

Okay, so some more practise for us.

In this section, I've got four different images and the different images are again of different contexts.

I want you to think does each image show the given fraction? Why is this or why is this not the case? I want us to keep using the sentence that you must know quite well by now, the whole has been divided into mh equal parts.

One of these parts is one of the whole.

So pause the video, have a think about each one individually.

Okay, we're going to go through them.

So let's start with the triangle.

It says is one half shaded? Let's use the census is to help us.

The whole has been divided into two equal parts? Are there two parts? Yeah there's two parts, one's red and one's white.

Are they equal though? They're not, are they? The red part is smaller in size than the white part.

So we cannot say that one half is shaded, so well done if you said that, even though one of the parts is red, they're not equal parts so we cannot use the fraction one half.

What about the next image? We've got some cubes, haven't we? Let's look at the cubes, it looks, one of them is yellow, one, two, three, four, five of them are blue so does that mean one fifth? Is that what we write? Let's go back to our centres to help us.

The whole has been divided into, how many equal parts are there? Let's count those blocks.

There's one, two, three, four, five, six, there's six blocks isn't there? So there's not five equal parts, there's six equal parts.

One of these parts is one sixth of the whole.

So that is not correct.

Let's think about our next image, is one quarter shaded? Show me with your thumbs, thumbs up or thumbs down.

Let's go through it together.

One quarter, the whole has been divided into, are they equal parts? No, the red part is larger than two of the white parts so we cannot say one quarter, because there's not one of four equal parts that's been shaded in, so that's not right.

Now I'm going to change my fraction, are you ready? Is one third shaded? What do you think? Thumbs up again, thumbs down.

Think carefully.

Okay let's go through it.

I am going to try and convince some of you that might have said the incorrect answer.

I'm going to change our shape ever so slightly it's going to stay exactly the same size, but one of my lines is going to disappear, look carefully.

Did you see it? There used to be a line that went from the centre of the circle, out here, but I've taken it away.

I haven't changed the amounts of this shape that has been shaded red, but I've taken away a line.

Does it look now like the parts are of equal size? It does, doesn't it? There's two white parts and there's one red part, and they are all equal size, so now we can go to our sentence.

Let's say this together, the whole has been divided into three equal parts.

One of these parts is one third of the whole.

So now that sentence is correct, or that question I should say, there is one third of that shape shaded.

Let's go to the final example.

It says does each plate have one third of the biscuits? That important question, we need to think about two things.

Is there the right number of parts and are all of those parts equal in size? Are they equal in size? No, they're not, are they? There's two biscuits in the first plate, there's three on the next plate and there's one on the final plate so they are not equal in size.

Could I change my image though so that they did become equal in size? Which plate would I have to take a biscuit from? I'd have to take it from the middle plate, wouldn't I? Where would I put that biscuit? If I moved that biscuit, let's say that I've moved the biscuit.

Now can we describe them, now can we see if the statement's true? It wasn't true before because the parts weren't equal, but now I've changed them.

Now do we think, does each plate have one third of the biscuits? Let's go back to our sentence.

The whole has been divided into three equal parts.

One of these parts is one third of the biscuits.

That then would be true after we've moved that biscuit.

Okay, so we've gone through lots of examples together.

And now I wanted to talk about what I want you to practise at home.

So similar to before, I want you to go through each image and think carefully, does each shape show that given fraction, and why or why not for each case? Still want you to use that sentence scaffold.

Maybe it'd be good to draw each shape if you can, if you've got a bit of paper, and then underneath you can write the right sentence, or you could tick or cross whatever you think, think about some way to record your results.

Each one think carefully, are the parts equal? Is there the correct number of parts? So then is the fraction able to be written? And is it correct? Go through each one, try not to be tricked.

Same again, similar to other example but slightly different.

This time, does each plate have one quarter of the biscuits? Same sentence scaffold, slightly different image, think carefully why is that the case? Why is that not the case? Can you write or say a reason for your choice? And then the final image, you will be talking with Ms Kingham in the next lesson about this.

So think carefully about this, is a quarter of the shape shaded? You're going to have to be prepared to reason to explain why you think a quarter is shaded, or why you think a quarter shape is not shaded.

Think carefully.

I hope you enjoyed that, practise as activities.

See you again.