Lesson video

Hello there, my name is Mr. Goldie and welcome to today's maths lesson.

And here is the learning outcome for today's lesson.

I can identify the number of equal or unequal parts in a whole in different contexts.

And here are the keywords.

I'm going to say each keyword, can you repeat it back? So the first key word is equal.

The second key word is unequal.

Let's take a look at what those words mean.

Equal means exactly the same amount or value.

Unequal means not exactly the same amount or value.

And here's our lesson outline.

So the first part of the lesson is equal and unequal parts.

And the second part of the lesson is called find the fraction.

Let's get started.

And in this lesson you'll meet Sofia and Jacob.

Now a lot of people find fractions a bit tricky, but Sofia and Jacob are here to help you.

They're here to help you understand fractions, understand how they work.

Sofia and Jacob are sharing a pizza with friends.

"I'm going to cut the pizza into five parts", says Sofia.

So Sofia has cut the pizza into five parts.

Sofia says, "Each part is one-fifth of the pizza." There are five parts, so each part must be one-fifth.

Jacob says, "Sofia, some of the slices are bigger than others.

They're not fifths because they are not equal parts." Who do you think is right? Sofia says, each part is one-fifth of the pizza, but Jacob says they're not fifths because they're not equal parts.

Who do you think is right? Jacob is right.

Each fifth must be equal in size.

Sofia has cut the pizza into five parts, but each part is not one-fifth because the parts are not equal in size.

A fraction is made from equal parts of a whole and that's really important.

To be a fraction, it has to be equal.

Look at these shapes.

Which have been divided into equal parts? So which parts are equal in size? Look, there are three shapes.

Which ones have been divided into equal parts? Jacob says, "Which have been divided into quarters?" Now if it's been divided into four equal parts, each part would represent one quarter of the shape.

For the first shape, the parts are equal, so each part represents one-quarter of the shape.

The second shape here, the parts are unequal, so the shape has been divided into four parts, but because they are unequal, each part is not one quarter of the whole.

What about that last shape, what do you think? The parts are unequal.

Two of the parts there are much bigger than the other two.

Sofia shades three parts of some shapes.

There are three shapes and Sofia has shaded three parts of each of them.

Which show three-quarters? What do you think? Look to see if the parts are equal.

Let's take a look at that first shape.

The parts are unequal.

One of the parts is bigger than the other three.

So each part does not represent one-quarter of the shape.

What about that second shape? The parts are equal.

Each part is the same size.

So this shows three-quarters.

Each part represents one-quarter of the shape and three of them are shaded.

So three quarters of the shape are shaded.

What about that last shape? The parts are unequal and again two of the parts are bigger than the other two.

And because they are not equal, each part does not represent one-quarter of the whole.

So three parts are shaded but three-quarters are not shaded.

Sofia shades part of some shapes.

Sofia says, "Which show three-fifths?" What do you think? Oh, and Jacob's got a bit of useful advice for you.

Jacob says, "Look to see if the parts are equal." So if the shape is representing three-fifths, the parts have got to be equal.

Pause the video and see if you can work out which of those shapes represents three-fifths.

How did you get on? Do you think you found the right answers? Let's take a look.

So that first shape, the parts are equal, there are five equal parts, three of them are shaded.

So this shows three-fifths.

Three-fifths of that first shape is shaded in.

What about that shape in the middle? Does that represent three-fifths? The parts are unequal.

There's a circle in the middle which is smaller than the others.

So although three parts have been shaded, three-fifths of the shape has not been shaded.

And that last shape, what do you think? Is that three-fifths? Yes it is, the parts are equal.

So this also represents three-fifths, three equal parts have been shaded.

Very well done if you got those correct.

Parts can be different shapes but still be equal in size.

And this is where it starts getting a little bit tricky because it might not look like the parts are equal sizes, but they could be.

So here's a shape here.

Has that been divided into equal parts? They're not the same shape are they? But are they equal? What fraction of the shape it's shaded? Sofia says, "These two parts represent one-half of the shape.

They're equal in size, so each must be one-quarter." So those two parts of the whole shape represent one-half of the shape.

And because they're the same size as each other, because that half has been divided into two equal parts, each part must represent one-quarter of the shape.

So each of those is one quarter.

And Sofia says these two parts also represent one-half of the shape.

They are also equal in size, so each must be one-quarter.

Each of the parts are equal even though they are different shapes.

Sofia thinks that three-quarters of the shape is shaded.

I wonder, is she right? Jacob says, "I'm still not completely sure all of the parts are the same size." So Jacob wants to prove that each part is the same size.

Jacob says, "I'm not sure whether these parts are equal in size." So this part here, is it equal to this part here? Jacob says, "I'm going to cut out these two pieces and check whether they are equal." So Jacob cuts those two pieces out so he is left with them, and Sofia said they were both one-quarter of the shape and they are both the same size.

Is she right? Jacob's going to try to prove that.

Jacob cuts one of the parts up so he can compare the two shapes.

So he takes the shape here and he cuts it into half and he moves that part of the shape underneath.

Ah, are they the same? The parts are equal in size, Sofia was correct.

What fraction of the shape is shaded? Have a good look at that shape there.

What fraction do you think is shaded? Are the parts equal in size? Is there a way of finding out whether they're equal in size or not? Pause the video and see if you can work out what fraction of that shape is shaded or whether you think the parts are actually unequal.

And welcome back.

How did you get on? What fraction of the shape do you think is shaded or are parts unequal? Let's see what Sofia and Jacob made the shape.

So Sofia starts off by saying these two parts represent one-third of the whole shape.

So each smaller part is equal in size, so it must be one-sixth.

So Sofia's doing a lot of thinking about these shapes.

So she's saying that these two parts here represent one-third of the whole shape and they're both equal in size.

So each part must represent one-sixth of the whole shape.

These two parts are also equal in size and they also represent one-third of the whole shape.

So each of them must be one-sixth.

These two parts also represent one-third of the whole shape.

Each part is equal in size, so it must represent one-sixth of the whole shape.

"Each of the parts is equal even though they are different shapes," says Jacob.

"I can show this by cutting out one of the parts." So Jacob cuts out this part here and he's going to cut it up and rearrange it to show it's the same size as the other shapes.

So he's going to cut it there and he's going to move that part down here.

So you can see it is the same size as one of those rectangular parts of the shape.

So in fact they are all the same size.

So very well done if you said five-sixth of the shape is shaded because that is the correct answer, well done.

Let's move on to task A.

So in task A you're going to sort the shapes into the table.

You're going to think about whether the shapes are made out of equal parts or whether they made out of unequal parts.

So which are divided into equal parts.

And can you name the fractions too? So can you actually describe what fractions are represented when the parts are equal? So here are the shapes you're going to be sorting out.

So you can see straight away that some of them are unequal, some of the parts they may be equal in size.

So pause the video and have a go at task A.

And welcome back.

Did you manage to sort all the shapes out? Let's take a look to see if you put them in the right places.

So here are the answers.

So there were six shapes that were divided into equal parts and six shapes that were divided into unequal parts.

And sometimes those equal parts may have been different shapes but they were still the same size.

So for example, this one that represents three-quarters.

We've got there a triangular shape being the same size as one of the rectangular shapes.

The two-thirds shape, we've got one of the thirds has been rotated around and turned around.

So it's a different in a different orientation to the other two.

And then we've got some which are very, very clearly of an equal size.

So very well done if you managed to sort those into the correct places on the sorting diagram.

Well done.

And let's move on to part two of the lesson, which is called find the fraction.

Sofia represents a fraction in different ways.

"How have I represented five-eighths," says Sofia.

So what is the eight in her fraction? What is the five, what do you think? Five-eighths of the pandas are not wearing hats.

There are eight pandas altogether and five of them are not wearing hats.

Jacob is not convinced that Sofia is correct.

He says, "Not all the pandas are the same size.

How can you work out what fractions are wearing hats?" Now, in the first part of the lesson we looked at equal and unequal parts and quite clearly you can see that some pandas are bigger than others.

Sofia says, "The size of the panda doesn't matter.

Each panda represents one part of the whole.

It's the number of pandas that matters here, not their size." "I think I understand," says Jacob, "You're not looking at the parts of a shape, you are finding the fraction of a number." "How have I represented five-eights?" says Sofia.

These are all parts of one shape.

They are not separate objects.

The parts of the shape are unequal in size.

This does not represent five-eighths.

How have I represented five-eighths? Pause the video and see if you can work out how that shape there shows five-eighths.

And welcome back.

Did you manage to find five-eighths? Let's take a look, see if you are right.

So five-eighths of the shape is not shaded.

There are eight parts altogether.

Three of them are shaded, five of them are not shaded.

Very well done if you found the right answer.

"How have I represented five-eighths?" says Sofia.

You may notice she seems quite like five-eighths, doesn't she? "I'm not sure," says Jacob.

"The shapes are all different sizes." It doesn't matter.

Here, each shape represents an equal part of the whole.

It doesn't matter that are different shapes and different sizes.

There are eight shapes, so each represents one-eighth of the whole.

"But only four-eighths of the shapes are shaded blue," says Jacob.

So four-eighths of the shapes are shaded blue, four-eighths are shapes are not shaded blue.

Where's five-eights? "Can you see five-eights represented in a different way?" says Sofia.

I wonder look really carefully.

Can you see five-eights? Five-eights of the shapes are triangles.

So sometimes the fraction's not obvious, you have to dig a little bit deeper and see if you can find it.

But you can see there there's still eight shapes, the whole is still eight and five of those shapes are triangles.

Five-eighths of the shapes are triangles.

Jacob is watching some frogs.

"Four-eighths of the frogs are on the lily pad," says Jacob.

Is Jacob correct? What do you think? Pause the video and see if you can work out whether Jacob is right or whether he is wrong.

And welcome back.

Did you think that Jacob was correct? Did you think he was incorrect? Let's take a look and see what Sofia managed to work out.

So Sofia says, "The size of the frogs doesn't matter." So some of the frogs are bigger than others, but they each represent one part of the whole.

"But Jacob has miscounted them." He hasn't counted up the frogs correctly.

There are actually seven frogs.

So four-sevenths of the frogs are on the lily pad, not four-eights like Jacob said.

And let's move on to task B.

For the first part of task B, you're going to be looking to see which pictures represent four-sevenths.

Try to explain your answers as well.

So if it doesn't show four-sevenths, why doesn't it? For A, there are seven hearts, the whole there is seven, but where is four represented? Where is four-sevenths represented? So have a go trying to find four-sevenths in each of those representations.

And if you can't find four-sevenths, explain why you can't find it.

And here's part two of task B.

So what fraction is represented in each picture? Now there's more than one way of explaining this.

You might find more than one fraction in each picture.

A for example, how many parts are there all together, how many parts are shaded, how many parts are not shaded? And then for B we've got a number of pandas.

How many of them are wearing hats? How many of them are not wearing hats? And remember for A, it matters that they are equal size because it's a fraction of a whole shape.

For B, it doesn't matter because we are looking at a fraction of a number.

So it doesn't matter if they're unequal in size.

And here's part three of task B.

This is one that's going to really get your brains working.

What fraction could be represented here? What different ways can you find and describe a fraction? So the shapes are different sizes and different shapes, but it doesn't matter because we are looking at a fraction of a number, not a fraction of an area or a shape.

How many different shapes are there altogether? How many shapes are triangles? How many shapes are shaded? How many shapes are quadrilaterals? How many shapes have an even number of sides? How many shapes have an odd number of sides? There's lots of different ways you can find fractions using those shapes.

Don't forget to think about the whole and don't forget to think about the parts.

Pause the video and have a go at task B.

And welcome back.

How did you get on? Did you get all the way to part three of task B? Excellent work if you did.

Let's take a look, see if you've got the right answers.

So here are the answers for part one of task B.

So for A, four-sevenths of the shapes are shaded.

That was quite nice, straightforward one wasn't it? For B, the parts of the shape are unequal in size, so it doesn't represent four-sevenths.

Four parts have been shaded in, but the parts aren't all equal in size.

And because it's an a fraction of a shape, it matters that they are unequal.

And then for C, only two of the shapes are shaded.

But we could say four-sevenths of the shapes are quadrilaterals.

That was quite a tricky one.

So you've got there, four of the shapes have four sides, four of them are quadrilaterals, four-sevenths are quadrilaterals, three-sevenths are not quadrilaterals.

So very well done if you managed to get the answer to C, because that was quite a tricky one.

Here are some possible answers for part two of task B.

Now you may have come up with different answers for these, but you may have said for A that seven-ninths of the shape is shaded.

And you could have said that two-ninths of the shape is not shaded.

For B, eight-tenths of the pandas are wearing hats.

Or you may have said two-tenths of the pandas are not wearing hats.

And then for C, the parts of this shape are unequal in size.

And because it's all one shape, we can't say a fraction has been shaded because the parts are different sizes.

So well done if you spotted that one.

And let's move on to part three.

This is where you had to really think and really use your observational skills and your knowledge of shapes to try and work out different possible answers.

So you may have said eight-ninths of the shapes are shaded.

That was quite an easy one to spot, wasn't it? You may have said five-ninths of the shapes are quadrilaterals.

So five of them have four sides.

So five-ninths of the shapes are quadrilaterals.

Four-ninths of the shapes have an odd number of sides.

So we've got there a triangle which has three sides and three pentagons, which have five sides each.

So altogether four of the shapes have an odd number of sides.

And finally one-ninth of the shapes is a triangle.

You may have come up with that one as well or you may have said three-ninths of the shapes are pentagons.

Lots and lots of different answers for that one.

So very well done if you got onto part three and you managed to find some of the different answers there as well.

Excellent work today.

And hopefully Sofia and Jacob have made you feel more confident about fractions and hopefully you are feeling more confident as well about when the parts need to be equal and when it doesn't matter if the parts aren't equal because you are looking at the fraction of a number.

Very well done in today's lesson.

Excellent work.

And finally, let's move on to our lesson summary.

So a non-unit fraction has a numerator greater than one.

A fraction is made from equal parts of the whole.

Parts can be different shapes and still be the same size.

When counting different objects that make a whole, the objects can be unequal in size.