Lesson video

Hi there, my name is Mr. Tilstone, I'm a teacher.

I teach all of the different subjects, but the one that I enjoy the most is definitely maths.

I just love it.

I like teaching all of the different parts of maths, but I think maybe my favourite is fractions.

So you can imagine how excited I am to be here with you today to teach you this lesson, which is all about fractions.

Hope you are ready.

If you are, will you help me to count down from five.

five, four, three, two, one, let's begin! The outcome or target, if you like, of today's lesson is this.

I can find one-third or one-quarter of a number and you might have had some very recent experience finding one-half of a number.

I wonder if we can use some of the same strategies.

And we've got some keywords.

So my turn, one-third, your turn.

And you can see there we've got one-third written as words and one-third written in numerals.

And finally, my turn, one-quarter, your turn.

And once again you can see one-quarter as words and as numerals.

Today's lesson is split into two parts.

The first will be find a fraction of a number by sharing objects.

And the second, find a fraction of a number in other ways that are perhaps a little bit more efficient.

So let's start by finding a fraction of a number by sharing objects.

And in this lesson, you're going to meet Jacob and Alex.

Have you met them before? They're here today to give us a helping hand with the maths.

And very good they are too.

Jacob and Alex are helping to get some food ready for a picnic with their friend.

They carefully cut some cakes into slices, and don't those cakes look delicious! What do you notice about those cakes? What can you see? Alex says, "We've both cut our cakes into 3 parts.

Each picnic guest will get 1 slice." Hmm, is it fair though? Jacob says, "My cake has been split into 3 equal parts," but Alex say, "My cake has been split into 3 unequal parts." That means each part of my cake says Jacob is one-third because the whole has been divided into 3 equal parts.

They're thirds, they're one-thirds.

But Alex says, "My parts are not called thirds because they are not equal." Jacob says, "I think we should make sure our food is divided into thirds.

That way we will each get the same amount." That seems fair, doesn't it? Now Jacob and Alex have finished cutting the cake, they need to divide these strawberries into thirds.

They look juicy and lovely, don't they? Let's have a look at this.

Jacob says, "I've tried this before.

It's difficult to cut strawberries into thirds!" But Alex says, "Do you think we need to cut them?" Well, no, we don't do we.

To find one-third, you need to divide the whole into 3 equal parts.

Can we do that with those 3 strawberries? Yes, "The whole is 3 because there are 3 strawberries in the bag." "We could share them into 3 equal parts." Quite easily in fact, one, one and one.

To find one-third you need to divide the whole into 3 equal parts.

Jacob says "There is 1 strawberry in each part." Alex says, "That means that one-third of 3 is equal to 1." And we could write that as an equation just like this.

We don't need to write a whole sentence, one-third using the numerals, so one-third of 3 equals, using the equals sign, 1.

One-third of 3 equals 1.

Or to swap that around, 1 equals one-third of 3.

Jacob and Alex divide these apples this time into thirds.

So how many apples have we got? 6.

"The whole is 6 because there are 6 apples in the bag.

I know we need to divide the whole into 3 equal parts," 'cause that's what thirds are, 3 equal parts.

So there we go, we can use this box, it's got 3 equal parts.

"Let's put one apple in each part first." One for you, one for you, one for you.

We've got some left.

And as Jacob says, "There are still some apples left in the bag." So what shall we do? Let's keep sharing.

Let's put another apple in each part.

One for you, one for you, and one for you.

Are the parts equal? Yes.

To find one-third, you need to divide the whole into 3 equal parts.

"There are 2 apples in each part." "That means that one-third of 6 is equal to 2." Do you think you could write that as an equation? How could we write that? Just like this, one-third of 6 equals 2, or 2 equals one-third of 6.

Let's have a little check.

Let's see what you've understood so far.

Who has found one-third of these sweets correctly? So look how many sweets we've got there.

Who's found one-third? "One-third of 9 is equal 1 because there is one sweet in each part," says Alex.

Okay, let's think about that.

And Jacob says, "One-third of 9 is equal to 3 because there are 3 sweets in each part." Hmm, pause the video and have a think and see who you agree with.

Let's see, it was Jacob.

Jacob was right.

One-third of 9 is equal to 3 because there are 3 sweets in each part.

And we could write that as an equation.

One-third of 9 equals 3.

And Alex wasn't correct.

Alex has not divided the whole 9 sweets into 3 equal parts.

He's only divided 3 of the sweets.

There would still be some left in his bag.

Jacob and Alex want to invite another friend to their picnic.

So that means there will be 4 children at the picnic.

"So far we've divided all the food into thirds." Alex says, "Let's make some more food, but we will divide it into 4 equal parts this time." There's a special name for that, isn't there, 4 equal parts? Can you remember? Jacob carefully cuts the watermelon into 4 equal parts or quarters just like that.

"I tried hard to make sure all 4 parts are equal." And I think he's done a pretty good job of that, don't you? They look equal to me.

"Well done Jacob," says, Alex, "you've divided the watermelon into quarters." I suppose we could call it a quarter melon.

"We will each be able to eat one-quarter of the watermelon," says Jacob.

Jacob and Alex can divide these grapes into quarters.

The whole is 12 because there are 12 grapes in the bag.

"I know we need to divide the whole into 4 equal parts." So that's what we're going to do.

So we've got a box or a bar with 4 equal parts.

"Let's put one grape in each part first." So that same sharing strategy that we used earlier on.

One for you, one for you, one for you, one for you.

Have we got some left? Yes we have, let's keep going.

"There are still some grapes left in the bag." "Let's put another grape in each part." One for you, one for you, one for you, one for you.

Are there still grapes left? Yes there are.

Let's keep sharing.

Let's put another grape in each part.

One for you, one for you, one for you, one for you.

Are there still grapes in the bag? No there aren't.

We've shared them all out.

Are they equal parts? Yes they are.

"There are 3 grapes in each part." "That means that one-quarter of 12 is equal to 3." Could you think of an equation that we could use to write that? How about this? One-quarter, that's how we write one-quarter, of 12 equals 3, or, 3 equals one-quarter of 12.

And that's much quicker than writing that whole sentence, isn't it? Jacob and Alex can divide these sweets into quarters.

How many sweets have we got this time? What's our whole? "The whole is 8 because there are 8 sweets in the bag." "I know we need to divide the whole into 4 equal parts." That's what quarters means.

So there we go, we've got our quarters box ready to share the sweets into.

"Let's put one sweet in each part first," just like before.

One for you, one for you, one for you, one for you.

Are there still sweets left in the bag? Yes there are.

Let's keep going.

One for you, one for you, one for you and one for you.

Are there still sweets in the bag? No there are not.

Are they equal parts? Yes they are.

"There are 2 sweets in each part." That means that one-quarter of 8 is equal to 2.

How could we write that as an equation? What about this, one-quarter of 8 equals 2? Is there another way? Yes.

2 equals one-quarter of 8, and they're both correct.

Jacob says, "There were some lollies in the bag.

I've divided them into quarters." Okay, so we don't know the whole this time, but these are what the quarters look like.

Alex says, "I can see that there are 5 lollies in each part," and we could count those, but I didn't need to count.

I don't know about you, but I could see 5 in each.

It sort of reminded me a little bit of a dice.

So it looked like a 5 on a dice.

That means the whole must be 20, because 5 and 5 and 5 and 5 make 20, 5, 10, 15, 20.

"You are right, there were 20 lollies in the bag to start with, well done Alex!" When you know the size of one part, you can work out the size of the whole.

So if we knew that one-quarter was 5, that meant 4 quarters was 20, the whole was 20, one-quarter of 20 equals 5 or 5 equals one-quarter of 20.

Let's do a check.

Jacob wants to divide these chocolates into quarters, but he has made a mistake.

How could you help him correct it? So he is got 16 chocolates in the bag.

Would you say they've been divided into equal parts? Is it fair sharing? Not really.

Okay, help him out, pause the video please.

What could we advise Jacob? What could he do here? When you find one-quarter of a number, you need to divide the whole into 4 equal parts.

And at the minute, Jacob's parts are not equal.

But if we do a little moving around, we could make them equal.

Are they equal now? Yes they are.

They've each got 4 chocolates in each part.

So we can now see one-quarter of 16 equals 4 or 4 equals one-quarter of 16.

Hey, you are doing really well and I think you are ready for some practise.

Let's see if you can show off your skills.

Number 1, use this empty bar model which is split into 3 equal parts.

So it's perfect for thirds and some small objects such as cubes or counters or something similar to that to complete each equation.

So we've got a, one-third of 15 equals something.

So you're going to need 15 of your objects.

One-third of 27 equals something.

One-third of 24 equals something.

One-third of something equals 4.

That's slightly different, isn't it? One-third of something equals 10 and then something equals one-third of 9.

So use that empty bar to help.

And number 2, use this empty bar, which you might notice is split into 4 equal parts.

And again, some small objects like cubes or counters to complete each equation.

So a, one-quarter of 24 equals something, b, one-quarter of 28 equals something, c, one-quarter of 32 equals something, d, one-quarter of something equals 3, that's different, e, one-quarter of something equals 5, and finally, something equals one-quarter of 8.

Righteo, pause the video and away you go.

Welcome back, how did you get on with your objects and your thirds and quarters? Let's have a look.

1a, one-third of 15, well there's 15, divided into 3 equal parts and each one is worth 5.

So b, one-third of 27, that's 27 divided into 3 equal parts and one of them has 9 in.

So one-third of 27 equals 9.

C, one-third of 24, this time this is 24 counters divided into 3 equal parts and each one is 8.

And for d, one-third of something equals 4.

So if we put 4 into each one we can see that in total that's 12.

That's the whole, one-third of 12 equals 4.

And for e, one-third of something equals 10.

So this time we need to put 10 in each one.

And altogether that makes 30, one-third of 30 equals 10.

And for f, something equals one-third of 9.

That's only the same as saying one-third of 9 equals something, and there's 9 counters, and one-third of them equals 3.

Number two, this time it's quarters.

One-quarter of 24.

This is 24 counters or whatever you might have used.

And one group of those is 6.

So one-quarter of 24 equals 6.

One-quarter of 28, here's 28 counters, and one group of those is 7.

One-quarter of 32, here's 32 equal counters, one of those groups is worth 8, and a bit different for d, one-quarter of something equals 3, so if we put 3 into each group, that gives us 12 for our whole, and for e, one-quarter of something equals 5, so 5 in each group this time, and that equals 20, one-quarter of 20 equals 5.

And for f, one-quarter of 8 equals something and that something is 2.

So two equals one-quarter of 8.

You're doing really, really well and I think you are ready for the next cycle.

Let's have a look.

Now we're going to be finding a fraction of a number in other ways, so not using objects this time.

Hmm, what else could we do? Alex thinks he's found another way to find one-third or one-quarter of a number.

Hmm.

Jacob says, "Let's both find one-quarter of 20 and we can compare our strategies." "Good idea, Jacob," says Alex, "let's start!" So Jacob and Alex each use a different strategy to find one-quarter of 20, see which one you like best.

So Jacob says, "I will start by counting out 20 counters." It's taking some time, isn't it? And Alex says, "I think my strategy will be more efficient as I do not start by counting." Hmm, I wonder what he's going to do.

Jacob says, "Now I need to draw a bar model with 4 equal parts." Yeah, that would be good for quarters.

And just like that.

Alex says, "I agree.

To find one-quarter we need to divide the whole into 4 equal parts." So he's also using a bar model.

So we agree that bar models are good strategy to split into 4 equal parts.

What do you think Jacob is going to do next? What we did before, basically, he says "I will place one counter in each part." Now Alex is going to do something a bit different.

He says, "I will draw one mark in each part." Ah, "I will count each mark as I draw." Okay, so 1, 2, 3, 4.

That's similar, isn't it? Jacob says, "I will continue sharing the counters until there are none left," just like you did before, just like this.

He keeps sharing those counters until there are none left.

He's arranged them nicely, a bit like a dice face, isn't it? That's going to make it easy to count, in fact, to subitise.

And Alex says, "I will carry on drawing one mark in each part until I reach 20." Hmm, so he's on 4 already.

He's got 1, 2, 3, 4.

Let's watch him, count long if you like! 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

That was a different strategy.

I really liked that because he didn't have to count the counters to start with, it was quicker.

So Jacob says, "I can see 5 counters in each part.

That means that one-quarter of 20 equals 5," so I got equation.

And Alex says, "I can see 5 marks in each part.

That means that one-quarter of 20 equals 5." So they've both got to the same answer but in different ways.

Alex says, "If I count all the marks, it is equal to the whole." Jacob says, "I like your strategy because you do not need to use any equipment." And Alex says "Sometimes when I use counters, I lose one and then I have to start again." Well that's not going to happen with his new strategy, is it, that's very good.

Jacob says, "Me too, Alex! I think you might have solved your problem with that strategy." Now Jacob wants to try Alex's strategy.

So do I, I like it.

To find one-third of 18.

Okay, let's think about how he could do that.

What would you do first? "Make sure your bar model has 3 equal parts because you are finding one-third." " Great tip, thank you Alex." Here we go, so we've sketched a bar model with 3 equal parts.

"Now I will draw one mark in each part until I reach 18." Let's go.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

Hmm, I quite like that.

Can you suggest anything that he could do to improve it though? He says, "I'm not sure how many marks I've drawn in each part." A bit hard to count, isn't it? Alex says, "Try to draw them in the same place in each box to create a pattern." Oh, that's a good tip.

"Thank you Alex.

I will try one more time." 1, 2, 3.

Do you notice he's putting them in the same part of each box each time? 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

Oh that's much better, isn't it, how he set it out now.

"Well done Jacob, your marks are much easier to count now." In fact, you might not even need to count them at all, it looks like a 6 on a dice.

"You are right, I can see that one-third of 18 is equal to 6." That's a great strategy, isn't it? I really like that.

Here are the equations.

One-third of 18 equals 6 or 6 equals one-third of 18.

Let's have a check.

Alex has drawn bar models and marks to work out 3 different equations.

Can you match the bar models and the equations together? So one of them is 2 equals one-third of 6, but which one? One is one-quarter of 8 equals 2, but which one? One of them is 3 equals one-quarter of 12, but which one, and one of them is one-third of 12 equals 4, but which one? Pause the video, have a good think and see if you can match them up.

Did you manage to match them up? Let's have a look.

So 2 equals one-third of 6 is this one here.

You can see 6 marks altogether.

And in one of those boxes you've got 2, two marks.

One-quarter of 8 equals 2, so 8 is our whole.

You've got 4 boxes and in each box you've got 2.

3 equals one-quarter of 12 is this one.

So you've got 4 boxes, again, we know our whole is 12 and in each box you've got 3, so 3 equals one-quarter of 12.

And finally, one-third of 12 equals 4.

We've got 3 boxes, our whole is 12, and in each of those boxes we've got 4 marks.

Time for some final practise.

Let's see if you can use those strategies.

First, draw your own bar model for each question.

So think about how many parts your bar model's got.

Then draw marks in the boxes to help you answer each question.

So a is one-quarter.

How many boxes would that be in your bar model? One-quarter of 12 equals something.

B equals one-third of 12, so one-third.

How many boxes would you draw in your bar model? One-third of 12 equals something.

C, one-quarter of 28 equals something.

D, one-third of 21 equals something.

E, one-quarter of something equals 2.

That's slightly different, isn't it? We don't know the whole this time, but how many boxes could you draw? Hmm, there's a clue in the fraction.

And F, one-third of something equals 2.

Number 2, who do you think has more money? Use bar models with marks to explain your thinking.

So Jacob says, "I have one-quarter of £20." and Alex says, "I have one-third of £15." Who's got more money? Think about how you would draw your bar models to prove it.

Okay, let's have a go at that.

If you can work with a partner, I always recommend that because then you can share ideas with each other.

Pause the video and I'll see you soon for some feedback.

How did you get on with those questions? Are you starting to feel really confident about this? Did you like using the marks instead of the counters? It's quick, isn't it, very efficient? Well, number 1, one-quarter of 12, we can draw 4 boxes.

One-third of 12, we can draw 3 boxes.

One-quarter of 28, 4, one-third, that's 3.

One-quarter, that's 4, and one-third, that's 3.

And then this is what one-quarter of 12 looks like, that's 3.

One-third of 12, when we draw those 12 marks, that gives us 4 in each part.

So one-third of 12 equals 4, one-quarter of 28, when we draw those 28 marks, each box has 7 marks in, so one-quarter of 28 equals 7.

And for d, one-third of 21, we've drawn 21 marks, in each box you've got 7, one-third of 21 equals 7.

And for e, one-quarter of something equals 2, a bit different this time, we are going to draw two marks in each box.

And then in total that gives us 8.

So one-quarter of 8 equals 2.

And then finally, one-third of something equals 2.

Again, we're going to write 2 in each box, 2 marks.

So one-third of 6 equals 2, that's our whole.

And who has more money? Jacob's has got one-quarter of £20 and Alex has got one-third of £15.

Jacob's got one-quarter of that.

So the bar model needs to have 4 equal parts.

So 4 equal parts.

I drew 20 marks, I worked from left to right so that the marks would be in equal groups.

So when you do that, each box has got 5 marks in, so that represents £5.

I can see that one-quarter of 20 equals 5, I have £5.

For Alex, Alex has got one-third of £15.

So he needs to draw a bar model with 3 equal parts just like that, is that what you did? He's going to draw 15 marks from left to right just like this.

And when he does that, one box has got 5 in.

So that means that one-third of 15 equals 5 and that means he's got £5.

So actually they've got the same amount of money.

They both have £5.

Very well done if you said that.

We've come to the end of the lesson.

You've been fantastic today.

Today we've been finding one-third or one-quarter of a number.

To find one-third of a number, you divide the whole into 3 equal parts, and we've done that with bar models.

To find one-quarter of a number, you divide the whole into 4 equal parts.

And we've done that with bar models.

It is helpful to use a bar model to help you define one-third or one-quarter of a number.

If you count all the marks, it will be equal to the whole.

So some examples here, we've got one-third of 12 equals 4.

And we've done that by drawing marks in the boxes from left to right.

You could use counters, but marks are quicker.

And then one-quarter of 8 equals 2.

Well, you've been fantastic today.

Hope you are proud of yourself and all of your accomplishments in your achievements today.

You've been brilliant.

I think you need to give yourself a nice gentle pat on the back to say, "Well done me." I hope I get the chance to spend another maths lesson with you in the near future because this has been lots of fun and I'd like to do it again.

But until then, have a great day, whatever you've got in store, take care and goodbye.