Lesson video

Hello there, my name is Mr. Tilston.

How are you? Are you having a good day? I'm having a good day, but it's about to get even better because we are going to do a lesson all about fractions and I just love fractions.

I know that you already know quite a lot about fractions, so let's see if we can teach you even more.

If you are ready to begin today's lesson, help me with a countdown.

Are you ready? Five, four, three, two, one.

Let's begin.

The outcome of today's lesson is this.

I can find three-quarters of an object, shape, set of objects or quantity, and you may have had some very recent experience of finding one-quarter.

I wonder how we could use that to find three-quarters.

And we've got some keywords.

If I say them, will you say them back? Are you ready? My turn, one-quarter, your turn.

My turn, three-quarters, your turn.

And you may have noticed that we've written them there as words, but we could write them using numerals.

We'll see lots of examples of that in this lesson.

Our lesson today is split into two parts.

The first will be recognise three-quarters.

What does it look like? And the second will be finding three-quarters of a quantity.

So if you are ready, let's start by looking at recognising three-quarters.

And in this lesson today 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.

Jacob and Alex have been learning about quarters.

Jacob says, "I think this shape has one-quarter shaded." What do you think? Do you agree? Alex says, "I agree.

The whole has been divided into four equal parts and one of those parts is shaded." Very good.

Jacob says, "Does that mean that this shape has three-quarter shaded?" What do you think? Alex says, "Yes, if each part is one-quarter, that means three-quarters of this shape are shaded." Jacob says, "Do you think this still has three-quarters shaded? Some of the shaded parts have changed." What do you think? Alex says, "Yes, the whole has been divided into four equal parts and three of those parts are shaded." So just like before, they're just in a different order, but it's still three-quarters.

Let's do a little check.

How could you shade three-quarters of this shape and could you find maybe a different way to do it? Pause the video.

Let's have a look, three-quarters of this shape.

Well this is one possible way.

There are others though.

Three of those four equal parts are shaded.

You could have shaded any three parts so, and you would still have shaded three-quarters of the shape.

The whole has been divided into four equal parts and three of those parts are shaded.

Jacob and Alex are going to play a game.

Hmm? Jacob says, "I'm going to show you some pictures.

You have to say if it represents three-quarters or not." Okay, this sounds like fun.

Will you play along too? Alex says, "Okay, I'm ready." What do you think? Put your thumb up if you think that's showing three-quarters.

And put your thumb down if you think it's not.

"This is three-quarters because the whole has been divided into four equal parts and three of those parts are shaded." So well done if you put your thumb up.

"Correct, well done!" What about this one? Put your thumb up if you think that's showing three-quarters and thumb down if you think it's not showing three-quarters.

Alex says, "This is not three-quarters because the whole has been divided into four unequal parts." "Correct, well done!" What about this one? Thumbs up if you think that's showing three-quarters, and thumbs down, if not.

Hmm.

"This is not three-quarters because the whole has been divided into three equal parts." It's not three-quarters.

"You're really good at this, Alex!" And you are really good at this too, well done.

Well let's have a quick check.

Which shapes have three-quarters shaded.

Have a good look.

Think about that stem sentence and pause the video.

How many did you find that had three-quarters shaded? The first one did.

That was split into four equal parts and three of them were shaded.

The same is true of this one.

Four equal parts, three shaded.

Four equal parts, three shaded.

These all have three-quarters shaded because the whole has been divided into four equal parts and three of those parts are shaded.

So why not the other ones? That shape has been divided into four parts, but they're four unequal parts.

This shape hasn't been divided into four parts.

It's been divided into five parts.

So that's not showing three-quarters.

Jacob says, "Do you always have to write the words three-quarters when you are describing this fraction?" What do you think? Have you got a quicker away? Can you use numerals perhaps? Alex says, "No! You can write it with numerals like this." The whole has been divided, so we start with our fraction bar, into four equal parts, the number of parts, and three of those parts are shaded.

So that is the order we go in.

Fraction bar, bottom number, top number.

You can write three-quarters or three-quarters to show that the whole has been divided into four equal parts and you have three of those parts.

"So far we've looked at three-quarters of a shape." "I wonder what else we could find three-quarters of?" Hmm, what have you had experience at finding one-quarter of? Jacob and Alex are going to explore finding three-quarters.

Jacob says, "I can break this chocolate bar into four equal parts." Just like that, nice and simple.

"You have three-quarters of the chocolate bar and I have one-quarter of the chocolate bar." This is three-quarters, this is one-quarter.

Jacob and Alex are still going to explore finding three-quarters, this time it's that square pizza.

"I can carefully cut this pizza into four equal parts." Just like that.

And here we go.

"You have one-quarter of the pizza and I have three-quarters of the pizza," says Alex.

One-quarter, three-quarters.

And that's how we write that with numerals.

Jacob and Alex are going to explore finding three-quarters.

We've got some lovely juicy strawberries here.

"I can divide this whole bag of strawberries into four equal pars." Hmm, let's have a look.

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

Still got some left, one for you, one for you, one for you and one for you.

Have we got four equal parts? Yes, we have.

Here we go.

"You have one-quarter of the strawberries and I have three-quarters of them." One equal part for Jacob, three equal parts for Alex.

That's one-quarter, and that's how we write that with numerals.

And that's three-quarters, and that's how we write that with numerals.

Jacob and Alex are still exploring finding three-quarters.

This time with sweets.

"I can divide this whole bag of sweets," says Jacob, "into four equal parts." "There are four rows and each row is one-quarter of the sweets." So you could think of that as one group.

There are four groups and that's one of them.

"You have one-quarter of the sweets and I have three-quarters of the sweets." So Jacob has one of the four groups and Alex has three of the four groups.

That's one-quarter and that's three-quarters.

Complete Alex and Jacob's sentences.

I can hmm, the whole tray of cakes into hmm equal parts.

So need a missing word and a missing number.

And you have hmm of the cakes.

And I have hmm of the cakes.

We are looking for two fractions, okay? Pause the video.

Let's start by dividing them up.

So one for you, one for you, one for you, one for you, one for you, one for you, one for you, one for you, one for you, one for you, one for you and one for you.

So we've divided those cakes up equally and that's the missing word.

I can divide the whole tray of cakes into four equal parts.

You can see four equal parts.

You have three-quarters of the cakes and I have one-quarter of the cakes.

So well done, if you said those, you're on track.

It's time for some practise, I think you're ready.

Tick the images that represent three-quarters.

Explain to a partner why you did not tick the other images.

And number two, Alex and Jacob both have a length of ribbon.

Some of their ribbon is hidden.

Jacob says, "You can see one-quarter of my ribbon." And Alex says, "You can see three-quarters of my ribbon." Hmm, whose ribbon is the longest and how do you know? Could you sketch how long you think each ribbon could be? Okay, pause the video.

Good luck and I'll see you soon for some feedback.

Welcome back, how did you get on with that first set of tasks? Are you starting to feel confident? This is three-quarters.

It's been divided into four equal parts and we have three of them.

This one has been divided into four equal groups and we have three of them.

This one has been divided into four equal groups and we have three of them.

This one has been divided into four equal groups and we've got three of them shaded.

Didn't tick this one because only one-quarter is shaded, but you could say that three-quarters are not shaded.

Depends how you look at it.

And I didn't tick these ones because the whole has been divided into three equal parts, not four.

I didn't take this one because the whole has been divided into two equal parts, not four.

And I didn't take this one because the whole has not been divided into equal parts.

It shows that three counters have been circled, but that doesn't represent three-quarters.

There aren't four equal parts there.

And number two, Alex and Jacob both have a length of ribbon and some of their ribbon is hidden.

Whose is longest and how do you know? If you can see one-quarter of Jacob's ribbon, that means the other three-quarters are hidden.

You could sketch Jacob's ribbon like this.

We'd need three more of that size.

Three more equal parts.

So now you can see a bit more clearly that he's got one-quarter.

But Alex says you can see three-quarters of my ribbon.

So we've already got three-quarters.

How many quarters are left? Just one, one-quarter is hidden.

So we could sketch an extra quarter onto the end and it would look like that.

So well done if your drawings were a little bit like that.

Jacob's ribbon is longer.

You're doing very, very well and you are ready for the next cycle now, which is finding three-quarters of a quantity.

You've hopefully got lots of experience and confidence with finding one-quarter of a quantity.

Jacob and Alex continue to explore finding three-quarters.

"To find one-quarter, you need to divide the whole into four equal parts," says Jacob.

Yep, you do.

And here are four equal parts.

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

We've still got some left.

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

We've still got some left.

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

Have we got four equal parts? Yes, we have.

"There are three grapes in each part so one-quarter of 12 is equal to three." That's finding one-quarter.

One-quarter of 12 equals three or three equals one-quarter of 12.

But we're trying to find three-quarters, not one-quarter.

"How did you know that you've found one-quarter of 12?" asks Jacob.

"Remember if you count the objects in all of the parts it will equal the whole." So three, six, nine, 12.

Now what's being shown here? "The whole has been divided into four equal parts and I have three of those parts." So Jacob has three-quarters.

"You have three-quarters of the whole," says Alex.

"I wonder how you would write that as an equation?" Hmm.

"There are three grapes in each quarter.

If you have three-quarters, you have nine grapes." Can you see that? Three, six, nine.

We could write it like this.

Three-quarters of 12 equals nine or nine equals three-quarters of 12.

So if one-quarter was three grapes, two-quarters are six grapes and three-quarters are nine grapes.

That bar model's really helpful.

Jacob and Alex continue to explore finding three-quarters.

"I bought 20 sweets earlier.

I bet we could find three-quarters of them!" "I'll go and find them now." "Hold on, Alex! I think I know how to find three-quarters of 20 without using the sweets." Hmm, maybe you've got a good idea, a strategy you've used quite recently that's nice and efficient.

Jacob and Alex try a different strategy to find three-quarters of 20.

"I will draw a bar model with four equal parts." "When you want to find three-quarters, you divide the whole into four equal parts." Just like if you're finding one-quarter.

So here's our bar model.

It's already, it's set out into quarters.

"I will draw one mark in each part." Have you done that recently? "I will count each mark as I draw." What will we count up to? Twenty, "One, two, three, four." "Looking good so far," says Jacob, "can you carry on drawing marks until you get to 20?" So we're on four, let's keep going.

We're going left to right.

Let's start again.

Five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

We made it all the way there.

That is 20.

Not quite answered the question yet though, have we? Jacob says, "I can see five marks in each part.

That means one-quarter of 20 equals five." Yes, but that's still not the question, is it? "Remember we wanted to find three-quarters of 20 so we need to look at three of the parts." Here we go.

That's three of the parts.

"I need to count three lots of five." If five is one-quarter, two-quarters is 10 and three-quarters is 15.

"Five, 10, 15." "There are 15 marks in three-quarters." And here are our equations.

Three-quarters of 20 equals 15 or 15 equals three-quarters of 20.

Alex drew marks on this bar model to help him find three-quarters of 16, but he's made some mistakes.

How could you help Alex to improve his work? Hmm, have you got any feedback for him? He says three-quarters of 16 equals four or four equals three-quarters of 16.

I'm not sure that's right.

See what you think.

What advice have you got for him? Pause the video.

Well, I like that he had a bar split into four equal parts.

That was a good start and I like that he was thinking about using marks.

That's really good too.

But he's not organises marks and that's made it hard to keep track and to count.

He should have tried to draw them in a pattern like this to make them easier to count.

Let's have a look.

Now doesn't that look better? Now straight away when it's organised like that, I can see that's wrong.

I can see they're not equal parts, can you? Now the marks are organised, it's clear that the four parts are not equal.

He should have divided the whole into four equal parts like this.

Now we've got four equal parts.

Alex's equation is wrong.

He's only looked at one part.

So he is found one-quarter of 16.

Alex needs to look in three parts to find three-quarters of 16.

So if one-quarter is four, two-quarters is eight and three-quarters is 12.

Four plus four plus four is equal to 12.

So this is our correct equation.

Three-quarters of 16 equals 12 or 12 equals three-quarters of 16.

So very well done if you've got that.

And it's time for some final practise.

Number one, circle three-quarters of each group of objects and complete the equations.

So A, there are four cakes, three-quarters of four equals what? B, there are four pens, three-quarters of hmm equals hmm.

C, there are hmm coins.

You got to count.

Three-quarters of hmm equals hmm, and D, there are 12 sweets.

Mm, equals three-quarters of 12.

And number two draw marks on the bar models to answer each question.

Three-quarters of eight equals hmm.

So you're going to need to draw eight marks.

Remember to go left to right, remember to keep them nice and organised and clear.

And then B, three-quarters of 24 equals hmm.

You're going to need 24 marks.

Number three, draw your own bar model, then draw marks to help you answer each question.

So A, three-quarters of 32 equals something.

So how many parts has your bar model got to have? And how many marks are you going to draw in it? Hmm, and then B, three-quarters of 36 equals something.

Righteo, pause the video and off you go.

Welcome back, how did you get on with that? Are you feeling confident? So three-quarters of each group.

So there's four cakes, three-quarters of four, we've got three-quarters circled and that's three.

Four pens, we can circle any three of those.

Three-quarters of four equals three.

And for C you had to count the coins.

So there are 12 coins, three-quarters of 12 equals nine.

You can see there.

And there are 12 sweets.

So something equals three-quarters of 12.

And if we circle three of those four groups, this is what we've got.

Three-quarters of 12 equals nine or nine equals three-quarters of 12.

And number two draw marks on the bar models to answer each question.

Three-quarters of eight equals something.

Here's the marks.

One-quarter of eight equals two, so therefore three-quarters of eight equals six.

And for B, three-quarters of 24 equals something.

Or here's the marks, that's 24 marks.

One-quarter equals six, three-quarters equals 18.

Draw your own bar model, three-quarters of 32.

Well, you need to draw a bar split into four equal parts and perhaps you likely shaded three of them.

That's showing three-quarters and there's 32 marks.

One-quarter equals eight, two-quarters equals 16 and three-quarters equals 24.

And for B three-quarters of 36, again we've got our bar model that's showing three-quarters.

We've got 36 marks, one-quarter equals nine, three-quarters equals 27.

We've come to the end of the lesson.

You've been fantastic.

Today we've been finding three-quarters of an object, shape, set of objects or quantity.

To divide an object, shape, set of objects or quantity into quarters, you need to divide it into four equal parts and I'm sure you already had lots of confidence with that before today's lesson.

Each part is called one-quarter and we can write that using numerals as such.

If you have three of those parts, you have three-quarters and you've shown lots of different representations of three-quarters.

It can be helpful to use a bar model to help you find three-quarters of a number.

We've drawn 24 marks from left to right.

That means that one-quarter in this case equals six, two-quarters equals 12 and three-quarters equals 18.

So three-quarters of 24 equals 18.

So those bar models are really helpful, aren't they? I've had so much fun today exploring this and I hope you have too.

You've done yourself proud and you deserve a little pat on the back.

So go for it, you've earned that.

I really do hope I get the chance to spend another maths lesson with you in the near future.

But until then, have a great day.

Be successful at whatever you are doing.

Take care and goodbye.