Lesson video

Hi, welcome to today's maths lesson with me, Ms. Jones.

let's have a look at what we're going to be doing today.

In today's lesson, we're going to be calculating unit fractions of quantities.

Remember, unit fractions is any fraction with a numerator of one, such as one half or one quarter.

We're going to start off by thinking about how we can represent these problems with bar models to make sense of them.

Then you've got a talk task where you'll be exploring different problems, matching them to the correct bar model.

Then you're going to solve problems with fractions and measures.

And then you've got a task and a quiz.

You'll need today a pencil and piece of paper, or something else to write on and write with.

Pause the video if you need to go and get that.

If you're ready, let's begin.

Okay, here we have a problem that I've represented with a bar model.

There are 24 hours in a day.

Poppy spends one third of her day at work.

How many hours is she at work for, okay? So let's just have a look at how I presented this using a bar model.

This bar represents our whole, 24.

I've actually drawn in 24 dots here.

Now you don't need to do that every time, but I thought for this first problem, it will just help to develop our understanding.

But later on, we might not draw the dots in.

So this represents 24.

We know the whole, but we do not know how many hours she's at work for.

We know that she spends one third of her day at work.

Hmm, let's think about what one third means.

Well, if we're dividing something into thirds, we're dividing them into three equal parts.

So what we need to do is divide 24 into three equal parts, and then identify what one third is, okay? So I know that 24 divided by three is eight, so I should have eight dots in each part.

So I'm just going to divide this into thirds.

One, two, three, four, five, six, seven, eight.

Now let's just check if they're all equal.

Okay, so I've got three equal parts here.

I know that one part would be worth eight.

24 divided by three is equal to eight.

So when we're finding one third of something, so we're finding one third of 24, we're dividing it into the amount of parts stated by the denominator.

So we're dividing by three, and we're identifying that we only want one of those parts, so it's just one lot of three.

One third of 24 is eight.

Let's have a look at another problem.

A class has 32 pupils.

One quarter of them walk to school.

How many pupils walk to school? Again, we're going to make sense of this using a bar model.

So this bar represents my whole.

What was my whole? 32, there are 32 pupils in the class.

Now, how many equal parts do we need to divide our bar into this time? Can you say it out loud? Well, I know that we're working quarters, so we need to divide it into four equal parts.

Now I don't need to do 32 dots.

I'm going to sketch in where I think one quarter might be.

So here's the halfway mark, so a quarter might be here and here.

These represent four equal parts.

Now I'm looking at one quarter to find out how many of them walk to school.

So this is my unknown.

I need to divide 32 by four to find my answer.

Have a go at that.

You can use your multiplication and division facts hopefully to help you with this one.

I know that 32 divided by four is eight.

One quarter of 32 is eight.

Eight pupils walk to school.

Okay, hopefully you're ready to have an explore yourself.

Here's your talk task problem.

You need to match the word problem with the correct bar model, and explain how you know.

Spend a couple of minutes doing that.

Pause the video and then we'll come back and we'll have a look at them together.

Okay, hopefully you've had a chance to pause the video and match these bar models to the problems. Let's look at this first problem.

A scooter costs 42 pounds.

Isla has one seventh of the price left to save.

How much more money does she have to save? Well, she has one seventh, so we know we need to divide 42 into seven equal parts.

We can see that this bar here is divided into seven equal parts, and one part will give us the answer.

Let's look at the second problem.

A newsagent receives an order of 85 newspapers a day.

At one o'clock, they have sold one fifth of the newspapers.

How many have been sold? Well, we know here our whole is 85 and we're dividing into five equal parts.

So this matches this one, with the whole being 85 and this representing one fifth of 85.

So finally, this one hopefully should match this one, but let's check the information.

Reena is competing a 30 kilometre run.

So far she has run one sixth of the distance.

How far has she run? So we're looking at six equal parts, which we have, and we are identifying one sixth, so yes, that's correct.

Hopefully you did okay with those.

Let's move on to solving problems. These next few problems are going to be in different contexts, including measures.

So let's have a look.

Mary cycles a kilometre and a half to a corner shop.

However for the first 10th of her journey, she has to cycle up a steep hill.

How far did you have to cycle uphill at the beginning of her journey? So let's make sense of this by using a bar model.

I'm going to draw a bar that represents my whole, and I'm going to divide it into 10 equal parts, because we're working in tenths.

We need to divide into ten equal parts and then we can figure out what one part is.

Now, let's label our whole.

Our whole journey, we know, was one kilometre and a half, so this represents one and a half kilometres.

Now we'll need to divide this into 10, so we can write our answer as a decimal like this, okay? But if you didn't want to work with decimal numbers in division, you could also think about this in metres.

One and a half kilometres is equivalent to 1,500 metres, so you could work with either version here.

She has to cycle up a steep hill, and we need to work out how much was uphill, which was one tenth, so it's just this section here.

So we need to divide 1.

5 kilometres by 10 to find a 10th, okay? Which is the same as.

I know if we're dividing by 10, we need to move each digit over to the right, so that's the same as 0.

15 kilometres.

Now, if we're working in metres, we would write that as 150 metres.

And we can either convert this answer into metres, or we could have started with our answer here, converted earlier, and divided by 10.

One tenth of one and a half kilometres is 150 metres.

Here we've got a different problem.

A film lasts for one hour and 48 minutes.

Now I'm already thinking, "Well, I need to convert that into minutes to help with my division." Ross arrives late and misses one ninth of the film.

How many minutes of the film does he miss? Okay, so let's represent this problem.

We need.

We've got our whole, we know that.

We don't know what one ninth is, so we need to divide our whole into nine equal parts this time.

Now it asks us to give our answer in minutes, and our original whole is written in hours and minutes.

I think it might be easier to think of this in minutes.

So we know one hour is the same as 60 minutes.

60 add 48, I know that 60 add 40 is a hundred, so 60 add 48 is 108 minutes.

I'll put mins.

So if I just put m, you might get confused with metres.

So what I need to find is just one ninth.

Okay, so I need to divide 108 by nine to find one ninth, and I know that 108 divided by nine is, I'll give you a moment to think about it, is 12.

One ninth of 108 minutes is 12.

He missed 12 minutes of the film.

Okay, it's time for you to have a go at some of these problems. Pause the video now to do your task.

Hopefully you've had a chance to complete your task, and now we're going to go over the answers together.

Now, Jenny has 722 building bricks.

She uses one eighth of them to build a model skyscraper.

How many bricks were used to make the skyscraper? So here we know we're dividing our whole into eight equal parts.

We need to find one eighth.

Now our whole was 720.

We need to divide that by eight to find out what one part was.

Now I know 72 divided by eight would give me nine, so 720 divided by eight would give me 90.

She used 90 bricks.

Question two.

A school raises 480 pounds for charity.

They decide to spend one eighth of the money on books for the library.

How much of the money is spent on books? Well again, we know our hole is 480, and again we're dividing into eight equal parts and we need to find one part.

So our whole is 480.

We need to find out what one part is.

Now let's use our known facts again.

I know that 48 divided by eight would give us six, so 480 divided by eight would give us 60.

60 pounds is spent on books.

Question three.

A water bottle contains 600 millilitres of water.

Paul drinks one fifth of the bottle.

How many millilitres of water did he drink? Well our whole this time is 600 MLs, so this bar represents 600.

Make that look a bit more like a six.

And one fifth would be one of these five equal parts.

600 divided by five.

Well, I know that 60 divided by five would give us 12, so 600 divided by five would give us 120.

There are 120 millilitres in the water that he drank.

Question four.

Maria runs for four hours and 16 minutes a week in four sessions of equal length.

How long does one running session take? Okay.

Now this doesn't mention fractions as such, but it's still the same as finding one quarter, because it mentions that she used four sessions of equal length.

So we need to divide four hours and 16 minutes into four equal parts.

Now we could convert this into minutes and then divide by four, but here I can probably do this mentally, because we've got four hours 16 as our whole.

Let's put 4h and 16mins.

Now I know that four divided by four would give us one hour, and I can also work out that 16 divided by four would give us four minutes.

One quarter would be one hour and four minutes.

Now if you did convert this into minutes, that's the same as 64 minutes.

Okay, hopefully you had a good go at drawing some of those bar models to represent your problems. And if you wanted to share any of that, please ask your parents or carer to do so following the instructions on this screen now.

It's now the end of the lesson and time to complete your quiz.

Thanks very much.

Take care, and goodbye.