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 compare unit fractions.

And here are the keywords.

I'm going to say the keywords.

Can you repeat them back? First one's a bit of a tricky one.

Are you ready? The first word is denominator.

And the next key words are unit fraction.

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

A denominator is the bottom number in a fraction.

It shows how many parts a whole has been divided into.

A unit fraction is any fraction where the numerator is 1.

The numerator is a top number in a fraction.

So the numerator, the top number in a fraction is 1, it is a unit fraction.

Let's take a look at the lesson outline.

In the first part of the lesson, we're going to be comparing fractions.

In the second part of the lesson, we're going to be ordering fractions.

Let's get started.

In this lesson you'll meet Sofia and Jacob and they're going to be helping you with your maths today and ask you some questions as well.

Jacob and Sofia are running a race.

I have run 1/4 of the distance, says Jacob, I have run 1/3 of the distance, says Sofia, who has run further? I wonder what you think.

Let's compare the distances.

So Jacob has run 1/4 of the race.

Here's the start and finish line.

0 represents the start of the race and 1 represents the finish to the race.

We can say there are four equal parts to the race.

So we can call those quarters.

1/4, 2/4, 3/4, and 4/4 or 1.

Jacob has run one of them.

He has run one of those four equal parts.

So Jacob is currently there in the race.

So is Sofia ahead of him or is she behind him in the race? Sofia has run 1/3 of the race.

We can say there are three equal parts to the race.

Let's divide the race into three equal parts.

1/3, 2/3, and 3/3.

Sofia has run one of them so she has run 1/3 of the race.

So Sofia is currently ahead in the race.

1/3 is greater than 1/4.

Sofia has run more of the race than Jacob.

So currently she's ahead.

I wonder she wins the race.

Jacob and Sofia compare unit fractions.

Here is a whole divided into four equal parts.

Each of those parts is a quarter.

Here is a whole divided into three equal parts.

Each of those parts is 1/3, 1/3 is greater than 1/4.

1/4 has a greater denominator than 1/3 when the whole is the same.

And that's really important, the wholes need to be the same.

The greater the number of equal parts, the smaller each equal part is.

For our whole divided into quarters, there are four equal parts.

For our whole divided into thirds, there are three equal parts.

When you divide something into four equal parts, the parts are going to be smaller than if you've divided it into three equal parts, into thirds.

Jacob and Sofia each take a slice of pizza.

I think obviously they're hungry after running that race.

So here is a pizza cut into five equal parts.

Jacob says, I'm taking a slice of this pizza.

Here is a pizza divided into eight equal parts.

I'm taking a slice of this pizza, says Sofia, whose slice of pizza is larger in size.

Jacob says, I took 1/5 of this pizza because the pizza was divided into five equal parts, each part represents 1/5.

The Jacob took 1/5 of this pizza.

I took 1/8 of this pizza says Sofia.

Each part of the pizza represents 1/8 of the whole.

My slice of pizza is larger, says Jacob.

1/8 has a greater denominator than 1/5.

So Jacob took 1/5 of his pizza.

Sofia took 1/8 of her pizza.

And because there are more eighths in a whole, each part must be smaller.

When the whole is the same, the greater the number of equal parts, the smaller each equal part is.

Jacob compares 1/8 and 1/7.

Which is smaller, 1/8 or 1/7? Here's 1/8.

So the whole is divided into eight equal parts.

Each represents 1/8.

Here is 1/7.

So the whole is divided into seven equal parts.

Each part represents 1/7 and both wholes are the same.

So we can compare them.

Which is smaller, 1/8 or 1/7? 1/7 has a smaller denominator than 1/8.

And because it has a smaller denominator, it means it must be a larger fraction.

1/8 is less than 1/7.

When the whole is the same, the greater the number of equal parts, the smaller each equal part is.

Compare these fractions.

Which is smaller, 1/5 or 1/4? Have a think.

Which do you think is smaller? And can you explain why you think that? Pause the video and see if you can work out the answer.

And welcome back.

Did you think that 1/5 is a smaller fraction? Do you think 1/4 is the smaller fraction? Let's find out.

So here is a whole divided into five equal parts.

One of them is shaded.

So this represents 1/5.

Here is a whole divided into four equal parts.

One of them is shaded.

So this represents 1/4 which is smaller.

Jacob says 1/4 has a smaller denominator and 1/5, 1/5 is less than 1/4.

The more parts there are the smaller the size of those parts.

Well done if you manage to work out that 1/5 is less than 1/4.

Jacob and Sofia compare these unit fractions.

Each whole is the same size, says Jacob.

This first shape is divided into six equal parts.

Each part represents 1/6 of the whole.

This shape is divided into six equal parts.

Each part represents 1/6 of the whole.

1/6 is equal to 1/6.

Now the parts are different shapes but they are the same size.

Each whole is the same and each whole is divided into six equal parts.

So each part represents 1/6 of the whole, which unit fraction is larger.

Each whole is the same size, so which fraction is greater than the other.

Think about how many parts each whole has been divided into.

Try and work out what the two fractions are.

Can you work out which fraction is greater than the other? Pause the video and see if you can work out what the answer is.

And welcome back.

Did you manage to work out both fractions? Did you manage to compare one or the other? Did you manage to say which one was greater than the other? Let's take a look, see whether you got it right.

So this first shape is divided into nine equal parts.

Each part represents 1/9 of the whole.

The second shape is divided into 10 equal parts.

Each part represents 1/10 of the whole.

1/9 is greater than 1/10.

How can you tell? Because when the whole is the same, the greater the number of equal parts, the smaller each equal part is.

And that first example that the whole has been divided into nine equal parts.

And the second example, the whole has been divided into 10 equal parts.

So each 10th must be smaller than each 9th.

Well done if you've got the right answer.

And let's move on to task A.

So in task A you're going to work out the shaded fraction and then you're going to compare the unit fractions saying which one is less than the other or saying which one is greater than the other.

So if you look at A, for example, how many parts are there in that first shape? One part is shaded, but how many parts there in total? And you can see that second fraction is less than that first fraction.

But what does that second fraction represent? So work out the fractions and then compare them.

In part two, work out the shaded fraction and then compare the two fractions explaining which is less or greater or whether they are equal.

Pause the video and have a go at completing task A.

And welcome back.

Let's take a look to see how you got on.

Here are the answers for the first part of task A.

For A, 1/8 is less than 1/6.

That first shape was divided into six equal parts and our second shape was divided into eight equal parts and 1/8 is less than 1/6.

Let's take a quick look at B.

So that first shape is divided into 3 equal parts.

So each part represents 1/3.

Our second shape is divided into 5 equal parts.

So each part represents 1/5 and 1/5 is less than 1/3.

When the wholes are the same, the greater the denominator the more parts that you have.

So the smaller each part will be.

And here are the answers for part 2 of task A.

Let's look at A to start off with.

So for a 1/8 is equal to 1/8.

Both shapes were divided into eight equal parts.

So each part represents 1/8 B 1/9 is less than 1/8 or 1/8 is greater than 1/9.

Both of those sentences are correct.

And then for C 1/12 is equal to 1/12.

Both shapes were divided into 12 equal parts.

Very well done for completing task A.

And let's move on to the second part of the lesson.

So in the second part of the lesson we're going to be ordering fractions.

We've done some comparing of fractions.

Now we're going to have a go at ordering them.

Jacob and severe order unit fractions.

Where would 1/2 appear on the number line, asks Jacob.

So have we got a number line from 0 to 1 and all the unit fractions will appear somewhere on that number line.

Sofia says there are two halves in one whole.

So if we take a shape and divide into two equal parts, one of those parts is equal to 1/2.

So 1/2 would appear here halfway on the number line.

Jacob says next, where would 1/4 appear on the number line? Sofia says there are four quarters in one whole.

So if we take the whole and divide it into four equal parts, one of those parts is equal to 1/4.

Where would 1/3 appear on the number line? So we've got there already 1/2 and 1/4 represented on the number line.

Where would 1/3 appear? Is it larger than a half? Is it larger than a quarter? Is it smaller than a half? Is it smaller than 1/4? Pause the video and see if you can work out where 1/3 would appear on that number line.

And welcome back.

Did you manage to work out the answer? Let's take a look to see whether you put 1/3 in the right place.

So Sofia says there are three thirds in one whole.

Let's take a shape and divide into three equal parts.

Each of those parts represent 1/3.

So 1/3 would appear here.

1/3 is smaller than 1/2.

1/3 is larger than 1/4.

Remember the larger the denominator is, the more parts you have, the smaller each part will be.

When the whole is the same, the greater the number of equal parts, the smaller each equal part is.

Very well done if you manage to place 1/3 in the correct place on that number line.

Jacob and Sofia order unit fractions.

They're going to add more fractions to this number line.

Where would 1/5 appear on the number line, asks Jacob.

There are five fifths in one whole, says Sofia.

Let's take the whole, divide it into five equal parts.

1/5 would appear here.

Where would 1/7 appear on the number line, asks Jacob.

There are seven sevenths in one whole says Sofia.

So let's take the whole, divide it into seven equal parts.

So 1/7 would be represented here on the number line.

Now it's your turn again.

Where would 1/6 appear? Pause the video and see if you can work out where 1/6 would be represented on that number line.

Welcome back.

Did you manage to place 1/6 on the number line? Do you think you got it in the right place? Let's take a look and see whether you were right.

So Sofia says there are six sixths in one whole.

So let's take a whole and divide it into six equal parts.

So 1/6 would appear here.

1/6 is smaller than 1/5.

The whole has been divided into more parts, but 1/6 is larger than 1/7.

If you split a whole into seven equal parts, each part will be smaller than if you split into six equal parts.

So when the whole is the same, the greater the number of equal parts, the smaller each equal part is.

Well done if you managed to place 1/6 in the correct place on the number line, Sofia puts these unit fractions in order.

So she's got there 1/9, 1/10, 1/6.

I need to start with the smallest number.

I'm going to add the fractions to the number line, says Sofia.

So here's our number line 1/6 is already on the number line, but she can certainly place 1/9 and 1/10 on it.

Let's take a whole and divide it into nine equal parts.

So 1/9 would be represented here on the number line.

And if the whole was divided into 10 equal parts, 1/10 would be represented here.

Sofia can now order those unit fractions.

So when comparing unit fractions, the greater the denominator, the smaller the fraction.

So 1/10 is the smallest fraction, the denominator is the greatest.

So because it's just a unit fraction we're comparing the numerator is one each time, that must be the smallest fraction.

1/9 would come next.

So 1/9 is greater than 1/10.

1/10 is less than 1/9.

And then finally 1/6, 1/9 is less than 1/6.

Sofia is looking for the missing denominator.

So she's got here 1/14 and then that is less than one something, we don't know what the denominator is, which is less than 1/11.

What fraction could be used to make this correct, asks Sofia.

The denominator is less than 14 but greater than 11.

So remember the more parts or rather larger the denominator, the greater the denominator, the smaller the unit fraction will be.

I could use 1/13, but I'll use 1/12 instead.

There's actually two possible answers, but Sofia has decided to use 1/12.

So she writes in the missing denominator and makes it 12.

But 1/14 is less than 1/12, which is less than 1/11.

When comparing unit fractions, the greater the denominator, the smaller the fraction.

It's your turn.

Can you find the missing denominator? So we've got there 1/8 is greater than a fraction which is greater than 1/11.

What could the missing denominator be? What fraction could be used to make this correct? Pause the video and see if you can work out what the answer would be.

And welcome back.

Did you manage to work out the answer? Now in fact, there are two possible answers for this one.

Sofia says the denominator is greater than 8, but less than 11.

You could use 1/9 or 1/10.

So the denominator could be 9 or it could be 10.

Sofia has decided to put 9 in there.

So 1/8 is greater than 1/9, which is greater than 1/11.

When comparing unit fractions, they're greater the denominator, the smaller the fraction.

Well done if you worked out that the answer could be 1/9 or 1/10.

Excellent work.

And let's move on to task B.

Put these unit fractions on the number line.

The positions are already marked for you.

So you've got there 1/5, 1/8, 1/10, 1/4, 1/6, 1/2, 1/3, 1/15, 1/25.

Think very carefully about those denominators.

See if you can work out where those fractions should be placed on the number line.

Here's part 2 of task B.

Find denominators to make these correct.

So if you look at A, for example, you've got there 1/2 is greater than what fraction, and this fraction is greater than 1/4.

There's only one possible answer for that one.

So part 2 of task B.

And here's part 3 of task B.

So find three different ways to make this correct.

There's lots and lots of possible answers for this one.

We've got 1/12 is greater than 1 something which is greater than 1 something else which is greater than 1 something else which is greater than 1/18.

So how could you make that correct? What denominators could you use and can you find three different ways to make that correct? Remember, when we're using unit infractions, the greater the denominator, the smaller the fraction is.

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 3 of task B? Excellent work if you did.

Let's take a look at those answers.

So here are the answers for part 1 of task B.

You have to place these unit fractions on the number line.

That is where the fraction should be placed.

So 1/25 was the smallest fraction, 1/2 was the largest fraction.

So with unit fractions, as the denominator gets larger, the fraction gets smaller.

So if you managed to place those fractions correctly on the number line, let's have a look at part 2 of task B.

So we've got that A, 1/2 was greater than 1/3, which is greater than 1/4.

B, 1/8 is less than 1/7, which is less than 1/6.

So well done if you managed to complete part 2 of task B.

And then finally, let's have a look at some possible answers for part 3 of task B.

So we've got 1/12th is greater than 1/13, which is greater than 1/14, which is greater than 1/15, which is greater than 1/18.

Okay, so very, very well done if you've got on to part 3 and found some possible answers there as well.

And excellent work today.

And hopefully you're feeling much more confident when it comes to comparing unit fractions and ordering them.

Excellent Work today.

Very well done.

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

So when the whole is the same, the greater the number of equal parts, the smaller each equal part is.

When comparing unit fractions, the greater the denominator, the smaller the fraction.

When comparing unit fractions, the smaller the denominator, the greater the fraction.