Lesson video

Hello, I'm Mr. Tazzyman and I'm going to be joining you today for your learning.

I hope that you enjoy it and if you are ready, we can get started now.

Here's the outcome for today's lesson.

By the end, we want you to be able to say, I can compare and order unit fractions by looking at the denominator.

Here are the keywords that you might hear during this lesson.

I'm gonna say them and I want you to repeat them back to me.

I'll say my turn, say the word and then you can say it back.

My turn.

Whole.

Your turn.

My turn.

Part.

Your turn.

My turn.

Denominator.

Your turn.

My turn.

Unit fraction.

Your turn.

Okay, let's understand these words now.

The whole is all of a group or number.

A part is a section of the whole and the bar model at the bottom of the screen shows the relationship between the whole and the part.

A denominator is the bottom number in a fraction.

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

A unit fraction is a fraction where the numerator is one.

Here's the outline for today's lesson on comparing and ordering unit fractions by looking at the denominator.

To begin with, we are gonna use a fraction wall and see how that might help us when we are comparing and ordering.

Then, we are gonna look at ordering in different contexts.

Let's start by looking at using a fraction wall and we can meet here Jun and Sofia.

These are two friends who are going to help us by discussing some of the maths that you are gonna be thinking about.

They'll also give us some hints and tips as we go through the slides.

Hi Jun! Hi Sofia! Is everyone ready? Let's go for it.

In science, Jun and Sofia are making a musical instrument using identical glasses filled with different amounts of water.

Jun says if we tap the glasses with a spoon, they make a ringing sound.

The fuller the glass, the lower the pitch of sound.

Let's order them from low pitch to high pitch.

Okay then, the full glass needs to go first, then the glass with the least water goes last.

Now we can compare the other two and put them in the right place.

There we go.

The glasses have been ordered.

Jun and Sofia use inequality symbols to show the change in water across the four glasses.

We need to place an inequality symbol between each.

There's greater than and there's less than just as a reminder for all of us.

I agree, says Sofia.

The amount of water decreases as we go along the line from left to right, that's what she means.

So the quantity of water becomes less and less.

The full glass has more water than the second glass.

There's a greater than sign in between there.

The second is more than the third.

Finally, the third is more than the last.

Can we order unit fractions in a similar way? I think so, but a fraction wall might be useful.

Let's check your understanding so far.

Which inequality symbol should go between each of these glasses to show the quantity of water in comparison to the next glass? Pause the video here.

Have a think and I'll be back in a minute to reveal the answer.

Welcome back.

Let's see.

So the symbol that went between all of those glasses was less than because as you go along the line from left to right, the quantity of water is increasing.

Sofia decides to compare unit fractions by creating a fraction wall.

I'll cut six identically sized strips of paper, then I'll fold each of them into equal parts except the top, which is my whole.

Next, I'll unfold them all and line them up carefully to compare equal parts.

The number of equal parts increases by one as you go down the wall.

Jun decides to label the fraction wall using notation.

The first strip is a whole which I can label as one because it isn't a fraction.

Then I can count the number of parts making up the whole in each strip.

2, 3, 4, 5, 6.

The whole has been divided into the labelled number of parts for each strip and you can see that there.

We've got the number alongside each row written as the number of parts that row's been split into.

That gives me the denominator, which tells me what each equal part is.

So Jun's gonna convert these numbers alongside to being denominators now.

Half and half, third, third and third, and you can see the rest of them there.

What do you notice? Look down that fraction wall.

Compare each row and think about what you notice is happening to the denominator.

I notice that the greater the denominator, the smaller the fraction.

Jun and Sofia discussed the fraction wall.

This is really useful, says Jun.

Now we can order unit fractions to see which is greater.

Yes, we can as long as the whole stays the same.

The great thing about a fraction wall is that the whole will always be the same because all of the strips are the same width.

Shall we show the unit fractions on their own to make it easier to compare?, says Jun.

Sounds like a good idea.

So now, they've taken each of those equal parts and put them on their own to show the unit fraction.

Jun and Sofia choose two fractions each to order.

I'll choose one half and one third.

Okay, I'll choose one fifth and one quarter.

Let's order these using the fraction wall.

Yes, from smallest to largest.

That's a really important point from Sofia.

You need to know before you order whether you are going from smallest to largest or largest to smallest.

On the fraction wall, I can see that one fifth is the smallest and Jun's noticed that because he's seen that one fifth is lower down than the other fractions that they decided upon and you can see that it's smaller by looking at the wall.

I can see that one half is the largest, says Sofia.

So she puts that further to the right with enough room in between to sort out the other two fractions that they've chosen.

One quarter is smaller than one third and it's helpful that they're next to one another in the fraction wall makes for an easy comparison.

Let's place the wall parts next to them to check.

Good thinking Sofia.

Always worth checking as a mathematician.

That's what brilliant mathematicians do.

So they take away all the other fractional parts and they put the parts above the fraction notation.

You can see that the parts are increasing as you go from left to right.

Jun and Sofia use inequality symbols to show the relationship between the unit fractions.

We need to put an inequality symbol between each.

I agree.

They get greater as you go from left to right.

I can see that one fifth is less than one quarter.

There it is.

O ne quarter is greater than one third.

So there it is again.

Finally, one half is greater than one third.

All three symbols were all less than because the fraction was increasing in size as you went from left to right.

What do you notice here? Jun says, I notice that the numerator are all one.

Sofia says, yeah, they are all unit fractions.

I notice that the denominator gets smaller as the fraction gets bigger.

If you look on the right hand side, the greatest fraction has a denominator of two.

One half has a denominator of two.

Now look back along the line to the beginning.

You can see one fifth which has a denominator of five.

That's smaller but it has a bigger denominator.

Yes, the greater the denominator, the smaller the fraction as long as the whole is the same.

That's a really good point from Sofia.

If we have fraction notation, we know that the whole will automatically be the same.

Okay, let's check your understanding.

You need to be a detective here.

You need to spot the mistake in the statement below.

Pause the video and have a go.

Welcome back.

Did you see a mistake in there? Jun says the inequality symbol is incorrect.

One third is greater than one quarter, which is greater than one fifth.

There they go swapping around.

Now we've got the correct symbols in there.

Jun and Sofia practise ordering unit fractions.

They create four unit fractions using a spinner to create the denominators.

One third, one seventh, one ninth and one fifth.

One ninth and one seventh aren't on our fraction wall.

That's okay.

We can use what we've learned from the wall.

So you can see that the wall's disappeared there because some of those fractions aren't represented on it, but I think they know that they can still compare them easily by considering the fact that the greater the denominator, the smaller the fraction.

Just as Sofia says there, the smaller the denominator, the larger the fraction.

Exactly.

Let's order from greatest to smallest.

Again, a really good point from Jun there.

You need to know whether you are doing, greatest to smallest or smallest to greatest.

One third has the smallest denominator, so we should start with one third.

One ninth has the greatest denominator, so it's smallest.

Can you see that Jun has placed that further to the right giving room to put the other two fractions in between these two fractions.

They know that one third is the greatest and one ninth is the smallest.

Now let's compare one seventh and one fifth.

One fifth has a smaller denominator so it's greater.

There they go.

In go those two remaining fractions.

Now to put an inequality between them.

It's greater than.

Now, they've completed it.

One third is greater than one fifth, which is greater than one seventh, which is greater than one ninth.

The fractions are getting smaller as you go from left to right, so the greater than symbol is the one that's needed.

Okay, it's time for your practise task now.

Use the fraction wall to order these unit fractions from greatest to smallest and there's a fraction wall there to help you, but you might have your own one.

What do you notice? Number two, order these fractions from smallest to greatest.

Put the correct inequality symbol between them.

Now you'll see that the denominators on these ones are greater than a lot of the denominators on fraction walls, so you might not be able to use that, but you know what happens when the denominator gets greater? Number three, below a three unit fractions ordered from greatest to smallest.

What could the denominator of the middle unit fraction be? How many different ways can you solve this? Okay, have a good go at those.

Make sure you're doing lots of thinking as you do it.

Pause the video and I'll be back with some feedback shortly.

Welcome back.

Let's do some marking.

For number one, you should have arranged the fractions in this order with a greater than symbol between.

So we've got one half is greater than one third, which is greater than one quarter, which is greater than one fifth, which is greater than one sixth.

What do you notice? Well, Sofia said, I noticed that the denominator is increasing as the fraction gets smaller.

Here's number two, order these fractions from smallest to greatest and put the correct inequality symbol between them.

So here was the order and you needed less than symbol between.

So you should have had one-15th is less than one-10th, which is less than one ninth, which is less than one seventh.

Pause the video here for some extra time for marking should you need it.

Okay then number three, below a three unit fractions ordered from greater to smallest.

Your task was to find as many different ways as you could to complete this statement.

And Sofia says, here are all the solutions that were possible.

You could have had one quarter is greater than one fifth, which is greater than one ninth.

One quarter is greater than one sixth, which is greater than one ninth.

One quarter is greater than one seventh, which is greater than one ninth and one quarter is greater than one eighth, which is greater than one ninth and you can see the denominator there is increasing by one.

Okay then, we finished the first part.

Let's move on to the second part of the lesson, ordering in different contexts.

Here are three representations of unit fractions.

Jun and Sofia order them by size.

They are all the same whole.

That means we can order them.

Yes, the circles are identical but they've been divided differently.

I'm going to turn them into fraction notation first.

The first circle has been divided into four equal parts.

Each equal part is one quarter.

I can see that the second circle is one half.

The third circle has been divided into eight equal parts, it's one eighth.

There we go.

Let's order them from smallest to greatest.

The smaller the denominator, the greater the fraction.

There they are, ordered according to size from smallest to greatest.

We've got one eighth, first one quarter, and then one half.

Now we can place the inequality symbols between them.

Less than symbols are put in between because they are increasing as size from left to right.

I don't think we needed to find a fraction notation here, says Sofia.

You can look and see which is a bigger fraction and you can probably see that as well.

You might have been able to order these before putting fraction notation on them.

That's true, says Jun, as long as the whole is the same, that's really important.

Okay, your turn.

Order these three representations of fractions from smallest to largest.

Then put the correct inequality symbol between them.

Pause the video and have a go and I'll be back in a little while to reveal the answer.

Welcome back! Let's see if you manage to order these correctly.

We've got one 16th, one quarter and one half, and the symbols between them would be less than.

One 16th is less than one quarter, which is less than one half.

You may not have used fraction notation, you might have just compared the sizes of the shaded parts.

That's absolutely fine.

Okay, ready to move on.

Let's go for it.

They look at three more representations and all of the fractions by size again.

Some of the parts are triangles and some oblongs.

Does it matter? What do you think? Can we have comparisons between differently shaped parts? It doesn't matter because we are comparing the fractions, says Sofia.

Fractions can be differently shaped parts.

Let's label each part with fraction notation to start.

The first whole has been divided into four differently shaped equal parts.

One part has been shaded, so it's one quarter.

The middle whole has been divided into eight equal parts.

One part has been shaded, so it's one eighth.

The final whole is divided into two parts with one shaded.

It's one half.

Let's sort them from greatest to smallest this time.

The smaller the denominator, the greater the fraction.

That's a really key piece of learning to remember, isn't it? So it goes one half, one quarter and then one eighth.

There they are, one half, one quarter, one eighth.

The fractions are getting smaller, so we need greater than symbols.

There we go.

They place greater than symbols in between each representation.

Okay, it's your turn.

You are gonna have a go at ordering these three representations of fractions from largest to smallest.

Remember that, largest to smallest.

Then put the correct inequality symbol between them.

Pause the video and have a go.

Welcome back.

Did you manage to order these fractions? Well there they are, in the correct order.

We start with one half, move to one quarter and then go to one eighth.

They're getting gradually smaller.

That means we needed greater than symbols in between.

How did you get on? I hope you managed to get it.

Okay then, let's look at the next part.

Jun is pouring juice into the glass.

He asks Sofia to shout stop when the glass is one fifth full.

'Can you help me please?', says Sofia.

Stop! 'How do you know that is one fifth', asks June.

I think five of those parts would fill the glass.

1, 2, 3, 4, 5.

She's right.

Sofia is pouring the juice now.

She asked Jun to shout stop when the glass is one quarter full.

Your turn now Jun.

Can you help me? Stop! How do you know that is one quarter? 'I think four parts like this would fill the glass', says Jun.

1, 2, 3, 4.

There we go.

Four parts filling the glass and one of those parts has got juice.

It's one quarter.

Jun challenges Sofia, why don't you try to do one-thousandth? One-thousandth, I think that will overflow.

It's got 1000th in it.

I think it will be too hard because it's so small.

What do you think? Do you think Jun is right? Do you think it's gonna be really, really small or do you think Sofia is right and it's gonna be massive and overflow? Remember, says Jun, the greater the denominator, the smaller the fraction.

You are right.

It's going to be tiny and hard to judge.

I'll just put a single drop in.

There it is.

Might be 1000th that.

Hard to know if that's exact, but it's definitely tiny.

Jun and Sofia order the three glasses showing different fractions.

Let's go from the smallest fraction to the largest.

One-thousandth was tiny, so that should go first.

The denominator of five in one fifth is greater than the four in one quarter.

That means one fifth is smaller.

You can see that it is.

If you compare those two glasses that have just been put down there, you can see that one fifth is ever so slightly smaller than one quarter.

The inequality symbol between them should be less than because they are getting greater.

There we go.

Okay, it's your turn for a second practise task.

For number one, I want you to look at the fraction representations below.

A, label the fraction notation for each; B, order them from smallest to largest, and C, write the correct inequality symbol between them.

For number two, it's the same kind of thing, but we've got some different representations this time.

And for number three, have a go at estimating the following fractions by filling a glass with water.

Then, order the glasses from largest to smallest, A, one quarter; B, one third; C, 100th and D, one-half.

Oh and an extra tip.

Try not to spill too much.

Okay, pause the video here and have a go at those tasks.

I'll be back in a little while with some feedback.

Welcome back.

Let's look at number one first.

We had one eighth, was less than one quarter, which was less than one half.

So you can see that they've all been labelled with their fraction notation.

They've been ordered from smallest to largest and less than is the inequality symbol that's been used between them.

Okay, here's number two, same sort of thing, and I'll reveal it in the same way.

We had one eighth, was less than one third, which was less than one half.

Strange looking half that, isn't it, but it was one half.

Okay to number three.

There's one half which is greater than one third, which is greater than one quarter, which is greater than 100th.

And of course these are images drawn on the screen, but you might be sat there with some actual glasses in front of you with some water in, and I hope that you enjoyed estimating these unit fractions and that you arrange them in the same way.

Okay then, let's move on to a summary.

Today, we thought about the fact that unit fractions are parts of a whole that can be represented with a numerator of one in their fraction notation.

Unit fractions can be compared and ordered like quantities or values using inequalities.

A fraction wall is a useful tool to order unit fractions from smallest to largest or vice versa.

When the whole is the same, the greater the denominator, the smaller the fraction.

When the whole is the same, the smaller the denominator, the greater the fraction.

I hope you've enjoyed today's lesson and that you've learned really well.

I really enjoyed it.

My name is Mr. Taziman.

I hope to see you again soon in another maths video.

Bye for now!.