Lesson video

Hello there.

My name is Mr. Tazzyman.

And today, we're gonna be learning together.

I'm looking forward to it and I hope you are too.

So if you're ready, we can get started.

Here's the outcome for the lesson.

By the end, we want you to be able to say, "I can compare unit fractions by looking at the denominator." Here are some of the keywords.

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

So I'll say, "My turn." Say the word and then you can say it back.

Ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, denominator.

Your turn.

My turn, unit fraction.

Your turn.

All right, now let's see what those words actually mean so we can use them in our thinking today.

The whole is all of a group or number.

A part is a section of the whole.

You can see a bar model on the screen there, which shows that relationship between whole and 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.

This is the outline for today's lesson on comparing unit fractions by looking at the denominator.

We are gonna start by looking at how to make a fraction wall, a really useful tool.

Then we're gonna think about comparing the denominator.

We'll start by thinking about making a fraction wall.

Here are some friends that you're gonna meet along the way.

They're gonna really help us by talking through some of the maths that's there to discuss and by helping us with our thinking, by giving us hints and tips.

Meet Aisha and Jacob.

Okay, you ready to get started? Here we go.

Aisha and Jacob compare diagrams showing fraction representations, notations and names.

You can see there on the left that there's a diagram with the name of a fraction 1/4, then the fraction notation.

And then there's a shape and the shape has one equal part shaded in out of four.

So it represents 1/4.

On the right side, we've got 1/2.

The fraction notation is there and there's another shape.

This shape has been split into two equal parts and one of them has been shaded, so that's 1/2.

What do you notice? Aisha says, "I have noticed that both of these fractions have a numerator of one." Jacob says, "Yes, they have a special name, unit fractions." I have noticed that both of them have different wholes.

We can't compare them like glasses of squash.

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

He starts by cutting six identically sized strips of paper.

Here they are.

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.

What do you notice? Look down that fraction wall.

What's happening as you go from top to bottom? Jacob says, "I notice that the number of equal parts increases by one as you go down the wall." Aisha and Jacob ask each other questions about the fraction wall.

Aisha asks, "Which strip has the fewest equal parts other than the whole?" Jacob replies, "The second strip." What do you notice about it? It also has the greatest size parts.

Which strip has the most equal parts? The bottom strip.

What do you notice about it? It has the smallest sized equal parts.

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

That's a really key piece of learning for us to understand.

Okay, let's check your understanding then.

True or false, when the whole is the same, the fewer the number of equal parts, the bigger each equal part is.

Think carefully about that and decide whether you believe that to be true or false.

Pause the video and I'll be back in a moment to reveal the truth.

Welcome back.

That statement is true.

When the whole is the same, the fewer the number of equal parts, the bigger each equal part is.

At the bottom of the screen, you can see there are two justifications.

These support the fact that that statement is true.

One of them is a good justification, one of them is not such a good justification.

You've got to decide which one you think is the correct one.

I'll read them both to you now.

A, the parts make up the whole so they must be bigger if there are fewer.

B, parts of what make the whole big parts make the whole change.

You've gotta decide, which do you think? Okay, pause the video here and I'll be back in a moment to reveal the answer.

Welcome back.

The first justification was the one that worked.

The parts make up the whole, so they must be bigger if there are fewer.

Aisha decides to label the fraction wall using notation.

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

She labels the top strip with one.

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

two, three, four, five, six.

She's counted the number of equal parts in each row and labelled it at the side.

The whole has been divided into the labelled number of parts for each strip.

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

1\2, 1\2, 1\3, 1\3, 1\3.

1\4, 1\4, 1\4, 1\4.

1/5, 1/5, 1/5, 1/5, 1/5.

And lastly, 1\6, 1\6, 1\6, 1\6, 1\6, and 1\6.

Okay, let's check your understanding of what Aisha has just shown us.

What fraction notation would you label each part of the new strip below the fraction wall here.

So you can see that there's been a new strip put at the bottom.

What fraction notation would you put on each of those equal parts? Pause the video here and I'll be back in a moment to give you the answer.

Welcome back.

What did you think? Well, Aisha says the whole has been divided into seven equal parts.

So each part is 1/7 of the whole.

So the denominator is seven and the numerator is one.

There they are seven sevenths.

It's time for your first practise task now.

It's a practical one.

What I'd like you to do is, use number rods or folded strips of paper.

12 centimetres works really well to create your own fraction wall.

If you're using number rods, you might have to leave out some of the rows.

That's the only thing for this practise task, but I want you to make sure you keep hold of your fraction walls because they could be really precious in later learning.

Okay, pause the video now and have a go at making your fraction wall.

Welcome back.

Let's get some feedback.

How did it go? How were the fraction walls? Did you find it easy or tricky? I hope you've got a really good one sitting in front of you that you'll be able to use in the second part of the lesson.

Jacob says, he made one with number rods.

He started with 1\6.

He had to leave out 1\5 and 1\4 and he put in 1\3, 1\2 and then the whole at the top.

Maybe, you've got something in front of you that looks a little bit like that.

Okay, let's move on.

It's time for the second part of the lesson comparing the denominator.

Aisha and Jacob discuss the fraction wall.

This is really useful.

Now, we can compare unit fractions to see which is greater.

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

And that's the really good thing about the fraction wall is that the whole is always 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? "Sounds like a good idea," says Jacob.

So Aisha has gone through and she has made sure that there's only one equal part from each row remaining.

They're all unit fractions and look at what happens.

It makes it really easy to compare them.

They start to compare unit fractions.

"Let's compare 1/3 and 1/5," says Aisha.

Okay, let's remove the other part so we can compare easily.

Great thinking, Jacob, here we go.

Shall we put them next to each other to make sure? Yes, let's do that.

1/3 is greater than 1/5.

Yes, as long as the whole is the same.

And again, we know it is because these two unit fractions came from the fraction wall that they made earlier.

They choose two more unit fractions to compare.

Let's compare 1/4 and 1/6.

Okay, I think I already know which is greatest.

I think it's 1/4.

I wonder how Jacob has managed to work that out.

Look at the fraction wall.

What do you think? "Let's see," says Aisha.

We'll remove the others and put them next to one another.

There we go.

1/4 is greater than 1/6.

All right, let's check your understanding of that process.

Use your own fraction wall or the one below and compare different unit fractions.

Describe the comparison using the sentence below.

Complete three comparisons.

So there's a stem sentence there for you to use.

It says, one something is greater or smaller than one something.

So you're gonna choose, have a go, pause the video and I'll be back in a little while.

Welcome back.

Did you manage to compare three times? Well, I hope so and I hope that you were able to use your fraction wall to do it.

"Here's one of ours," says Jacob, 1/5 of the whole is smaller than 1/4 of the same whole.

Okay, next part.

Jacob and Aisha use inequality symbols to describe the comparisons they found.

Using the fraction wall, we found that 1/3 is greater than 1/5.

We also found that 1/4 is greater than 1/6.

What do you notice? I have noticed that when comparing unit fractions, the greater the denominator, the smaller the fraction.

Again, a really key piece of learning there.

Aisha and Jacob both have a full glass of squash.

The glasses are identical.

They each drink some.

"You have more leftover than I do," says Aisha.

"Yes, you've had more," says Jacob.

Let's put an inequality symbol in-between our glasses.

Okay, but which one should we use? What do you think? Which inequality symbol would fit in there? I have less squash than you do, so I think it will be less than.

"I agree," says Jacob.

And in it goes.

They look back at their glasses of squash.

The squash left was a part of the whole glass.

So we could describe the relationship between part and whole using a fraction.

So Aisha and Jacob have realised that the amount of squash in their glass could be described as a fraction of the whole glass.

I'll visualise how many parts equal to this one could fill the glass.

She's gonna visualise.

Here we go.

How many parts is that filling the glass? Four equal parts would fill the glass.

One equal part is 1/4.

There it is, 1/4 in fraction notation.

I'll do the same.

I'll visualise filling the glass.

There we go.

How many equal parts is that? Two equal parts fill the glass so the leftover squash is 1/2.

There it is in fraction notation.

So the comparison of leftover squash works with fractions too? Yes, when the whole is the same, the greater the denominator, the smaller the fraction.

They use their learning for fraction notation.

So you can see now that they've got a series of different fractions that they need to compare.

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

"So let's circle the greatest denominator in each statement," says Jacob.

That's being really systematic.

An excellent skill for mathematicians to use.

Three is greater than two.

Four is greater than three and five is greater than four.

Now, I was comparing the denominators there.

That doesn't necessarily mean that the fraction with the greatest denominator will be the biggest.

In fact, we know that it will be the opposite.

"So each of the unit fractions with a circle denominator is the smallest," says Aisha.

There we go.

And there we go.

We've got 1/2 is greater than 1/3.

1/4 is less than 1/3.

1/4 is greater than 1/5.

"Let's put the parts from the fraction wall alongside to check," says Jacob.

Again, a great skill as a mathematician to make sure that you check your answers.

That works.

The piece that's 1/2 is bigger than the piece that's 1/3.

That works too.

The part that's 1/4 is less than the part that's 1/3.

And this one works as well.

The part that's 1/4 is greater than the part that's 1/5.

Let's check that you've understood that.

We've got another true or false here.

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

Is that true or false? Pause the video and I'll be back in a moment with the answer.

Welcome back.

That statement was true.

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

And there are two justifications below you're gonna choose which one you think is the best justification.

Is it A, because the denominator tells us how many wholes there are? Or B, it is the same as when comparing unit fractions, the greater the denominator, the smaller the fraction? Make a choice between those two.

Pause the video and I'll be back in a moment to reveal the answer.

Welcome back.

The best justification was B.

It is the same as when comparing unit fractions, the greater the denominator, the smaller the fraction.

Aisha and Jacob look at more comparisons.

"Hang on," says Aisha.

These aren't in our fraction wall.

How can we compare? "The same way," says Jacob, Let's circle the greatest denominator in each statement.

11 is greater than 10.

11 is greater than nine and 12 is greater than seven.

I see.

The greater the denominator, the smaller the fraction.

So 1/11 is less than 1/10.

1/9 is greater than 1/11.

And 1/12 is greater than 1/7.

"Yes, we got them," says Jacob.

Okay, your turn.

Let's check your understanding.

Write in the correct inequality symbol here, we've got 1/7 and 1/10 and we're comparing them.

Pause the video and have a go.

Welcome back.

Aisha says, "When comparing unit fractions, the greater the denominator, the smaller the fraction." 10 is the greatest denominator in these unit fractions.

1/7 is greater than 1/10.

How did you get on? Is that what you thought? I hope so.

Okay, let's move on to the next part.

Jacob sets a challenge for Aisha using digit cards.

You can see there that we've got some denominators that we don't know yet.

And we've got the digit cards, three, four, five, and six.

All the numerator are one and that means that we're dealing with unit fractions here.

Jacob says, "Arrange these digit cards as denominators to make the statements correct.

You can only use each digit card once." Well, I know that the greater the denominator, the smaller the fraction.

So I'll put the greater digits into smaller fractions.

She puts 1/5 on the bottom statement in the less than side.

And she puts 1/6 in the top statement in the less than side as well.

Then I'll put the lesser digits in as the missing denominators and she does that.

So she's got 1/4 is more than 1/6.

And 1/5 is less than 1/3.

Aisha challenges Jacob back.

There are other ways to complete this.

Can you find three other ways? I'll start with yours and then move the cards around.

First, I'll swap the greatest denominators.

Both those denominators are still greater so it works.

Next, I'll swap over four and three as denominators.

Another combination that works.

You found two other arrangements, well done.

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

For number one, I'd like you to write the correct inequality symbol between the two unit fractions into the boxes.

The parts from the fraction wall have been included to help.

If you wanted to use your own fraction wall as well, you could.

That would be a great thing to do because it's a very useful tool and worth familiarising yourself with it.

For number two, there aren't any fraction wall parts, but again, you can still use your fraction wall.

You've got to write the correct inequality symbol between the two unit fractions into the boxes below.

Where possible, as I said, use your own fraction wall to help.

Notice it says, where possible.

I wonder why that might be.

I'm sure you'll discover.

For number three, you've got to use the digit cards below to complete the inequalities.

You can only use each digit card once.

How many different ways can you complete this? Who can find the most ways? So similar to the challenge that was set by Aisha for Jacob, but this time we've got three inequality statements and the digits at the bottom are 2, 3, 4, 5, 6, and 7.

Can you sort them so that they are in an arrangement that works.

In how many different ways can you do it? Okay, pause the video here and I'll be back in a little while for some feedback.

Enjoy.

Welcome back.

Let's do some marking.

Be ready.

For the first one, we had 1/2 is greater than 1/4.

For the second one, we had 1/5 is less than 1/3.

And for the last one, we had 1/4 is less than 1/3.

Pause the video here so you can mark those carefully.

Here's number two.

For A, we had 1/4 is less than 1/3, 1/4 is less than 1/2.

1/5 is less than 1/3.

For B, we had 1/6 is less than 1/3, 1/3 is more than 1/5.

And 1/4 is more than 1/7.

And that bottom one B might have been the first one where you found it tricky because you couldn't use a fraction wall with it.

Unless of course, you were somebody who created a fraction wall that featured sevenths as well.

Let's look at C.

1/9 was greater than 1/10.

1/11 is greater than 1/12.

And 1/11 is less than 1/7.

Pause the video here so you can catch up with marking should you need to.

Okay, number three.

Well, there are lots of ways to solve this.

Here's one of the ways that Aisha did it.

1/2 is greater than 1/3.

1/5 is less than 1/4.

And 1/6 is greater than 1/7.

I wonder which of you managed to find the most ways.

"Here's a different way," says Jacob.

1/3 is greater than 1/4.

1/7 is less than 1/2 and 1/5 is greater than 1/6.

Okay, let's summarise all of the learning that we've enjoyed today.

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 like quantities or values using inequalities.

A fraction wall is a useful tool to complete comparisons of unit fractions.

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.

Really key piece of learning at the bottom there.

One that you're gonna need to use all the way through school.

Okay, I've really enjoyed learning with you today and I hope you did too.

I also hope that I'll be able to see you again soon for another maths lesson.

My name is Mr. Tazzyman.

Goodbye for now.