Lesson video

Hello there, my name is Mr. Goldie.

Welcome to today's math lesson.

And here is the learning outcome for today's lesson.

I can compare non-unit fractions, including those equal to one.

And here are the keywords.

I'm going to say the keyword.

Can you repeat it back? They're both a little bit tricky, so get ready.

The first keyword is denominator.

And the next keyword is numerator.

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

A denominator is the bottom number written in a fraction.

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

A numerator is the top number written in a fraction.

It shows how many parts we have.

Let's have a look at our lesson outline.

So in the first part of the lesson we're going to be comparing and ordering fractions.

And in the second part of the lesson we're going to be solving problems by comparing fractions.

Let's get started.

In this lesson you'll meet Sophia and Jacob, who will be helping you with your maths and asking you some difficult questions as well.

And I think Sophia has something to tell you.

Sophia, what did you want to say? I love strawberry milkshake.

Strawberry milkshake will feature in this lesson as will pandas.

Sophia is finding fractions a little bit tricky.

"I'm finding it hard to remember everything," she says.

"That's okay," says Jacob, "I'm here to help." "Let's explore fractions using milkshakes." "I do like milkshakes," says Sophia.

Sometimes when you find something a little bit tricky, it's nice to relate it to something that you enjoy or like.

Jacob starts with fractions equal to one.

"Can you complete each fraction to make it equal to one?" says Jacob.

So we've got a certain number of fives is equal to one.

And nine some things are equal to one.

So we've got a missing numerator and a missing denominator.

"When the numerator and the denominator are the same, the fraction is equal to one," says Sophia.

So five fifths is equal to one whole.

Here's five fifths represented using strawberry milkshake.

The milkshake is divided into five equal parts and each one is full of milkshake.

Five fifths is equal to one.

"Nine ninths is equal to one whole," says Sophia.

Here's another strawberry milkshake.

This time divided into nine equal parts.

Each ninth contains strawberry milkshake.

Nine ninths is equal to one.

So with the numerator and the denominator are the same, the fraction is equal to one.

Now it's your turn to have a go.

Complete the fraction to make it equal to one.

Seven whats are equal to one.

What's the missing denominator? Pause the video, see if you can work out the answer.

And welcome back.

Did you manage to find the answer? Let's take a look to see whether you got it right.

Sophia says, "When the numerator and denominator are the same, that fraction is equal to one.

Seven sevenths is equal to one whole.

The milkshake has been divided into seven equal parts.

There is milkshake in every part.

Seven sevenths is equal to one the milkshake is full.

It is a whole milkshake.

Very well done if you worked out the missing denominator.

Jacob uses fractions with different numerators.

"Would you rather have two fifths or four fifths of a milkshake?" he asks.

Sophia says, "Oh, that's easy.

The denominator is the same.

So the parts are the same size." Here's two fifths of a milkshake.

A milkshake divided into five equal parts and two of those parts are left.

Here's a milkshake divided into five equal parts.

Four of them are left, four fifths is greater than two fifths.

So I would rather have four fifths of a milkshake.

Four fifths is greater than two fifths.

"Would you rather have seven ninths or four ninths of a milkshake?" asks Jacob.

"That's a bit trickier to imagine," says Sophia, "But the denominator is still the same for both fractions." So there's a milkshake divided into nine equal parts, seven parts left, and there's a milkshake divided into nine equal parts and four parts left.

"Seven ninths is greater than four ninths, so I would rather have seven ninths of a milkshake," says Sophia.

Seven ninths is greater than four ninths.

So Jacob uses two fractions with different numerators.

Would Sophia rather have three sevenths or four sevenths of a milkshake? What do you think? The denominator is still the same for both fractions.

Which do you think Sophia would rather have? Three sevenths of a milkshake or four sevenths of a milkshake? Pause the video and see if you can work out the answer.

And welcome back.

Did you think she would rather have three sevenths? Did you think she would rather have four sevenths of a milkshake? Let's take a look at the answer.

So here are two milkshakes, each divided into seven equal parts.

In that first milkshake, we've got three parts left, three sevenths, in our second milkshake four parts left, four sevenths.

"Four sevenths is greater than three sevenths so I would rather have four sevenths of a milkshake," says Sophia.

Four sevenths is greater than three sevenths.

The denominators are the same, but the numerators are different.

So the fraction with the greater numerator is the larger fraction.

Jacob uses fractions with different denominators.

"Would you rather have five ninths or five sevenths of a milkshake?" asks Jacob? "This is what I find tricky," says Sophia, "I'm not sure which fraction is greater." Let's use some images of milkshakes to help us work out the answer.

So here is a milkshake divided into nine equal parts, and a milkshake divided into seven equal parts.

The numerators are the same, is one ninth or one seventh larger? "One seventh is larger in size as the whole is divided into fewer parts," says Sophia, "I'd rather have five sevenths of a milkshake.

Five ninths is less than five sevenths." One seventh is larger than one ninth.

So five sevenths is definitely larger than five ninths.

Five ninths is less than five sevenths.

So again, Jacob uses fractions with different denominators.

"Would you rather have seven ninths or seven elevenths of a milkshake?" asks Jacob So here's a milkshake divided into nine equal parts and here is a milkshake divided into 11 equal parts.

Sophia says, The numerators are the same.

One ninth is larger than one eleventh." The milkshake divided into nine parts has been divided into fewer parts than the milkshake divided into 11 parts.

I'd rather have seven ninths of a milkshake.

Seven elevenths is less than seven ninths.

Let's take a look at seven ninths.

And we clearly see that seven elevenths is less than seven ninths.

Jacob gives Sophia a challenge.

Can you put these fractions in order? Nine elevenths, nine tenths and eight elevenths? "This is really tricky, says Sophia, "I need to compare two fractions at a time." You may have spotted that all the fractions do not have the same denominator and they do not all have the same numerator, but two of them have the same numerator and two of them have the same denominator.

Sophia says, "Eight elevenths and nine elevenths have the same denominator.

Eight elevenths is smaller." So, here is eight elevenths represented through milkshake.

And here is nine elevenths represented through a milkshake.

Eight elevenths is less than nine elevenths.

The denominators are both the same.

So the fraction with a smaller numerator will be the smaller fraction.

Sophia says, "Nine tenths and nine elevenths have the same numerator.

Nine elevenths is smaller." Let's look at what nine-tenths of a milkshake would look like.

Here's nine-tenths.

Now nine-tenths and nine elevenths both have the same numerator, but the denominators are different.

When a milkshake is divided into 11 equal parts, there are more parts and when it is divided into 10 equal parts, so nine-tenths will be larger than nine elevenths.

Nine elevenths is less than nine-tenths.

"Nine-tenths is the greatest fraction," says Sophia, So I'd rather have nine-tenths of a milkshake." Jacob gives you a challenge.

Can you put these fractions in order? Six sevenths, five eighths and five sevenths.

"Compare two fractions at a time," says Sophia.

So look at two fractions with the same numerator, and look at two fractions with the same denominator.

And think carefully about which fraction is the smallest and which fraction is the largest.

If you want to draw pictures to help you work out the answer, you can do.

Pause the video and see if you can put those fractions in order, starting with the smallest fraction.

And welcome back.

Did you manage to order those three fractions? Let's take a look to see whether you got it in the right order.

So Sophia says, "Five sevenths and five eighths have the same numerator.

Five eighths is smaller." Let's represent our fractions again using milkshake.

But here is five eighths of a milkshake.

Here is five sevenths of a milkshake.

Five eighths is less than five sevenths.

Five sevenths and six sevenths have the same denominator.

Five sevenths is smaller.

So here's six sevenths.

Five sevenths is smaller than six sevenths, so you should have ordered the fractions starting with five eighths, which is smaller than five sevenths, they both have the same numerator, the denominators are different.

And then five sevenths is smaller than six sevenths, they have the same denominator, but the numerators are different.

Very well done if you manage to get those three fractions in the right order.

Let's move on to task A.

So in task A, you're going to compare the fractions using greater than less than or equals.

Shade the milkshakes to help you.

If you don't like strawberry milkshake, you can make a different flavour of milkshake instead.

So A, you are comparing three eighths and five eighths.

The denominators are the same, the numerators are different.

B.

11 elevenths or three thirds is one greater than the other, less than the other, or are equal? And then C, we've got 10 elevenths and 10 thirteenths.

Which fraction is larger or are they equal? And this time the are the numerators are the same, but the denominators are different.

Here's task A part two.

So order the fractions, shade the milkshakes to help you.

So for a, there are three fractions which you've got to put in the right order.

You've got three quarters, four quarters, and three fifths.

So which fraction is the smallest? Start with the smallest fraction and working your way up to the largest fraction.

So compare those numerators and compare those denominators and try to get those fractions into the correct order.

And then part three of task A, use each digit card once to make these correct.

So you've got the digit cards there, one to nine.

And there are some denominators missing, and some numerators missing.

You can use each card once to make all of those correct.

And the first one we've got a certain number of ninths is less than nine somethings which is equal to, something fifths, which is equal to one.

For some of those there's only one card you can use to make it correct.

For some of them there's more than one card you've got to use.

So I would suggest starting with the cards that you have to use first and then see what cards you've got left to make those other ones correct.

So pause the video and have a go at task A.

And welcome back.

How did you get on? Did you get all the way to part three of task A? Let's take a look to see whether you got the right answers.

So here are the answers for part one of task A.

So A, three eighths is less than five eighths.

B, 11 elevenths is equal to three thirds.

And C, 10 elevenths is greater than 10 thirteenths.

So while done if have you got those correct.

Here's part two of task A.

So for A, three fifths is the smallest fraction and that is less than three quarters, which is less than four quarters.

Four quarters of course is equal to one.

And then for B, four elevenths is less than five elevenths, which is less than five nights.

Well done if you've got part two correct as well.

Now finally, let's move on to part three of task A.

Now here is one possible solution using those nine numbers, you may have come up with a solution that is slightly different.

So you may have put the numbers in slightly different places, but you may have done, six ninths is less than nine ninths, which is equal to five fifths, which is equal to one.

And then one is equal to three thirds, which is equal to two halves, which is greater than one half.

And then finally one is greater than four sevenths, which is greater than three sevenths, which is greater than three eighths.

So very well done if you got onto part three of task A and managed to find a solution to that as well.

Excellent work.

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

Part two of the lesson is solving problems by comparing fractions.

And I must warn you there are pandas.

Some pandas have climbed a tree.

Here are some pandas in a tree.

Priya has climbed six sevenths of the tree.

Paul has climbed three elevenths of the tree.

Polly has climbed five ninths of the tree.

Ping has climbed five elevenths of the tree and Pedro has climbed six ninths of the tree.

"Let's work out which panda is which," says Jacob.

Let's just take a look at the fractions.

So here are the five fractions and we've gotta work out which panda is at the correct height.

Sophia represents each fraction, the tree represents one whole.

So here's the tree, the tree represents one.

Seven sevenths is equal to one.

Priya has climbed six sevenths of the tree.

Nine ninths is equal to one.

Polly has climbed five ninths of the tree.

Pedro has climbed six ninths of the tree.

11 elevenths is equal to one.

Paul has climbed three elevenths of the tree.

And Priya has climbed five elevenths of the tree.

We can use these visuals to help us compare.

So Jacob is still keen to work out which panda is which.

"Let's start with the smallest number.

I think it's three elevenths," says Sophia.

Why do you think that's Sophia? Three elevenths is split into the most parts and has the smallest numerator.

Three elevenths has the largest denominator and it also has the smallest numerator.

So Sophia thinks it's the smallest fraction.

Here is three elevenths.

Also when the denominators are the same, the smaller the numerator, the smaller the fraction.

So Sophia says, "Paul has climbed three elevenths of the tree." So this is Paul.

"Which panda comes next?" asks Jacob.

Let's start with the next smallest number.

I think it's five elevenths.

There is five elevenths.

Why do you think that Sophia? Five elevenths is split into the most parts.

11 is the largest denominator.

Here's five elevenths, five elevenths, and five ninths have the smallest numerators.

But five elevenths is smaller, so five elevenths is going to be smaller than five ninths.

Where the numerators are the same, the greater the denominator, the smaller the fraction.

So five ninths and five elevenths both have the same numerator, five.

But the denominators are different.

11 is a larger number than nine.

So elevenths are going to be smaller parts than ninths.

So Ping has climbed five elevenths of the tree.

So this here must be Ping.

"Which number comes next?" asks Jacob.

Five ninths comes next, says Sophia.

Sophia's getting very confident with comparing her fractions, isn't she? One ninths are smaller than one sevenths because the whole is divided into more parts.

So one ninth is smaller than one seventh.

Five ninths is less than six ninths.

The denominator's the same, but the numerators are different.

Six ninths is going to be larger than five ninths.

When the denominators are the same, the smaller the numerator, the smaller the fraction.

So Sophia says, "Polly has climbed five ninths of the tree." So this here must be Polly.

Work out the positions of the last two pandas.

So there's still two pandas in the tree, which have not yet been named.

Can you work out their names? So Priya has climbed six sevenths of the tree.

Here's six sevenths.

Pedro has climbed six ninths of the tree.

Here's six ninths, but which panda is Priya? Which panda is Pedro, can you work it out? Pause the video and see if you can work out the answer.

And welcome back.

Did you work out which panda was Pedro? Did you work out which panda was Priya? Let's take a look to see whether you got it right.

So Sophia says, "When the numerators are the same, the smaller the denominator, the greater the fraction." So six sevenths and six ninths both have six as a numerator, the seven is a smaller number than nine.

So six sevenths must be the greater fraction.

Six sevenths is greater than six ninths.

So Priya is higher than Pedro.

A panda who has climbed six sevenths of the tree is going to be higher up the tree than a panda which has climbed six ninths of the tree.

So this must be Pedro here, and Priya must be right at the top.

Very well done if you worked out the positions of those last two pandas, excellent work.

And let's move on to task B.

So in task B you're going to be looking at a similar problem.

Some pandas have climbed a tree.

This time there are six pandas in the tree.

So Peter has joined them in the tree.

Priya has climbed four-fifths of the tree.

Paul has climbed one eighth of the tree.

Polly has climbed five fifths of the tree.

Ping has climbed three eighths of the tree.

Pedro has climbed four sevenths of the tree.

Peter has climbed three sevenths of the tree.

Can you work out which panda is which? Now to help you, here are some fractions which you can shade in to help you compare the height of the different pandas and work out which fractions are larger than others, that might prove to be really, really helpful.

Don't forget to look carefully those denominators and numerators and work out which fractions are greater.

Pause the video and see if you can solve that problem.

And welcome back.

Did you manage to solve the whole problem? Did you work out the name of each of the pandas? Very well done if you did.

Let's take a look to see whether you got them all right.

So here is how you should have completed the fractions for comparing.

So Priya had climbed four fifths of the tree.

So imagine divided that tree into five equal parts.

And Priya had climbed four of those parts.

Paul had only climbed one eighth of the tree.

So imagine divided that tree into eight equal parts.

Paul had only climbed one of them.

Polly had climbed five fifths of the tree.

So five fifths is equal to one whole, so you should be able to work out quite easily where Polly was on the tree.

So here are the answers.

So Paul is nearest the bottom of the tree.

One eighth is the smallest fraction, and then Ping was next in the tree.

And then Peter was just above Ping and Pedro was just above Peter.

Priya, who was top of the last tree, was second from the top this time.

And Polly has reached the top of the tree.

So Polly climbed the whole height of the tree and got to the very, very top.

Very well done if you've got some of those patterns correct and if you've got every single one in the correct place, give yourself a pat on the back.

That is excellent work.

'Cause that was quite a tricky problem.

And very well done for working so hard in today's lesson and thinking very carefully about the numerators and the denominators and comparing different fractions and seeing which ones are smaller and which ones are larger.

I'm sure your brains are aching now after all of that thinking.

Excellent work today.

Very well done.

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

So to compare non--unit fractions, the whole must be the same for each fraction.

When the numerators are the same, the greater the denominator, the smaller the fraction.

When the denominator are the same, the greater the numerator, the greater the fraction.