Lesson video

Hello there.

My name is Mr. Goldie, and welcome to today's maths lesson.

And here is our learning outcome.

I can use my knowledge of unit fractions to find one whole.

And here are the keywords for today's lesson.

I'm going to say each keyword.

Can you repeat it back? Couple of tricky ones today.

So the first keyword is denominator.

The second keyword is numerator.

And the last keyword is whole.

That's whole with a W, not without a W.

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

So 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.

And the whole is all of a group or number.

Here's our lesson outline.

So in the first part of the lesson, we're going to be looking at fractions equal to one whole.

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

Let's get started.

In this lesson, you will meet Sofia and Jacob.

Now lots of people find fractions a bit tricky.

Sofia and Jacob are here to help you, and so are Sofia's chickens.

Sofia has three chickens called Charly, Chilly and Chocolate.

Here are Sofia's three chickens.

"I collect the eggs that they have laid and put them in an egg box." says Sofia.

Here's the egg box that Sofia collects the eggs in.

"On Monday, Sofia collects three eggs." says Jacob, one, two, three.

"Three-sixths of the egg box contains eggs." says Sofia.

The egg box is divided into six equal parts.

Each part of the egg box is equal to 1/6 of the whole.

3/6 of the egg box contains eggs.

"That's the same as being half full!" says Jacob.

Well spotted, Jacob.

Can you see there that half the egg box is full? Three parts have got eggs in.

Three parts are still empty.

3/6 of the egg box contains eggs.

3/6 is equal to half.

On Wednesday, Sofia collects the eggs, so one egg, two, three, four, five.

5/6 of the egg box contains eggs.

Because there are six equal parts, each part is equal to 1/6 of the whole.

So five parts contain eggs.

5/6 of the egg box contains eggs.

"The egg box is nearly full!" says Jacob.

5/6 of the egg box contains eggs.

The egg box is almost full.

On Friday, Sofia collects the eggs, one, two, three, four, five, six.

"What fraction of the egg box contains eggs?" says Sofia.

6/6 of the egg box contains eggs, so each part, remember, represents 1/6 of the whole.

All of them have an egg in.

6/6 of the egg box contains eggs.

Jacob says, "The whole egg box is full." 6/6 of the egg box contains eggs.

6/6 is equal to one whole.

The following week Sofia fills a different egg box.

"Over several days, I fill this egg box." she says.

There are 12 different parts to this egg box.

So each part represents 1/12 of the whole.

Each egg represents 1/12 of the whole egg box.

"I'm going to count as the eggs appear." says Jacob.

Here's a number line starting with zero.

Jacob's going to count.

If you would like to count along with him, please do that.

1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12.

When we have 12/12, the whole egg box is full.

12/12 is equal to one whole.

Sofia thinks about fractions equal to one whole.

When the numerator and the denominator are the same, the fraction is equal to one whole.

Here's a pizza split into five parts.

5/5 is equal to one whole.

If you have 5/5 of the pizza, you have one whole pizza.

Here's a pack of pencils.

There are 10 pencils in the pack.

If you have all the pencils in the pack, you have 10/10.

10/10 is equal to one whole.

And here are some eggs in an egg box.

This time there are 15 eggs altogether.

If all the eggs are in that egg box, we have one whole.

15/15 is equal to one whole.

Sofia has said, "When the numerator and the denominator are the same, the fraction is equal to one whole." 5/5, 10/10 and 15/15 are all equal to one whole.

Now here are some fractions for you to have a think about.

Which fractions are equivalent to one whole? An equivalent just means they're equal to one whole.

There are three fractions.

Which of those fractions are equal to one whole? And is there a fraction there which is not equal to one whole? But think about what Sofia has just told you.

Pause the video and see if you can work out which fractions are equal to one whole.

And welcome back.

What do you think? Are they all equal to one whole? Are some of them not equal to one whole? Let's have a think about what Sofia told us earlier on.

She said "When the numerator and the denominator are the same, the fraction is equal to one whole." Let's have a look at that first one.

So we've got there 4/4.

there's a whole divided into four equal parts, and we've got all of them.

4/4 is equal to one whole.

Let's look at that next fraction.

This time we've got 7/7.

Is it equal to one whole? Here's a whole divided into seven equal parts and all of them are shaded in.

7/7 is equal to one whole.

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

Seven is the same as seven.

Let's look at that last fraction.

We've got 2/3.

Is it equal to one whole? No, it is not.

So then we have a whole divided into three equal parts, but only two of them are shaded.

The whole is not shaded.

2/3 is not equal to one whole.

Well done If you spotted that 4/4 and 7/7 are both equal to one whole.

Let's move on to task A.

So in task A, you're going to be looking for fractions that are equal to one whole, and you're going to be sorting the fractions.

There are two sorting circles.

You put the fraction in one if it is equal to one whole, and you put the fraction in the other if it is not equal to one whole.

And if you look carefully, you've got 12 different fractions to sort through and have a look at.

And if you finish all those ones, you can always have a go trying to come up with some of your own fractions as well.

Just to get you started, Sofia and Jacob are both going to say something.

Sofia starts off by saying, "9/9 is equal to one whole because the numerator and denominator are the same." So 9/9 would go in the sorting circle here.

The fraction is equal to one whole.

Jacob says, "5/6 is not equal to one whole." Because the numerator and the denominator are different numbers, the fraction is not equal to one whole.

So 5/6 will go in this sorting circle here.

The fraction is not equal to one whole.

So have a go trying to sort those fractions.

Think carefully about whether they are equal to one whole or not.

And remember if you finish those ones, you can always have a go trying to write some of your own.

Pause the video and have a go at task A.

And welcome back.

How did you get on? Did you manage to sort all the fractions there? Did you come up with some of your own as well? Let's take a look to see how you got on.

So here are the answers for the fractions you were given.

So all of these fractions are equal to one whole because the numerator and the denominator are both the same number.

So 10/10 is equal to one whole.

So is 6/6.

So is 12/12.

So are 3/3.

So are 8/8.

You could have also have had 11/11.

You could have also have had 15/15.

You could also have had 100/100.

They're all equal to one whole.

On the other side we've got the fractions that are not equal to one whole.

So 6/7 is not equal to one whole.

11/15 is not equal to one whole.

10/12 is not equal to one whole and neither are 11/12 or 3/4.

And any fraction you put in that circle, as long as the numerator and the denominator are different numbers, that fraction is not going to be equal to one whole.

So very well done if you sorted those fractions.

And well, I don't know if you came up with some of your own as well.

Let's move on to part two of the lesson.

So part two of the lesson is comparing fractions.

Jacob wants to compare fractions.

"I'm using the symbols greater than, less than and equals to compare." So this symbol here means less than.

This symbol here means greater than.

And this symbol here means is equal to.

We use that if both sides of the equation are equal to each other.

Jacob starts comparing fractions with one whole.

"I'm using greater than, less than and equals to compare the fractions with one whole." Which symbol should Jacob use? So 1 and 7/8, is 1 greater than 7/8, is 1 less than 7/8 or is 1 equal to 7/8? So start off with a whole and divide it into eight equal parts.

So 1 is equal to 8/8.

When the denominator and the numerator are the same number, that fraction is equal to one whole.

Let's have a think about what 7/8 would look like.

Here's 7/8.

8/8 is greater than 7/8.

And if 8/8 is equal to one whole, then 1 must be greater than 7/8.

One whole is greater than 7/8.

If the numerator is less than the denominator, the fraction is less than one whole.

Jacob compares a fraction with one whole.

"Which symbol should I use?" says Jacob.

This time he's got 1 and 5/5.

Let's think about one whole and divide it into five equal parts.

So each part is 1/5.

1 is equal to 5/5.

One whole is equal to 5/5.

Remember when the numerator and the denominator are the same number, the fraction is equal to one whole.

Jacob compares a fraction with one whole.

"Which symbol should I use?" says Jacob.

This time he got 6/7 and 1.

And again, let's start off by looking at one whole divided into seven equal parts.

There we have one divided into seven equal parts.

So each of those represent 1/7.

And 1 is equal to 7/7.

Here's 6/7.

Is 6/7 less than 7/7? Is it more than 7/7? It's less than 7/7.

So 6/7 is less than 7/7.

And if 1 is equal to 7/7, then 6/7 must be less than 1.

6/7 is less than one whole.

If the numerator is less than the denominator, the fraction is less than one whole.

The numerator 6 is less than the denominator 7.

So the fraction must be less than one whole.

Here's one for you to try on your own.

Compare this fraction with one whole.

Which symbol should you use? You've got 11/11 and 1.

What is the missing symbol? Pause the video and see if you can work out what the missing symbol is.

And welcome back.

How did you get on? Did you manage to work out the missing symbol? Let's take a look, see if you've got it right.

So first of all, let's start with 1 and divide it into 11 equal parts.

Here's 1 divided into 11 equal parts.

And 11/11 is equal to 1.

11/11 is equal to one whole.

Remember when the numerator and the denominator are both the same number, the fraction is equal to one whole.

In this case here, the numerator and the denominator were both 11.

They were both the same number.

Very well done if you used the correct symbol.

Jacob and Sofia are comparing fractions.

"Which is larger, 5/5 or 6/6?" asks Jacob.

"Let's work it out using the pizza we have for lunch!" says Sofia.

So here is Jacob's Pizza.

So Jacob cuts his pizza into five equal parts.

Quite tricky to cut a pizza into five equal parts but he's done a brilliant job there, hasn't he? Sofia cuts her pizza into six equal parts.

Sofia is a bit luckier because six is an even number.

So Sofia can cut the pizza in half first of all.

So Sofia has cut her pizza into six equal parts.

Which is larger, 5/5 or 6/6? Who has more pizza? "We both still have a whole pizza." says Jacob.

When the numerator and the denominator are the same, the fraction is equal to one whole.

5/5 is equal to 6/6.

They're both equal to one whole, so they must be equal to each other.

Jacob is looking for the missing numbers.

What numbers would complete these equations? So we've got there a set number of ninths equals one.

What's the missing number? So here are 9/9 as one whole divided into 9/9.

And here is one whole which is not divided up at all.

How many ninths are equal to one? 9/9 is equal to one whole.

So remember when the numerator and the denominator are the same, the fraction's equal to one whole.

Let's take a look at another one.

So 6/6 is equal to 10 what? What's the missing denominator? Let's start off by looking at 6/6.

10 of what would be equal? Well, 10/10 would be equal to 6/6.

6/6 is equal to 10/10.

So the missing denominator is 10.

Let's look at one more.

We've got this time, 4/4 is equal to how many thirteenths? Let's have a look at trying to represent those two fractions.

So here we've got 4/4 and we've got one whole divided into 13 equal parts.

How many of them need to be shaded to make it equivalent to, to make it equal to 4/4? 4/4 is equal to 13/13.

So remember, when the numerator and the denominator are the same, the fraction's equal to one whole.

And if you've got two fractions where the numerator and the denominators are the same, the fractions are equal to each other.

They're both equal to one whole.

They're equal to each other as well.

What is the missing number? What number would complete this equation? 15 somethings are equal to 7/7.

What is the missing denominator? Can you work it out? Pause the video and see if you can work out what the missing denominator is.

And welcome back.

Did you manage to work out the missing denominator? Let's have a look, see whether you got it right.

So let's think about a whole and how many parts would you have to divide it into so it is equal to 7/7.

Well here's 7/7.

There's a whole divided into seven equal parts and we've got all seven of them shaded in.

7/7 is equal to 15/15.

15/15 is equal to 7/7.

Both fractions are equal to one whole, so they are equal to each other.

Very well done if you worked out the missing denominator.

And let's move on to task B.

So use the symbols greater than, less than and equals to compare these fractions with one whole.

So are the fractions equal to one whole.

Are they greater than one whole? Are they less than one whole? So think carefully about which symbols you need to use.

Here's part two of task B.

Find the missing numerators and denominators.

So most of those, they're either equal to one whole or equal to another fraction.

So think carefully about what the missing numerator or denominator will be.

And remember, if the denominator and the numerator are the same, the fraction's equal to one whole.

If the numerator is less than the denominator, the fraction is less than one whole.

And here is part three of task B.

Find three different ways to make each of these correct.

So in each of these there are quite a few different answers, but can you come with three different ways to make them correct? So in a, 1 is greater than how many fifths? Can you think of three different ways to make that correct? B, how many tenths are less than one whole? So think carefully about three different answers that you could use to make these correct.

Pause the video and have a go at task B.

And welcome back.

How did you get on? Did you get to part three of task B? Well done if you did.

Let's take a look at those answers.

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

So a, we've got there 1 is equal to 3/3.

And c, 7/7 is equal to 1 whole.

So very well done if you completed part one.

Let's move on to part two and look at some of the answers.

So you had to find the missing numerators and denominators in part two.

So we've got there a, 5/5 is equal to 1 whole.

B, 1 whole is equal to 12/12.

C, 4/4 is equal to 11/11.

And well done if you had a go at e as well 'cause e was a bit tricky.

E, we've got 10/10 is equal to 20/20, which is equal to 30/30, which is also equal to 40/40.

All those fractions are equal to each other and they're also all equal to one whole as well.

So well done if you completed part two of task B.

Here are some possible answers for part three of task B.

So a, we've got 1 is greater than.

We could have 4/5.

You could have 1 is greater than 3/5.

You could have 1 is greater than 2/5.

5/5 is equal to one whole.

The numerator has to be four or less to make the fraction less than one whole.

So while I don't know if you came up with three different answers for a, let's have a look at 3b.

You could have had 9/10 is less than 1 whole, 7/10 is less than 1, and 5/10 is less than 1.

All those fractions are less than 1.

10/10 is equal to one whole.

So the numerator here has to be 9 or less.

To make the fraction less than one whole, the numerator has to be 9 or less.

Well, I don't know if you completed b.

And let's take a look at c.

So again, here are some possible answers.

Your answers may be different.

So you could have had 4/7 is less than one whole.

4/9 is less than one whole.

4/11 is less than one whole.

There are lots and lots of different answers to this one.

Now, Sofia says, "4/4 is equal to one whole." So the denominator has to be 5 or more.

The fraction is less than one whole.

So the denominator has to be larger than the numerator.

If the denominator is larger than the numerator, the fraction is less than one whole.

So you could have gone all the way up to 4/100 is less than one whole.

So very well done if you got onto part three of task B and you managed to complete some of those questions, and excellent work in today's lesson.

And hopefully you're feeling much more confident about when a fraction is equal to one, and when it is less than one.

Very good work in today's lesson.

And let's move on to our lesson summary.

So when the numerator and denominator have the same value, the fraction is equal to one whole.

If the numerator is less than the denominator, the fraction is less than one whole.

Fractions that have numerators and denominators with the same values are also equal to each other.

So 5/5 is equal to 10/10.