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 non-unit fractions with the same denominator.

Let's take a look at those keywords.

Quite tricky keywords today.

I'm going to say each keyword, can you repeat the keyword back? So the first keyword is denominator.

And the second 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.

And here's our lesson outline.

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

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

Let's get started.

In this lesson, you will meet Sofia and Jacob, who are going to be helping you with your maths today, with special guest appearances from Laura.

So Laura's going to pop up from time to time as well.

Jacob and Sofia are talking about their journey to school.

"I walk 7/10 of a kilometre," says Jacob.

"I walk 6/10 of a kilometre," says Sofia.

Who walks further? What do you think? Let's compare the distances.

So Jacob says, "I walk 7/10 of a kilometre." Here's Jacob walking to school, and he's walked 7/10 of a kilometre.

And the number line there starts on 0 kilometres and ends on 1 kilometre.

And Sofia says, "I walk 6/10 of a kilometre." So it's the same number line, and we're going to look at Sofia's journey to school.

So Sofia walks 6/10 of a kilometre.

Who walks further? "I walk further," says Jacob.

"7/10 of a kilometre is greater than 6/10 of a kilometre." Laura wants to see if she walks further than Jacob.

"I walk 5/10 of a mile to get to school," says Laura.

So there is Laura's journey, starts on 0 miles, and she walks 5/10 of a mile.

So her number line starts on 0 miles and ends on 1 mile.

"Sorry, Laura.

I don't know how we could compare that," says Jacob.

"Your measurement is in miles," says Sofia, "and ours are in kilometres.

To compare, the whole must be the same." Because Laura knows her journey to school in miles and Sofia's journey to school is in kilometres, it's very difficult to compare them, so Sofia is saying we can't compare them at the moment.

"You could change your measurement into kilometres, but I don't know how to do that yet," says Sofia.

So it is possible to compare them, but at the moment it's too tricky because the whole is different.

Laura's measurement is in miles, Sofia's and Jacob's measurement is in kilometres.

At lunchtime, Jacob and Sofia have pizza.

Here's a pizza.

"I ate 3/8 of a whole pizza." "I ate 5/8 of a whole pizza," says Sofia.

Who ate more pizza? What do you think? Let's use a number line to help us compare.

So Jacob said, "I ate 3/8 of a whole pizza." So here's a number line, starting on 0 and ending on 1.

And the interval marks on the number line show eighths, 1/8, 2/8, 3/8, all the way up to 8/8, which is equal to 1.

Jacob eats 3/8 of a pizza.

"I ate 5/8 of a whole pizza." So there's another number line, also divided up into eight equal parts, so each one of those represents 1/8.

Sofia ate 5/8 of a pizza.

Sofia ate more pizza.

"5/8 is greater than 3/8," says Sofia.

Did Laura eat more pizza than Sofia? "I ate 4/8 of this pizza," says Laura.

There's the pizza that Laura ate 4/8 of.

"I ate 5/8 of this pizza," says Sofia.

Now, who ate more pizza? What do you think? Pause the video and see if you can work out who ate more pizza.

And welcome back.

What do you think? Do you think Laura ate more pizza? Do you think Sofia ate more pizza? Or is there a different answer? And we know that Sofia ate 5/8, so she took 5 slices of pizza.

We know that Laura took 4/8, she ate 4 slices of her pizza.

Jacob says, "The pizzas are different shapes.

To compare, the whole must be the same.

' Now, just by looking at those pizzas, you can't really work out who ate more 'cause it looks like Laura's slices are larger than Sofia's slices, so how can you compare? So when we are comparing fractions, the whole must be the same.

Jacob and Sofia think about how to tell which fraction is greater.

"When we compare fractions with the same denominator, the greater the numerator, the greater the fraction." Sofia says, "Let's compare 4/5 and 3/5." So 4/5 and 3/5 both have the same denominator, 5.

So here is a representation of 4/5, and here is a representation of 3/5.

And the denominator is the same in both of those fractions, and the whole is the same size as well.

So which is larger? Our 4/5 is greater than 3/5.

We can also write that with a greater than symbol as well.

4/5 is greater than 3/5.

So Jacob says when the denominator is the same, in this case, 5, the greater the numerator, the greater the fraction, because 4 is greater than 3, 4/5 must be greater than 3/5.

Jacob and Sofia compare another pair of fractions.

"Let's choose two fractions with a denominator of 9." "Let's compare 5/9 and 7/9," says Sofia.

So here's a whole, divided into nine equal parts, 5/9 are shaded.

And here's a whole, divided into nine equal parts, seven parts are shaded.

Let's compare those two fractions.

5/9 is less than 7/9.

They both have the same denominator, but 5 is less than 7.

We could also write it like this.

5/9 is less than 7/9.

Compare these fractions.

Compare 5/8 and 6/8.

So think about what 5/8 would look like.

Think about what 6/8 would look like.

Both wholes are divided into eight equal parts, and both wholes are the same size.

Which is larger, which is smaller? Pause the video and see if you could compare those two fractions.

Welcome back.

Which one do you think is larger? Which one do you think is smaller? Let's take a look.

So let's shade in five parts to represent 5/8, let's represent 6/8.

We can see that 5/8 is less than 6/8.

We could also write it like this.

5/8 is less than 6/8.

You may have said 6/8 is greater than 5/8 as well, and that's absolutely fine.

So, very well done if you managed to compare those two fractions and work out which one is less than the other or which one is greater than the other.

Jacob and Sofia compare fractions using number lines.

"When we compare fractions with the same denominator, the greater the numerator, the greater the fraction." "Let's compare 4/6 and 3/6." This time, Sofia is going to represent the fraction on a number line.

Number line goes from 0 to 1, and the interval marks show sixths.

There are six equal parts marked on the number line.

4/6 will be marked here.

Let's use the same number line and mark where 3/6 is.

Which is larger? 4/6 is greater than 3/6.

We could also write it like this using the greater than sign.

And again, the denominators are the same, both fractions have the denominator of 6.

But 4 is greater than 3, so 4/6 is greater than 3/6.

Compare these fractions using number lines.

So compare 8/11 and 6/11.

So think about where 8/11 would be on the number line.

Think about where 6/11 would be.

Which fraction is greater? Which fraction is less than the other? Pause the video and see if you can work out how to compare those two fractions.

And welcome back.

Let's see whether you got it right.

So, 8/11 will be represented here on the number line.

6/11 will be represented here on the number line.

Which one is greater than the other? Which one is less than the other? 8/11 is greater than 6/11.

Could also write it like this.

8/11 is greater than 6/11.

You may have said 6/11 is less than 8/11, that is also correct.

So well done if you compared those two fractions and managed to get it right.

And let's move on to Task A.

So the first part of Task A, you're going to shade the fractions and then compare them.

So A, for example, you've got to compare 2/5 and 3/5.

So shade in 2/5 in that first bar, shading 3/5 in that second bar, and then say which fraction is greater than the other.

And then C and D as well.

So, again, shade the fractions and then compare them.

And then part two of Task A, compare these fractions using greater than or less than.

So which symbol would you put in the middle of those two fractions? So let's look at A.

So we've got 7/8 and 6/8.

Is 7/8 greater than 6/8? Is 7/8 less than 6/8? Which symbol would you use? So, pause the video and have a go at completing Task A.

And welcome back.

How did you get on? Did you complete all of Task A? Very well done if you did.

Let's take a look at those answers.

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

So 3/5 is greater than 2/5, 'cause the numerator in 3/5 is greater than the numerator in 2/5, and the denominators are the same.

5/6 is greater than 4/6.

C, 10/12 is less than 12/12.

And 5/7 is less than 6/7.

So well done if you got those correct.

So let's move on to part two.

You had to compare the fractions using greater than or less than.

So for A, 7/8 is greater than 6/8.

B, 6/9 is less than 8/9.

And C, 3/4 is less than 4/4.

3/4 and 4/4 both have a denominator of 4, so the denominator is the same in both fractions, but 4 is greater than 3, so 3/4 is less than 4/4.

Very well done if you completed part two of Task A.

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

So part two of the lesson we're going to be looking at ordering fractions.

Laura finds out how far away from school she lives in kilometres.

If you remember earlier on in the lesson, Laura said how far she walked in miles to get to school, and Sofia said we can't compare them 'cause there's a different whole.

So Laura has found out how far she lives away from school in kilometres.

"I walk 8/10 of a kilometre," says Laura.

So Laura has to walk 8/10 of a kilometre to get to school.

So here's the number line, going from 0 kilometres to 1 kilometre and marked in tenths of a kilometre.

So Laura walks this far to get to school, 8/10.

Jacob says, "I walk 7/10 of a kilometre." So Jacob walks 7/10 of a kilometre.

Sofia walks 6/10 of a kilometre.

So 6/10 is represented here on the number line.

"I do walk the furthest to school," says Laura.

Sofia orders the three fractions, starting with the greatest.

So 8/10 is greater than 7/10.

So she uses a greater than symbol to show this.

7/10 is greater than 6/10.

So again, she uses the greater than symbol to show this.

So 8/10 is greater than 7/10, and 7/10 is greater than 6/10.

Sofia orders these three fractions, starting with the greatest.

So you've got 6/7, 4/7, and 7/7.

I wonder how Sofia would order those three fractions.

Well, Sofia says, "7/7 is greater than 6/7." All three fractions have the same denominator, 7, but the numerators are different.

We're looking for the largest numerator first.

7/7 is greater than 6/7.

So Sofia writes this down using the greater than symbol.

"7/7 is equal to 1," says Jacob.

Well spotted, Jacob.

When the numerator and denominator are the same, the fraction is equivalent, is equal to, 1.

"6/7 is greater than 4/7," says Sofia.

So 7/7 is greater than 6/7, and 6/7 is greater than 4/7.

So Sofia has ordered those three fractions, starting with the largest, starting with the greatest fraction.

Order these three fractions, starting with the greatest.

What order would you put those three fractions in, starting with the largest, starting with the greatest fraction? The denominators are all the same.

The numerators are different.

Pause the video and see if you can work out how to order those three fractions.

And welcome back.

Did you manage to order them? Did you definitely get them in the right order? Let's take a look, see whether you are right.

So Sofia says, "7/9 is greater than 4/9." So 7/9 is the greatest fraction there, so we start off with that one first.

And 7/9 is greater than 4/9.

4/9 is greater than 2/9.

So if we order those three fractions, we end up with 7/9 is greater than 4/9, and 4/9 is greater than 2/9.

Very well done if you got those three fractions in the correct order.

Sofia works out the missing symbols.

So there are four fractions there and symbols are missing between each of the fractions.

So we're going to see if we can order those fractions using the correct symbols.

So Sofia is going to start with 5/12.

And she says, "5/12 is less than 11/12." So the missing symbol there is less than, 5/12 is less than 11/12.

What symbol comes next? 11/12 is less than 1.

And finally, 1 is equal to 12/12.

When the numerator and the denominator are the same number, the fraction is equal to 1.

So 1 is equal to 12/12.

So the equal symbol will go in there.

Jacob works out the missing numerator.

So this time, we've got three fractions, and we've got the less than symbol being used.

So 7/15 is less than a fraction with a missing numerator, and then the fraction with the missing numerator is less than 9/15.

Jacob says, "The numerator is between 7 and 9.

The numerator must be 8." So 7/15 is less than this fraction, but 9/15 is greater than this fraction, so the missing numerator must be 8.

7/15 is less than 8/15, and 8/15 is less than 9/15.

Can you work out the missing numerator? Bit of a tricky one, this one.

So we've got 1 is greater than a certain number of elevenths, and that certain number of elevenths is greater than 9/11.

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

And welcome back.

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

So Jacob says, "1 is equal to 11/11." So 11/11 is greater than this fraction, and this fraction is greater than 9/11.

So the numerator must be between 11 and 9.

The numerator must be 10.

So the missing numerator is 10.

Very well done if you worked that out.

Excellent work.

That's a bit of a tricky one.

Let's move on to Task B.

So part one of Task B, you're going to order each set of numbers, starting with the smallest.

So for A, you've got 6/6, 2/6, and 5/6.

What's the smallest fraction out of those three fractions? And don't forget, when the denominator is the same, the fraction with the smallest numerator will be the smallest.

So have a good think about part one of Task B.

Here's part two of Task B.

So work out the missing symbols.

Use greater than, less than, and equals.

So for A, we've got 9/10, and the missing symbol then, 7/10, and then the missing symbol, 4/10, and the missing symbol, and 1/10.

So with 9/10, is that greater than 7/10? Is it less than 7/10? Is it equal to 7/10? So try and work out those missing symbols in part two of Task B.

And then part three of Task B, find different ways to make this correct.

You must use odd numbers as the numerators.

So we've got there a set of fractions and four of them have missing numerators.

We've got 6/20, which is less than a fraction, and we've got several other fractions which are less than 20/20.

So what could be the missing numerators? And you must use odd numbers.

So you could do 6/20 is less than.

Could you do 10/20? No, you couldn't, because 10 is not an odd number.

So remember the numbers have got to be odd numbers.

So think carefully about the numbers that you could use to make those correct.

And can you find different ways of doing it? Okay, there are lots of possible answers for that one.

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 the end of Task B? Did you have a go at part three of Task B? Well done if you did.

Let's take a look at those answers.

Here are the answers for part one of Task B.

So let's look at A.

So 2/6 is less than 5/6, and 5/6 is less than 6/6.

Let's have a quick look at B.

1/8 is less than 3/8, 3/8 is less than 6/8, and 6/8 is less than 7/8.

So well done if you completed part one of Task B.

Let's move on to have a look at part two of Task B.

So work out the missing symbols.

Use greater than, less than, and equals.

So for A, we've got 9/10 is greater than 7/10, which is greater than 4/10, which is greater than 1/10.

And B, 1/5 is less than 4/5, which is less than 1, but 1 is equal to 5/5.

When the numerator and the denominator are the same, the fractions equal to 1.

Well done if you completed part two of Task B.

And let's move on to part three of Task B.

Now, there are lots of different ways you could solve this problem, and here are some possible answers.

So you could have had 6/20 is less than 7/20, which is less than 9/20, which is less than 11/20, which is less than 13/20, which is less than 20/20.

All those numerators are odd numbers.

You could have had 6/20 is less than 9/20, is less than 11/20, is less than 13/20, is less than 15/20, which is less than 20/20.

So very well done if you came up with three different ways, or more than three different ways, of answering that problem.

And excellent work today.

And I hope you're feeling more confident about comparing fractions and ordering fractions and thinking about which fraction may be larger than another or smaller than another.

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 you compare fractions with the same denominator, the greater the numerator, the greater the fraction.

If the whole is not the same, you cannot compare the fractions.