Lesson video

Hello there.

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

And here is the learning outcome.

I can place fractions between zero and one on a number line, and here are the keywords for today's lesson.

I'm going to say the keywords, can you repeat them back? The keywords are proper fraction.

Let's take a look at what proper fraction means.

In a proper fraction, the numerator is less than the denominator.

So remember, the numerator is the top number in a fraction, and the denominator is the bottom number in a fraction.

So, if the top number is less than the bottom number, the fraction is a proper fraction.

And here's our lesson outline.

In the first part of the lesson, we're going to be representing fractions on a number line.

In the second part of the lesson, we're going to be looking at fractions as numbers.

Let's get started.

In this lesson, you'll meet Sofia and Jacob, who will be helping you with your learning today.

Jacob and Sofia share a pizza.

Here's their pizza.

"First, we cut the pizza up into eight equal parts." "Each slice represents 1/8 of the pizza." Sofia takes three slices of pizza.

"I'm going to count forwards on a number line "to show this," she says.

Here's a number line, starting with zero, and we've got one at the other end of the number line.

"8/8 of the pizza is equal to one whole pizza." Let's count forwards with Sofia.

So 1/8, 2/8, 3/8.

Sofia took 3/8 of the pizza.

Jacob takes five slices of pizza.

"I'm also going to count forwards on a number line "to show this," says Jacob.

"8/8 of the pizza is equal to one whole." So, Jacob's going to count forwards on the number line.

Try and keep up with him, try and count along with him.

So, we start off with 1/8, 2/8, 3/8, 4/8, 5/8.

Jacob took 5/8 of the pizza.

"That's okay, he was hungrier than I was," says Sofia.

Any fraction can be represented on a number line.

"Let's count in sevenths," says Jacob.

There's number line, starting with zero, see if you can count forwards with Jacob.

1/7, 2/7, 3/7, 4/7, 5/7, 6/7, one.

"7/7 is equal to one whole." So, Jacob could have said 7/7 at the end of his count, but he said one instead.

7/7 is equal to one whole.

Jacob represents fractions on a number line divided into sevenths.

What proper fraction is shown on each number line? And remember, a proper fraction is just any fraction where the numerator is less than the denominator.

What fraction is shown on that number line? "This shows 3/7," says Sofia.

Let's look at another one.

What fraction's represented this time on the number line? "This shows 6/7." There are seven equal parts, and the bar starts at zero, and goes all the way to 6/7.

Jacob represents proper fractions on different number lines.

What fraction is shown on each number line? Here's the number line starting with zero, ending with one.

What fraction is represented on that number line? "This shows 3/5." Let's try another one.

What fraction is represented this time? "This shows 5/6," says Sofia.

Jacob represents proper fractions on the same number line.

What fraction is shown on each number line? There's number line here, starting at zero, ends in one, and the number line divides up into ninths.

What fraction is represented on the number line? "This shows 7/9," says Sofia, and it's the same number line again, still divided up into ninths.

What fraction is shown this time? What fraction do you think that represents? "This representation does not begin at zero.

This shows 1/9," says Sofia.

Bit of a tricky one, that one.

This representation starts on 7/9, but it ends on 8/9, so it only actually only represents 1/9, not 8/9.

What fraction is represented on these number lines? So, there are two number lines there.

Can you work out what fractions are represented on each of them? Now, pause the video, and see if you can work out what fraction is shown.

And welcome back.

Let's take a look at that first number line.

What fraction is represented? This shows 7/10.

There are 10 equal parts, and the bar starts on zero, and ends on 7/10, so 7/10 is represented.

What about our second number line, and it might be a bit of a problem with this one.

This representation does not begin at zero.

So, this actually only shows 1/10.

The bar goes from 1/10 to 2/10.

That only shows 1/10.

So, very well done if you've got both those correct, and you spotted that slightly tricky one with that second example, well done.

Jacob looks at a different number line.

He might have spotted something is missing on this number line.

"What fraction is shown on the number line?" "The interval marks are not labelled on the number line," says Sofia.

"I'm going to try counting in steps of 1/8." So, Jacob's gonna use a bit of a trial and improvement to try and see if he can work out what fraction is represented on that number line, so he's going to count up in steps of 1/8 and see whether it works out.

So, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8.

It's not quite right, is it? Now, "The count is not in steps of 1/8.

8/8 is equal to one whole." So, whatever fraction it is, the count will make the numerator and the denominator being the same number, that's got to end on one.

That's got to be the same as one.

So, what do you think the count might be in? "The whole is divided into nine equal parts," says Jacob.

So, nine equal parts.

"I'm going to try counting in steps of 1/9." So, 1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9, 8/9, and 9/9 will be equal to one, so that does work.

"Well done, Jacob.

9/9 is equal to one whole." "The fraction shown is 4/9." So, that bar starts on zero, it ends on 4/9, so 4/9 is represented on that number line.

What proper fraction is shown on the number line? And again, proper fraction just means the numerator is smaller than the denominator.

Pause the video and see if you can work out what fraction is shown.

You might need to do some counting up or think carefully about what the number line has been divided up into.

And welcome back.

Did you manage to find the answer? Is it definitely right? Let's find out.

Jacob starts out by saying, "The whole is divided into six equal parts." So, the count is in steps of 1/6.

1/6, 2/6, 3/6, 4/6, 5/6, and one would be equal to 6/6.

So, "The fraction shown is 5/6." Very well done if you had the correct answer.

And let's move on to Task A.

So, the first part of Task A, what proper fraction is represented on each number line? Have a good look at A.

You can see that the count is in steps of 1/10.

How many tenths are represented by that bar? So, can you work out what proper fraction is represented on each number line? Here's part two of task A, shade each number line to represent the correct proper fraction.

So A, you've got to shade 4/6, B, you've got to shade 5/8.

So represent each of those fractions on the number line.

And then three, bit of thinking needed here, what proper fraction is represented by each number line? Work out what fraction the steps are counting in.

So you might need to use a bit of trial and improvement.

You might wanna count to see how many interval marks there are in between zero and one.

Try and work out what the count is in.

Don't forget to double check, and don't forget if it's 5/5, or 6/6, or 7/7 that is equal to one.

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

Pause the video and have a go trying to solve the problems in task A And welcome back.

How did you get on? Let's take a look at those answers.

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

So A, that fraction represented on the number line was 8/10, B, the fraction represented was 2/6.

Let's move on to part two of task A.

So shade each number line to represent the correct fraction.

So for A, you should shade it all the way up from zero to 4/6, and that would then represent 4/6.

For B, you should start it from zero and shade it all the way up to 5/8, and that would represent 5/8.

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

And let's take a look at part three.

So you have to do a bit of thinking here and a bit of working out, bit of problem solving.

So A, the fraction represented was 3/6.

B, the fraction represented was 4/5.

C, the fraction represented was 6/7.

And D, the fraction represented was 8/11.

Very well done if you got onto to part three and you managed to work out the answers there, excellent work.

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

So part two of the lesson is fractions as numbers.

Fractions are numbers.

"Every fraction has its own position on a number line." "Proper fractions appear between zero and one." So all proper fractions are larger than zero and they are all smaller than one.

To be a proper fraction, remember the numerator has to be less than the denominator.

"Where would this fraction be represented on a number line?" Sofia there has got a representation of a fraction.

I wonder what fraction it is.

Well Jacob says, "This shape is divided into seven equal pieces.

The number line needs to count in steps of 1/7." Now here's the number line counting in steps of 1/7 with 7/7 being equal to one.

Five parts are shaded, so the fractions shown is 5/7.

So every fraction is a number, fractions are numbers two.

So 5/7 will be represented on the number line at that position there.

That is where 5/7 belongs.

5/7 appears here.

Sofia challenges Jacob with another fraction.

"Where would this fraction be represented on a number line," asks Sofia.

Or fraction does that shape represent? "The shape is divided into nine equal pieces.

The number line needs to count in steps of 1/9," says Jacob.

So here's the number line, counting in steps of 1/9.

Six parts are shaded, so the fraction shown is 6/9.

I wonder where 6/9 would appear on the number line.

6/9 appears here.

How would you represent this fraction? "Where would this fraction be represented on a number line?" Here's our shape.

I wonder what is divided up into.

And here's Jacob, Jacob's saying, "The shape is divided into 12 equal pieces.

The number line needs to count in steps of 1/12.

So here is the number line.

Where would you represent that fraction on the number line? Pause the video, see if you can work out what the fraction is and whereabouts it should go on that number line.

And welcome back.

How did you get on? Did you get the right answer? Let's take a look.

So Jacob says, "Seven parts are shaded.

So the fraction shown is 7/12.

Out of 12 equal parts, seven of them are shaded, the fraction is 7/12, and 7/12 would be represented here.

7/12 appears here.

Very well done if you've worked out the correct fraction and you worked out where it would appear on the number line, excellent work.

Jacob and Sofia look at an unlabeled number line.

"How can we work out what the interval marks are counting forwards in," says Jacob.

"Count the interval marks," says Sofia.

"Remember to include the interval mark for one but not for zero." "So there are seven interval marks," says Jacob, "The count must be in steps of 1/7." So there are six interval marks between zero and one, but Sofia has said to Jacob to include one in the count as well.

Why does Sofia say to count one as well? Well she said to count one because of course one is equal to 7/7.

So we've got to remember to include one in your count as well.

"The arrow shows the position of 2/7," say Sofia.

Jacob and Sofia look at another unlabeled number line.

"How can we work out what the interval marks are counting forwards in." says Jacob.

Remember Sofia said last time? Sofia says, "Count the interval marks.

Remember to include the interval mark for one but not for zero." So I wonder what would the count be? How many interval marks are there if you remember to include 1/11 as well? Jacob says, "There are 11 interval marks.

So the count must be in steps of 1/11." 'Cause remember, 11/11 will be equal to one.

So Jacob completes the number line.

What number is represented on the number line? "The arrow shows a position of 9/11." And here's one for you to try on your own.

Look at this unlabeled number line.

"How can you work out what the interval marks are counting forwards in?" "Count the interval marks.

Remember to include the interval mark for one, but not for zero." Pause the video and see if you can work out the answer.

And welcome back.

How did you get on? Did you find the answer? Let's take a look.

So Jacob says, "There are six interval marks.

That count must be in steps of 1/6." Remember, 6/6 is equal to one.

That's why you've got to remember to include one in the count as well.

"The arrow shows the position of 2/6." Very well done if you've got the right answer.

Jacob has a challenge for Sofia.

"What number is shown by the arrow," asks Jacob.

Now Sofia doesn't have a lot to help her there, does she? There are not even any interval marks and there's certainly no fractions marked on there apart from 5/5.

I wanna give Sofia a bit of a clue as to what the answer's going to be.

Sofia says, "The arrow is slightly nearer 5/5 than zero, I think the number must be 3/5." So Sofia is thinking the count must be in fifths and 3/5 would be about there, can't be 4/5, that would be much closer to 5/5.

So Sofia thinks it's 3/5.

"I could check by trying to show where the interval marks would be," says Sofia.

So Sofia tries to work out where the interval marks would be.

So 1/5 would be about there, 2/5 would be there, 3/5 would be there, 4/5 would be there.

"I'm confident that the number shown by the arrow is 3/5," says Sofia.

"Well done, Sofia, that's correct," says Jacob.

Jacob has a challenge for you.

"What number is shown by the arrow?" Now you haven't got a lot to go on there.

You know the count starts on zero and it ends on 7/7.

There's a bit of a clue.

So maybe it's a certain number of sevenths.

I wonder how many sevenths is represented by that arrow.

Pause the video and see if you can work out the answer.

And welcome back.

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

So Sofia says, "The arrow is slightly nearer zero than 7/7.

The number must be 3/7." So Sofia says it's 3/7.

Let's check by showing where the interval marks would be.

So 1/7 would be there, 2/7, 3/7, 4/7, 5/7/, 6/7.

So very well done if you managed to work out the answer as being 3/7 as well.

Excellent work.

And let's move on to Task B.

So the first part of Task B, write each fraction and show its position on the number line.

You've got there a shape, gonna work out what fraction is represented, write down the fraction that's represented, and then show where it would be on the number line.

Got two shapes there, A and B.

And there's two more, C and D.

And again, work out the fraction that is shown, write down the fraction, and then work out where it would be represented on the number line.

Here's part two of Task B.

So what fraction is represented by the arrow? So you've got the interval marks, but the fractions are not marked.

So you've got to work out what the fractions are, then carefully about what the count would be.

So remember when you count up interval marks, don't forget to include one in your count.

And then in C and D you've got to work out what fraction's represented, but the interval marks aren't put on the number line either.

All you've got to go on is the zero and the 5/5 or 8/8.

So you've gotta reason that out, try and work out what the answer would be.

So pause the video and have a go at Task B.

And welcome back.

How did you get on? Did you complete part one? Did you get into part two? Well done if you did.

Let's take a look at those answers.

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

So A, the fraction represented was 5/6, and that's where it should be put on the number line.

B, the fraction represented was 5/9.

C, the fraction represented was 5/12 and that's where it would be represented on the number line.

And finally, D, the fraction represented was 7/11.

So well done if you managed to complete part one of Task B, and let's take a look at part two of Task B.

So A, the fraction represented was 6/7.

So well done if you worked out that the count was going up in steps of 1/7.

B, the answer was 3/10.

Again, very well worked out if you got that as your answer.

And then C, the arrow is pointing at 2/5, whatever fraction it is is nearer to zero than 5/5.

So 2/5 would be the right answer.

And then finally, D, the number line starts on zero and ends on 8/8 and this fraction is slightly nearer to zero than it is to 8/8.

Slightly less than halfway along that number line.

So the number represented would be 3/8.

Very well done if you completed all of Task B.

Excellent work and well done in today's lesson.

I hope you're feeling much more confident about placing fractions on a number line and you understand that fractions are numbers just like any other number.

Excellent work today.

Very well done.

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

So a fraction is a number and has an exact position on a number line.

Fractions can be ordered and positioned on a number line.

Proper fractions appear between zero and one on a number line.

And in a proper fraction, the numerator is less than the denominator.