Lesson video

Hi everyone.

MR. Easter here again.

Let's make a start of today's lesson by looking at the practise activities from the previous lesson, I asked you to use the generalisation to help you and to then complete each of the following equalities.

So let's remind ourselves the generalisation, when the numerator and denominator are the same, the fraction has a value of one.

So the first question is the numerator and denominator the same value? Yeah.

They're both four.

So that must have be equal to a value of one.

What about the second one? Okay.

We're told the denominator, we're told the fraction is equal to one.

So that must mean the numerator has the same value as the denominator, which must be an eight.

And then the final one this time, we know the numerator.

We don't know the denominator, but we do know that is equal to one, which means that the denominator must be the same value as the numerator, which is seven.

In the second question, you're also asked to use that generalisation to help you.

And then use it to try and work out the unknown values on the number lines.

So let's think about what we know and what we don't know.

Zero, 1/3, one.

So let's look at the number line.

So it goes from zero to one, it's been split into three core parts, which is why the first one is 1 1/3, then another 1/3.

So that'd be 2 1/3 So we need to put in 2/3.

The next number line.

Okay.

Let's think again, how many parts has it been split into, it's split into four equal parts.

Some of you might've used the fraction that we are told, 3/4 to know the denominator.

All of the fractions must be 4/4.

So that's count up in quarters, zero, 1/4, 2/4, 3/4, 4/4 , not 4/4.

It's just one box.

What can we write to the end of our number line? We can write one because 4/4, the numerator would be four, the denominator would be four, they're the same value which is why we can also say the fraction has a value of one.

Okay.

Final number line.

Okay.

We're not told much information here.

Let's think about what our number line has been split into.

How many equal parts.

So I can count.

Let's count together.

I can count one equal part, two equal parts, three equal parts, four equal parts, five equal parts.

Up until that line.

We'll ignore the fact that it carries on that's because we could continue to count past that final number.

So if it's been split into five equal parts, there must be fifth each time we're adding on another fifth.

So let's count to fifth together, zero, 1/5, 2/5, 3/5, 4/5 could write 5/5, but for my generalisation, we know we can also write one, we'll then have to look at the three number lines and think what's the same and what's different.

That should have been done after you'd completed them.

Something I can see same as the previous lesson, all of the lines are the same length, which is why zero and one are found on the same point on each number line.

And then the location of each fraction is slightly different based on its value.

And that's based on the size of each part.

Other things you might have spotted? The denominator for the fractions on each line are the same that's because each line has been split into a certain number of vehicle parts.

Some of you might've noticed the numerator one appears on each number line, the numerator two appears on each number line, but then the other number lines, sometimes they have a numerator of three and one of the fractions, sometimes they have a numerator four, but the key things to focused on is we now know that we can put one at the end of those number lines to show that that is the place where the fraction could have been written, where the numerator and denominator are the same.

But instead we now know, we can say it has a value of one.

The challenge was this.

You were asked to complete the following expression in different ways, and this is building on what we just said.

So let's think back that generalisation is super important when the numerator and denominator are the same, fraction has a value of one.

So actually you could have put any fraction you wanted, as long as the numerator and denominator were the same.

So let's start with ones we've seen already.

5/5 is equal to one, 9/9 is equal to one, 12/12 is equal to one, that final one and all of those, you could have any numbers you like, as long as the numerator and denominator are the same, I've chosen 99/99, how many different ways could that have been? There's an unlimited number of different ways, but the important thing is, each way the numerator and denominator must have the same value.

So this is a familiar image.

And again, I want us just to make sure we know that we can see at the end of these number lines, I've written 5/5, 9/9, and 12/12, just to make sure we're all on the same page together.

The generalisation that's that one more time together.

When the numerator and the denominator are the same, the fraction has a value of one.

So 5/5.

I can write one instead, 9/9, I can write one instead, and 12/12, I can also write one.

So let's build on that a little bit more.

Still the same generalisation.

Don't worry.

I won't make you read it this time.

But let's think about completing some descriptions of some fractions.

9/9 is equal to one.

We said that today, 10/10 is equal to one.

Haven't seen that one, but we now know that, 5/5 seen this one, 5/5 is equal to one, 12/12 is equal to one.

Hopefully you're sporting this pattern.

So some true or false statements for us to think about that build on that generalisation a little bit.

For each one, I want you to identify if you think it's true or false, but I also want you to think why.

So the first question, 8/9 is equivalent to one.

Do you think that's true or do you think that's false, show me with your thumbs? That is false, but why is it false? Let's look at the numerator and the denominator.

Are they the same value? No, the numerator is eight.

The denominator is nine.

So they are not the same.

So that fraction is not equivalent to one.

My next statement.

One has the same value as 8/8, true or false.

What do you think? That one is true.

Why? Because in the fraction, the numerator and the denominator have the same value.

So we can say that the fraction is equal to one, or it has the same value as one.

Final one, 9/9 is the same point on the number line as one.

What do you think? 9/9 is one equivalent to each other? They are on there because the numerator and the denominator in the fraction 9/9 is the same.

So it has the same value as one.

And we now know that means on a number line, they would be at the same point.

Now, I want us to do some sorting.

So at the bottom, I've got three sorting circles.

And at the top, I've got six fractions.

I want you to think about which fraction goes into each sorting circle, pause the video, have a go at that.

Okay.

Now we're getting pretty good at this.

So the one we're going to start with is the non-unit fractions, which equal to one, because we all now know that when the numerator and the denominator of the fraction are the same, that we can say that it has a value equal to one.

So out of the fractions, in that list, which ones have the numerator, and the denominator the same, 6/6 and 15/15.

So they both go into our non-unit fractions that are equal to one circle.

Okay.

Let's now think about unit fractions.

Who can remember what a unit fraction means.

In a few lessons ago, we talked about repeated addition of unit fractions.

They were the fractions where the numerator was one.

So out of those fractions, which fractions have a numerator of one, 1/4 and 1/100.

So they are both unit fractions.

Let's hope then that the two fractions left are non-unit fractions that are less than one.

So let's see, are the numerators the same as the denominators? No.

Is the numerator one? Are they unit fractions? No.

So they're definitely non-unit fractions.

And that means they have a value less than one, which means on a number line, they would come before one.

So both of those fractions can go into our red circle.

So I want to focus on this sorting circle, where we talked about non-unit fractions, which had a value equal to one.

So think about how many expressions can you write? How many equality's with the equal sign can you write based on what we know about those fractions? So pause the video and see what you can write.

Okay.

Now let's go through those together and each time I'll pause and you can pause the video, see if you can complete what I've written, if you haven't got it.

So let's start off with 6/6.

What's that equal to? It's equal to one.

We're getting good at this now, aren't we? We know when the numerator and denominator are the same, a fraction has a value equal to one.

If we can write that, we can also write one is equal to 6/6, although some people that didn't write that.

But based on our understanding of the equal sign, we can also write that statement.

So what about 15/15? What's that equal to? That's also equal to one.

And if we can write that, we can also write that one is equal to 15/15.

Now I bet there's more that people could write.

I wonder if anyone has written this, if you haven't see if you can complete it, what can I write in that circle in between 6/6 and 15/15, we can use that equal sign.

We know that those two fractions are equal to each other because we've just written about both of them individually are equal to one because they have the same value.

We can say that they are equal to each other.

So let's read that 6/6 is equal to 15/15 or 6/6 is equivalent to 15/15.

Can you say that final one with me? 6/6 is equivalent to 15/15.

Now, so work for you to do.

I would like you to look at all of the numbers in the grey square, and remember fractions are numbers as well, and I'd like you to use those numbers to complete the stems or the missing boxes underneath.

So the first one, what is equal to what, then think about a fraction that's equal to a number, then a number that's equal to a fraction, and then finally two fractions that are equal to each other.

Be careful.

I have included one fraction which you cannot use in these questions.

Maybe start off by seeing if you can spot what that fraction is.

So pause the video, have a go.

Okay.

Did you have a go at that? I hope so.

Which fraction did you realise you couldn't use in these equations? We couldn't use 4/5 couldn't we? Why couldn't we use that? Because that's the only fraction where the numerator and the denominator don't have the same value, you then could have actually used any of these numbers to complete them.

So I'm going to choose some, maybe you did them, let's if I can guess.

7/7 is equal to 20/20, you could have also said 3/3 is equal to 9/9.

There's lots and lots of things you could have said.

Maybe some of you used the number one for that.

Maybe you said 12/12 is equal to one, 200/200 is equal to one, there's lots you can have.

So then let's think about a fraction is equal to, then there's only one box.

Where are we going to start with this? There's one that we have to use.

It's the number one, the number one is going to have to go into that final box 'cause we want that to be a single digit.

And then again, we can choose any of those fractions where the numerator and the denominator are the same value, let's see if I can guess what you've written, 20/20 is equal to one.

Did I guess right? Possibly not.

Let's think about the next one, this time, our single digit with a one box is before the equal sign.

Let's see if I can guess what you've written this time.

One is equal to 200/200 and then we have another occasion where we've written two fractions and we've got our circle in the middle.

So if we're thinking about is equal to that's the operation, we're going to put in our circle.

And then again, you can choose any of the fractions, where the numerators and denominators are the same.

Let me guess one.

Maybe I can see if I could say one you haven't written, 9/9 is equal to 20/20.

I wonder if anyone wrote that.

All of these are based on that generalisation that we're really good at it now, when the numerator and the denominator are the same, the fraction has the value of one.

So some practise activities for you to do again.

First questions I want you to see if you can find the value that can go in our missing box.

And for your challenge, this is very similar to the challenge question I asked in the previous lesson.

Can you try and complete the following expression in different ways? You'll notice that each of those have the number 4/4, and then you've got our missing boxes.

So think about the different ways you can complete those expressions.

And then again, can you think how many different ways do you think there are to complete the expression and why do you think that? So have a go to those questions and someone we'll go through them at the beginning of the next lesson.

Bye.