Lesson video

Hi, everyone.

Mr. here.

Let's start off by going through the practise activity from the previous lesson.

So the first one, 3/8 equal to something added three times repeat addition.

We know their unit fractions.

I can look at the denominator eight.

So they must all be eight.

The numerator is three.

So three 1/8 would be equal to 3/8.

Next one, down 4/8.

Again, we notice repeated addition of a unit fraction.

How many would there be this time if the numerator is four? There would be four lots of 1/8.

So four 1/8 added together.

Next one down same thing.

And let's looked at the pattern, yep still the denominator eight.

So the denominator of our fractions will be eight.

How many of the unit fractions will there be? There would be five, won't there? The numerator is five.

So 5/8 is equal to five 1/8.

Now next one, this time we've got sevenths.

So let's see how many sevenths we've got.

We've got one, two, three, four, 1/7.

That means my numerator will be four, my denominator will stay as seven.

And then finally, lots of missing boxes.

We can start either, but we can start at the denominator.

Maybe I'll start with that.

We have the denominator as eight, which means that my fraction must be 5/8.

And if my numerator is five, that means there'll be five, 1/58.

Now this question definitely was more challenging.

Stan makes a repeating pattern with some white and grey cubes.

Write a repeated addition of a unit fraction to show what fraction of his model is made of grey cubes.

So to do that, the first thing we have to do is to work out how many cubes there are in the whole Now I can see here, the top phase of this grey cube and the front face, but that is still just one queue.

I can try and count all of those cubes that I can see, but some of you might have noticed that there are some hidden cubes.

You might be able to work at how may they are, but I'm going to split our whole into the top and bottom layer so that you can see all of them.

There you can see all of the cubes.

And like I said, some of you might've worked that out.

Some of you might've seen that if there are eight cubes in the top there, that means there's also eight cubes in the second layer, eights and eight is equal to 16.

So there are 16 cubes altogether.

So now we know there's 16 cubes.

We can think about what our repeated addition will look like.

Let's start with this grey cube.

If we're writing a fraction, we can write our fraction but first, we'll start with the denominator.

How many cubes are there in total? There's 16 cubes and that one grey cube is one of those 16.

So we can start off with a unit fraction of 1/16.

Then let's think about this grey cube.

That's also 1/16.

So we can add that.

Then we can continue making sure we include all of our grey cubes.

So the next grey cube means we add another 16th, the next grey cube and other 16th and so on and so on.

So we've included all of our grey cubes.

So what is that going to be equal to 1/16 add 1/16 add 1/16, all the way to the end.

How many 1/16 have we added together? We've added eight 1/16.

So the final part will be, is equal to 8/16.

So to start today's lesson, we're going to think about something you have looked at in a previous lesson.

On the left of the screen, we can see I've got a bar model and underneath the bar model, we've got a number line.

I'm going to show different numbers of parts.

And we're going to think about what that will be as a fraction and where that fraction will be on our number line.

So to start with, I have shaded in one part, why is it 1/5? Because the whole has been split into five equal parts.

I can see those equal parts on our bar model.

And we can see on the number line that there are five equal parts on the number line.

I remember we said that we can put 1/5 at the end of where that part is in our bar model.

And that's the unique place that 1/5 is written on our number line.

So we can say this is one 1/5, and we can write it with one as the numerator and five as the denominator.

Let's continue our pattern.

This time two of our equal parts are shaded.

Certainly there's 2/5.

We can say that's two 1/5 and we can write it as two as the numerator and five as our denominator.

I'm sure we can start to spot the pattern.

This time, say it with me three 1/5.

And that is written as three as the numerator and five as the denominator.

Four 1/5, four as the numerator, five as a denominator.

And we can see where 4/5 is on a number line when 4/5 is a number.

And then finally, we've shaded in all of the parts.

So we can say, and you said in previous lessons that this is five 1/5 and it's written as five as the numerator and five as the denominator.

And that's the part I want us to focus on here.

Last lesson or previous lesson, you would have said this generalisation.

When the numerator and denominator are the same, how can I finish that generalisation? What can we say if the numerator and denominator are the same? Did anyone say this? The fraction is equivalent to one whole.

Let's look at the bar model in that case.

The whole of the bottom shaded in.

We've moved the whole way along this line.

So we can say when the numerator and denominator are the same, the fraction is equivalent to one whole.

Okay, let's look at that in one more way.

I got the same number line and I got the same bar model.

At the beginning of my number line.

I'm going to put a zero and the next whole number is going to be one.

So I'm going to put that at the end of our number line.

Let's count up in fifths together.

Zero, one 1/5, two 1/5, three 1/5, four 1/5, five 1/5.

But look at the number line.

Have I written five 1/5? No, in the red circle, I've written one.

What do we then know about five 1/5 and one? They would go at exactly the same point in our number line.

That means they are equivalent to each other.

Let's go back to our generalisation.

When the numerator and denominator are the same before we said is the whole, well, what can we say now? We now know the fraction has a value of one.

Let's say that together.

Say it with me.

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

Let's talk about the different fraction.

What do you think our fractions are going to be our number line? How are we going to work out what fractions are we saying? Or we can look at either the number line or we can look at our shape.

Let's start with a number line, 'cause that's what we're trying to get used to, and trying to get more familiar with.

Remember, we have to think about the number of parts on the number line.

So I got along two parts so far, three parts, four parts, five parts, six parts, seven parts, eight parts, nine parts.

So there's nine parts in our number line.

Now remember, we're not counting the number of lines, we're counting the number of parts.

Let's check our diagram.

One part, two parts, three parts, four parts, five parts, six parts, seven parts, eight parts, nine parts.

Great, they match.

So can you count up with me? So zero, 1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9, 8/9.

Did anyone say 9/9? You wouldn't be wrong, 9/9 or we can say one.

Why is that the case? In broad generalisation, say this with me, when the numerator and denominator are the same, the fraction has a value of one.

So if you said 9/9, you weren't wrong, but we're now trying to learn that we can also say one.

One more time with me.

Here I've got an empty egg box, so let's see what's going to happen when we add one egg each time.

What's the fraction of the whole egg box? That's going to increase as we add one egg each time.

Let's check our egg box shall we? On the top row, I can see one, two, three, four, five, six empty spaces.

Six plus six is equal to 12.

So my fractions must be twelfths.

Counts up with me and remember our generalisation and see if you can say the same thing as me at the end of our number line.

Okay, off we go together.

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

Did you say one this time? Let's hope so.

Why is that the case? Can you remember? Who can remember that generalisation? Try and say it to yourself before I put it on the screen.

Here it is in case you couldn't do that.

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

So here are the three number lines we've looked at.

Let's think, what's the same, what's different? For the video how many similarities and differences can you spot? Okay, now I'm going to start with the differences.

Something I've noticed is the number of parts that each number line has been split up into is different.

So let's think about how we can move along each number line and what fraction we would write at each individual parts on the number line.

So the first one, we're going to think about how many parts it's been split into? One part, two parts, three parts, four parts, five parts.

Oh, it's the same as we've just done.

So you should be good at that.

Count along with me.

Zero, 1/5, 2/5 3/5, 4/5, one.

The next number line.

How many parts are there? Did you say nine parts? Again, it's the same as the previous example.

So again, count with me.

Zero, 1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9, 8/9, one.

And finally, our final number line.

How many parts has that been split into? It's been split into 12 equal parts.

So now count in twelfths with me.

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

So what's the same about both of these number lines? Is there something that's same that we said for each of them? I can think of two similarities.

Zero was at the beginning of all three of our number lines and because our number lines are the same length, one was also at the same parts of our number line.

That's something really important.

Let's looking at that in a bit more detail.

So on our number line, we didn't have 5/5, did we? What did we have instead? We had one and we said that you weren't wrong if you said 5/5, but we are learning from my generalisation that when the numerator and denominator are the same, the fraction has a value of one.

So let's look at our next fraction.

We got 9/9.

Did we write that in our middle number line? No, we wrote one.

So we can say that 9/9 is equal to one.

What about 12/12, did we write that in our final number line? No, and again, what can we say that's equivalent to? We can say it's equal to one.

And why is that the case? Let's go back to our generalisation.

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

It's time for some practise activities for you to do.

For all of these practise activities.

I want you to use the generalisation to help you.

So let's say it one more time together.

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

So there's three missing boxes there for you to fill in.

The next thing I want you to do still using the generalisation is to look at these three number lines.

I want you, first of all, to see if you can work out where the unknown values are on each of the number lines.

Then the third thing I'd like you to do is look at the three number lines above and write down, what's the same and what's different? Think about what we've discussed in this lesson and see if you can refer to our generalisation in your explanation.

Final thing, I like you to do is complete the following expression in different ways.

I've given four ways there.

But then think about this.

How many different ways do you think there are to complete the expression? Why do you think there's that many ways? See if you can convince me and we'll talk about this in the beginning of the next lesson.

Good luck.