Lesson video

In progress...

Oh, hi, sorry, one minute, one second, let me just finish, done.

I've been reading this book for a little while I'm hooked.

And I just had to finish that page its the last page in the chapter.

I hope you don't mind me keeping you waiting for a second.

That said, that book is a complete distraction, I need to push it away, cover it with a pillow or something so that I cannot see it, I need to focus on this maths lesson, I need you to be able to focus on this maths lesson as well.

So if you have any distractions close by that you need to cover up like I have, or perhaps you need to move out of the room into a quieter space.

Press pause, get yourself set up somewhere where you'll be able to focus on your maths learning.

Then press play again, and we'll get started.

In this lesson, we will be identifying, naming and writing equivalent fractions.

Our agenda for the lesson, we're going to start off with a chatterbox activity before we have a look at equivalent fractions when we're focused on a shape and when we're focused on a set, and a quantity.

Things that you're going to need, a pen or pencil, a ruler, a pad or book, something to write onto.

And as well as that, you're going to need a square piece of paper, it's really important that the paper is square.

And in terms of the size, I would say at least 10 centimetres for each of those lengths.

Finally, if you're able to get, say around 20 different items, in school I would give you 20 counters.

You probably haven't got 20 counters at home, but you might have something that would work in a similar way.

It could be pieces of Lego, it could be little stones, it could just be pieces of paper that you've torn out and then rolled into balls, you need around 20 of them.

Come back and come back even and play again when you're ready to start.

So, chatterbox activity, this is what I mean by chatterbox.

Give me a quick wave if you've made one of these before.

Fantastic! Then you are a pro already and you're set to start.

Some instructions are on the screen for you.

Essentially, I want you to make a chatterbox, then I would like you to unfold it.

So that little image next to my video right now is the unfolded chatterbox.

When you've done that I would like to know what fraction of the whole square each of those small triangles represents.

Press pause, have fun making the chatterbox.

Come back and play again when you're ready to take a look.

How did you get on? Hold your chatterboxes up.

Let me have a look.

They're really really fun, aren't they? Especially when you start writing things underneath different flaps and playing with it properly.

A really fun game.

And guess what? When I was in year three, or four five, I was making these chatterboxes as well.

But it has been sometime since I've made one myself, although of course, I always see them in the classrooms of the classes that I have been teaching.

Let's focus in then on the maths of this chatterbox.

I want us to work out the fraction of each triangle.

What fraction of the whole square does this smallest square represent? Tell me.

It does 1/4.

We're visualising the square divided into four equal parts, each equal part worth 1/4.

How about this smaller square? What do you think? So, around or visualise the whole square divided into smaller squares of that size.

How many would there be? Would have four along the top row and another four.

there are four columns four rows, 16 each square one 1/16 of the whole square.

How about the triangles then? So the triangle is, is half of the smallest square, So were going to have more than them, more than the 16 squares, we could do some counting.

We could think if, if one square is equal to two triangles and we had 16 squares, how many.

We're going to multiply two by 16/32? How do we say 1/32? How do we say that? 1/32, often ordinal numbers first, second, third, fourth, fifth, sixth, seventh, we would use those typically when we're using when we're when we're naming fractions.

How we say it doesn't really matter.

What does matter is that we've identified the whole square has been divided into 32 equal parts.

And we are talking about one of them, that purple triangle is 1/32 of the whole square.

Let's go deeper with this now then, what fractions, which fractions can we represent from our chatterbox unfolded? Press pause.

What other fractions can you see? Come back when you're ready to share.

Should we take a look at some together? So remembering that that small triangle represents 1/32 of the whole.

Which fractions could we represent with a fold or a drawn line here? Good! 1/2.

Now, that is, each of those two equal parts represents 1/2.

But with the extra lines drawn on from our folding, we can see some fractions that we could say are equivalent to 1/2.

So for example, here, in each of those halves, there are 16/32, 1/2 is equal to 16/32, you don't believe me? Take a look.

Look on the left half.

How many triangles in that top row? Four.

The next row? Another four.

So we've got 8, 16.

16/32 and 1/2 are equivalents? How about now? What fraction can we see? 1/4.

What could we say is equivalent to 1/4 focusing on one of the quarters? Good! 8/32.

But it doesn't stop there.

1/2 is equal to how many quarters, which is equal to how many thirty-seconds? Press pause while you quickly work that out, then come back.

So what did you get? 2/4.

Good.

And so if 1/4 is 8/32, 2/4, 16/32.

Good.

Next one.

Okay, so 1/4.

Ah, what are we representing now? Eighths.

The whole has been divided into eight equal parts.

Let's focus in on one of those eight equal parts.

What's its equivalent to? So the whole square has been divided into eight equal parts.

Let's focus in on one of those eighths.

What's it equivalent to? 4/32.

Good.

Let's continue.

1/4 is equal to how many eighths and how many thirty-seconds? 1/4, how many eighths? Good! 2/8.

How many thirty-seconds? So if 1/8 is four, 2/8 is 8/32, doesn't stop.

How about 1/2? How many quarters is 1/2 equivalent to? 2/4.

How many eighths is that? Good.

And how many thirty-seconds? Fantastic 16/32.

So many connections.

I hope that the unfolded chatterbox is helping you to see them.

Next one, I need to move my video down.

What fraction of the whole shape does one of these squares, one of these equal parts represent? 1/16.

Okay, so focus in on one of those 16 equal parts.

What's it equivalent to? 2/32.

Good.

Now let's build up.

1/8, 1/8 is equal to how many sixteenths? Good, which is equal to how many thirty-seconds? Four.

Continuing, 1/4, how many eighths is that equal to? Good! How many sixteenths? And how many thirty-seconds? Super.

Last row.

If you want to pause and work through those missing numerators, please do.

Well, if you think you can reveal them to me as we go and please call them out nice and clearly do that instead.

So 1/2, you ready? How many quarters? Good.

How many eighths? How many sixteenths? And how many thirty-seconds? So many connections.

Well done everyone.

Look across these numerators and denominators.

Notice the patterns and connections.

These fractions are equivalent in each of the rows and look at the relationships that are there the multiplicative relationships between those numerators and denominators to help explain their equivalence.

Let's have a look at this now.

I'm just going to move my video back up.

We can use the area of rectangles to represent equivalent fractions.

Tell me the fraction that's blue.

1/4.

1/4 of the whole rectangle is blue.

How about the darker blue now? What fraction does one of the dark blue pieces represent? Okay, and so two of them? Good.

Each equal part is 1/8.

Two 1/8 are making up the dark blue.

Two 1/8 and 1/4 are equivalent in proportion when we're looking at the proportion of the shapes shaded, of the rectangle shaded 1/4 and two 1/8 are equal.

So now, what can you tell me about 1/4, two 1/8 and the yellow part of the third rectangle, four 1/16, they're all equal.

Look, you can see the amount of the whole, the wholes are the same, the amount shaded is equal.

It's just a different number of equal parts shaded because each rectangle has smaller and smaller equal parts as more equal parts are made.

Your turn to have a go.

Looking at these two examples, each example has three rectangles.

I'd like to know which fractions are represented.

Press pause, come back when you're ready to check.

Should we take a look? Can you hold up your paper so I can see anything you've written down to explain this.

Looking good.

Well done.

So focusing in on this one.

Which fractions do we have here represented? Good.

This green is representing 1/3 of the whole rectangle.

In the next shape, I've used pink to represent 2/6.

And in the last shape I've used purple to represent? Good.

4/12.

These three fractions are equal, they all represent the same proportion of the whole rectangles.

And in this one? What does my green represent? Good, 1/5 of the whole rectangle.

And what about my pink? 2/10 of my whole rectangle and my purple? 4/20 of my whole rectangle.

These three fractions are equivalent.

The amount of each whole rectangle shaded is the same across the three rectangles.

The difference is the total number of equal parts.

So get focused and be ready.

I'd like you to pause and have a think maybe get some of those counters or screwed up pieces of paper.

Whatever it is you organised.

How could you represent 1/4 using a set of counters or items? Come back when you're ready.

Now it'll be difficult for you to show me this because it's probably down in front of you somewhere.

So let me show you instead on the screen how I represented 1/4.

I had this many counters, this many and this many.

Of the first purple set, I represented 1/4 like this, 1/4.

But I have more than four items. How many items are there in the purple set? 12.

And how many of those 12, are we talking about? Three, 3/12, 1/4 is equal to 3/12.

Of a set of 12, 1/4 is three.

In the next set, I've represented it this way, 1/4 of four is one, of a set of four counters.

One counter is 1/4 of the whole set.

And in this last one, how many of them would I use to represent 1/4? Good, two.

1/4 of a set of eight shape.

Eight items, could be shapes of eight items, 1/4 of eight items is two 2/8 and 1/4 are equivalent.

How else could I represent 1/4 though? So the most I had on the previous slide was 12 counters.

And I've had 1/4, 2/8, 3/12 as equivalents but what if I had this many counters? What fraction, equivalent fraction to 1/4 is represented here? 4/16.

Good.

What if I had this many? What would my equivalent fraction be now? 5/20.

And now? 6/24.

This family of equivalent fractions all representing 1/4 with a different number of items in the set.

But 1/4 of the set being represented each time.

I'd like you to pause now and have a go at the independent task.

Be prepared to make use of those items you collected at the start of the session to help you find some equivalent fractions.

How did you get on.

So we had these three fractions to represent and find some equivalent fractions for, again it's going to be hard for you to show me what you've done.

But perhaps you've taken some photographs that later a parent or carer can share on Twitter for you.

In terms of the equivalent fractions, at least we can go through those.

So for 2/5, when I was working, I found these three equivalent fractions to 2/5, I increased the number of items that I had by five each time and looked at how many of those in total, how many of that total would represent 2/5 of the whole, it was useful to start with 2/5, just to start with five items and look at two of those five, and then increase by five by five by five at a time.

Similarly, with 3/4 starting with four items, thinking about three of them and increasing the set by four each time, and looking at the difference that makes my numerator, and the same with 4/7.

You need quite a few items here.

So at one point, I had 28 items in front of me.

And I was thinking about in that case 16 of those twenty-eight.

I mentioned the photos earlier, if you would like to share those as part of your learning from this session with Oak National, please ask your parents or carer to share your work on Twitter tagging @OakNational and hashtag Learn with Oak.

Fantastic learning everyone.

I'm really really proud of you all for your participation, your contributions and all of that fantastic learning.

You should be really proud of yourselves as well.

If you've got anything else learning wise lined up for the day, do have a break first.

I'm going to carry on reading before I do anything else.

I hope to see you again soon for some more maths learning.

Until then Look after yourselves.

Bye.