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Hello, I'm Mr. Coward.

And welcome to today's lesson on ordering decimal fractions.

For today's lesson, all you'll need is a pen and paper or something to write on and with.

If you can please take a moment to clear away any distractions including turning off any notifications, that would be great.

And if you can, try and find a quiet space to work where you won't be disturbed.

Okay, when you're ready, let's begin.

Okay, time for the "Try This" task.

The bar model and the hundred square both represent 1.

So here we've got our bar model which represents 1.

And here we've got our hundred square which represents 1.

How can I shade the hundred square with the same fractions as the bar? So we've got to shade this using these colours and using these fractions.

And I don't want you to do it in just one way.

I want you to see if you can be a bit creative and see if you can do it in two, three, even maybe four ways.

Okay, and try and be adventurous with the ways that you do it.

Okay, so pause the video and have a go.

Pause in three, two, one.

Okay, so here are my answers.

Now, here I've split up the pink.

I have kept the green over there and did the purple there.

Green here, purple there.

Pink there.

This time, this was me going a bit funky.

I did my 50, I did my half like this and then I did this as my other two fractions.

And this was a quite tricky one.

You've got to make sure that each section has the right area.

So you have to be really careful with the area of triangles there.

Now, what were our fractions? Well, our fractions were 3/10, 1/2, and something.

Hmm? Well what was that something? What was that missing area? Well.

If I make this over ten.

Times the numerator and the denominator by 5.

So 2 times 5, 10.

1 times 5, 5.

Then I can see I have 3 + 5, 8/10.

So I'm missing 2/10 from the whole.

The whole is 10/10.

So that's my other missing fraction there.

Now I can go more than just writing them as tenths.

I can also write them as hundredths.

Which is more helpful for when I'm doing it on a 100 square.

And now, you can see that the pink section was the 50.

That was the 1/2.

So for the pink section, you need to shade in 50 squares.

For the green section, you need to shade in 30 squares.

And for the purple section, you need to shade in 20 squares.

And it doesn't matter how you do it.

As long as you shade in that amount of squares.

Okay.

When the denominator of a fraction is a power of 10, e.

g.

10, 100, 1000.

We can write the fraction differently.

So what does that mean? Okay, let's have a look at this one here and let's think about this.

Well, 7, 10.

So 7 times 10 is 70.

So that means 70 squares are shaded.

So I can say this is 70 out of 100.

Okay, using equivalent fractions, could I describe that in a different way? Well, I could describe it like this.

One, two, three, four, five, six, seven out of ten.

Okay, they're the same.

And there's lots of other different ways as fractions that I could write that.

But now I'm going to try and write it as a decimal.

Hmm? Well, let's think about our place value.

So we have our ones.

Not with an 'M' with an an 'N.

' We have our ones.

So they are ones.

Then we have our decimal place.

Then we have our tenths.

Like this.

That should be an 's' I'm sorry.

Having a funny day again.

We have hundredths.

Okay so we have 1/100's.

Tenths, hundredths, and this here.

Well we wouldn't write 70 in there.

What we'd do is we'd exchange.

We'd exchange those 70 for tenths.

And we can exchange them for 7/10.

So what we'd actually have is we'd have 0.

7.

And you can see that more clearly here.

Here, we have zero ones.

And 7/10.

Okay, can you see that? Can you see how we have literally 7 tenths.

That's how we say it.

So we have 7/10 here.

And that is 0.

7.

And you can do this with lots of others.

So say we had 72 out of 100.

Well we can split this up into 70 out of 100.

And 2 out of 100.

Now these, every 10 we have would get exchanged.

So we'd do 7 exchanges.

So 7 exchanges would give us 7/10 and 2/100.

So 72 out of 100 would be 0.

72.

Okay? Well, what about now if we had 172 our of 100.

Well, we have a whole one there.

Then we have our 70's.

And we can exchange this for 10/10.

And we can exchange 10/10 for a whole.

So that would be 1.

72.

Okay? 7/10, this one.

We can write that as 7/10.

We can write that one as a whole.

And can we can write that as 2/100.

So we have 1.

72 or one whole one, 7/10, and 2/100.

So can you see how there's lots of ways that you could write this? And you could even use all the equivalent fractions such as 35/50 or 140/200.

When we have a power of 10.

So like 10, 100, 1000, 10000, etc.

It makes it really, really easy to write it as a decimal.

And that is because we use our base 10 system.

10 is a very special number in our number system.

Okay, so I want you to try and find at least two different ways that we can represent the fraction.

So you might want to write one as a fraction.

You might want to write one as a decimal.

Or you might even want to do two or three as a fraction and then then one as a decimal.

Okay, so pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

First one, I have 3/10 or 30/100.

Or we can write that as 0.

3.

Okay, here I have 25/100 which would be 0.

25.

Can you see how it's a quarter? Well yes, it's a quarter of the total area shaded.

What about this one? 6/10 and an eighth.

which we could write that as 0.

68 or we can write it as 68 over 100.

Or we can write it as an equivalent fraction.

For instance, 34 over 50 or 17 over 25.

Or make it a bigger one, 136 I think, over 200.

The last one.

One, two, three, four.

So that'd be 40, 47, 47 out of 100, or 0.

47.

And again you could use equivalent fractions to find more.

So really done if you got a few of them correct.

And that is awesome work.

Okay, so what I'm going to do now, try and do this without any pictures.

So here, we've got 3/10.

Tenths are in this column there.

Here, we've got 3/100 which is our hundredths column.

So we've got out ones, our tenths with our decimal place here.

And our hundredths.

So our hundredths column is here, and we have 3 of them so it would be like that.

Well here, we've got 30.

But we wouldn't write 30 in there.

We could do an exchange.

We could exchange 30/100 or 3/10.

Okay, 'cause every time we get more than 10 in there, we can do an exchange.

So we could exchange for 3/10.

Well, this one, how's it changed? Well, it's got a 7 now.

So I can still exchange my 30.

30 of these, I can exchange them.

So if I write that as 30 and 7, I can exchange 30 of them for 3/10 and I'll have 7/100.

So that would be 0.

37.

This time I have 37/10.

So I'd have 37 in this column.

Now what I can do, is I can exchange 30 of those for ones.

And then I've got 7/10 left.

So I'd have 3 whole ones and 7/10 left.

Okay, so hopefully that made sense.

And I'd just like you to have a go at this.

Okay, so your turn.

Have a go at these questions.

Pause the video and have a go.

Pause in three, two, one.

Okay, so welcome back.

Hopefully you got these as your answers.

0.

9 0.

09 0.

9 0.

92 and 9.

2.

Okay, do you notice anything? Do you notice how when here we've got 9/10, but here we've got 9/100.

The value of the 9 is worth less.

The value of the 9 is worth less.

They are hundredths now, not tenths.

So we get a smaller number.

And in fact, we need 90/100 to have the same value as 9/10.

Because for every 10 we have, we can exchange once.

So we do 9 exchanges, so we'd get 9/10 now rather than 90/100.

Here, we can do 9 exchanges to get 9/10 and we'd have 2/100 left over.

But here, well what's different between these two? Well, our denominator on this one is 10 times smaller.

And because our denominator is 10 times smaller, our answer is actually 10 times bigger because the denominator is like, remember when we thought of fractions as division.

Well if you divide it by 100, you're going to get a small answer than dividing by 10.

So here, you can see that we have a bigger answer than we would for 92/100.

So there's loads of different ways that you can think about fractions.

So it's division, there's parts of a whole that help you see why these are what they are.

Okay so we're going to use our knowledge now of fractions and decimals to build to ordered decimals.

So, this one.

Well, it's good to think of this as 8/10 and 2/100.

And this one is 9/10.

And this one, what's that? Tenths, one hundredths, one thousandths.

So which one's bigger? Oh, just by the way, ascending order means from smallest to biggest.

Okay, so ascending is smallest to biggest.

So for instance, one, two, three, four.

That it is ascending order because it goes from smallest to biggest.

Okay, so which is the smallest now? Hmm? Well, 9/10 is bigger than 8/10.

So this one is bigger than that one and that one because there's no more exchanges to be made.

But then 2/100 of 5/1000.

Well 1/1000 are 10 times smaller than a hundredth.

So this one is smaller than that one.

And that means that one's our smallest.

Here, this one's our next smallest.

And then finally, our biggest one is 0.

9.

Okay, so when we're ordering them, we care about what is in the first column and we compare that first.

And if two of them are equal, we look at the second column, and then we compare that.

And here, we've got 0, so we've got 0/10.

So 2/10 is obviously bigger than 0/10.

And I know we've got thousandths to go afterwards, but you can see from this second digit that that 2 is bigger than that 0.

Okay, so now it's time for the independent task.

So, there are three questions.

And I'd like you to pause the video to complete your task and resume once you've finished.

Okay, and here are my answers.

You may need to pause the video to mark your work.

Okay, and all that's left is the explore task.

So you need to put the cards below in ascending order.

So ascending, what does that mean? From smallest to biggest.

Okay, and once you've done that, you should notice, well you shouldn't notice, but I'm telling you that the sum of the cards is 3.

And these can be organised into 3 groups each with a sum of 1.

So you're going to have to put them into three groups.

Groups of three.

So three groups of three.

And in each group, you want that sum to be 1.

Okay, so it's going to be a bit tricky guys, but have a go, alright? See if you can do it.

So, pause the video, complete your task, resume once you're finished.

Okay, so here are my answers.

Here are they are in ascending order and here are the groups that sum to 1.

Okay, that second part of that task was pretty tricky.

And the first wasn't particularly easy either.

So really well done if you got that correct.

Okay, and that is all for this lesson.

Thank you very much for your hard work, and I look forward to seeing you next time.

Thank you.