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Hello there.

My name is Mr. Tilston.

I'm a teacher and a math specialist.

So it's my great pleasure to be with you today, teaching you a lesson all about unit conversions.

Units of measurement can be seen everywhere, every single day.

For example, I've got here some custard, and you might see that the measurement of the custard has been given in grammes, 500 grammes.

And here I've got some flour, and you might see that the measurement for the flour has been given in kilogrammes, 1.

5 kilogrammes.

It would be useful then if we had a way to convert from one unit of measure to another, and that's what we're going to do today.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can use known facts to derive common conversions over one.

You might have had some recent experience of conversions that are one and more recently still less than one.

This time it's going to be over one.

We've got two keywords.

The first is my turn, equivalent.

Your turn.

And the second is my turn, convert.

Your turn.

You may be familiar with those words already, but let's have a quick reminder to see what they mean.

If two or more things have the same value, they are equivalent and convert means to change a value or expression from one form to another.

For example, grammes to kilogrammes, or millilitres to litres.

Our lesson today is split into two parts, two cycles.

The first will be fraction and decimal conversions greater than one kilogramme.

And then the second part will be converting other units greater than one.

So let's begin by really focusing on one kilogramme.

In this lesson, you're going to meet Izzy and Lucas.

They're here today to give us a helping hand with our maths.

Izzy has previously created unit conversion circles to investigate equivalences less than one, and hopefully you've done the same as well.

So she's drawn a circle to represent one kilogramme and then looked at dividing the circle in different ways.

So this is showing half a kilogramme and 0.

5 kilogrammes, and 500 grammes are all equivalent.

She says, I wonder if we could combine whole circles like the one kilogramme and parts of circles like the half a kilogramme to show equivalences greater than one.

Hmm.

So putting them together basically.

Izzy starts by investigating examples where the fraction is a unit fraction.

So in this case look, she's looking at half one is the numerator, it's a unit fraction.

So when you combine though, that whole circle and that part of a circle together gives you one and a half kilogrammes.

So just take a moment just to look at that.

See if you agree.

Can you see one and a half kilogrammes they're altogether.

Good.

What about now? What can we see now? Well, we can see a decimal, that's 1.

5 kilogrammes.

What about now? What can you see now if you combine those together? You've got one kilogramme, 500 grammes.

So mixed units.

What about now if we convert that one kilogramme into grammes, we've got 1,500 grammes.

So we've got four different ways of saying the same thing, they're all equivalent to each other.

Let's do another one.

Let's do a different one.

So we've still got that one kilogramme and we're going to combine it with a fraction to start with.

So that's a quarter.

So we've got one and a quarter kilogrammes.

What decimal do you think we've got? Hmm, something kilogrammes.

We've got 1.

25 kilogrammes.

What about as a mixture of kilogrammes and grammes? What do you think? I can see one kilogramme, 250 grammes.

And then what about adjusting gramme? Let's convert that one kilogramme into grammes, put them together and we've got 1,250 grammes.

So again, four different ways of saying the same thing.

They are all equivalent to each other.

What about now, what have we got? Start with a fraction.

What can you see? Combine those two together and you've got one and a fifth kilogrammes.

What about the decimal? What do you think? There's a clue.

2 kilogrammes.

What about kilogrammes and grammes? Well, that's one kilogramme and that's 200 grammes, so that makes one kilogramme 200 grammes.

And then what about in just in grammes? Convert that one kilogramme into grammes, it's a thousand grammes.

Put them together and you've got 1,200 grammes.

They are all equivalent, all different ways of saying the same thing.

What about now? What can you see now? Start with a fraction.

We've got one and a 10th kilogrammes, as a decimal 1.

1 kilogrammes, as a mixture of kilogrammes and grammes, we've got one kilogramme 100 grammes.

And what about just in grammes? Convert that one kilogramme and you've got 1,100 grammes.

Again, four different ways of saying the same thing, they're all equivalent.

Now Izzy is investigating one-unit fractions.

They were all unit fractions.

And she's taken this example.

So this is a circle split into four parts.

So they're quarters, but she's looking at three quarters.

Here we go.

So what fraction can you see now? That's one in three quarters of a kilogramme.

What about a decimal? Put those together and we've got 1.

75 kilogrammes.

What's about as a mixture of kilogrammes and grammes? Well, we've got one kilogramme and then 250, 500, 750 grammes, if you put those three together.

So that's one kilogramme, 750 grammes.

And what about just in grammes? What is that? Put all together and you've got 1,750 grammes.

So that was a non unit fraction for our starting point.

And what about now? What can you see now? What fraction to start with? That's fifths.

So I can see one in four fifths of a kilogramme.

There's a decimal.

8 kilogrammes, kilogrammes in grammes.

There's your kilogramme.

Add those together and you've got 800 grammes.

So that's one kilogramme, 800 grammes.

And then just in grammes, that's 1000 plus those two hundreds makes 1,800 grammes.

Those four are equivalent to each other.

Let's have a check, what is being represented here? Can you express that in as a fraction, as a decimal, kilogrammes and grammes and then just in grammes, pause the video.

And as you get on this, let's have a look.

Well as a fraction, that's one and three tenths of a kilogramme.

It's a decimal, that's 1.

3 kilogrammes.

Kilogrammes and grammes, that's one kilogramme and 300 grammes.

And just in grammes, that's 1,300 grammes.

Very well done.

If you've got all of those, you're on track.

Other whole numbers of kilogrammes can be combined with fractions.

So before we looked at changing the fraction, but you could also add more whole numbers too.

So what can you see here? What about as a fraction? Hmm, that's two and a half kilogrammes.

What about as a decimal? 2.

5 kilogrammes.

What about as kilogrammes and grammes? What I could see two kilogrammes and 500 grammes, that's two kilogrammes 500 grammes.

And just in grammes, 1000 plus 1000 plus 500 equals 2,500 grammes.

They're all equivalent.

What about this? Can you see now there's another whole number, another whole number of kilogrammes.

What have we got now? We've got three and a half kilogrammes, 3.

5 kilogrammes, three kilogrammes, and 500 grammes and 3,500 grammes.

Different weights are saying the same thing, all equivalent.

And let's have a check what is being represented here.

Can you say it in four ways? Pause the video.

Let's have a look.

As a fraction, two and three quarters kilogrammes, as a decimal 2.

75 kilogrammes, as a mixture of kilogrammes and grammes, that's two kilogrammes 750 grammes, and just in grammes, that's 2,750 grammes.

And well done if you've got all of those.

Izzy thinks she can visualise those circles rather than drawing them.

So she's picturing them in her mind and use a part-part-whole model to partition the number instead.

So you've used these before, I'm sure this is a part-part-whole model, and we've got 4.

7 as our whole.

I'm gonna split that into two parts.

I'm going to partition it.

So what is 4.

7 kilogrammes in grammes is our question.

Well, with partitioning that into two parts, you can see four kilogrammes and 0.

7 kilogrammes.

We could change that four kilogrammes into 4,000 grammes and we could change the 0.

7 kilogrammes into 700 grammes.

Put them together and you've got 4,700 grammes.

No need to draw the circles.

Well, let's see if you can do it.

Convert 3.

8 kilogrammes into grammes.

Pause the video.

Let's see.

So 3.

8 kilogrammes becomes three kilogrammes and 0.

8 kilogrammes that's been partitioned and now you've got to convert into grammes.

Three kilogrammes is 3000 grammes, 0.

8 kilogrammes is 800 grammes.

Part them together and you've got 3,800 grammes and a big well done if you've got that.

Lucas is using the part-part-whole model to convert 3.

25 kilogrammes into grammes.

Is he correct? Let's see what he does.

So he is partitioned it into two parts, three kilogrammes for one part, 0.

25 kilogrammes for the other part.

So okay, so far, do you think then let's see what he does next.

He's turning the three kilogrammes into 3000 grammes and he's turned the 0.

25 kilogrammes into 25 grammes.

And it's saying 3.

25 kilogrammes is three kilogrammes, 25 grammes or 3025 grammes.

Is that right? Hmm.

No, it's not right.

Lucas has made an error.

Did you spot it? 0.

25 is equivalent to one quarter, which I'm sure you knew, but one quarter of a thousand grammes is actually 250 grammes, not 25 grammes.

I can see where that mistake came from.

He saw the 0.

25 kilogrammes and thought that was 25 grammes, but it's not.

It needs to convert.

So yes, it's 250 grammes and put those together and you've got 3,250 grammes.

So he's had another go.

He says 3.

25 kilogrammes is three kilogrammes 250 grammes, or 3,250 grammes.

Well done, Lucas, you got there in the end.

Izzy thinks she does not need to use a part-part-whole model as she can visualise the circles and use a stem sentence to describe them.

What is 6.

5 kilogrammes in grammes? Let's see what Izzy does.

She's got this stem sentence.

One kilogramme is 1000 grammes.

Mm kilogrammes is mm grammes.

So mm kilogrammes is mm gramme.

Let's see how she fill that in.

So she's saying six kilogrammes.

I can see where she's got that from, is how many grammes? 6,000 grammes and then 0.

5 kilogrammes.

That's the other part is 500 grammes.

So 6.

5 kilogrammes is 6,500 grammes.

I like that.

That's good.

No need to use the circles.

Let's have a check.

Let's see if you can use that stem sentence too.

So use that stem sentence to convert 5.

2 kilogrammes into grammes.

Pause the video.

Hopefully you've got an answer there.

And hopefully you had the chance to practise and rehearse that answer.

Let's have a look though.

So one kilogramme is 1000 grammes, five kilogrammes then is 5,000 grammes.

So we've got the five part sorted and 0.

2 kilogrammes is 200 grammes.

So 5.

2 kilogrammes is 5,200 grammes.

If you've got that, brilliant, you are well on track.

So we've still got that stem sentence and we are weighing this book.

Let's have a look.

Here we've got one kilogramme is 1000 grammes.

So one kilogramme is 1000 grammes and 0.

5 kilogrammes, that's the other part is 500 grammes.

So put together, 1.

5 kilogrammes is 1,500 grammes.

When expressed as a decimal, this book has a mass of 1.

5 kilogrammes.

And when expressed in grammes, it has a mass of 1,500 grammes.

Let's do another one.

Same stem sentence, different object that we are weighing.

Different set of scales.

What do you think this time? Let's have a look.

So one kilogramme is 1000 grammes.

I can see the one kilogramme here and then the other part is 0.

6 kilogrammes, which is 600 grammes.

So 1.

6 kilogrammes is 1,600 grammes.

So we're still partitioning just without the part-part-whole model.

So when expressed as a decimal, these potatoes have a mass of 1.

6 kilogrammes.

When expressed in grammes, they have a mass of 1,600 grammes.

Let's have a check, which of these is the accurate mass of this box of food? Is it A, 2,100 grammes, B, 2,200 grammes or C, 2000 and grammes? Pause a video.

It's B, that's 2,200 grammes.

2 kilogrammes is what's being shown on those scales.

And that's the same as 2,200 grammes.

It's time for some practise.

Write what is being represented by the shaded parts below? So you've got two different examples to complete there.

Number two, complete those part-part-whole models.

The first one's got a little bit more information, so use that as a clue when doing the second one.

And number three, use that stem sentence as you've done before to convert 6.

75 kilogrammes into grammes.

And number four, convert the scale readings into grammes.

Good luck with all of that.

Pause the video and I'll see you soon.

Welcome back.

How did you find that? Let's have some answers, shall we? So number one then, that's four and a half kilogrammes being shown there, which is 4.

5 kilogrammes, which is four kilogrammes and 500 grammes, which is 4,500 grammes.

And then B, that's three and seven tenths of a kilogramme.

That's 3.

7 kilogrammes.

That's three kilogrammes 700 grammes or 3,700 grammes.

And these part-part-whole models, eight kilogrammes is 8,000 grammes.

Note 0.

6 kilogrammes is 600 grammes.

Part 'em together and you've got 8,600 grammes.

And then for the next one, that's nine kilogrammes and 0.

2 kilogrammes.

That's 9,000 grammes and 200 grammes and put them together, you've got 9,200 grammes.

And that stem sentence to convert 6.

75 kilogrammes into grammes.

We've got six kilogrammes is 6,000 grammes note 0.

75 kilogrammes is 750 grammes.

So 6.

75 kilogrammes is 6,750 grammes.

And converting these scale readings into grammes, the first one, that's 2.

2 kilogrammes and that's 2,200 grammes.

The next one, that's 1.

9 kilogrammes, that's 1,900 grammes.

And the third one, 3.

5 kilogrammes is 3,500 grammes.

You're doing really well so far.

I think you are ready for the next part of the lesson that's converting other units greater than one, and we will use some of those same skills.

We're just changing the units of measure.

So just as there are 1000 grammes in one kilogramme, there are also 1000 metres in one kilometre.

So look, the values have stayed exactly the same, just the units changed.

1000 millilitres in one litre.

And so have a look again.

Nothing's changed apart from the unit of measure, the numbers have remained the same.

1000 millimetres in one metre.

And again, all of the numbers have remained the same, just the unit of measure that's changed.

The same models and conversions can be used as only the units of measurement have changed.

So here's 4.

7 litres.

So you're very familiar with this part-part-whole model.

Just like before, you can turn that into millilitres by partitioning.

So we've got four litres and 0.

7 litres, that's 4,000 millilitres and 700 millilitres.

So 4,700 millilitres.

We can also modify and use the stem sentence.

So what's 6.

5 kilometres in metres? We're gonna make a little change to the previous stem sentence and say this, one kilometre is 1000 metres.

So mm kilometres is mm metres.

Mm kilometres mm metres.

So mm kilometres is mm metres.

So let's think about partitioning that number.

So that six kilometres is 6,000 metres, 0.

5 kilometres is 500 metres.

So 6.

5 kilometres is 6,500 metres.

Let's have a check.

Can you convert please 3.

75 metres into millimetres.

Use whatever strategy you like.

Pause the video.

I wonder which strategy you used, or whatever you chose to do.

You might have used a stem sentence for example, you should have something like this.

So one metre is 1000 millimetres, three metres, 3000 millimetres, 0.

75 metres is 750 millimetres.

So therefore is the answer to the question.

75 metres is 3,750 millimetres.

Brilliant if you got that.

Time for some practise.

So number one, write down what is being represented by the shaded parts below, just like before.

Number two, just like before, complete the part-part-whole models.

This time you've got metres and kilometres to convert.

Number three, use that stem sentence just like before.

This time you are converting metres into millimetres.

And number four, you've got an image there of four different jugs with liquid in.

And can you convert it into millilitres at the minute it's in litres, pause the video and good luck.

Welcome back.

That was your final practise of this lesson.

Let's see how you got on then.

So here we've got three and a half kilometres, 3.

5 kilometres, three kilometres, 500 metres, and 3,500 metres.

And the next model we've got five and six tenths of a litre.

6 litres, five litres 600 millilitres, or 5,600 millilitres.

The part-part-whole models, we've got seven metres is 7,000 millimetres.

Note 0.

8 metres is 800 millimetres.

Part them together, you've got 7,800 millimetres.

And the second one, let's partition it first, that becomes six kilometres and 0.

4 kilometres.

That's 6,000 metres and 400 metres.

Put them together, you've got 6,400 metres.

And that stem sentence then, we're converting 3.

25 metres into millimetres.

One metre is 1000 millimetres, so let's partition three metres is 3000 millimetres.

25 metres is 250 millimetres.

Therefore, 3.

25 metres is 3,250 millimetres.

And convert the amount of liquid into millilitres.

So you can see it's in litres at the minute, or we could think of that as a thousand millilitres and a thousand millilitres and a thousand millilitres and 900 millilitres.

So put them all together and you've got 3,900 millilitres.

We've come to the end of the lesson.

Today's lesson has been using those known facts that hopefully you've got really memorised and locked and loaded to derive common conversions over one.

A partitioning strategy can be used when converting from kilogrammes to grammes.

So for example, 4.

2 kilogrammes can be thought of as being equivalent to four kilogrammes and 200 grammes or 4,200 grammes.

The same process can be applied when converting from kilometres to metres, litres to millilitres and metres to millimetres.

The process is just the same.

Very well done on all of your accomplishments and achievements today.

I've really enjoyed spending this math lesson with you and I really hope to get the chance to spend another maths lesson with you in the future.

But until then, take care.

Enjoy the rest of your day.

Well done once again and goodbye.

I've finished the video