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Hello there.
My name is Mr. Tilstone.
I'm a primary school teacher and I'm a maths specialist, and I'm really delighted to be with you today learning all about unit conversions.
Units of measure are everywhere.
I'll bet in front of you right now you've got a ruler.
And on that ruler, I bet it shows centimetres and millimetres, two different units of measure.
When you go home tonight, have a look in your cupboards, in your fridge, and you'll see dozens of examples of grammes, kilogrammes, litres, millilitres, and so on.
Today we're going to be learning all about converting from one unit to another.
So if you're ready, I'm ready.
Let's begin.
The outcome of today's lesson is I can use known facts to carry out conversions that correspond to 10 and 100 parts.
And recently you might have been looking at 1000 parts.
Our keywords today are my turn equivalent, your turn.
My turn, convert, your turn.
If you've been working with me recently, you've heard those words quite a lot, but let's have a little reminder about what they mean 'cause they're very important and they're going to come up a lot today.
If two or more things have the same value, they are equivalent.
And you could even use an equal sign.
Convert means to change of value or expression from one form to another.
So I'll give you an example, changing from grammes to kilogrammes is converting or changing from millilitres to litres is converting.
Our lesson today is split into two parts or two cycles.
The first will be centimetres to millimetres and the second pounds to pennies and metres to centimetres.
If you are ready, let's have a look at centimetres to millimetres.
In this lesson, you are going to meet Izzy, Lucas and Laura, have you met them before? They're here today to help us out with our maths.
Here we go to ruler and it measures centimetres.
Now, of course, that's not to scale, but this ruler is showing centimetres as shown by the larger interval marks and the numbers.
So can you see 0, 1, 2, 3, they're centimetres? But what are the smaller interval marks in between the numbers showing? So for example, look at one and two.
Numbers one and two.
Can you see some little marks in between? Well, what are they? They're showing millimetres.
The word millimetre means 1,000th of a metre, but it can also be thought of as one 10th of a centimetre.
So one centimetre is equivalent to 10 millimetres.
You might have already known that.
This might be the first time you've heard that, but try and memorise that.
Try and get that one locked and loaded.
You're going to use it a lot.
So one centimetre equals 10 millimetres.
Here we go.
Look, that's one centimetre.
And can you see 10 little millimetres in between? It's a very small unit of measurement.
This fact can be used to explore the relationship between whole numbers of centimetres and the equivalent number of millimetres.
So here we've got one centimetre, 10 millimetres, two centimetres, 20 millimetres, three centimetres, 30 millimetres, four centimetres, 40 millimetres, five centimetres, 50 millimetres.
You get the idea.
Six centimetres, 60 millimetres, seven centimetres, 70 millimetres, eight centimetres, 80 millimetres, et cetera, et cetera.
15 centimetres, 150 millimetres.
They're equivalent.
This relationship could be explored by drawing circles.
You might have had some experience, lots of experience doing that recently with other units.
So here we've got one centimetre and one centimetre equals 10 millimetres.
You know that already.
Well, here's two centimetres.
How many millimetres is that? That's 20 millimetres.
Here we've got three centimetres.
How many millimetres is that? That's 30 millimetres.
Here we've got four centimetres.
How many millimetres is that? That's 40 millimetres.
And parts of circles can use to explore parts of one centimetre.
Again, you might have done that quite recently with things like kilogrammes, but this is centimetres, so that's half a centimetre.
That's the fraction.
What about the decimal? 0.
5 centimetres.
And what's about the millimetres? How many millimetres will be half a centimetre? Remember a centimetre is 10 millimetres, so it's half of ten, five.
So that's showing five millimetres.
So half a centimetre, 0.
5 centimetres and five millimetres are three different ways of saying the same thing.
They are equivalent.
What about this one, a different example? So we've got one centimetre, the fraction is one 10th of a centimetre.
The decimal would be 0.
1 centimetres, which we could also read as one 10th of a centimetre.
What about millimetres? Well, remember one centimetre is 10 millimetres, 10 divided by 10 equals one.
So that's one millimetre.
One 10th of a centimetre, 0.
1 centimetres and one millimetre all mean the same thing.
Now whole circles and parts of circles can be combined to show various conversions.
And again, you might have done that with other things like kilogrammes or litres.
But here we've got centimetres, we've got a whole centimetre and part of a centimetre and we can combine them.
So what can you see there? What fraction can you see? Let's start with that.
That's one-and-a-half centimetres.
What decimal can you see? 1.
5 centimetres.
What about a mixture of centimetres and millimetres? What can you see there? That's one centimetre, five millimetres.
And then finally, what about as just millimetres, well, we'd need to convert that one centimetre into 10 millimetres.
10 millimetres and five millimetres equals 15 millimetres.
So that's four different ways of expressing the same value.
What about this one? Let's have a look at this one.
What can we see here? Again, we've got a whole number of centimetres and a part of a whole number of centimetres.
Well, the tenths.
How many tenths specifically? Seven tenths.
So there we've got one and seven tenths.
What about as a decimal? What can we see there? That's 1.
7 centimetres.
What about as a mixture of centimetres and millimetres? That's one centimetre and seven millimetres.
What about just millimetres? Let's convert our one centimetre into 10 millimetres.
Put them all together and we've got 17 millimetres.
So that is four different ways of saying the same thing.
They're all equivalent.
What about this one then? So this one's got an extra centimetre, an extra whole centimetre and a fraction as well.
What we got here, we've got two-and-three-tenths of a centimetre.
What about the decimal? 2.
3 centimetres.
What about the mixture of centimetre millimetres? We've got two centimetres and three millimetres.
And what about just millimetres? Let's convert.
We've got 23 millimetres, four different ways of saying the same thing.
A part-part-whole model can be used to partition the centimetres.
Once again, you might have done this very recently with something like kilogrammes.
Well this is centimetres.
So we've got 2.
3 centimetres.
Let's partition that.
So let's put that into two different parts.
The whole number part is two centimetres and the decimal part is 0.
3 centimetres.
Now let's convert each part of that into millimetres.
Two centimetres is 20 millimetres and 0.
3 centimetres is three millimetres.
Put those together and we've got 23 millimetres.
So 2.
3 centimetres is also 23 millimetres.
Let's have a check.
So we've got a ruler here.
Express each value as both centimetres and millimetres.
So what's A, what's B and what's C? Pause the video and have an explore.
Welcome back.
Did you manage to give each of those values in both centimetres and millimetres? Let's have a look.
So A, that's exactly two centimetres.
So that's exactly 20 millimetres.
B is not a whole number.
It's 6.
5 centimetres.
That's decimal, or 65 millimetres.
So I can see the six centimetres is 60 millimetres and there's an extra five.
So 65 millimetres.
What about C? That's 10 and something, isn't it? Or just a bit less than 11 centimetres.
So it's 10.
7 centimetres or 107 millimetres.
If you've got those three answers correct, you are on track in today's lesson.
Well done and you are ready to carry on.
So let's do just that.
Izzy is confident that she can convert centimetres to millimetres without circles or part-part-whole models using a stem sentence.
Hmm.
And the question is, what is 2.
3 centimetres in millimetres? And let's have a look.
This is her stem sentence.
One centimetre is 10 millimetres.
Hm, centimetres is hm millimetres.
hm, centimetres is hm millimetres.
So hm centimetres is hm millimetres.
Well, let's have a look at filling that in.
So two centimetres, we're partitioning that number into two and 0.
3.
Two centimetres is 20 millimetres.
0.
3 centimetres is three millimetres.
So 2.
3 centimetres is 23 millimetres.
Well done, Izzy.
Well, let's have a check.
Let's see if you can use that stem sentence too.
Use a sentence to convert 6.
5 centimetres into millimetres.
Off you go.
Let's have a look.
Six centimetres is 60 millimetres.
0.
5 centimetres is five millimetres.
So 6.
5 centimetres is 65 millimetres.
That's using partitioning.
Well done if you've got that.
I think you are ready for some independent practise.
So let's have a go.
So number one, record each measurement in both centimetres and millimetres.
So you've got A to H, each one, write twice in two different ways.
And number two, what's being represented by the shaded parts below? Got two to do for that.
Number three, some part-part-whole models.
The first one's got a bit more information.
So do use that as a reminder when doing the second one.
Number four, use that stem sentence to convert 7.
8 centimetres into millimetres.
And number five, Izzy has measured the length of her pencil.
It's 12.
9 centimetres.
Lucas measures the length of his pencil.
It is 130 millimetres long.
Whose pencil is longer and by how much.
Good luck tackling those questions.
And I will see you soon for some answers.
Welcome back, let's have a look.
So number one, let's start with A, that's two centimetres or 20 millimetres.
That was a whole.
Number B is 2.
5 centimetres or 25 millimetres.
C is 4.
8 centimetres or 48 millimetres.
D, that's six centimetres or 60 millimetres.
E, that's 8.
7 centimetres or 87 millimetres.
F, that's 9.
4 centimetres or 94 millimetres.
G, that's 12 centimetres or 120 millimetres.
And H, just a bit less than 15, look.
That's 14.
9 centimetres or 149 millimetres.
And let's have a look at these circles and part circles.
The first one is showing four-and-a-half centimetres, 4.
5 centimetres, four centimetres five millimetres or 45 millimetres.
They're all exactly the same.
They're all equivalent.
Just different ways of saying it.
And the second one, that's three-and-eight-tenths of a centimetre, 3.
8 centimetres, three centimetres eight millimetres or 38 millimetres.
And these part-part-whole models.
So we've got nine centimetres, which is 90 millimetres and 0.
6 centimetres is six millimetres.
Combine them and we've got 96 millimetres.
And then 10.
2 centimetres, first let's partition, that's 10 centimetres and 0.
2 centimetres.
10 centimetres is a hundred millimetres, 0.
2 centimetres, two millimetres, put them together and you've got one 102 millimetres.
Using that stem sentence to convert 7.
8 centimetres into millimetres.
We've got one centimetre is 10 millimetres, seven centimetres is 70 millimetres.
So 0.
8 centimetres is eight millimetres.
So 7.
8 centimetres is 78 millimetres.
And Izzy measured the length of her pencil.
It's 12.
9 centimetres.
Lucas measures the length of his pencil.
It's 130 millimetres long.
Whose pencil is longer and by how much? Well, there's not much in it.
Not much at all.
12.
9 centimetres is equivalent to 129 millimetres.
So Lucas's pencil is longer by one millimetre, tiny amount or 0.
1 centimetres you might have put.
Well done if you got that.
You're doing ever so well.
And I think you are ready to tackle the second part of the lesson.
So this is pounds to pennies and metres to centimetres.
So in the first cycle we looked at something that corresponded to 10 parts.
These ones are going to correspond to a hundred parts.
So one pound is equal to 100 groups of 1p.
So although there's lots more coins in the second part of that, they're actually worth the same.
They're equivalent to each other.
There's the same in value.
That relationship could be explored by drawing unit conversion circles.
And you've done that plenty of times now.
So here we go.
That's £1.
£1 equals 100p, £2.
£2 equals 200p or pence, £3.
£3 equals 300 pence.
£4, how many pence is that? How many pennies? That's 400 pence.
Parts of circles can be used to explore parts of £1.
So here we go.
Look, we've got that as a decimal.
Now that's not how we'd write that.
And you might have had some practise perhaps earlier on this year at writing different money amounts.
We don't just use one decimal place, we use two.
And a zero is used to show there's no extra 100ths of a pound.
That is how we would write that.
So that's a decimal.
And that's just pennies or pence.
So unlike with other unit conversions, people don't tend to refer to fractions of pounds.
It wouldn't say like half a pound or quarter of a pound or three quarters of a pound.
So fractions aren't used, but decimals are.
So what about this one? So we've got £1 is our large circle, and that's split into four parts.
So each part is worth 25 pence, or we could write that as a decimal.
So £0 and 25 pence, 0.
25.
And what about this one then? So this is £1 split into five equal parts.
That's 20 pence.
Or we could write that as £0 and 20 pence, as a decimal.
And this is £1 split into 10 equal parts.
That's 10 pence or £0 and 10 pence.
And that's how we'd write that as a decimal, 0.
10.
Whole circles and parts of circles can be combined, just like before, to show various conversions.
So here look, we've got two whole circles, that's two whole pounds and then half of a circle.
So that's either 50p or £0 and 50p.
Combine them together and you've got £2.
50 or you've got 250 pence.
So that's a visual representation of that conversion.
What about this one then? Got three whole circles.
So three whole pounds and then two tenths of a pound or two 0.
1 of a pound.
That's 20 pence.
So that makes £3.
20 or 320 pence.
Once again, a part-part-whole model can be used to partition an amount into the number of pounds and the number of extra pennies with it, just like before.
So partitioning this number, think about how many pounds to start with.
That's got £2.
And then how many pence? That's got 50 pence.
And that's how we'd write it in decimal form.
That's 200 pence and 50 pence.
Combine them together and you've got 250 pence.
So that's converting from £2.
50 into pence or pennies.
Once again Izzy's confident that she can convert pounds to pennies without circles or part-part-whole models using the stem sentence.
So that question again, what is £3.
25 in pence? One pound is 100 p.
Hm Pounds is hm p.
Hm Pounds is hm p.
So hm pounds is hm p.
Well let's have a look.
£3.
25, start by partitioning.
£3 is how many pence? 300 pence.
And then the other part of that number is the 0.
25.
So that's zero pounds and 25p, which is how many pennies? 25p.
So £3.
25 is 325 pence.
Just as one pound is equivalent to 100p, one metre is equivalent to 100 centimetres.
So they both involve 100 parts.
The same calculations can be used to convert from the larger unit, that's metres in this case, to the smaller unit, that's centimetres in this case.
So just the same things we've just done with pounds and pennies.
So let's have a look at this metre, this 100 centimetres, one metre can be split into different parts.
It can be split into how many parts is that? Two, that's two equal parts.
One either side of the divide.
As a fraction, each part is what? There's two equal parts that is half a metre.
There's decimal, each part is 0.
5 metres.
And each part is equivalent to how many centimetres? So think about what, half of 100 is, that's 50.
So each part's equivalent to 50 centimetres.
You could split it a different way.
How many equal parts have you got now? We've got three divisions.
So how many parts does that make it? How many parts does that turn it into? How many can you count? There's four.
That's four equal parts.
As a fraction, each part is what? So if you split something into four equal parts, each part is one quarter.
So that's one quarter of a metre.
As a decimal, each part is? So what's a what's one quarter is a decimal, that's 0.
25 metres.
And then each part is equivalent to how many centimetres? Well, a hundred centimetres divided by four equals? 25 centimetres.
So they're all equivalent.
Or we could split it like this, into how many parts is that? Count them.
That's five equal parts.
So as a fraction then, if something's been split into five equal parts, what's each fraction? That's one fifth of a metre.
As a decimal.
What's that as a decimal? One fifth, 0.
2.
0.
2 metres.
And then each part's equivalent to how many centimetres? Hm, that's 100 centimetres divided by five, which is 20 centimetres.
So they're all equivalent.
What about this? How many equal parts are there now? 10.
One metre can be split into 10 equal parts.
So as a fraction then each part is one 10th of a metre, there's a decimal, each part is 0.
1 metres.
And then each part's equivalent to, well 100 divided by 10 equals 10.
So each part's equivalent to 10 centimetres.
They're all equivalent.
A part-part-whole model, once again, can be used to partition the metres into metres and centimetres or just centimetres.
So here look, we've got eight-and-three-quarter metres and we're partitioning that into eight metres.
And what's the other part? Three-quarters of a metre.
Right, now we can turn those into centimetres.
So eight metres, what's that in centimetres? 800 centimetres.
And what's three quarters of a metre in centimetres? Well, one quarter is 25 centimetres, three quarters is 75 centimetres.
Combine those together.
Eight-and-three-quarter metres equals 875 centimetres.
Izzy thinks she can change her stem sentence to convert from metres to centimetres.
So what is 8.
75 metres in centimetres? She's not gonna use any models.
Just a stem sentence.
So one metre is 100 centimetres.
hm metres is hm centimetres.
hm metres is hm centimetres, so hm metres is hm centimetres.
Well partitioning that number, we've got eight metres is how many centimetres? We just did it before.
800 centimetres.
And then the other part of that number is 0.
75 metres.
And what is that in centimetres? We did it before.
That's 75 centimetres.
So 8.
75 metres is 875 centimetres.
'Cause 8.
75 metres is the same as eight-and-three-quarters of a metre.
Well let's do a check.
Izzy is converting 9.
2 metres into centimetres.
And she said this, she says, "One metre is 100 centimetres, nine metres is 900 centimetres, 0.
2 metres is two centimetres.
So 9.
2 metres is 902 centimetres." Okay, I don't think that's quite right.
I think some bits of it are right and some bits of it are not right.
So can you give her some feedback, please.
Pause the video.
Welcome back.
Well, what did you say? Let's start with some positives.
Well, she's correctly converted nine metres into 900 centimetres, fabulous.
However, when partitioning 9.
2, it seems like she thought that the two represented the number of centimetres, but it's not, is it? 0.
2 metres is in fact equivalent to 20 centimetres.
So 9.
2 metres isn't nine metres two centimetres, it's 920 centimetres.
Time for some final practise.
So number one, complete the tables using your knowledge of unit conversions and one's been done for you.
Can you fill in the rest of the gaps and you'll notice something about the tables.
They're very similar.
Number two, complete the stem sentences, convert £4.
90 into pennies and convert 4.
9 metres into centimetres.
And once again, you're going to find they've got some things in common.
Number three, what could the shaded parts of this model be showing in terms of pounds and pence, or metres and centimetres? And how many different ways can you think of to answer that? Number four, Lucas is one-and-a-quarter metres tall, Izzy 140 centimetres tall, who is taller? Pause the video and give those a go.
Welcome back.
That was your final practise of the lesson.
Would you like some answers? Of course.
So number one then, let's start with the pounds and pennies.
50p is the same as £0.
50.
£3 is the same as 300p.
£2.
40 is the same as 240p.
£5.
80 is the same as 580p and £6.
75, it's the same as 675p.
And the metres and centimetres.
You might notice a lot of these numbers are the same or very similar at least.
0.
5 metres is 50 centimetres, three metres is 300 centimetres, 2.
4 metres is 240 centimetres, 5.
8 metres is 580 centimetres, and 6.
75 metres is 675 centimetres.
And these stem centres to start with £4.
90.
So four pounds is 400p, £0,90 is 90p.
So £4.
90 is 490p.
And then this one little bit similar, four metres is 400 centimetres, 0.
9 metres is 90 centimetres.
So 4.
9 metres is 490 centimetres.
And for number three, what could the shaded parts of this model be showing in terms of pounds and pence? Let's start with that.
Well, you could say £4.
30, I can see that.
Or you could say 430 pence.
That's a unit conversion, they're equivalent.
And the metres and centimetres, you might say that's 4.
3 metres.
I can see that.
Four-and-three-tenths of a metre, I could see that, or 430 centimetres, I could see that too.
And then Lucas is one-and-a-quarter metres tall.
Izzy is 140 centimetres tall, who is taller? So we need to do some conversion here.
We need to convert one of those into the other.
So when converting to centimetres, it's possible to see that Lucas is shorter as he is 125 centimetres and Izzy taller as she is 140 centimetres.
We've come to the end of the lesson and haven't you been amazing? Today's lesson has been all about using known facts to carry out conversions that corresponded 10 and 100 parts.
A partitioning strategy can be used when converting from centimetres to millimetres, starting with a known fact that one centimetre is equivalent to 10 millimetres.
So you explored that with a part-part-whole model and then just a stem sentence.
So for example, 4.
2 centimetres is equivalent to 40 millimetres and two millimetres or 42 millimetres.
The same process can be applied when converting from pounds to pennies or metres to centimetres.
So for example, £4.
20 is equivalent to 400p and 20p or 420p.
4.
2 metres is equivalent to 400 centimetres and 20 centimetres or 420 centimetres.
So partitioning really is a great way to convert from one unit to another.
Well done once again on your accomplishments and achievements in today's lesson.
I think it is deserve a pat on the back.
Give yourself one, please.
And well done once again.
I've enjoyed spending this lesson with you and I really hope to get the chance to spend another maths lesson with you in the future.
But until then, enjoy the rest of your day.
whatever you've got in store.
Take care and goodbye.
