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Hi, my name's Mr. Peters.
Thanks for learning with me today.
In this lesson, we're gonna be thinking about a really important topic, thinking about centimetres and metres and how these can relate to each other, and how we can convert between the two of them.
Centimetres and metres are a universal measure used all over the world by lots of different countries to measure the length of different things.
I have no doubt you are already measuring things using metres and centimetres, so let's get used to thinking about how we can convert between the two of them.
When you're ready, let's get started.
By end of this lesson today, you should be a lot more confident and be able to say that you can use your knowledge and understanding of decimal place value and apply that to converting between centimetres and metres.
Throughout the session, we've got three keywords we're gonna be thinking about.
I'll have a go at saying them first, and then you have a go at repeating them.
My turn, metre.
Your turn.
My turn, centimetre.
Your turn.
My turn, convert.
Your turn.
Let's have a think about what these mean.
You may already be quite familiar with metres.
So a metre is a measure of length, which can be abbreviated to the letter m, which stands for metre.
A centimetre is also a measure of length, which again can be abbreviated, but this time we use the letters cm.
And finally, convert is when we exchange a unit for an equivalent unit, for example, converting between millimetres and centimetres.
Today's lesson is gonna be broken down into two cycles.
The first part of this lesson, we'll be thinking about exploring metres and centimetres.
And the second cycle, we'll take it a bit further, linking metres and centimetres beyond one metre.
As always, if you're ready, let's get started.
Throughout this lesson today, you'll also meet Laura and Jacob.
They're gonna be helping us along the way, sharing their thinking and their questions throughout our learning.
So let's start our lesson today here.
We've got a number here and we're thinking about how can we describe this number.
Laura thinks she can describe this number in three different ways.
Take a moment yourself to think about how you might be able to describe it.
Laura thinks we can describe this number as two point five.
We could also describe it as two wholes and five hundredths.
Or we could describe it as two hundred and five hundredths.
Well done if you managed to come up with those.
Let's have a think about the third one quickly.
Two hundred and five hundredths.
Hmm, well, I can see the number has five hundredths, but we've also got two wholes, isn't we? And we know that one whole is equivalent to a hundred hundredths, so two wholes would be equivalent to 200 hundredths.
So altogether we would have two hundred and five hundredths.
Great thinking, Laura.
A quick check for understanding.
0.
84 can be read as A, B, or C? Off you go.
That's right, it's A and C, isn't it? We could read it as zero pint eight four or eighty four hundredths.
Well done if you've got that.
So, here on the screen, we've got an image which we're gonna use to represent one metre.
Obviously, on the screen itself, it's not actually a metre in length.
So I want you to take a moment to think for yourself actually, well, how long is one metre in real life? Can you estimate it? You might like to use your hands to think about the size of one metre.
As I said, throughout this lesson here, we've got this image if we're going to use to represent one metre.
It's not an actual metre, but we're going to pretend that it is one metre for the purpose of this lesson.
We might also use this purple bar to represent one metre as well.
We know that wholes can be divided into technical parts, so we are going to divide our one metre into 10 equal parts.
The whole metre has been divided into 10 equal parts, and each part represents one tenth of a metre.
We also know that we can divide wholes into 100 equal parts.
So again, this time we're gonna divide our whole metre into 100 equal parts, and each one of those parts represents one hundredth of a metre.
Have a look at the differences between these three here.
Look at the size differences.
They're significantly smaller, aren't they, as they go down.
We would require 10 tenths of a metre to be equivalent to one metre, and we would also require 100 hundredths of a metre to be equivalent to one metre.
So when we divide one metre into 100 equal parts, each one part represents one hundredth of a metre as we already talked about.
The name we can apply to this is one centimetre.
There are 100 centimetres in one metre.
I wonder if we can use our sentence stem here that Laura has provided with us to help us.
One metre has been divided into 100 equal parts.
Each part is one centimetre.
Could you have a go saying that? Say that again with me.
One metre has been divided into 100 equal parts.
Each part is one centimetre.
Well done.
So now that we know that one centimetre is one hundredth of a metre, we can think about how we write this as a decimal number.
We can write this as 0.
01 of a metre.
So one centimetre is equal to 0.
01 of a metre.
I say 0.
01, but I think zero wholes and 100th.
So we have zero whole metres and one hundredth of a metre.
Let's have a look at how we relate this then to our place value chart.
Look at the place value headings and how I'm now going to replace these with the images which represent one metre, one tenth of a metre, and one hundredth of a metre.
So we can see that we have zero whole metres, we have zero tenths of a metre, and we have one hundredth of a metre.
So we record it as 0.
01.
So whilst I can say 0.
01, we want to think that it's zero wholes and 100th, or we can extend this into metres.
I say 0.
01 metres, but I think zero whole metres and one hundredth of a metre.
And again, Laura is just reminding us that we know that one hundredth of a metre is equivalent to one centimetre.
Now have a look at our metre stick underneath.
And what do you notice this time? What's changed? That's right.
We no longer have one centimetre, do we? We have three centimetres.
So I wonder how we could describe this.
Well, if one centimetre can be written as 0.
01, then three centimetres could be written as 0.
03 of a metre.
So three centimetres is equal to 0.
03 metres.
I say 0.
03, but I think zero wholes and three hundredths.
And again, extending that to metres.
We have zero whole metres and three hundredths of a metre.
Looking at our place value chart again, if we change our place value headings to the images, we can now see what each number represents.
The first zero represents zero whole metres.
The second zero represents zero tenths of a metre.
And the three represents three hundredths of a metre.
I say 0.
03, but I think zero wholes and three hundredths.
Again, we can think of that understanding as metres as well.
I wonder if you could say this with me.
I say 0.
03 metres, but I think zero whole metres and three hundredths of a metre.
Take a moment.
How else could we describe this? That's right.
We know that three hundredths of a metre can also be described as three centimetres.
Here's another example.
What's changed this time? What do you notice? That's right.
This time, we've got 10 centimetres, haven't we? We've got 10 lots of one centimetre.
Hmm, one centimetre can be written as 0.
01.
So 10 centimetres can be written as 0.
10 metres.
Laura's reminding us that we know that 0.
10 is the same as saying 0.
1.
So 0.
10 metres or 10 centimetres is equivalent to 0.
1 metres.
I say 0.
1, but I think zero wholes and 10 centimetres.
Hmm, so we know that 10 centimetres is equivalent to one tenth of a metre, isn't it? And we know that 'cause we can see that those 10 centimetres would be the same size as that one tenth of a metre that we looked at earlier on.
Let's have a look how we apply that in our place value chart again.
First of all, notice how here I've recorded it as 0.
10.
Obviously, we don't need this zero in the hundredths column, do we? So we're gonna take that one away and we're gonna leave it as 0.
1.
Now, when we change the headings, we can see that we've got zero whole metres.
We've now got one tenth of a metre because we've now regrouped those ten one centimetres into one lot of 10 centimetres or one tenth of a metre.
Obviously, the zeros disappeared 'cause we don't need to record that we have zero additional hundredths of a metre.
So I say 0.
1, but I think zero wholes and one tenth.
Or in terms of metres, I say 0.
1 metres, but I think zero wholes and one tenth of a metre.
And once again, as Laura is quite rightly pointed out, we know that one tenth of metre is equivalent to 10 centimetres.
Here's one more example.
What'd you notice this time? Yeah, we've got a lot more this time, haven't we? We've actually got 42 lots of one centimetre, haven't we? So, take a moment for yourself again.
How do you think we have a go at right in this? Well, if we know that one centimetre can be written as 0.
01, then 42 centimetres can be written as 0.
42 metres.
I say 0.
42, but I think zero wholes and 42 hundredths.
Again, let's look at that in our place value chart.
Zero represents zero whole metres, the four represents four tenths of a metre, and the two represents two additional hundredths of a metre.
So I say 0.
42, but I think zero wholes and 42 hundredths.
Or in terms of metres, we can say 0.
42 metres, but I think zero wholes and 42 hundredths of a metre.
Or as Laura said, 42 hundredths of a metre is equivalent to 42 centimetres.
So, we've already begun recording these as decimal numbers, haven't we? We've been thinking about metres and centimetres and how we can record them as decimal numbers.
As you can see, I've placed my decimal point below between the whole metres and the fractional parts of the metres.
The zero whole metres sits on the left-hand side of the decimal point, and the centimetres sit in the two places immediately to the right-hand side of the decimal point.
Okay, time for you to check your understanding now.
True or false? 73 centimetres can be written as 0.
73 metres.
Take a moment to have a think.
That's right, it's true, isn't it? Now, which one of our justifications below helped you to reason that? Yep, that's right.
It was A, wasn't it? We know that 73 centimetres is the same as 73 hundredths of a metre, which we write as 0.
73 metres.
Well done if you got that.
Okay, and here's our first task for today as well.
What I'd like you to do is to fill in the missing numbers.
You need to convert between either the centimetres into metres or from the metres into centimetres.
Good luck, and I'll see you again shortly.
Okay, welcome back.
Let's go through the answers then.
So one centimetre can be written as 0.
01 of a metre.
Four centimetres can be written as 0.
04 metres.
Hmm, 10 centimetres.
We have to think about that one, don't we? We can write that as 0.
10 metres or 0.
1 metres.
17 centimetres can be written as 0.
17 metres and 71 centimetres can be written as 0.
71 metres.
We have to be really clear that we get our numbers in the correct place values there, don't we? And the next row, 0.
09 metres can be written as nine centimetres.
0.
90 metres can be written as 90 centimetres.
Notice there how the place value of the nine digit has changed from hundredths of a metre to tenths of a metre.
0.
38 metres can be written as 38 centimetres.
0.
83 metres can be written as 83 centimetres.
And finally, 0.
6 metres.
Hmm, I say 0.
6, but I think zero wholes and 60 hundredths of a metre.
So, that would be 60 centimetres, wouldn't it? Well done if you managed to get those.
Okay, onto part two of our lesson now, thinking about linking metres and centimetres beyond one metre.
As I said, we were gonna use a number of bars, didn't we, to represent one metre.
So we're now gonna use this green bar here to represent the one metre that we've been looking at so far.
Have a look at my image now.
How might we describe what you can see here? That's right.
You may have noticed that we've got three whole metres, haven't we, and we've got an additional 24 hundredths of a metre.
We know that one metre is equivalent to 100 centimetres.
So three whole metres would be equivalent to 300 centimetres.
And then we've also got an additional 24 centimetres, haven't we? So altogether we've got 324 centimetres.
We can say that three metres and 24 centimetres is equal to 324 centimetres.
We can also write this, as Jacob is pointing out, as 3.
24 metres.
We have now got three different ways of recording this image here.
We can record it as metres and centimetres.
So we've got three metres and 24 centimetres.
We can record it simply in centimetres.
So we've got 324 centimetres.
Or we can record it in metres.
We've got three metres and we've got 24 hundredths of a metre as well.
Again, let's have a look at how we record this within our place value chart.
So we can see here that we've got 3.
24.
On the left-hand side, we'll have the whole metres.
And in the two places immediately to the right of the decimal point, we'll have the centimetres.
Okay, have a look this time.
What do you notice? That's right.
We've got three metres and seven centimetres, haven't we, which is what Jacob has just pointed out.
We know that each one of those metres represents a hundred centimetres, so we could convert those into centimetres.
So now we've got 300 centimetres and an additional seven centimetres.
Altogether, we could write that as 307 centimetres.
That's two ways we can record it so far.
And the last way, we can also record it as metres, can't we? We know it's three metres and seven hundredths of a metre.
So we'd record that as 3.
07 metres.
Let's have a look at that in our place value chart.
The three represents three whole metres.
The zero represents zero additional tenths of a metre.
And the seven represents seven additional hundredths of a metre.
And again, on the left-hand side of the decimal point, we would record the whole metres.
And on the two places immediately to the right-hand side of decimal point, we would record the centimetres.
Okay, time for you to check your understanding again.
Which of these represents 7.
5 metres? That's right, it's D.
7.
5 metres can also be represented as seven metres and 50 centimetres.
Laura's asking, "Well, how did you know?" Well, we know that the five in 7.
5 metres represents five tenths of a metre.
Now, one tenth of a metre is equivalent to 10 centimetres, so five tenths of a metre is equivalent to 50 centimetres.
So it's D, seven metres and 50 centimetres.
And another check.
True or false? 603 centimetres is equal to 6.
03 metres.
Take a moment to have a think.
You're right, it's true, isn't it? And which one of our justifications helps us to reason this? That's right, it's A.
The six represents six metres and the three represents three hundredths of a metre, doesn't it? So we would record it as 6.
03 metres.
So now that we're starting to feel more confident with converting between centimetres and metres, we can then start thinking about how we can apply this to when we are not always using the same unit of measure and how we can convert between them to compare these numbers.
Here, Aisha and her friends were measuring how far they could throw a football using an over arm throw.
Laura's pointed out that everyone's recorded their scores in different units of measure, haven't they? So how will we know who's thrown the furthest distance and who's thrown the least furthest distance? Jacob thinks we should start converting them.
And he's noticed that some of them are already recorded as decimals, so he thinks maybe we should record them all as decimals, which would be the same as recording them as metres, wouldn't it? Let's have a look.
Alex, Laura, Jun's score have already been converted into metres.
So that means we've got three more scores to convert into metres.
Let's start with Aisha, shall we? Aisha has 650 centimetres, and we know that 100 centimetres is equivalent to one metre.
So we place a six on the left-hand side of the decimal point for our whole metres.
And we also know that she's got an additional 50 centimetres, which we record on the right-hand side of the decimal point.
This now represents 50 hundredths of a metre, so we record as 6.
50 or 6.
5.
I say 6.
5 metres, but I think six whole metres and 50 hundredths of a metre.
Let's have a look at Jacob's score then.
This looks very similar to Aisha score, doesn't it? But it is slightly different and we need to be careful with this.
So, Jacob's score is 605 centimetres.
We know that 100 centimetres is equivalent to one metre, so 600 centimetres is equivalent to six metres.
So we placed that on the left-hand side of our decimal point.
And then we've got an additional five centimetres, haven't we? So that means that would be five hundredths of a metre.
So we'd record that as zero tenths of a metre and five hundredths of a metre on the right-hand side of the decimal point.
I say 6.
05, but I think six whole metres and five hundredths of a metre.
Finally, Andeep's score.
Well, that's already been converted into metres and centimetres, which makes our life slightly easier, doesn't it? We know that on the left-hand side of the decimal point, we have placed the five metres.
Now we've just got the small matter of the eight centimetres.
We know that eight centimetres is equivalent to eight hundredths of a metre.
So we would need to place on the right-hand side of the decimal 0 to represent zero tenths of a metre and the eight to represent eight hundredths of a metre.
Be careful not to place the eight immediately after decimal point, 'cause that would represent eight tenths of a metre, which would be 80 centimetres.
And we've only got eight centimetres here, haven't we? So I say 5.
08 metres, but I think five whole metres and eight hundredths of a metre.
So, now that all of our scores are in the same unit of measure, we can start thinking about comparing these, can't we? We're gonna find out who threw the furthest distance and who threw the least furthest distance.
When we compare numbers, we start always looking at the largest place value first.
So looking at the place values here, we're gonna be looking at the metres, the whole metres.
And we can see that three of them have six metres.
Now that we've looked at the metres, we now need to start thinking about looking at the centimetres.
So Aisha has thrown an additional 50 hundredths of a metre or 50 centimetres.
Jacob has thrown an additional five hundredths of a metre or five centimetres.
And Laura has thrown an additional 46 hundredths of a metre or 46 centimetres.
So Aisha has thrown the furthest distance, hasn't she? She's thrown the distance of six metres and 50 centimetres or 6.
5 metres.
Now let's think about who threw the least furthest.
Well, now we can see, looking at the largest place value that these three people here threw five metres, which was the least furthest amount of metres that were thrown.
Once again, because they all have five metres, we need to start looking at the centimetres or the hundredths of a metre.
So, Alex, threw 83 hundredths of a metre or 83 centimetres, additionally.
Jim threw eight tenths of a metre or 80 hundredths of a metre further.
Again, this would be 80 centimetres.
And then finally Andeep threw an additional eight hundredths of a metre or eight centimetres.
Out of all of these three, we can say that Andeep through the least furthest distance.
Well done if you managed to work through that for yourself as well.
Okay, another chance to check your understanding here, 870 centimetres converted into metres is A, B, or C? That's right, it's A, isn't it? 8.
7 metres.
"Why is it not option B or option C?" Laura is asking.
Well, 870 centimetres we know is eight metres and 70 centimetres or eight metres and 70 hundredths of a metre.
So that would be 8.
70 metres.
So therefore it can't be B because that represents eight metres and seven hundredths of a metre.
And it can't be option C 'cause that actually represents 87 whole metres.
Another check for you.
True or false? 6.
24 metres is equivalent to 624 centimetres.
Yep, and that's true again, isn't it? We know that the six represents six metres or 600 centimetres, and then we've got an additional 24 hundredths of a metre or 24 centimetres.
So, using justification A would've been helpful for you to think that through.
Okay, onto our last task for today then.
What I'd like you to do here is convert between centimetres and metres by filling in the missing numbers again.
And then for task two, I've given you three digit cards here.
I've given you a zero, a two, and a five.
And I've given you a structure here of something point, something, something metres.
And what I'd like you to do is use those three digit cards to find at least four different lengths.
And then once you've got those lengths, what I'd like you to do is order them in descending order.
So, from the largest to the smallest.
Good luck with that, and I'll see you again shortly.
Okay, welcome back.
Let's see how you got on.
I'm gonna go through these answers here and you can tick them off as you go if you got them.
There we go.
Were any of those more tricky than others? I found that on the left-hand side, you had to be really careful with the place values, didn't you? You had to think really carefully about what those numbers represented.
What did the seven represent each time and what did the five represent each time? The five was jumping between representing hundredths of a metre and tenths of a metre, wasn't it, which then changes the number of centimetres that we have, doesn't it? And again, on the right-hand side, the threes were being placed in different positions, weren't they, and we have to think carefully about whether they represented three hundredths of a metre or three tenths of a metre to help us understand how we'd record that in metres.
Well done if you've got those.
And then finally, here's the answers to our last task.
She used 5.
20 metres, 5.
02 metres, 2.
50 metres, 2.
05 metres, 0.
52 metres, and 0.
25 metres.
And then Laura's asking, "Well, how did we know that we found all the possible solutions?" Well, Laura started thinking systematically.
She started with the largest digit in the metres.
So she put the five there, and then rotated the other digit cards in the centimetres to identify all the different ways that we could record that.
She then did the same with the two being the metres, and then the same with the zero being the metres.
So we found all possible solutions here that we could.
And in total, there were six solutions.
Well done if you managed to find all six.
So, that brings our lesson to a close for today.
Hopefully you've enjoyed yourself and you're feeling a lot more confident about converting between centimetres and metres, and that's something you can begin to use in your everyday lives, even more so from now on.
Just to summarise what we've learned today, one centimetre is one hundredth of a metre, 10 centimetres is one tenth of a metre, metres can be expressed as a decimal, and you can convert between units of centimetres and metres.
For example, 650 centimetres can be written as 6.
5 metres.
Thanks for learning with me today.
I've really enjoyed myself.
Hopefully you have too.
Take care and I'll see you again soon.
