G’day, I’m Dr Peter Price of Classroom Professor. Welcome to this video in the Free Math Worksheet

series, this week the topic is “Metric Measures of Length”. The worksheets themselves if you see, they

will have questions about converting “Metres to Centimetres” and back, “Kilometres to Metres”

and “Centimetres to Millimetres”. So there are obviously a lot more metric units

that we’ll look at in future episodes but, these are the ones we are looking at today. The first comment I must make, is that the

metric system is not yet used in the entire world, I say “Not yet” because I believe that’s

the way we’re going, basically all the countries of the world have moved in that direction

apart from the United States and a couple of other minor countries, so I’m expecting

that at some time in the future the whole world will be metric. And in the United States I’m, I’ve done a

little bit of research and a bit of reading and so, it’s clear that in the American education

system they are moving towards the metric system as well. I gather you probably teach both sets of units

in the United States but metric units are an important part of what you teach. So the other thing to say is that there is

a difference in the spelling and that’s reflected on the worksheets themselves, so on the worksheets

to avoid offending anybody, cause I know what it’s like when you read a word that is spelled

differently from the way you know is correct. It can be a bit of, it can be difficult to

deal with and I don’t want to offend anybody in the audience with this video, so I’ve used

both spellings for the worksheet so you’d pick the one you like basically. This is the original spelling of the word

“Metre”; it’s a French word “Mettre”, “Mettre”, like the word “Centre” in a lot of the English

speaking part of the world, we spell it C-E-N-T-R-E, the Americans very sensibly anglicised the

spelling or made it more English if you like, by changing the R-E so it says “ME-TER” with

E-R saying “ER”. Ok that’s the way it is and similarly metre,

the units that are derived from the metre, the centimetre, kilometre and so on. Alright enough of that, let’s look at the

units we’re going to be converting and there are 3 pairs and so I’ve just mentioned. “Centimetres to Metres, Kilometres to Metres,

Centimetres to Millimetres” and in the opposite direction, so if you look through the worksheets

you’ll see are going back directions in the worksheets. The conversion that the students are doing

is based around a conversion factor between the two units, so to know how we need to change

the numbers, we need to understand how big the relative units are and the metric system

makes that really nice and easy for us. And I’ll explain what I mean, so the “Centi”-metre

has a prefix which is spelled the same everywhere, “Centi” in front of the word metre, the kilometre

similarly has “Kilo” and the millimetre has the prefix “Milli” and those prefixes have

very precise mathematical meanings. So “Centi” means “1/100”, “Kilo” means “1000”

and “Milli” means “1/1000”, so unlike the old fashioned British units where 12 inches

equals a foot, then 3, 3 feet equal a yard and, 1200 and I’ve forgotten how many they

were, 5280 feet in a mile and so on. All those different numbers had to be remembered

they, they sort of grewed during history I think and so they had different numbers of

units making up other ones, In the next metric system because it was planned in advance,

it’s all based on ten. So a “Centi” anything is a hundredth of something,

so a centi-litre is a hundredth of a litre, a kilo of anything is a thousand, so a kilowatt

is a thousand watts and so on. So we use those numbers when we’re doing the

conversion, so basically when we’re converting and I’m going to just add a little more to

this messy set of notes, if we’re converting a number like 150 centimetres to metres we’re

still going to have the 1 and the 5 and we could even have the 0 as well, they’re just

going to be in different places because this is a power of 10 and so all the prefix is

in the metric system refer to powers of 10. So centimetres to metres the conversion factor

here of course is divide by a hundred, because these are hundredths of a metre, “150 hundredths

is how much?” And this will be 1.5. Let me make up a couple of questions here;

let me say we had 2.6 kilometres, “How many metres would that be?” The conversion factor this time is a thousand,

times or times a thousand, “2.6 x 1000 will be 2600”. And the last one of this quick examples, let’s

say we had, oh let’s have a nice easy one “9 centimetres”, Centimetres to millimetres,

now there isn’t a nice, the prefix itself doesn’t tell us, we have to look at the different

between the prefix and so this is a hundredth and this is a thousandth, the difference of

course is 10, so we multiply centimetres by 10 to give us millimetres and that’s 90. So each of the conversions as I said is based

on this idea of powers of 10, so we’re going to reuse the digits in the same order the

same relative positions to each other, they’ll just be in a new place. Let me talk a little bit more about that,

now what I’m going to say now maybe to some people a little controversial but I’m going

to say it anyway, because basically I’m right. Let’s go back to our question before of 150

centimetres, and we’re going to convert this and I just had the answer before “1.5” with

or without the 0. Now students may want to put the 0, but they

don’t need to it’s an unnecessary 0, either way it may or may not have a 0 and as I’ve

said before here of course, we’re dividing by a hundred. None of that’s controversial; the controversial

bit is where students learn to move the decimal point, let me urge you not to teach that to

your students, now as I said it’s a bit controversial I may have just offended half my audience,

I’m sorry if I’ve done it I don’t intend to offend anybody, but it’s simple a really really

bad idea. My experience of teaching young adults who

are going on to be teachers who have learned to move the decimal point, is that when they

do activities just like this with metric units, having grown up with metric units in the Australian

schooling system, they get their answers wrong over and over and over again because they

can’t remember how many decimal places and they don’t remember which way to move them

left of right. So some people literally get an answer that

is 10,000 times too big or too small, because they move it the wrong way, two places and

they get completely ridiculous answer, because they’re not thinking about the process, the

quantity, the operation and so on. Rather than that let me strongly suggest,

that you teach your students to move the digits, if we’re dividing by a hundred, every digit

is going to move to the right two places, so move the digits not the decimal point. We are allowed to move the digits, cause digits

can go anywhere because of the place value system, the decimal point never moves it’s

always between the ones and the tens place. Alright so if we move the digits two places,

“Where’s the decimal point at the moment?” Well clearly it doesn’t have one because we

haven’t written it, but that’s a whole number so the decimal must be just after the 0 and

if we move everything this way two places the 1 will end up right there, the 5 will

be just after the decimal, of course as I said the 0 we can actually drop the 0 because

it’s after the decimal point. Ok, the other way that I would help reinforce

this idea of thinking about the quantity and what’s our answer going to be, what sort,

what you really want is what, “What place is the digit going to end up in?” “What is it roughly equal to?” I would ask a question like this, how many,

I’m writing this very quickly, “How many hundreds are there?” or “Where are the hundreds?” Simply because this is a conversion factor

of a hundred we’re dividing by a hundred I say, “How many hundreds are there?” Look at this number and tell me the hundreds,

I’m going to write a little label here, that’s the hundreds, well if there’s 100 to divide

by a hundred, everybody knows that will be 1 and so it ends up there. So if you use questions like that and if you

teach your students to move the digits to the right place, I believe it will be a lot

clearer to them and ultimately, when they’re older and they’ve used this over and over

again it will be familiar to them, and they’re thinking about the size of the quantity and

where it ends up. So I’m not going to re-do this of course with

kilometres, metres, but the conversion factor is a thousand and so it’s 3 places, so depending

on which conversion it is, from kilometres to metres you’re going to move all the digits

to the left 3 places, it will get bigger because the number of metres is bigger by 3 places

and so on. The other recommendation I’ll make to go along

with this is you make up a, what I call “Place value slides”, where you have a sliding piece

of paper that you, or cardboard of something that you can move left and right with digits

written on it, and have something else in front of it showing that the places, and the

decimal point and then move the digits and I think that will make it far far clear. Oh by the way, we’re actually working on a

piece of Software that will help with that as well, so if you keep in touch with me,

I’ll let you know when that’s available. I’ve probably talked to long on this one,

thank you for being with me; I appreciate your support with the Free Math Worksheets. I hope that this has been helpful and I look

forward to talking to you next time.

We don't teach both sets in the US. (or at least my school doesn't)

That's why I watched this video! It's very informative and was beneficial to me. Thanks!