Teacher Math Lesson: Metric Measures of Length

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.

One thought on “Teacher Math Lesson: Metric Measures of Length

  1. 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!

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