Alright, this is
Fifth-grade module 1 lesson 4 and in this lesson we're going to be doing some metric conversions
But the point is to continue practicing with our powers of 10
now we're just happen happening to be doing it inside the context of metric conversions as
Opposed to just doing it with plain old boring numbers, so let's get started on this
So the first thing I like to do before I just go teaching some sort of rule is to help students understand the basic
relationships of
The metric
Various metric measurements for example I start off with that big Ol meter stick
And I show them that one meter this whole length is the same thing as a hundred
Centimeters, and then I show them that one little centimeter is the same as 10
millimeters, so that means if you have
One meter you're Gonna have a lot of millimeters
There's 10 here 10 here 10 here all the way, and there's a hundred of them so a hundred times 10
and and once you get this basic idea of the general
Relationships, that's how I teach
the relationships of these metric conversions
I don't try and teach them just some boring rule, so let's get to sing that so the idea is
Convert and write an equation with an exponent use your meter strip when it helps you so it just so happens
I have a meter strip right here
And I'm gonna shrink that a little bit boom all right
And the idea is it says
Two meters is equal to how many centimeters well if you have one meter that's a hundred centimeters
so if you have another meter that's another hundred centimeters, so that's why it's
200 so you have two meters times by a hundred and that gives you 200 so
Let's do this problem. B. So you have a hundred and eight centimeters, and we want to know how many meters is
That well we know that if you have a hundred centimeters
that equals one meter, so that's a hundred centimeters divided by a hundred gives you one meter, so
If you have a hundred and eight that means and I'm gonna zoom in here
so if you have a hundred and eight centimeters that means you're gonna do
108
divided by a hundred
but that's the same thing as
108 divided by a hundred to the second power, and that's really what they want us to give them and then
that equals
whoa that equals
one point zero whoa one point zero
eight and
That's because the decimal moved two places to the left
because we divided by a hundred so let's zoom out so that you can see all that going on right there and
That's the kind of concept going on on this series of problems. Let's do
Oh, let's do another example here. Let's do question d
Which is saying 50 centimeters?
- how many
Meters okay, so first thing. We're gonna do is we're gonna put in 50 centimeters and
In order to go from centimeters to meters
Since meters are much bigger than centimeters
we're gonna have fewer meters and
that means we're Gonna have to divide and
We're gonna divide by a hundred. So that's Gonna be
50 divided by a hundred
but really what they want us to show is 50 divided by
10 Squared and that gives us
point
five
Let's do one last one let's do E
So problem E says six point three meters, so we're gonna write in
60.3 right here, and then if we want to turn that into
Centimeters, so that means we're gonna have a lot of centimeters because there's a hundred centimeters that fits in each
of these meters
So that means we're gonna do six point three
times
100
Which is six point three times ten?
squared
Which means our answer is?
630 because our decimal is going to move two places
to the right
More of the same kind of practice just a little less
Scaffolded, so there's my little
representation that I like to use to help students understand and if we're Gonna go from meters to
Millimeters, Remember one meter is Gonna. Have a bunch of these little millimeters in fact it's Gonna have a thousand
millimeters, so
four meters
into how many millimeters well each Millon each meter
has a
Thousand millimeters
And another way to write that is 4 times 10 to the third power?
Which gives us four thousand?
So our answer right here is four
Thousand oh my goodness
Now similarly except the exact opposite. Let's take a look at problem. C. So now we have
1050 millimeters okay, so that's
1050
Millimeters, and we want to turn those millimeters into meters
Well when you have a lot of millimeters, and you want to turn it into meters
Since meters are big
Much bigger than millimeters that means you're gonna have a smaller number of meters
Which means you're going to take this number and divide?
So we're Gonna take
1050 and we're Gonna divide and
Since there's a thousand millimeters in a meter
We're Gonna Divide by a thousand which is to say
1050 Divided by
10 to the Third Power which
means our answer is going to be one point zero five zero because
The decimal place moves three places to the left as our nice efficient Shortcut
So that's going to be one point zero five zero
Here, it's just more of the same
Practice, I'm just gonna kind of quickly. Go through this oh
Let's take a look at question B question b says centimeters
You've got seven centimeters, and we're gonna turn it into meters. Well since meters are big
That means we're gonna have a smaller number of them to equal seven centimeters I
Mean since there's a hundred centimeters in a meter means, we're gonna take that seven
We're Gonna Divide by a hundred
Which is to say seven divided by ten to the second power and that means our?
answer
is
going to be point zero seven because
That decimal is Gonna move two places to the left
Or you could think of it as the digits move two places to the right and so our answer is
Point zero seven now a lot of teachers like to put the zero in the front, and that's cool, too. Oh
Let's do one last one. Let's do D
So on D
we have
Point zero eight meters now. Let's ignore. The decimal. Let's just think about meters
You have meters and then we want to turn it into millimeters
Well since millimeters are small
And a whole bunch of them fit into a meter in fact a thousand of them
That means this number right here is going to be big
Because you're going to need a lot of millimeters to equal these meters
So we're going to take that
0.08 and
We're going to multiply by a thousand because there's a thousand millimeters in each meter
Another way of writing that is
0.08 times 10 to the third power and remember that means that decimal place moves
three places to the right
So our answer
becomes 80 because we don't need that leading zero
We definitely need this trailing zero, so the answer is 80
All right, let's practice with some word problems. You've got ye ting and as height is one point four nine
meters
And we're supposed to express his measurement in
millimeters
Well meters are big
Millimeters are small
we're gonna have a thousand millimeters for every meter and
Which means this magnitude of the magnitude of this number is going to be big?
You're gonna have a lot of millimeters in order to equal the meters
So means, we're gonna have to multiply
1.4 nine times in this case. It's Gonna be a thousand
Because we know that there's a thousand millimeters in one meter
So that becomes one point four nine
times
Ten to the third power which means that decimal place is Gonna move
so
That decimal place is Gonna move
Three places it used to be here
And it's going to move three places to the right which means we have to add in a zero
So our answer becomes
one Thousand four Hundred Ninety millimeters
and our last problem for this video is we've got a ladybug and its length is two centimeters and
We're supposed to Express this measurement in
Meters well let's use logic
Centimeters are small meters are big in fact. There's a hundred centimeters that fit into a meter
Since we want to convert into meters and meters are big which means this number right here is
Going to be a small number
Because you don't need very many meters
To equal centimeters these two centimeters so our conversion
We're gonna divide by a hundred because we know that there's a hundred centimeters in a meter
so two divided by a hundred is the same thing as saying two divided by 10 to the second power and
That means we're gonna take that to
where the decimal is right here and
We're gonna move that decimal place two spaces to the left
Which means we have to add a zero?
So it's gonna be point zero two meters is equal to two centimeters and that
wraps up
Fifth-grade module one lesson four where we're using the metric system as the context for multiplying
and dividing
by ten or
Multiplying and dividing by a hundred we're multiplying and dividing
by a thousand