Teaching the Metric System

Date: 08/18/2000 at 18:21:51
From: Bart
Subject: Inches, mm, cm, km, Celsius and Fahrenheit

I am homeschooling my child, who is in second grade. The curriculum 
that I have purchased for science talks about the metric system. 

I have no idea how to read a metric ruler or how to convert inches 
into the metric system or vice-versa.

I also need help with converting Celsius into Fahrenheit and 
vice-versa. 

Thank you,
Bart W. Buskey

Date: 08/18/2000 at 23:43:26
From: Doctor Peterson
Subject: Re: Inches, mm, cm, km, Celsius and Fahrenheit

Hi, Bart.

The metric system, in itself, is much easier to use than the 
traditional system, because you don't have to remember all the 
different conversions (16 ounces in a pound, 12 inches in a foot, and 
so on). You only have to remember a short list of prefixes that 
represent powers of ten: there are 1000 milligrams in a gram, 1000 
grams in a kilogram, and so on, and the same prefixes work for all 
units. There are 1000 millimeters in a meter, and 1000 meters in a 
kilometer.

It's also much easier to read a metric ruler. We get questions all the 
time about how to read a foot ruler, because people are confused by 
the fractional markings. On a meter stick, all you see are tens. The 
meter will be divided into ten "decimeters" (tenths of a meter), 
marked with big lines, and each of those will be divided into ten 
"centimeters" (hundredths of a meter) marked with short lines, and 
counted from 1 to 100. All you do is read off the number. A shorter 
ruler may have millimeters marked with short lines, with a longer line 
every ten for the centimeters. The centimeters will be numbered, and 
you just count the centimeters, then count the millimeters since the 
last centimeter. The 4-centimeter mark is the same as 40 millimeters, 
and 3 millimeters beyond it is 43 millimeters. It doesn't take long to 
get used to.

For you, it will take some time to get used to the feel of the new 
units - how big is a centimeter, how much can I expect a book to 
weigh. Your son probably doesn't have that "feel" yet for inches and 
pounds, anyway, so he'd want to develop it one way or the other. The 
metric system is no harder in that regard.

The only hard part is when you have to convert between metric and 
other systems. There, you need to learn a few special numbers, or at 
least know where to look them up. I don't think it's too important to 
know all these conversions, as long as you know how. To give an 
example, suppose we want to convert feet to meters. I only know one 
number for converting lengths: 2.54 centimeters (cm) make one inch. I 
can use that, and my knowledge of the rules within each system, to 
convert any lengths. I just have to make a chain from my starting unit 
to my destination unit that "crosses the river" where the bridge is; 
that is, it must make the jump from one system to the other by 
converting between cm and inches, because that's where I know how to 
cross:

     feet --> inches ----> centimeters --> meters

Now I know that a foot is 12 inches, that an inch is 2.54 cm, and that 
a meter is 100 centimeters. I can write each of these facts as a "unit 
multiplier," a fraction that represents 1 because it is the ratio of 
two equal quantities:

     1 ft     1 in      1 m
     -----   -------   ------   all equal 1
     12 in   2.54 cm   100 cm

Now suppose I measure something as 7 feet, and want to convert it to 
meters. I just have to find a chain of these multipliers that cancel 
out the units to give meters in the end, just as if the units were 
numbers:

              12 in   2.54 cm    1 m
     7 feet x ----- x ------- x ------ = 7 x 12 x 2.54 / 100 meters
              1 ft     1 in     100 cm

I had to turn some of the fractions on their heads so that feet 
canceled feet, and so on. Once I did that, I just have to multiply and 
divide.

By the way, they will NOT teach this in second grade. All you will 
have to worry about will be working within the metric system, so your 
son will see only the easy part and none of the hard parts. That's why 
they teach metric: to make it easier, not harder. Scientists rarely 
have to convert, because they work within one system. If America had 
switched over to the metric system long ago, only those who work with 
antiques would have to convert anything. (That's not to say the metric 
system is perfect; I'd prefer the ancient Babylonian system myself, 
but that's another story.)

If you ever do need to do these conversions, just go to the bottom of 
our Dr. Math FAQ page at

   http://mathforum.org/dr.math/faq/   

and look for the section on Other Math Sites: unit conversions. There 
are pages that explain the metric system or the many other units 
people have used, and pages that convert between units for you. Make 
sure you read what they say about the metric system, at least as far 
as the prefixes and basic units.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/