Metric Conversion Chart

Date: 07/17/97 at 15:24:29
From: Carrie Brzozowski
Subject: Conversion chart

Dear Dr. Math,

I am an 8th grade math teacher and I teach my students how to convert 
within the customary system and within the metric system.  I want to 
know if you know of a conversion chart where I can convert from metric 
to customary and vice versa. Thank you very much. By the way, are 
you a real person?  

Carrie

Date: 07/19/97 at 01:08:26
From: Doctor Terrel
Subject: Re: Conversion chart

Dear Carrie,

I am a 7th grade math teacher and I also teach my students 
"conversion" work of various kinds. 

You say you teach conversion "within" the two systems, but need help 
"between" the systems. Since I don't know how you teach within a 
system, that is, exactly what procedure you use (there are several 
writing methods), I will simply show you how I do it.  It is different 
from the ways shown in my current textbook [UCSMP's Transition 
Mathematics]. I call it the QFP method. Several people to whom I've 
shown it like it and do it with their students.

Here is a typical example.  Change 14 inches to centimeters.

First, one must know the basic relation between inches and 
centimeters: 1 in. = 2.54 cm.

Now I ask my kids, "What's the question before us?"  
  Answer: how many centimeters are in 14 inches.  So we write:

        Qstn:     ?  cm   =   14 in.

Next, "What fact do we know that connects inches to centimeters? 
  Ans.: 1 in. = 2.54 cm.  So we write:

        Qstn:     ?  cm   =   14 in.
        Fact:   2.54 cm   =   1 in.

This presentation begins to look like a "proportion", doesn't it? 
[This implies the students must have a little background about basic
proportion solving; otherwise, this is a good time to teach a little 
bit about it, because here is a USE for it.]  So we write:

        Qstn:     ?  cm  =   14 in.
        Fact:   2.54 cm  =    1 in.
                   x         14
        Prop:  --------  =  ------
                2.54          1

                      x  =  2.54 * 14   [by cross multiplication, or 
                                         any other phrase you prefer]
                      x  =  35.56

So 14 inches is 35.56 centimeters.

Later we discuss whether the 35.56 should be rounded or not. 
Technically it should, if the 14 in. was a humanly made measurement. 
No such measurement is ever "exact".  Although the in/cm conversion
factor is an exact one, it is so by definition; the others, such as
mi/km, lb/kg, etc. are not exact. Here I tell my kids to say "about 
36 cm" or "about 35.6 cm"; and the "about" is required.

Another example with inches/centimeters.

Change 45 cm to inches.  We proceed as before.

        Qstn:    ? in.   =   45 cm
        Fact:    1 in.   =    2.54 cm
                 x           45            Here I like to point out
        Prop:  -------   =   --------      the"criss-cross" model is  
                  1           2.54         unnecessary, if we look
                                           at the equation cerefully.  
                                           x/1 = x, so we have
                   x     =   45 / 2.54
                   x     =   17.716535
                             

Now the necessity of rounding is more obvious.  I suggest an answer
statement of "45 cm is about 17.7 in."

When I was a lad in the early '50s, studying conversions (usually 
within the customary system only; we didn't worry about metrics in 
"them days"), I could never remember whether I should divide or 
multiply when going from larger to smaller units or vice versa. [And I 
had no Dr. Math to turn to!] But when I learned about proportions, via 
slide rules (the predecessor of our calculators today), all my 
troubles vanished. The proportion "told" me what to do if I could get 
it set up by what I now call the QFP method. Piece of cake...  

By the way, QFP works within systems, too, but it is admittedly less 
useful within the metric system.  It's great for converting between 
unfamiliar monetary systems, though.

Now, Carrie, I hope this helps you a little bit. Try it, and let me
know. All you need are some more relations between metric and 
customary units, which can be found in most textbooks, even 
dictionaries.

As to your final question...

Asking if Dr. Math is a real person is like asking if Santa Claus
exists. As Santa Claus is the collective spirit of many good people 
doing good things for many others, Dr. Math is a collection of math 
volunteers ("elves," as it were) dedicated to helping all you kids, 
young and old, out there with your difficulties in math. Yes, I am a 
real person. Thanks for asking...

-Doctor Terrel,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/