From: moe <moe2@shaw.ca>
To: Teacher2Teacher Public Discussion
Date: 2002031405:55:14
Subject: teaching metric conversion of prefixes

	Lynn writes:

How can I effectively teach so that my students understand this topic
on conversion of units of measurement such as cm, m and km?

For example: most students find it difficult to comprehend that

   715 cm = 7.15 m  and
   2.12 m = 212 cm

It becomes frustrating for me to teach since they cannot understand   
1cm = 1/100 m or 1 m = 1/1000 km

Would you recommend some great activity that I can carry out to make
them understand better?

=================

hi Lynn

the most effective approach is to introduce the prefixes first. Only
the prefixes. this is a conversion of prefixes problem. we get so
easily trapped in the Imperial way of teaching with conversion of
'units', in metric it is conversion of 'prefixes'.  for a class of
grade 3 and up, all these can be learned, yes memorized, in a few
minutes

symbol  factor      name
------  -----       -----
     Y  10e24       yotta      
     Z  10e21       zetta       
     E  10e18       exa         
     P  10e15       peta        
     T  10e12       tera        
     G  10e9        giga        
     M  10e6        mega        
     k  10e3        kilo        
     h  10e2        hecto       
     da 10e1        deca                
        10e0 = 1
     d  10e-1       deci        
     c  10e-2       centi       
     m  10e-3       milli       
     u  10e-6       micro      
     n  10e-9       nano        
     p  10e-12      pico        
     f  10e-15      femto       
     a  10e-18      atto        
     z  10e-21      zepto       
     y  10e-24      yocto 


i find it useful to present them all at once. i see teachers pick away
at this table year after year, let the kids have them all, then they
will see what the whole picture is from the start.  the important
concept to stress is: MEMORIZE THE PREFIX CHARACTER AND ITS ASSOCIATED
POWER OF 10.  later the kids can learn the name.  A brief explanation
of what a power of ten means is required.  this table should be
printed out in non kerned font (monaco) and given to each student to
take home and printed in large font for the classroom. copy this table
into a word processor, the characters do line up.  you might wish to
start with the central  7  factors to assure yourself that this
material is easily handled

you will find that after a quiz given the next day that using visual
aids of  mm, cm and metre   ....   mL, cL, dL, L and daL  etc that the
students will grasp the metric system very quickly.  And NO AIDS WITH
IMPERIAL UNITS until the class completely understand the metric
measures.

personally i teach conversion of prefixes with a SINGLE METHOD, BY
MULTIPLYING BY 'A FACTOR ONE'. this method works for easy prefix
conversion and even better for difficult questions. Difficult
conversion like 
                       2  Gm3  =  2 •  10e?  um3
can be done by grade five in a few seconds, and no pencil and paper.
the student knows to ignore the metres. they simply say in their mind 
9 - (-6)   taken three times is  -45, so   ? = -45      
the student would say in their mind:   nine  minus  negative six times
three is  negative forty five.  a work sheet of 30 conversion of
prefix questions takes a few minutes. In the past a similar worksheet
in the imperial system would take the whole period. By this time one
can mix in all sorts of units  m2, L, g, Hz, N it doesn't matter, they
know to ignore these and just find the 'correct' answer.    sorry,
about the exponents not showing up properly, this forum & text will
not allow them to appear properly, you may have to check this in your
printout

some comments: fractions are not permitted in the metric system. there
should always be a space between the quantity and the unit except for 
°C.   Lastly a metre is a unit of measure and a meter is a measuring
devise. This make the sentence "the trundle meter measured the
distance to be one metre".

i would gladly share my materials. enjoy
moe2@shaw.ca

moe

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