Discussion:  Roundtable 
Topic:  exponents 
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Subject:  RE: exponents 
Author:  Mathman 
Date:  Oct 2 2004 
> I always have trouble teaching exponents. To me, the rules are both
> logical and easy, but my students usually seem to find them too
> numerous and confusing.
Sorry, no gimmics. However part of the problem may be the ease with which you
see it. Try assuming that it is not so easy, and perhaps give more, or more
specific, examples from basic principles using lots of examples with numbers.
Be sureto start in base 10 with powers of 10[ 10^2 * 10^3 = 10 ^ 5]. Get them
to write in that form and also in full [100 * 1000 = 100,000], and to see how
one is really a simpler easier notation, and how addition works for those
numbers. Give lots of numerical examples for every step before declaring the
rule. Get them to keep their notes and also to have a summary on the back page
of the formulas that they can use on at least their first test, more at your
discretion. If they do it, they think it more to their advantage, and so more
useful. Don't generalise until you have to, but do discuss "Why not use any old
numbers instead of nice round ones?". They might find that they don't need the
notes after all.
For examples such as x^0, give again numerical examples such as 3^2 / 3^2, and
5^6 / 5^6.... By examples, I mean work that they can do. They must do enough
until they agree that the method works, and so much always work. That's when
the formula is written as an expression of that idea. They then have a choice
...the hard way or the easy way, with examples like 16^12 / 16^11 = ...and so
on.
David.
 
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