Reflections of a Second-career Math Teacher

Yesterday, and today, I taught negative exponents to my Algebra 1 class. Students started out with a “discovery” activity where they filled out two tables, one for $latex 2^n$ and another for $latex 3^n$, for n = 5 to -5 where they eventually figured out that each successive result was half of the prior result, for the $latex 2^n$ table, and one-third of the prior result for the $latex 3^n$ table, which made the answer for n=0 and any negative n more understandable. I say “eventually” since most students did not recognize the pattern in the table until we covered it explicitly.

This activity led into an introduction of the following definition for a negative exponent.

For this definition, I mentioned that when any number a, a≠0, is raised to a negative power n, you took the reciprocal of the number a raised to the positive power n. Students learned what reciprocal meant earlier…

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