I start with what students know. I ask students to evaluate 3^1, 3^2, 3^3, and 3^4. They can do this and they can even show why it works. We recorded that part in this table (sorry all I have pictured is the final, but imagine half of it is blank :)
Then we continue dividing. 1 divided by 3 is 1/3 (yes I have to force them to use fractions--I just say that they will recognize the pattern better if they use fractions). Then by 1/9 there is a bunch of "oh"s and almost every students (or at least every students who is still paying attention) can say that the next in the pattern is 1/27.
We use the word reciprocal (instead of opposite as they tend to) and come to the rule that to evaluate negative exponents, we evaluate the positive first. At this point I gave them several problems to practice in their notebooks.
That about sums it up. If you have other questions about this, let me know :) Or other ideas to make it better I'd be happy to hear it!!!!
-Kathryn
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