This paper describes an approach for pre-service or in-service mathematics education thatteaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start witha standard problem from high school mathematics and let the solution to this problem serve as a platform forasking good mathematical questions and searching for deeper mathematical structure beyond the obvious"answer" to the question. Surprisingly, it turns out that high school mathematics is remarkably open to thissort of analysis, and the results are more interesting mathematically than one might initially think.
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