Robert Aumanns theorem on agreeing-to-disagree (the original article can be found here) is a fun result that can be motivated by simple puzzles. Moreover, it is the basis of the no-trade-theorems in finance that show that rational expectations rule out speculative trading. A leisurely introduction to this, Aumann's theorem, and related issues can be found here. This article also motivates these issues in terms of a puzzle for children. I think it should be possible to select some topics that are (at some level) understandable by someone in high school. Moreover, this is a topic that raises questions and gives no answers, so you will not indoctrinate your student.
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