An interesting change has been occurring in the author's middle school mathematics classes. Some students have become creative, free-thinking inventors. If they have had little experience with an operation, they invent strategies of their own. Sometimes these strategies have been well informed and supported by strong mental math skills and a good knowledge of mathematical properties. At other times, the strategies are uninformed and lack grounding in good number sense. These changes have produced both benefits and challenges. Students are thinking independently and willing to be creative in all areas of problem solving. However, from a pedagogical perspective, following these same students' thinking has become more difficult because they have learned a variety of strategies for each operation. This article shares examples of division computations completed early in the school year by sixth, seventh, and eighth graders. An early inspection of students' work gave teachers much insight concerning ways in which these students' K-5 preparation had changed. (Contains 5 figures and 1 table.)