In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide important details of how diagrams are used. A key aspect of this work shows the importance of using two diagrams in the solution process. Here, a related rates lesson that teaches how to solve such problems by pushing students toward thinking like a mathematician is presented.
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