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Dividing by Differentials: Instructor's Guide

Main Ideas

  • Students learn why differential division is a difficult manipulation to consistently use correctly

Students' Task

Estimated Time: 15 minutes

Students work in small groups to determine if differential division is a legal move in each of the given scenarios.

Prerequisite Knowledge

  • Basic understanding of the concept of a differential
  • Familiarity with partial derivatives
  • Familiarity with total differentials
  • Familiarity with the difference between a total derivative “d” and a partial derivative “d”


Activity: Introduction

Activity: Student Conversations

Activity: Wrap-up

Once most groups have at least attempted to judge each of the scenarios, convene the class into a discussion. Go through the worksheet scenario by scenario, having the class vote whether they think differential division is a legal step in each. After each vote, ask students from both sides (of the vote) to (voluntarily) justify their vote to the class. After both sides have (hopefully) had a few “spokesmen,” discuss the correct answer with the class before moving on to the next scenario. Once all scenarios have been voted on and discussed, and assuming that the class was quite divided with each vote, lecture to the class about how easy it is to make mistakes when dividing by differentials. If the class wasn't very divided and most of the students voted correctly, then the activity was not complex enough to show students that differential division is a poor choice for the average novice physicist.


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