This
small group activity is designed to ensure that students know when they can (or can't) divide by differentials.
Students decide in which of the given situations dividing by a differential is a legal move.
The whole class discussion focuses on how difficult it is to consistently use differential division correctly.
Students often discover that they can divide by differentials to obtain correct solutions to some assigned problems. The goal of this activity is to show students that it is very difficult to consistently produce correct solutions with this method, and that they should do so only at the risk of their own grades.