How to make students love square roots



Final exam scores in my calculus class were lower than I would have liked, with a few high-scores and a lot of medium-to-low scores. Reducing the number of possible points would bump the high scores over 100%, which is undesirable.  Since the scores are not normally distributed,  Another teacher in my department had a better idea: adjusting each score by taking the square root of its percentage.  Thus, a 0.36 becomes a 0.6, a 0.49 becomes a 0.70, etc.  Students were underwhelmed when I passed back the exams with only raw scores shown.  After discussing the problems they encountered, I had students "adjust" their scores.  Needless to say, they now love square roots.

In a traditional grading system, below 60% is considered failing:


Here's how the square root affects grade assignments:


This idea gives rise to a discussion about the square root function itself (why is x² > x if 0 < x < 1?), and other possible functions to adjust scores.  For example, if the square root (x^0.5)  is too extreme, what about x^0.9?  Perhaps you choose whatever power will bring the mean to 75%?