Curves to Curve By
A teacher's guide to grading curves, each graphed as a function of the old grade: shift, linear rescale, power, reflection, constant, absolute sine, and identity.
Content note: Joker/Dark Knight reference; 'violent overthrow' joke.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-10-22-curves-to-curve-by/ (CC BY-NC 4.0)Transcript
[1] "CURVES TO CURVE BY: a math teacher's guide to curving your class's scores" Students: "Professor, this test is totally arbitrary and unfair!" Professor: "Ridiculous! The scores always make a perfect bell curve!"
[2] THE ELEVATOR CURVE: just add 10%. Pros: clear, simple, understandable. Cons: pushes some grades above 100%, creating hubristic students who think themselves gods.
[3] THE FLOOR-RAISING CURVE: divide by 2, then add 50%. Pros: strictly monotonic; raises floor without raising ceiling. Cons: you must gaze upon a glass that is utterly empty and call it "half full."
[4] THE RADICAL CURVE: new score = old score^0.7. Pros: has all the mathematical properties you want. Cons: inscrutable to all students except those who definitely don't need it.
[5] THE BIBLICAL CURVE: subtract score from 100%. Pros: first shall be last. Cons: last shall be first.
[6] THE HARVARD CURVE: new grade = 100%. Pros: low effort, low conflict, makes students happy. Cons: may or may not bring about the collapse of elite higher education.
[7] THE JOKER'S CURVE: new grade = |sin(25 × old grade)|. "I'm an agent of chaos. And you know the thing about chaos? It's fair." Pros: those too young to have seen The Dark Knight may not share the philosophy (or get the reference).
[8] THE IDENTITY CURVE: f(x) = x. Pros: feels principled and righteous. Cons: riled masses may effectuate your violent overthrow.