I blame @bowmanimal for all of this. A few months ago he blogged about conceptualizing volume in calculus before formalizing. At the time, I had just started looking over past AP Calc exams, wondering how I was going introduce volume (solids with known cross sections and solids of revolution). Volume is a calculus topic I've not taught before, and I want my students to do more than memorize the formulas. Because, as our own textbook puts it so beautifully: "Some students try to learn...