Last year in Calculus I gave kids an open note assessment on volume with respect to the x and y-axis. There were two handouts. The regions and the questions.

It took.......forever. I had a lot going on here. We had had a jam packed week where we talked about the area between curves, cross-sections stacked on top of the region, AND solids of revolution. Plus there was the x-axis/y-axis context to wrap your head around.

This year I streamlined it a bit. We took our time and focused on area between curves. We did some extensive practice on identifying expressions for various x-axis and y-axis based regions. That was a huge problem last year. My kids weren't comfortable with simply defining the area, so slapping the volume idea on top just added to confusion. Since defining the area is really the hard part of any volume expression, it was important to invest our time here. Afterward we focused solely on built-up solids with known cross sections. We can save rotational solids for later.

To stream line the assessment process I prepared the regions in Desmos and shared the collection with them. I also requested far less information about each region: a single integral expression for each one, either an area or a volume.

For collection I set up an Activity Builder where they can type their integral and its result for submission.

I'm hoping the more methodical approach helps here. Gathering input through Activity Builder is promising as well. Integrating functions with respect to y is probably my favorite Desmos feature these days.