I start class by having students recap the work we did yesterday when we tried to find the area under a curve. There are a few big ideas that I hope they understand, so if I don't fully get the impression that they have a grasp on these, I will ask questions to bring them out. The big ideas are:
In this video I talk about what my true intent was for this lesson and yesterday's. This is also something I communicate with my students before they start working on the assignment.
After recapping yesterday's work, I give students this worksheet for them to work on with their table groups. While we are only working on one specific type of problem (finding the area under a curve), it is a challenging task and I want them to have practice going through the steps of making an infinite number of rectangles. I give my students about 30 minutes to work on this in class with their groups.
Here are a couple things that I noticed as they were working on the assignment.