The WarmUps, and to some extent the Puzzles, are undergirded by education research and target a variety of specific issues. The list of targeted issues might contain: developing concepts and vocabulary, modeling -- connecting concepts and equations, estimation- getting a feel for magnitudes, relating technical scientific statements to "common sense", understanding the scope of applicability of equations, etc. The targeted issues are highly content specific. They may involve the characteristics of a particular class (e.g. the background skills of a particular student body).
In preparing WarmUp assignments for an upcoming class meeting, we first create a conceptual outline of the lesson content. This task is similar to the preparation of a traditional passive lecture. As we work on the outline, we pay attention to the pedagogical issues that we need to focus on when in the classroom. Are we introducing new concepts and/or new notation? Are we building on a previous lesson, and if so, what bears repeating? What are the important points we wish the students to remember from the session? What are the common difficulties typical students will face when exposed to this material? (Previous classroom experience and teaching and learning literature can be immensely helpful here). Once this outline has been created, we create broadly based questions that will force students to grapple with as many of the issues as possible. We are hoping to receive, in the student responses, the framework on which we build the in-class experience.