As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite the titles of these mini-courses, they do not give students any actual school credits and they should primarily be seen as somewhat informal (I say "somewhat" because I will have to evaluate their progress) small-group meetings where I help students get ready for their real credit-bearing Algebra 2 and Calculus classes that they will take in the future.
Ideally, these classes would not be designed with the idea that students should achieve mastery. The summer program also requires to be in other kinds of mini-humanities, science, and art courses, so the program and the students are not all exclusively focused on math.
The problem I am having is deciding how to map the course and plan instruction for both classes given that I would want to make sure that I engage every kind of student regardless of prior ability or interest. This objective is important to me because I am not actually teaching a "real-deal" Algebra 2 or Calculus class and so I want to help the students feel confident when they enter high school again in the fall.
What kinds of topics do you think I should cover for our short time together? (If you can't answer this, how do you suggest I go about paring down the list of topics before I even get to see all my students?)
My own Google searches always seem to turn up pacing for standard high school courses, but I won't be able to follow these. If I did, it's possible I wouldn't cover both differentiation and integration in Calculus. Would covering only integration be a good call?
I don't know where to begin in designing my Algebra 2 course. I don't think I would want to risk boring these highly-motivated students with possibly unnecessary Algebra 1 review. Would you suggest giving a diagnostic assessment on our very first class meeting?