AP Exam Review
Week 4 - Monday (Day 16)
Graphs of f’
Our students loved playing this game that was both competitive and content rich! The class is split into two teams and each team should gather at one end of the room. A prompt will be shown with some information about a function, either in graphical, analytical, or tabular form. Then students are given a two minute individual prep period to gather ideas. Teams then go back and forth saying “something true” (and Calculus related!) about the given data. For example, if the prompt shows a graph of f’ on a closed interval a student might say “f has a relative maximum at __ because f’ changes from positive to negative” or “x=___ is a candidate for an absolute extrema since it is an endpoint.” If a team can not come up with “something true” in the given time frame (30 seconds max), the other team receives a point. You can then choose to move on to the next prompt or continue brainstorming ideas. There are MANY true things to say about each prompt.
It is important that all players on a team take turns saying “something true”. There can not be one spokesperson for the group, or a few students doing all the thinking for the entire group. Students should feel free to jot down ideas while other players are talking and also brainstorm with teammates. In our class, we award bonuses for creative answers or ones that are rich in Calculus. Given a graph of f’, one student said “Approximating the integral from x=__ to x=__ of f’(x) using a left Riemann sum would give an overestimate because f’(x) is decreasing”!