20 Questions Instructions

20 Questions (Calculus Style)

Overview: In this activity, students will work in groups of four to practice sketching graphs of functions and their derivatives. One person will be given a graph card and this student is the only one who may look at the graph card during that round. The other three students get to ask 20 questions to ascertain as much information as possible about the graph that they must sketch on their whiteboard. Students practice using precise vocabulary and making connections between graphs of f, f', and f''.

Round 1 (Graph A): Given graph of , group members sketch the graph of .

Round 2 (Graph B): Given graph of , group members sketch the graph of .

Round 3 (Graph C): Given graph of , group members sketch the graph of .

Roles: Graph holder: Only one allowed to see the graph. Answers question with Yes/No or a numerical value Sketcher: Sketches the graph on the whiteboard Note taker: Keeps track of the questions and responses; tallies number of questions asked Checker: Makes sure the sketched graph accurately reflects the clues given by the graph holder

*The sketcher, note taker, and checker are all allowed to ask questions to the graph holder!

At the end of each round, every group member switches roles.

Optional Round 4 (Graph D): The graph holder creates their own graph on the blank axes provided. They can choose whether it is the graph of f or f' and which graph the sketcher must create.

Possible Modifications: Change the number of questions students are allowed to ask (10 is still very doable) Have students sketch a graph of Make it competitive by having groups race against each other (we recommend not doing this right away because this activity is already very challenging for students)

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