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How to Incorporate Released Free Response Questions in your AP Calc Class

One of the best ways to prepare students for the AP Exam is to have them work on free response questions from previous years. Not only will this familiarize them with the types of questions, wordings, and content they will see on the AP Exam, but a look at the scoring guidelines also gives valuable information about what kinds of justifications earn points. One of the major ways that an Advanced Placement Calculus course differs from a Calculus class in college is the College Board’s emphasis on clear communication of reasoning and rigorous justification. Memorizing rules and knowing how to do a procedure is not enough!


Starting second semester, we instigate FRQ Fridays in my AP Calculus class. Students know that they will be working on an FRQ individually for 15 minutes. Whether we go over them in class or I take them home and return them on Monday depends on the week. Once students complete unit 6, you will find that many more free response questions become available that students will be able to complete in their entirety (or should be able to complete!).


While individual practice that mirrors exam conditions is certainly valuable, there are a variety of other ways you can incorporate free response practice in your class. The goal is to expose students to challenging, AP style questions in an engaging way, and give them insight into the kinds of responses that earn full credit. Here are my go-to activities for incorporating FRQs in my class, how to facilitate them, and when they are the most useful.



Activity

How it works

For best results...

Stations

Find five or six free response questions that relate to the current skill you’re working on (particle motion, solving differential equations, graph analysis, etc.). Tape each question on the wall around your room and have students travel in pairs or small groups around the room to complete them. We like having students work on whiteboards because it garners conversation and allows me to have a good overview of where students are at.

Works well when free response questions are shorter and focus on a few key skills, otherwise this will become overwhelming. We often remove parts of the problems, so students are only working on parts a and b, for example.

Gallery walk

Similar to stations, but each group works on the same question, preferably on a whiteboard or poster paper. After an allotted time (20 minutes usually), have groups travel to the other workspaces and look at their peers’ solutions. Have them provide feedback on sticky notes. Then have students return to their original FRQ, read the feedback, and make any revisions they would like. You can have students take a picture of their work and submit it or turn in the poster paper.

Works well when parts of the question are particularly tricky and students could benefit from seeing other students’ work.

Student Sample Scoring (SSS)

Give students 15 minutes to work on an FRQ in small groups. Then print the sample student responses provided by the College Board for your students to critique. Go over the scoring guidelines and how points are earned, then have students grade the sample answers.

Works well when the FRQ focuses on justification and making clear arguments (like graph analysis with an accumulation function, IVT/MVT questions, etc.)

FR Quad

Choose 4 free response questions that have parts a-d. You can add your own part to the question if the original does not have enough. Project a grid that has slots for all 16 parts. Groups write up answers in the appropriate slot on the projected grid and get points based on how many squares they filled, as well as bonus points for getting four in a row, completing an entire FRQ, or landing on the magic squares. For a full set of directions, click here.

Works well when questions can be answered numerically or with a short phrase. Students do not have a lot of room to write!

Partner-solo

In partner-solo, students get 5-8 minutes to discuss a free response question with a partner, but without being able to write anything down. They can only discuss. Then students return to their seat and get 15 minutes to complete the FRQ.

Works well as a formative assessment; we’ve used this structure on quizzes before!

Solo-partner-quad

This is basically the reverse of partner-solo. Students first get 5-8 minutes to work individually, then 5-8 minutes to work with a partner, then another 5-8 minutes to join with another pair to form a quad. We generally go over answers together in class using the scoring guidelines. Alternatively, you can have students turn in one FRQ per group, or have each person turn theirs in.

Works well when the FRQ is particularly challenging (like the potato problem from 2017 or the spinning toy problem from 2021)

Do you have any other strategies for incorporating FRQs in your classroom? Let us know in the comments!

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