Free-Response Question Fridays

Very few tests are well designed, but I believe the AP Calculus exam is a pretty well designed and consistent exam. One thing that amazes me is that in 6 Free response questions (FRQs) they test a majority of a course. While that is great for the test, it isn’t good for teaching. It makes it hard to use these items in class in the fall continuously, but I want students be familiar with the format and types of questions asked way before they could confidently complete an entire AP Question. I’ve watched my previous iterations of Calculus struggle with the FRQs, but never implemented a system to “train them” because I always started in the middle of the year. This year, my first full academic year of AP Calculus, I’ll be implementing FRQF’s -> Free Response Question Fridays to address that gap.

Every Friday, students will work on an actual AP FRQ (even if they aren’t computing answers to all the parts). I casually had read of Polya’s How to Solve it and his 4 step problem solving strategy on the #MTBoS, but hadn’t implemented it rigorously. I sat down this week and read it (well…I read the first two sections and skimmed the dictionary….). I planned on implementing Sarah Carter’s S.O.A.R. acronym – which is how I’ll be introducing it to kiddos in August. (P.S. I made some nifty INB notes for SOAR last year, hung a kite in my room…and never referenced it again after September. Hence the deliberate planning this time around).

Speaking of giving credit to where credit is due, in my internet search to find something like an AP Calc version of this AP Stats FRAPPY resource, I found this problem solving guide by Florida DOE “Research Based Strategies for Problem Solving in Mathematics”  (PDF). They break down all four parts of the process and have activities and prompts for each of the areas. I’ve taken some of their ideas as I’ve written my FRQF’s.

I’ve written the first month or so of my FRQF’s – focusing mostly on Polya’s first step in the process – understanding the problem. The first involves mostly just ensuring that students know what the problem is asking and understanding the situation. We’ll be breaking down this year’s ridiculous Volume problem (#5). Problem not included, because College Board be CRAZY.

Students are answering questions like these:

  1. Summarize what this problem is about in your own words.
  2. What do the variables r and h stand for?
  3. What are the units to describe this funnel?
  4. What is the height? What is the radius?
  5. What are the restrictions on the values for h?
  6. What is the shape of the cross sections of the funnel?

I’m hoping that by focusing on the thought process behind answering questions like these by May we’ll be able to let our knowledge shine instead of being bogged down by words.


P.S. Interested in looking at FRQF’s? Comment or tweet at me (@jakewinfield) and I’ll share my work. I’d love feedback too 🙂 Since I’m using AP Released Items I’m erring on the side of caution.


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