Overview

For our first day of review, students worked in teams to solve Bryan Passwater’s Big 10 worksheet on the FTC. In this activity, each integer from 0-9 is a solution to one of the problems. Students love working on these challenging problems in groups and getting instant feedback about the validity of their answer. 

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Teaching Tips

We love this activity from Bryan Passwater because the questions get at both parts of the FTC from many different angles. Students must think conceptually and strategically to solve the problems, and flexibly reason through ones they have not encountered before. 

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There are many strategies to ensure all members of a group are participating. Proximity, of course, is usually most effective. Walk around the classroom during the review to answer questions and keep students on-task. If you are collecting an answer document, require work from each student to support their answers. Perhaps you enjoy an element of surprise? Collect only one answer sheet from each group --- but don’t reveal which one until the end. The optimal strategy, though, is to build a classroom culture of peer-to-peer conversation and support. At this point in the year, group work should be natural and valuable. 

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Student Misconceptions

As you visit each group, listen carefully to student dialogue: some misconceptions can be corrected on-the-spot with individual students. If you notice common errors, you could pause the activity and teach a mini lesson on that topic. We noticed our students struggled most on parts d and e, but instead of interrupting their learning process, we gave them time to sort through the problems and eventually land on the right solution. This was a great reminder for students about applying the FTC when the upper limit of integration is a function in terms of x.