Connect derivative concepts (differentiability, derivative rules, tangent lines) across multiple representations
Explore patterns in the product rule and quotient rule in an open middle task
I can solve derivative problems in numerical, analytical, graphical, and verbal representations
I can look for and make use of structure to solve a challenging problem
Quick Lesson Plan
Two activities will frame today’s review of Unit 2 material. First, students will work on 5 multiple choice questions that vary in difficulty and complexity. Next, students will work on a derivative puzzle to gain a deeper understanding of the product and quotient rule.
We recommend having students work individually on the five multiple choice questions to reflect the format of the AP exam. These questions are non-calculator and are timed at 2 minutes a question, just like the AP exam. In the debrief, consider having a student present question 5, focusing on strategies and sense making of this non traditional problem.
Next, have students work in small groups on the open middle task. Our students enjoy working on these kinds of tasks because they are non-routine problems with multiple entry points. We find it works best when situated within a class discussion where after groups spend time working on the problem, solutions are presented, explored, and connected. We like to use the 5 Practices for Orchestrating Productive Mathematics Discussions approach, introduced by Smith & Stein, by anticipating student responses, monitoring group work, and then selecting, sequencing, and connecting student responses.
The goal of today is to get students thinking flexibly and creatively to prepare them for the rigor of the AP Exam. There WILL be questions on the exam that are unlike ones they have seen before, assessing students’ ability to connect concepts and apply their understanding in a new way. By preparing students to tackle non-routine problems and embrace their challenges, we can help reduce students’ test anxiety.