Determine general and particular solutions to differential equations
I can use separation of variables to find a general solution to a differential equation
I can use the initial condition to solve for “C” to find a particular solution to a differential equation
Quick Lesson Plan
Today students work on a Round Table activity to solidify understanding of how to solve a differential equation. Then students work individually or in pairs on an FRQ question. Responses were self-scored by students using the rubrics provided by College Board. After class discussion, assign additional work as necessary to review your learning targets from Topics 7.6 and 7.7.
For the Round Table activity, students should be in groups of four. Each group member gets a different question and has to solve part a (separate variables). After an allotted time (1 minute), they must rotate papers so they are working on a new problem. After checking the work of their peer in part a, the student completes part b. Students should not move on even if they are done before the given time (we suggest 3-4 minutes). This continues until parts a-d are done. Allow for slightly more time on each part since students must check the work of everyone before them. Have students affirm or high-five each other as they pass papers to build class community. At the end, have students look at their original paper to review the solution. Give students 3-5 minutes to ask each other any questions they had while solving.
After the Round Table activity, students are more equipped to handle an entire FRQ. To best prepare students for the expectations of a Unit 7 Test and the rigor of the AP Test, strive to offer authentic practice problems. We suggest 2014 AB6, 2016 AB4, or 2018 AB6. The College Board has made available to teachers past FRQs and the accompanying scoring rubrics. Students who practice authentic FRQs become familiar with the notation and communication expectations for this section of the test.
The Chief Reader’s commentary offers insight into the scoring rubric and details the learning targets which the FRQ was designed to assess.
Investigate the College Board site to review sample student responses for any FRQs assigned to students. Common errors are discussed and should inform your instruction before and after an assessment.