Connecting Position, Velocity and Acceleration (Topic 4.2)
Unit 4  Day 3
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Learning Objectives

Calculate rates of change in the context of straightline motion
Success Criteria

I can use first and second derivatives to find the velocity and acceleration of an object given its position.

I can determine when an object is at rest, speeding up, or slowing down
Quick Lesson Plan
Overview
We are using Bryan Passwater’s engaging Big Ten: Particle Motion worksheet as a vehicle for reviewing the concepts of motion in Topic 4.2. Students are presented with 10 particle motion problems whose answers are one of the whole numbers from 0 to 9. When students correctly solve a problem, they cross off the corresponding number from the list  only once  on the front page until every digit has been eliminated. Bryan has created a fun and effective review activity that students genuinely enjoy!
Teaching Tips
Students are usually quite motivated to work independently on these problems, but struggling students may find needed support by working within a small group. The format of this worksheet encourages independent work, often with little instruction or assistance requested of the teacher. As mentioned previously, flex time can be used as you wish. Going over homework problems or allowing students time to work on homework problems is an easy choice. Presenting related FRQs from AP Tests or interesting journal prompts is also valuable for students.
Exam Insights
Justifying whether a particle is speeding up and slowing down requires specific conditions for velocity and acceleration. (The Big Ten worksheet visits this idea in problem c.) Justifying whether a particle is moving toward or away from an origin requires a discussion of position and velocity. (The Big Ten worksheet visits this idea in problem f.) Students may confuse the two scenarios, so a debrief of those concepts is helpful.