To really learn a subject deeply, you need to be able to teach it to others. One of your assignments is to prepare a written lesson plan (around 6-8 pages) for a short lesson (under an hour) on the given objectives. For an audience, you should address someone who has been through this course before, but needs a review of the material.
I strongly recommend that you include several illustrative examples or homework problems that you have worked out fully. You might also summarize important concepts, facts, and theorems, note shortcuts, include pictures that illustrate the main points, and anticipate questions that might be asked.
A lesson plan should cover all of the objectives listed in the objective sheet.
Your lesson plan must be your own work in your own words. You do not need to write down every word you would say. Take this assignment seriously—you will most likely see a direct correlation between how careful you are in your lesson plan and how well you retain the material.
You are expected to teach a 20-30 minute lesson to one of your classmates or another appropriate person covering material from your lesson plan (part of your points for the lesson plan comes from this teaching). You will know the material much better after presenting it to someone else, leading a discussion, and answering questions. You will probably not be able to cover the entire lesson plan in your 20-30 minute lesson, but I encourage you to choose a part that is difficult for you and teach a lesson over that part.
After you have taught the lesson for 20-30 minutes, have the “student” sign the top of the front page of your lesson plan, with a statement like, “<your name> taught me for 20 minutes from this lesson plan.”