Number Theory for Teachers

This summer I'm taking a course in Number Theory designed for secondary school math teachers, specifically those of us who went through the Traders-to-Teachers program at Montclair State University. As such, it will cover a subset of the topics usually found in introductory number theory courses, with, I suspect, less rigor. From the syllabus: "Our class discussions will relate number theory topics to middle and high school level curriculum."

At the beginning of the first class the instructor asked what we hoped to get out the course. I kept silent, as my situation - unemployed - and interests differ from the rest of the class. However, I continued to ponder the question and hope to answer it here. Aside from the obvious and trivial response - to satisfy a requirement for full teacher certification - here's what I want to get out of the course: