Help Me Design a Number Theory Class for High Schoolers

At the end of the last school year, I agreed to the massive undertaking of teaching a Number Theory class at my school. I worked on it a bit this summer, but was going to do most of the planning once I returned to school and was able to pick the brains of my colleagues.

Now to the present day and my dilemma…

I have suddenly been offered a new job at another school. My last day with the Number Theory kids will be this Friday. So I have been assigned the arduous task of designing the curriculum in one weeks’ time. :eek:

You see, my successor has yet to complete his mathematics degree (has yet to complete the college-level number theory class for that matter) and desperately needs my help here.

My students are all of high-school age, but most have only completed the first half of Algebra 1, some barely. This includes lots of basics about functions and graphing, but nothing on systems of equations, radicals, polynomials, etc.

I’d like to include lots of fun stuff if at all possible. So far we’ve covered Set Theory (Venn Diagrams with a twist), Divisibility Rules (see here ), and number bases (loads of fun here for me and the students alike).

I’ve heard people mention game theory, but I’m not quite sure where to go with that.

Any help at all would be greatly appreciated by me, my successor, and my students alike.

DoperChic

You could spend a bit of time teaching them enough modular arithmetic to cover the extended Riemann hypothesis.