Being my first time teaching this, I am still trying to conceive how I want to teach this class. I was given a "map" on how to cover the standards (all the plus standards in CCSS for secondary math). I am moving things around, but its still a work in progress. The unit I will be describing is definitely not the first, nor should it be the last one in the class. This is out of what I'm envisioning as 6 units.
Complex Numbers and Graphing
All basic operations, conjugates and graphs. Review distance formula in relation to Pythagorean Theorem. (Which is reviewed in a previous unit). Lots of standards to be covered.
Not many standards here, but wonderfully fertile ground for what is to come. Keeps students using and thinking about trig. Pythagorean Theorem makes another appearance, keeps the students grounded with a comfortable concept.
**shameless plug here: Global Math Department did a week on the Pythagorean Theorem a few weeks ago and I left with at least 5 good ideas for using it to help my students think more mathematically.
Vectors: good number of standards here too. More Pythagoreas here too. Many of my students see vectors first in physics, but not all. Students helping others at its greatest. I'm tempted to challenge 3 students (in a class of 27-30) to be the helpers and offer them each class average on the quizzes plus 20 points, for their grade on those quizzes.
Matrices: our students see matrices in Alg1, Alg2 as well. Basic operations and solving matrix equations without inverses is well covered. So is systems. At this level we are doing row operations (gaussian/Jordan elimination) and understanding these ideas. Also a really silly standard about writing a vector as a matrix is required.
Currently, this unit contains the most standards of any of my units, by a high margin. It also was one of my students better units. Looking back I did parametric equations very poorly. I know I need to do more then just mention them, but I just haven't found the hook or way of engaging them.
My thought is that this unit should take 4-5 weeks. Each topic should include a quiz and 1-2 days per topic where formative assessment should drive the discussion. (I teach in a school where this class is done over 2 trimesters and the class meets 5 days a week with 72 minute classes).
One last thing... I wonder if the administration would accept that being able to most effectively teach vectors would require purchasing for me, and my classroom;a new pool table, balls and cue sticks. It can't hurt...