As for the seniors, most of the chapter was an extension of Algebra II. We solved systems of equations graphically as well as algebraically. As usual, most prefer the algebraic methods of substitution and elimination. I wouldn't mind the graphical approach if someone could guarantee that every solution would be an integer! Next, we worked on our tree problems (solving systems of three equations with three variables), followed by matrix arithmetic. We began slowing down with matrix transformations, and really ground to a halt with the last three sections based on inequalities. Finding the coordinates of the bounded polygons as well as unbounded regions was not always the easiest. Neither were the linear programming problems to boot. To my surprise, however, many students gravitated to the idea that linear inequalities have a real place in the work-a-day world. I've never been a fan, especially since real-life presents far too many variables to be controlled in a high school textbook.
The eighth grade class (Pre-Algebra) is working on solving one-, two-, and multi-step equations, including everyone's favorite: word-problems. I'm excited that many are getting some simple concepts of when to add with a variable verses when to multiply with a variable. Again, this class has gone slowly through the beginning of chapter 3, but don't mind to an extend; we will be solving for x almost every day of our high school careers.
All in all, the school year is off to a great start. Most students are still willing to work. I've encouraged several classes with some thoughts by David from Psalm 34:17
The righteous cry, and the LORD heareth, and delivereth them out of all their troubles.