## May 26, 2013

### Matrix Mess

One of the challenges of PreCalculus is making it seem like a cohesive course rather than a list of skills to review and master. My theme lately has been "solving problems efficiently." Students have learned a variety of methods to solve, for example, systems of equations. My goal is for them to master each method and know how to choose amongst them. Since we had just finished the unit on conics, we solved systems of second degree equations (smoother transition plus a more challenging set of problems than the ones they'd seen in both Algebra 1 and 2). That all went fine and students worked on elimination, substitution and graphing. However, I also wanted to review matrices and so I upped the ante to three variables (but returned to first degree equations). The problem was, I didn't want to take the time to properly review matrices, I just wanted to remind students that they're useful when solving systems. This obviously backfired.

After a rough week of allergy haze, it was already after school on the day before I needed to give this lesson and I still didn't have a plan. I had a vague idea of what I wanted to happen but couldn't even put it into words when explaining my thoughts to a coworker. Despite my incoherence she helped me out by putting together this worksheet (which she fully expected me to edit but I was too exhausted to do much):

I also put this problem on the board:

And had this diagram ready to show students who needed help remembering how to multiply:

You already know this is going to go badly because the material is split into three places and is dependent on me showing up with a diagram at the right moment. Students were totally baffled why they were multiplying matrices. They didn't understand that the calculator would be taking the inverse (some tried to multiply the matrix by -1). They didn't read the instructions all the way through and were calling me over to help with the calculator.

My attempt at a rewrite:

Thoughts and further suggestions would be much appreciated.