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:

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.

I'm at a parade, so can't see your documents. In a pre-calc course I think the way to show this, so that the kids see the reason for doing it, is to start off with the equations, put into matrix form and to do Jordan-Gaussian eimination by hand to show what is occurring. (I ignore the multiplying by the inverse matrix explanation). Then when the kids get capable, ask how many would like an easier way. (The 84 and nspire can both simply simplify rows and/or jump directly to the solution.... share whichever you wish with the students, though I think not just jumping to the solution is a better petagogical way of doing this)

ReplyDeleteI've not taught pre-calc but this is how I show it in Alg2 when I cover matrices. (Now if I can just get he Alg1 teachers to stop showing how the calculator can just short-cut to the solution of a system of equations with matrices. The Alg1 students NEED the practice with the algebraic manipulation and graphically understanding a solution of a system of equations.)

Scott

@planting_ideas

My original plan was to do the lesson you described, but since my kids did this method in Algebra 2 and my goal was to review I went with the inverse method. I almost wonder if this lesson was even worth doing if I'm not willing to do it justice though.

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