Sunday, January 12, 2014

Solving One-Variable Linear Equations

Confession:  I taught an entire semester of Algebra 1 without spending time solving linear equations. 

Why?  Because I knew my students had seen a lot of it in 8th grade, and I also knew that they were all at different places and ready for different challenges.  I also knew that they had forgotten some of what they had learned and a little reminder might take them a lot further.  All of this is hard to address in a class of 20+ students.

However, I knew it was something I needed to address at the start of this semester so that we could solve systems and eventually some quadratics.  I gave a pretest, but it was evident that not a lot was immediately recall-able for them.  So I spent a few days focusing on solving 2-step equations.  Here are a few reasons why I chose to start with 2-step equations:
  • I can say they can all be solved in 2-steps, which helps the students process what they need to do
  • I can address issues like "Ah, there's a fraction!" (but it really just means division) and I can even throw in some parenthesis
  • I can challenge all students with things like -t + 10.2 = -23.1 (the negative variable is really tricky the first few times they see it)
  • It is not out of the reach of most students (I do have a few students who still struggle to solve one-step...but those are students who did not take 8th grade math in my district last year.)
  • It is enough to bring back a lot of what they learned about solving equations
I have one Algebra class that is a little bit quicker than the others, so I got to move away from 2-step equations with them on Friday.  I couldn't decide exactly how to do it, because there are SO MANY ways to solve different equations.  I really just want to ensure they are aware of the various options they have and give them some practice at choosing what to use in what scenarios.  I don't want to say:  "always distribute" or "put the variable terms on the left and the constants on the right" or anything that shows that there is only one way to solve.  I want problem solvers, not procedure followers.

Anyway, here is what I ended up doing.  I just gave them 4 "challenge" equations to solve.  And for the most part, they worked HARD for 30 minutes to work out solutions.  Here are the equations:
  • 2(-1x + 6) = 22
  • 2x + 2 = 32 + 5x
  • 3 - 2x + 6x = 15
  • 5x - 7 = 2(x + 1)
I put the four equations on the board and said "I challenge you to use the resources available in this room to find the solutions (and perhaps a solution method) to these equations today."  We discussed what resources were available and then they got to work.  The review we had done with 2-steps was enough for several students to remember even how to move variable terms to the other side.

There were a few students who "tried" and then gave up and didn't accomplish much at all, but I would say at least 85% of my students worked hard during the time I gave them.  I was SO PROUD of them.  I just wanted to brag a little about my students, because it was everything I hoped it would be.  

We will continue to work with advanced linear equations on Monday and Tuesday to get them more fluent at being aware of the strategies that are available and choosing an appropriate one.  Perhaps with some whiteboarding...


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