Today’s lesson focused on solving simple linear equations where single variable expressions were on both sides of the equation. The warm-up showed the following

2x+5=7 2x+5=7x

and students were asked to state what was similar and different between the two equations, and to write the first step for each. They were also told anything they wrote would be acceptable.

Most students stated the numbers were the same and/or that one had a 7 and the other a 7x. No one mentioned that both had 2x+5 as a common expression on the left side, however, that is not to say no one noted it. After this I facilitated working out a few homework problems calling on students to tell me what to do for each step of each problem. While I want students involved and speaking up, most are very reluctant to do so, for many reasons, which I share occasionally as a student myself. While there were one or two students who would say something, correctly, I could not tell who did or did not understand what was going on, even when asking them. I hope more speak up over time.

Afterward, my CT led instruction on solving equations with variables on both sides. She worked through several examples including equations with one, none, or infinite solutions. When the infinite solution example came up, and my CT stated it as such, one student exclaimed, “This is why I hate math!” followed shortly by “this makes my head hurt.” I waited a minute then decided to offer a means for students to relate to the “infinite solutions” example (e.g. x+3=x+3). I mentioned that these expressions defined lines and when they equaled each other, they could be viewed as two lines that are on top of one another, then placed my arms together showing what that might look like to them. I know this worked well, when my CT referred to parallel lines for the “no solutions” example, which was next. Her doing so made me feel pretty good. I’m still treading very lightly to not rock the pedagogical boat. But I did take a calculated risk today and it turned out OK.

Onward and upward!

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## About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.

“I know this worked well”

Could you please elaborate on this statement?

Have you followed up with that student? How has his/her work been so far? What did you/your CT do to assess student understanding of this lesson?

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