Linear Systems Stay and Stray

Systems. Ugh.

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My very first go-round at systems of linear equations and inequalities, lo those many years ago, was an eye-opener. I was ready to drop the quiz score, all the scores were so bad. Clearly I must have done a terrible job teaching it. I’ll take the hit for this one, I figured. I related my misfortune to a colleague who had a couple of years experience under her belt. She wrinkled up her face and said, “All algebra I students are bad at solving systems. It happens every year. Don’t drop the quiz.”

Turns out, she was right. Truth: When you find a wise teacher, trust them.

My Algebra II students are struggling more than usual this year though. I covered another teacher’s IED class for a couple of days at the start of the unit, leaving one class of my students with a sub and some pretty thorough video notes, I thought. My first real try at an in-class flip. Thud. But my live class struggled too.

Scale of 1 – 10? They gave themselves a 3.5. No bueno.

So, let’s back up. We need some practice opportunities and a shot at understanding, not copying. We spent an entire class period working thru homework questions and setting up a word problem. That moved the needle a little. Got them to maybe 5. Still room to improve.

Sounds like a job for a Stay or Stray gallery walk. Picked this one up from my instructional coach in Hammond, Rhonda Fehr.

I provided a 9-question practice set, split 3/6 between graphing and substitution. Students group up, take ten minutes to work through problems as a group while I circulate to help troubleshoot. Each group should now have one problem on lock. My job is to subtly notice which problem that is, and assign it to that group as “their problem”. Now they put their work on a piece of poster paper which I strategically place around the room. One student is the “answerer”, the other group members ask questions to get to the point where they could teach it to other groups as they rotate around the room. Now one stays, they other group members rotate to the next station. After each round, a new student (not from the original group) stays at the station to become the new answerer, while everybody else moves on to ask questions at another station.

It was hectic. It was loud. That definitely turned off some of my students. “Mr. Dull, they don’t know what they’re talking about.” “I didn’t learn anything from him”. “We didn’t have enough time to figure out a problem/ask questions/make our poster”.

I wanted to give them an opportunity to learn one problem deeply, know it so well they could explain it someone else. I didn’t hit everyone. Maybe just a few in each class. But I posted the original problem set on our Canvas, with a worked-out answer key, and several committed to going home and at least trying the rest of the problems.

So some learned today by explaining to others. Some learned by being taught by peers. Some will go home and get in some reps and check their own work, and learn that way.

I’ll take that.

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I Already Know How To Do This Stuff

There are rumors floating around that Once Upon A Time, when dinosaurs roamed the earth and your teachers were in school, that summer vacation lasted all the way through August, and school didn’t start until after Labor Day.

Maybe? I don’t know. That was a long time ago. Alls I know for sure is my district switched from trimesters to semesters this year, and we already have 3 1/2 weeks in the books. So Labor Day is actually a well-timed check point for my students and me. We’ve got our first quiz coming up this week in my Algebra 1A repeat class, covering one-step, two-step, and multi-step equations. Way back when, I would have pulled some sample questions out of the back of the book, stood at the board, worked thru the problems, asked the students to copy them down, said “any questions?” then given the quiz the next day and wondered why they *still* didn’t understand.

One year, like a lightning bolt from the sky, the realization: you know, that didn’t work the first time around. How is them watching me do problems going to help them learn? Eventually I came around to the camp that had students working the type of problems we had learned, that they would see on the quiz, and checking each others’ work. Also in that span of time, I fell in with the good people of the #MTBoS, which poured a mountain of brilliant review activities into my Google Reader.

Eventually, fortified by people doing and sharing cool stuff (looking at you Kate Nowak and Matt Vaudrey) I stepped out and tried to create some of my own review activities. Tomorrow’s is driven by a desire for my students to understand why they follow the algorithm for solving equations, and by a desire to have all of them working, engaged with the math, and helping each other out when needed.

So here’s the plan: DIY equations. Documents here:

Algebra 1A DIY Equations Review

Algebra 1A DIY Equations Review Solutions Cards

Got some white index cards and some neon index cards (inspired by Math Equals Love), wrote some types of equations (two-step, multi-step, variables on both sides) and conditions (parentheses, fractions, addition, division) on the white cards, and solutions (x= -1/2) on the neon cards. Students will group in fours, each will draw a condition and a solution, and then write that type of equation with the indicated solution. They will then solve the equation they created to make sure it works. Then they will rotate the papers around the table so they are solving someone else’s equation. Rinse. Repeat, through the group of four.

If all goes well, they should be able to repeat the process (in a 50-minute class, if I can get around the table twice, I’m good). If that works out, each of my students will have written two equations and solved eight, and had a chance to check each one on the spot.

Plan is to check back in and blog the post-mortem. As I tell my students often, “Hey, you know what, I already know how to do this stuff. Went to school, did three, four semesters of rocket-science math. I want to know if *you* can do it.”