Last week I had introduced the idea of linear equations for the first time. The day after introducing the concept we had tried a Desmos activity. The activity did not go well and many of the kids clearly did not understand how to identify linear equations just from looking at the equation. (They were perfectly clear on linear equations making straight lines, but recognizing what the equations looked like or grappling with the definition of linear was much harder for them.)
Today I essentially started over because I felt that they needed to try it again. After repeating the definition and listing the ways to recognize as a class, we practiced as a group. I threw a table on the screen and had them enter their thoughts on Go Formative. Engagement was rather low today. Even students were not actively disrupting they were simply not answering the questions. It is Monday but I think I need to change it up a little on my formative assessment formats. I am not sure. I do want to help them get into a routine so that they know what to expect, which means I only give “notes” on Monday’s and Wednesday and I try to use every other instructional activity that I can on the other days. (And also we don’t JUST do notes on Mondays and Wednesdays. The blocks are too long for that.)
I also wanted them to start to connect that solutions of linear equations lie on the graph of linear equations. So I wrote a linear equation on the board -2x+3y=21, put them in pairs, showed them what a solution looks like without giving them any (values for x and y that make the equation true), and then told them whoever found the most solutions got candy.
I was plotting solutions that they give me on the projector using Desmos, but it was not until the final block that I realized that I should also have the graph of the line on there so that they could see that their solutions showed up as points on the line. Oops. At least I improved throughout the day, haha. I had mixed success in every block. Some kids got really into it and found lots of solutions and others were not excited about the challenge at all.
I really like this activity (largely inspired by Dan Meyer’s Wolverine poem about teaching math class) because my students do what mathematicians do. They look for solutions to problems without any type of machinery to work with. I didn’t tell my students to pick a value for x and then solve for y. Or to look at the graph and pull off points. Or to use the slope of the line to just keep moving up and finding new values. But they did all those things. Or some of them did. A few. Most them guessed wildly and that’s okay. Because that’s what real mathematicians have to do sometimes. Just guess wildly.
Things I will do better next time:
Scaffold more. This activity could have taken up the whole block and been really useful if I built up to -2x + 3y = 21 by first having x + y = 21 and then extending so they aren’t just trying whole numbers and then having them do x-y = 21 and so on, building up difficulty so that finding solutions themselves aren’t as much of a challenge. (At first, anyway. Later I do want it to be a challenge.)
Wrapping up as a class more. I did a poor job helping the group summarize as a whole until last block and even last block was not perfect.
No matter though, I plan to repeat the activity tomorrow and do exactly those things.
On a non-curriculum side, I feel I need to be careful because I keep finding myself looking forward to next semester and my new set of classes. I think I’ve gotten so tired and run-down that I’m starting to feel I’ll do better when I get a fresh start with new classes and can start from the beginning on classroom management. But I need to make it through this semester first and there are still plenty of instructional days left were I need my students to be learning. I am really looking forward to Thanksgiving break, I need it. I requested to use 2 of my personal days so I have some extra time to travel and get to Indiana, where I go to Thanksgiving every year. I’m really hoping those get approved, but they are right before a holiday and I am low man on the totem pole.
Thanks for reading.