We are finally getting to move beyond basic graphing and finding equations of lines. It was a long slog, but the skills tests show that the majority of my students are starting to get the hang of it. I always look forward to the systems of equations unit, because it is a chance for students to synthesize what they have been learning all year - and, in a situated context, no less. My plan this year is to deepen the emphasis on representational fluency and summarizing, to help build all of those neural bridges we want the students to have. We started the unit Monday, and I was really blown away by my classes today - all of a sudden, I have students doing algebra! I had them solving systems in pairs, using mini-whiteboards, where one does the graphical solution and the other does the algebraic solution, and then they compare their answers. They did a great job, and it wasn't until this activity that many students realized the answers should be the same. I got a couple of those hilarious, indignant "you should have told us!" comments. Next week is winter break, which doesn't come a moment too soon; however, I'm worried about how much will be lost over the seven days that nobody is asking them about starting points or rates of change. No matter, it's worth it to have a rest. Here are a couple of examples of what we're doing, and the links to the lesson materials thus far.

Lesson 1 (Intro to Systems of Equations) doc / GeoGebra files / Keynote / Powerpoint

Lesson 2 (Solving y = mx + b Systems) doc / Keynote / Powerpoint

Lesson 3 (Practice Solving Systems) doc

A beautiful combinatorics argument

19 hours ago

## 7 comments:

I love systems too. I've spent almost 4 weeks on systems this year, but I feel it is worth the time. I tell my students that this is where it all comes together. And I feel such pride when I look out and see them using their graphing skills, their solving equation skills, and even their calculator skills. When I get to systems, I know the end is near and they are almost ready to go on to the next course.

I share in your joy about moving beyond the basics and also about break! I too, used the mini-white boards and had students working solutions using different methods. It really helps to form connections between the methods. I'm enjoying your blog and like all the materials you so willingly share. Thanks!

Great stuff! Thanks. One activity that I do that seems to work well is to play "merry go round" - I put the kids in groups at stations around the room. They have to solve a system by the method of their choice (graphing, subs. or elimination). When everybody's ready, they all rotate to the next station. They'll see the work that the previous group did, and then they have to solve the problem a different way. We keep rotating until each problem is solved all 3 ways. This helps them see that each method will find the same answer. (I also use this for solving multi-step equations, having groups solve one step at a time and rotating until the problem is completely solved)

I think I've commented before, but I really like the cars to LA...

There are units on both axes that are on the right scale for the kids. And the derived units for the slope are well within their grasp.

Jonathan

I stumbled across your blog today and I am excited to sift through all your stuff. You definitely do "fun" things, yet the learning of the skill is still taking place! Thanks for sparking an interest in teaching topics in a fun way! I will be "stealing" lots from you! Thanks! :)

I stumbled across your blog today and I am excited to sift through all your stuff. You definitely do "fun" things, yet the learning of the skill is still taking place! Thanks for sparking an interest in teaching topics in a fun way! I will be "stealing" lots from you! Thanks! :)

I know these are older, but would it be possible to get these as a PDF? I tried downloading the files and a lot of the graphics don't show up correctly. Great ideas.

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