Right now in algebra, students are just wrapping up graphing systems of inequalities. According to my exit slips/formative assessments they are pretty good at it.

I spent a whole lot of time the last couple weeks digging around for activities and resources on rich problems involving systems of inequalities. Here are a couple of my favorites:

–Ohio Jones by Dan Wekselgreene

–Lego Pieces by Fawn Nguyen

I regret not using either of these this year.

However, I am in a weird position that I haven’t ever really found myself in…

Normally when I find an activity/task I am excited about I go for it, without any hesitation. Right now though, I feel a pressure just to get through the content. I dunno, I guess I am trying to say I don’t really feel like spending extra days exploring and setting up struggle for students with this particular concept.

And I am normally all about that.

I started teaching linear inequalities by asking students how many solutions various equations have…

**y = x + 3**

**lxl = 5**

**y = x + 3**

then dropped

**y > x + 3**

It took so much time to get through one linear inequality and I am not sure what value this approach has over just telling students the short cuts of shading/line types. It does not feel to me that the time we sunk into it was worth it. The transition from pure math or interesting problems into using a system of linear inequalities to solve them is rocky. Hopefully by next year I will have some time to think and come back with a better understanding of my struggles right now!

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I appreciate that you are so honest in your blog.

I can totally relate to your comment: “It took so much time to get through one linear inequality and I am not sure what value this approach has over just telling students the short cuts of shading/line types. It does not feel to me that the time we sunk into it was worth it.”

It is tempting to just give students the formula or algorithm to memorize so they can “get through” the material. However, if we really think about it, we are not doing them a favor by just teaching procedurally. The tricks and shortcuts around a specific topic will quickly be forgotten. In fact, most of the math we teach will not even be used by our students in their future careers. What will best benefit our students and what will have the greatest impact on their future success is to teach them how to learn, how to think and reason through new concepts (be in math or not)… helping them to make connections between these new concepts and previous ones (math or not).

In my opinion, the best resource provided to math education by the Common Core are the 8 Practice Standards. If we ask students daily to make sense of problems, persevere, reason abstractly and quantitatively, construct viable arguments and critique their classmates’ arguments, we are providing them with a blueprint for problem solving in any discipline. If we ask them to create mathematical models of real world situations using appropriate tools that they have learned to rely on for simplifying or illustrating the math concepts in question, we are teaching them to be creative and to communicate well. If we ask them to notice the structure of a mathematical equation or model and to be able to understand how that structure can help them get to the core of what the equation or model is trying to communicate, we have opened our students up to a whole new way of thinking. If we can get them to be precise in not only their calculations, but also in their communication, we are teaching them a life-long skill. Finally, if we can help them to look for patterns in abstract expressions and posed problems, noticing how the patterns repeat and then using that repetition to solve the problems, we are giving them tools for making sense of problems and persevering.

I had never before put the 8 Practice Standards into a paragraph like the one above. We always see them in a list of 8 statements that are not necessarily connected to each other. However, if we really instill them into what we do on an everyday basis, we are providing our students with a blueprint for facing problem solving in all aspects of their lives.

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Thank you for taking the time to write out this comment. Your points really hone in on the reasons why I pursued teaching in the first place. Definitely worth the time to build and focus on the practices rather than memorizing steps over and over.

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