I’ve been fascinated by inequalities lately. I always find it interesting how students tend to get them backwards. I feel like they learn some bad habits and have some misconceptions about inequalities before they get to Algebra. It’s hard to get them out of those habits.

I’ve heard my students say that you always shade in the direction that the inequality is pointing. Because of this situation, I try to get them used to switching the inequality if the x is on the right side of it. This really is not an easy concept for them and I think it’s because they really do not understand what’s happening.

What is this sign? What does it really mean? Why do I switch it sometimes and not at other times? These questions are hard. I developed a lesson where the students do a discovery of what causes the inequality to switch directions. As they are solving problems in the Google Sheets activity a picture is evolving. The kids can’t wait to finish to see what the picture becomes.

The rest of the activity is setting up, solving and graphing inequalities. To see if students truly do understand, I ask them to either show work or explain their steps. This is really challenging for many students. It’s interesting to see if they truly know what they are doing.

I have several activities that go nicely with this one. Check out the resources below:

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