# Day 29: Why? Why? Why?

In Algebra I used the textbooks exploration in solving one step inequalities. The goal was for students to realize the same properties of equality apply to inequalities.

This went ok.

It is had to differentiate and account for different student ability levels when giving every student the same worksheet. But at times I am feel like I am out of other options, especially when dealing with inequalities. These are my weak spot.

I am throwing around a few ideas of how to have students ask the question for the triangle inequality but that idea is still n the works. If anyone has any activities/ideas for inequalites let me know! I think the hardest thing for me is the similarity between solving a multi-step inequality and solving a multi-step equation.

In Geometry I introduced algebraic proofs by throwing this up on the board:

Solving for the variable was a piece of cake, justifying each step was brutal.

I really enjoyed asking students WHY they could subtract 8 from both sides. There was a flurry of reasons; they understood that it has something to do with the equal sign but couldn’t quite construct a viable argument as to the exact justification.

This is my first year teaching Geometry so these lessons are definitely at a still-in-the-works point, but I am excited to see how the year develops!

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## 2 thoughts on “Day 29: Why? Why? Why?”

1. So, our book basically says that to solve an inequality, you solve the corresponding equation, then test values in the intervals. Doesn’t matter what inequality it is.

There are several reasons. Locally (within A1) there are kids who still need practice with equations, so they get that instead of a whole new system with new rules. Globally (A2 / PC / Calc) the “number line marking” method is used to solve inequalities like determining when a function is positive or increasing, so use the same tactic for A1.

Example: solve -4x + 12 > 20. To do this solve -4x + 12 = 20 instead (x = -2). Now mark a number line, -2 is the cutoff, and test values in each possible zone (x -2). The rule of “switch the sign” never comes up, and isn’t needed.

Even better the same tactic works for systems of inequalities, except the “cutoffs” become lines like x+y = 5 and the “zones” are regions of the plane.

Good luck!

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1. Thanks for the response! I like the example you provided. Especially because it encourages students to look deeper into the concept rather than memorizing a rule. I will have to try that in the upcoming weeks!

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