Today was rough.

Algebra is just getting into solving quadratic equations. We looked first looked at solving linear equations like **3x + 4 = 10** and talked about how these were solved and what was happening to x in equation.

After a while I threw up **x² + 4x = -3.**

Students tried to solve it by moving the 4x over and were frustrated that they couldn’t get the equation down to just one x. They whole group divided and conquered on different values of x, and eventually they reached two solutions.This took a lot of time, time students don’t have, they asked for a better way.

Then I messed everything up.

No matter how I modified the lesson between periods, students struggle with the process of setting the equation equal to 0, graphing the related function, heading back to the equation to remember they were looking for x-values that produced y-values of 0, then using the graph to help them.

Too much.

I had blank stares all day, something is wrong on my end. Maybe I haven’t emphasized WHY graphs are useful, but, we talked a lot about how graphs generate y-values based on chosen x-values. This is almost the same thing.

I also probably shouldn’t have made them suffer by graphing each equation by hand…

Let me know below how you navigate into solving equations by graphing.

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Get them totally familiar with graphing equations, and the interpretation of interesting points, before thinking about solving equations.

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if solving graphically, why set equal to zero? Maybe let students graph y=x^2 + 4x or x(x+4) and y = -3 and ask where on the graph does it show where both equations are equivalent. I find my students get it better that way so the x axis isn’t there to confuse. Then for solving by factoring intro the value of setting equal to zero for the zero product property.

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Good point, I get hung up on setting equations equal to zero. I was talking with another teacher in my department who brought up the fact that it doesn’t really matter for graphing.

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I have found that if you start by remind students about plotting two lines (even better doing one) and finding the overlapping point, which is the solution to both those lines; then point out that you are looking for the intersection of that cool curve with the line y=0; plot y= 0 first (because it is easy) and then put the other curve on it and look for the overlap. The whole time remembering out loud that I want to find the overlaps. This only works if you have done this with two lines. Inevitably students remember that there were other ways to find the overlaps and ask if there isn’t another way (if you are lucky) and then you are on to the next lesson. Just some ideas…

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Sounds like a good way to review and introduce a new concept. Noted for next year!

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