We started off our Absolute Value unit with solving absolute value equations and inequalities this year. Then, we learned how to graph absolute value functions, and I had the students do this problem:

And the students were all, “Ohh this is why we get two solutions.” So I learned my lesson to start by graphing, and then solve simultaneously. Luckily, I didn’t have to wait til next year to try this approach. Our next unit of study was Quadratics, and once they learned how to graph them in vertex form, I gave them a similar problem:

At this point, we had not solved a single quadratic equation yet. My students graphed and launched right into solving like it was no big deal at all. I thought they had finally made the connection between the solutions and the intersection of the line and the parabola.

But, then we moved onto quadratics in standard form and solving by factoring. The factoring and solving went well, but on their assessment, I gave them a “Find the Error” problem where they had to identify which work was correct and explain their reasoning. Here are some of their responses:

Most of my students correctly selected Kristen; however, I was extremely disappointed in their explanations. I expected their explanations to be more in depth after the many discussions we had about solving for the x-intercepts. They mostly went with the procedural explanation of setting it equal to zero. I wanted them to explain WHY we set it equal to zero. I don’t know how to ask that without directly giving away which student’s work is correct in the first place. There’s also a problem with the many responses claiming Kristen is correct because she found two solutions. This tells me I need to do more examples with only one.

At this point in the year we’re moving onto exponentials, but I’ll be thinking about this problem for a while. Any advice would be greatly appreciated!