I am just finishing up my quadratics unit in Algebra II. We spend a lot of time on quadratics, doing everything from factoring, to completing the square, to the quadratic formula, to all sorts of graphing, the discriminant, 1D and 2D quadratic inequalities, quadratic linear systems, systems of inequalities, etc. Tons. And we didn’t even get to do the project I enjoy involving pendulums and quadratic regressions. Le sigh.
I’ve posted much of my quadratics materials before, but I thought I’d share some new/updated ones. I’m a bit exhausted, so forgive the shortness of my descriptions.
1. My Vertex Form worksheet was motivated by my frustration with students just memorizing that has a vertex of because you “switch the sign of the -2 and keep the 3.” Barf. (FYI: we haven’t done function transformations yet.) So I created this sheet to “guide” students to a deeper understanding of vertex form.
2. My Angry Birds activity was inspired by Sean Sweeney, but modified. I had taught students how to graph (by hand) quadratics of the form and . Students also had been exposed to the vertex form of these basic quadratics. But they hadn’t been exposed to quadratics where the coefficient in front of the term wasn’t “nice.” So all I did was give them four geogebra files, and had them play around. By the end of the activity, students recognized how critical the “a” coefficient was to the shape of the parabola, they started conjecturing that if you had the “a” value and the vertex and whether the parabola opens up/down that you could graph any parabola, and one pair of kids were able to convert a crazy angrybirds quadratic (with a really nasty “a”‘ value) to vertex form.
If I’m teaching Algebra II next year, I want to ask if I can get rid of quadratic inequalities or some of the other more technical things we do, and make an entire unit/investigation on using geogebra and algebra and angrybirds to investigate quadratics.
3. My discriminant worksheet is below. It worked okay, but students still didn’t quite understand the difference between and , which was the goal of the sheet. So it needs some refinement.
4. Finally, below are my attempts to get students to better understand quadratic inequalities. I started with a general sheet on “visualizing function inequalities,” and then I made a guided sheet to bring more detail to things. I found out that students didn’t quite understand the meaning of the schematic diagram we drew, nor did they understand why to solve we have to draw a 2D graph. Well, to be more specific, students could do the process but didn’t fully grasp why we graph . I changed up this worksheet this year, but maybe I should go back to last year’s worksheet.
C’est tout. With that, I’m exhausted and going to bed.