This lesson focuses on students making decisions about what tools to apply to solve different problems related to quadratic expressions and equations. It is also intended to build awareness of the form an answer will take in order to help students make sense of the kind of problem they are solving.
At the time of this lesson, students are nearing the end of a unit on quadratics in their Algebra classes. In that unit, they have developed tools for factoring expressions and solving quadratic equations using the zero product property and the Quadratic Formula, often guided by the question, “How can I make a quick sketch of this parabola?” Students have applied their new tools to find the x- and y-intercepts and vertex of parabolas in order to make those sketches. This lesson was intended to give students an opportunity to look at different kinds of problems side by side and determine the tools that would be most useful to solve those problems.
Prior to the lesson, students had demonstrated some uncertainty about which tool to apply to different problems, or in some cases how to identify the kind of answer they were seeking. Student focus had been on correctly applying a tool such as factoring completely or solving using the quadratic formula, rather than on looking at a problem and deciding how to begin. The activities in this lesson were intended to allow students to focus on this kind of decision-making.