Students manipulate progressively more flexible parabolas whilst a ‘special number’ is displayed on the screen. The problem for students to solve is ‘what is so special about this number’. Students continually review their conjectures as the parabola becomes more and more flexible.
Understand the role of the discriminant using technology and algebraically. (ACMMM010)
Vertex, Turning Point, Discriminant, Conjecture
About the Lesson
Students use an investigative problem solving approach to determine the role of the discriminant for quadratic functions. The discriminant is displayed on the screen and constantly updates as students translate and dilate the parabola. The investigation is scaffolded by initially limiting manipulations of the parabola to transformations where the coefficient of x-square is positive one. In the next stage this is changed to negative one then finally, it becomes a variable so students can dilate and transform the parabola. Students are required to constantly refine their conjecture(s) with regards to the function of the ‘special number’. The final question is an extension opportunity for students to use algebra to move their conjecture to a theorem.