Teaching the “Why,” not the “Way”

The focus of the Algebra I Module 4 session was on understanding the method of completing the square when solving quadratic equations. Participants started the session by being asked what they would do in the classroom on day one of teaching this topic. As high school teachers, participants realized that they tend to memorize an algorithm instead of experiencing the “why” behind it; the teachers who have taught completing the square tend to stick to the way to do it, not the why.

Participants looked at lesson 11 and saw an excellent progression of quadratic equations that lead to the need of building a square in order to solve the problem. Connections were presented that would allow students to see the geometric meaning behind the process, focusing on what “complete” really means. This process was extended to quadratics where the lead coefficient was not 1. Prior experience with solving equations and properties would allow students to generate equations where a perfect square could be built. This method would avoid fractions, helpful for some of the students in class. Participants used this method to derive the quadratic formula; very cool indeed! Excellent scaffolding was seen throughout the presentation.

The afternoon was devoted to Topic C, which uses technology to demonstrate and apply previous understandings of the transformations of functions. Lesson 18 presents a great opportunity for the discussion of inverse functions and finding the line of reflection.  Everything was pulled together when looking at lessons 23 and 24 with modeling exercises that explored modeling height over time of projectile objects and the early study of business applications.  The end goal of this module is to be able to have students formulate a general process for solving a quadratic within the context of a given problem.

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