Make Math Moments Academy › Forums › Full Workshop Reflections › Module 5: Planning Your Problem Based Lessons › Lesson 56: Proceed or Pivot › Lesson 56: Question › Reply To: Lesson 56: Question

The two lessons I taught back to back were completing the square and the quadratic formula. Students can derive the quadratic formula from completing the square of a quadratic function. I taught completing the square with Algebra tiles and I modeled the function x^2+8x and I walked through this example with the students. Then I had students practice with x^2+4x and asked them to complete the square with it. Students could imitate what I did in class but the understanding of an array would have really helped. I didn’t slow down but went straight to the abstract with the lesson.
The following day I derived the Quadratic Formula using completing the square and the students were stymied. They couldn’t participate in the lesson because they didn’t understand first how to complete the square. Usually, a student completes the square with a numerical problem and I model how to derive the Quadratic Formula algebraically.
Had I pivoted at completing the square by spending more time with the students and connected the Algebra tiles with an array, students would have felt more comfortable with how completing the square derives the Quadratic Formula.