Quadratic Functions: Toothpicks and Transformations

In this math lesson, learners explore transformations and quadratic functions through toothpick patterns. Learners examine the mathematical pattern that emerges as they build a geometric design with toothpicks. The pattern is quadratic, and the learners determine the mathematical model in several different forms. Learners investigate the recursive nature of the relationship. An explicit model for the relation is developed, and a third model is developed by examining the scatterplot and determining the equation from the transformations. Finally, the group uses graphing calculators to develop another model and to verify that all of the models--factored form, vertex form, and general form--are equivalent.