Students will launch the inquiry by testing multiple factoring methods on the same quadratic, comparing efficiency with mathematical evidence, and recording an initial claim they will investigate in the next phase.

Students will compare factoring methods on matched quadratic cases, build an evidence log, take and test an early position about efficiency, and draft a short claim that predicts what mathematical evidence could confirm or challenge it.

Students will present and defend their final quadratic factoring arguments to an authentic audience, evaluate competing claims about efficiency with mathematical evidence, and reflect on how their reasoning about factoring methods developed.