Chapter+7,+Special+Cases

Rachael's philosophy of special cases (it is okay to disagree, our texts do!)

Regular Algebra students would be best served introducing special cases in whole class settings and leaving it at that. This idea is easy to understand visually, and could be introduced along with graphing in the very first introduction of systems. However, for students who may be weak with manipulating variables, arriving at these solutions through substitution and elimination may be on their edge of understanding. Certainly, push student thinking, but in an environment where you are asking the right questions, and students have enough opportunity to understand their computations and what they mean. In this matter, I prefer the way McDougal handles special cases of systems of equations. However, I would not assign this topic as HW unless it was very guided (a matching situation,etc.) Remember, students are supposed to be able to complete their HW with 80% mastery!

The common core says.. A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.