My capstone lessons were centered around solving equations where we mostly focused on radical, rational, and quadratic equations. We learned strategies for solving equations such as rewriting and undoing. For my capstone assessment, I decided to give my students two equations to solve, one radical and one rational. Both questions had students utilizing the skills of rewriting and undoing that we had practiced.
I graded the first question out of 6 points. I gave 1 point for undoing the square root. I gave 1 point for completing the area model for the squared binomial. I also gave 1 point for rewriting the equation into a quadratic equation equal to zero where I gave 1 point if they were able to factor it. I then gave a point if they set the factors equal to zero with the last 1 point being given for solving the equation. An additional point would be given if they found an extraneous solution. For this student, I wrote "Are there any extraneous solutions?", so that he could think about plugging them in since he did the whole problem correctly. I also wrote "How did your get your solutions?" since he didn't set his factors equal to zero. I gave this feedback so that I could extend this students thinking and have them reflect on their work. I gave them this feedback because they had mostly done everything I asked, but there was some attention to detail that was missing. I hope this students reads my feedback and thinks about how he needs to check his solutions when solving and show all his steps so that he doesn't get lost in his work.
On the second question, I gave one point for getting x out of the denominator, 2 points for simplifying, 1 for getting the solution, 1 for checking the solution, and 1 for part b. This student did every thing I asked, so they got full marks. This student's strategy was to cross multiply. For feedback, I am going to ask him, "what's another way to get x out of the denominator other than cross multiplying?". I am also going to ask "can we this cross multiplying strategy with all rational equations?" My goal with this feedback would be to expand the students' thinking and widen their mathematical skillset. I would also want them to think about how the context of the problem allows for certain strategies.