The focus today is for students to learn a method to solve these problems that is different from their preferred method. I tell students this goal from the beginning of the day. Then, I ask them to use the warm-up time to try to figure out a different method.
In my classrooms, it always seems to work out that different students prefer different methods. I am always surprised how uniform the distribution of strategy preference is, although I do believe that slightly more students prefer the method of finding a linear relationship between two factors and then writing the quadratic function as the product of these factors.
I tell them that I am happy to explain any of the methods to small groups of students, but I also create a list of student experts for each method on the board. I add to this throughout the class period. I tell students that I want them to understand all of the methods, but that they only need to master two of them today.
Once students have figured some things out on the warm-up, I ask them to work on the same assessment they started yesterday, but to solve the same problems using a different method:
One interesting confusion that arises for many students during this lesson is the difference between solving a problem using two different methods and writing two difference equivalent functions to fit a situation. At first, I was confused by this, then I realized that they were used to writing equivalent expressions to fit a set of data. This means that many students solved the problem one way and then algebraically manipulated the equation into a different form. Once I figured this out, I asked students to find a whole different method. Some students complained about this requirement, but it was worth the time and effort.