More Multiple Methods to Solve Problems involving Quadratic Functions

Objective

SWBAT use more than one method to solve problems involving quadratic functions.

Big Idea

Now that students have solved different problems using a preferred method, they can apply their understanding to try and learn from different solution methods.

Warm-Up

30 minutes

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.

Teaching and Learning A Second Method

30 minutes

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.