Goals

The goal of this activity is for students to draft the second part of their proposal: the Investigation.

 

Details

Duration: 120+ minutes

Assessments: Student writing, Mathematical proof, Group work

Materials: graphing calculators

 

Description

The purpose of this section was for the students to show all of their work they did to solve the problem in addition to making it accessible to the general public by explaining some basics about matrices.

The Investigation section should include the following:
* a detailed explanation of the basics of matrices and how they can help solve the problem
* detailed explanations about why combinations of constraints are examined or ignored
* all matrices used with labels for rows and columns
* a detailed description of what the inverse is and how it helps you solve a matrix equation
* a detailed explanation of matrix multiplication used to solve a matrix equation
* solutions to all matrices and evaluations of those solutions
* costs for each possible solution

This is a very involved activity--I allowed two 90-minute class periods for this activity, in addition to assigning homework between them. The first class period students spent their time explaning the basics of matrices, eliminating combinations of constraints. I coached them through setting up the first matrix equation and they were assigned to do the rest for homework. The second class period was spent solving the matrix equations and clarifying explanations.

Author Reflections

During this activity, I found a few times that I needed to clarify for the entire class certain misconceptions/confusions about matrices. This part was the meat of the math portion, so I wanted them to make sure they touched on all the important parts of matrices. This was the point where a lot of kids struggled because they haven't had a lot of practice explaining math. I did some explicit modeling around that and had students who clearly understood share their explanations.