Goals

The goal of this activity is for students to be introduced to the project.

 

Details

Duration: 45 minutes

Assessments: Student writing, Mathematical proof, Group work

Materials: butcher paper to write constraints

 

Description

As this project was part of a larger unit based on linear algebra and matrices, by the time students were ready for this project, students had already been exposed to and understood:
* How to solve a system of equations in 2 and 3 variables using substitution and elimination methods
* How to determine the feasible region for a system of inequalities in 2 and 3 variables
* How a system of equation is translated into a matrix
* Why using matrices can be more efficient than substitution or elimination
* How to add and multiply matrices
* How to find the inverse of a matrix and why that is helpful
* How to input and multiply matrices onto a calculator

To begin the project, students were asked to individually read "San Francisco's Land: Greenbacks or Greenspace?" and highlight the information they thought they would need to solve the problem. In groups, students wrote out what information was given and translated the constraints into equations or inequalities on "Decoding Greenbacks or Greenspace". As a class, we went over the constraints and I made sure that students wrote them in the same order so we could refer back to them later without confusion.

Then I passed out the assignment sheet (see "Greenbacks or Greenspace: Proposal" in Resources) and I clarified questions that students had about the total project. The assignment sheet included a description of each section of the proposal and a calender with due dates and in class work periods. I also made a checklist for students to help them guide themselves in the project.

Decoding Greenbacks or Greenspace?
Questions to help students decode the written problem...
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Greenbacks or Greenspace? Proposal
Description of requirements for proposal...
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Project Rubric
A rubric based on our grading categories...
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San Francisco's Land: Greenbacks or Greenspace?
Description of problem...
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Student Work 1
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Student Work 2
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Student Work 3
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Student Work 4
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Student Work 5
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Student Work 6
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Author Reflections

One of the reasons that students were hooked into the problem was that is was San Francisco based. I suggest using local areas for the story. The next time I do this project, I will probably write a letter from Mayor Newsom (or, even better, get him to write it) asking the students for help in this situation. Many students had trouble determining constraints 7-12, so I talked explicitly about the fact that since this is a real world situation, each of the variables must be greater than 0. This project was really the first large, high stakes project my students had done, so they it was really helpful to break it into separate parts to make it more managable.