**Author** David Graser, Yavapai College, Prescott, AZ (David.Graser@yc.edu)

**Abstract**

This project is a modification of the Arsenic Removal from Drinking Water to allow students to work together in groups.

- Content Area – College Algebra, Finite Math
- Time Frame – 2 to 3 weeks with mini-lectures
- Published – June 22, 2015
- Keywords – system of linear equations, matrices, row echelon form, systems with an infinite number of solutions

**Project Content**

**Project Background** (PDF)

**Scaffolding Resources**

**Technology Assignment: Write Out Equations** (PDF)

This PDF handout lays out a strategy for finding the system of equations for the project.

Once students have written out the system of equations, they will use a shared document in Google Drive to demonstrate their work. Each member of their team should use a different contamination level for Well 3 in completing this assignment as well as the other two technology assignments.

The video below shows how theywill use Google Apps to document and share the equations you come up with.

Since they are using a shared document, all members of their team can see and comment on what they are doing.

Upon completing this assignment, they have a system of equations describing the amounts of water pumped from the wells described in the project letter.

**What is Parts per Million or Parts per Billion?** (PDF)

**Technology Assignment: Row Operations**

In this technology assignment students carry out the row operations on their system of equations.

They carry out the row operations on their system by hand. Once they have found the row operations, they put them into a shared Google Doc. The steps for solving the system of equations are shown in the video below. This video describes a slightly different problem.

Once they have completed this assignment, they should have a solution to the system of equations. It may not be exactly what they were expecting. They will verify that the steps are correct in the next tech assignment.

**Technology Assignment: Row Operations in Google Sheets**

The goal of this assignment is to carry out the row operations for the project in Sheets. Hopefully, this will verify the work they have already done in earlier technology assignments. They take their system of equations and watch the video below to learn how to do row operations in Google Sheets. They use the shared spreadsheet to do this so each of their team members can see what they have done.

The row operations you do in Google Sheets should yield the same matrices as the row operations you did by hand.

They may have some trouble interpreting the final matrix. To help them see how to interpret this matrix, have them take a look at a similar problem in this handout.

**Dependent Systems Handout** (PDF)

**Notes**

- None