# PBL Pathways

##### Content Area

College Algebra, Finite Math

##### Time Frame

2 to 3 weeks with mini-lectures

August 15, 2009
Updated 11//3/10

##### Keywords

System of Linear Equations, matrices, row echelon form, systems with an infinite number of solutions

#### Project Title

Arsenic Removal From Drinking Water

#### Author

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

#### Abstract

My Ford Ranger is no more and my students were getting wise to the Gas Prices Project, so I created a similar project using a bit of knowledge supplied by my hydrologist wife. This uses the same basic idea but incorporates blending of drinking water from several sources to result in a system of equations with many solutions.

#### Project Content

Project Letter - DOC | PDF

Project Background - PDF

#### Scaffolding Resources

Technology Assignment: Substitution DOC | PDF - This assignment introduces students to documenting their work with Mathtype.

Technology Assignment: Gauss-Jordan Method DOC | PDF | VIDEO- The goal of this tech assignment is to help students put a matrix into row echelon form. Once they have done this, they document their work usinfg Mathtype.

Link - What is Parts per Million or Parts per Billion? PDF

Technology Assignment: Row Operations on the Ti-83 DOC | PDF - In this assignment, students create their own system of equations and then use row operations to solve the system. This assignment is almost identical to the one above, but this version includes instructions for carrying out the row operations on a TI graphing calculator and documenting the steps using Mathtype. This document has been updated to show how to use the Equation Editor in Word 2007 or 2010 (as well as Mathtype).

Technology Assignment: Write and Solve a System Using Excel DOC | PDF - This assignment is designed to get students to write down their system of equations for the project so that they can be checked before turning in the final assessment for the project.

Dependent Systems Handout - PDF

Reduced Row Echelon Form on a TI Graphing Calculator PDF - This document takes a student through the steps of putting an augmented matrix into a TI calculator and using the rref command to find the reduced row echelon form for the augmented matrix.

Reduced Row Echelon Form in Excel PDF - This document shows how to do row operations in Excel in order to end up with the reduced row echelon form of an augmented matrix.

#### Notes

You can drop the number of wells down to 2 to make the problem a bit easier or increase the number of wells. Adding costs for pollution removal (and still blend) could make for an interesting linear programming problem.