Solving Systems of Equations

Introduction

Chief Financial Officers (CFO) are responsible for every aspect of the financial decision making of a corporation. Even if they do not directly make a decision, they are responsible for the actions of those responsible for the company's money. 

The time has come to invest in cell phones for the company. To this point, each sales representative has just been reimbursed for his monthly cell phone bill. This is becoming very expensive. The CFO feels that getting a plan through the company will be more cost effective. 

Here is what you will need to consider before you get started:

  1. There are 20 field agents that will be receiving a phone from the company.
  2. The average monthly usage is 2.5 gigs of data per month.
  3. The highest monthly use ever reported by an agent was 4 gigs of data.
  4. Agents will need to be able to have access to email and the internet while out in the field on their mobile devices.
  5. Agents will also need a hands free device to use the phone while driving.
  6. All agents work in major cities as well as rural areas throughout Tennessee.

 

Task

The CFO, your teacher, has brought in his most trusted field agent, you, in from the field to investigate possible options. Your task is to investigate what wireless carrier would be the best fit for the company. You will be asked to investigate different wireless providers. You will analyze the packages that each carriers have for businesses. You will check on data packages, access charges per line, call features, etc. You will then complete a rate comparison chart to help you in your decision

Finally, you will submit a report to the CFO with your findings.

Process

Step 1: Investigate

You will investigate business pricing and possible discounts for business pricing at the following wireless carriers:

Step 2: Rate Comparison

Fill out the rate comparison worksheet to help you find the company's best deal.

Step 3: Report

Write a report to the CFO that will document your findings. Since he likes options, you are to report on the two best deals that you find. Tell him the circumstances in which the first company is better. Then discuss the reasons when the second is better. You will also want to discuss when they are equally good options.

Make sure to include the graphs from your two picks of cell phone companies. Graph these on the same graph to make a system of equations. Make sure you explain what the graphs mean and what it means if the graphs cross, do not cross, or make the same line.

Finally, you will tell him your opinion on the cell phone company that will be best. Remember, the cheapest price is not always the best deal. He wants the best deal for the company.

You will type your report and put it in a binder with a cover page. Also, you are to include printed price comparisons for each company as well as coverage maps for Tennessee. If possible, go to these stores or the websites and download any brochures they have.

Now, you have worked for your company long enough to know that the CFO does not like mistakes. Make sure that you have at least two of your fellow field agents review your report. Have them fill out the Field Agent Double Check form. You will turn this in with your report to the CFO because you want him to know that you have made every effort to make this report error free.

Evaluation

Your project will be graded using the following rubric:

CATEGORY 4 3 2 1
Mathematical Concepts Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). Explanation shows some understanding of the mathematical concepts needed to solve the problem(s). Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.
Mathematical Errors 90-100% of the steps and solutions have no mathematical errors. Almost all (85-89%) of the steps and solutions have no mathematical errors. Most (75-84%) of the steps and solutions have no mathematical errors. More than 75% of the steps and solutions have mathematical errors.
Explanation Explanation is detailed and clear. Explanation is clear. Explanation is a little difficult to understand, but includes critical components. Explanation is difficult to understand and is missing several components OR was not included.
Checking The work has been checked by two classmates and all appropriate corrections made. The work has been checked by one classmate and all appropriate corrections made. Work has been checked by one classmate but some corrections were not made. Work was not checked by classmate OR no corrections were made based on feedback.
Neatness and Organization The work is presented in a neat, clear, organized fashion that is easy to read. The work is presented in a neat and organized fashion that is usually easy to read. The work is presented in an organized fashion but may be hard to read at times. The work appears sloppy and unorganized. It is hard to know what information goes together.
Diagrams and Sketches Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s). Diagrams and/or sketches are clear and easy to understand. Diagrams and/or sketches are somewhat difficult to understand. Diagrams and/or sketches are difficult to understand or are not used.
Completion All problems are completed. All but one of the problems are completed. All but two of the problems are completed. Several of the problems are not completed.

Conclusion

This webquest is a very real scenario that you may face in the "real world." By knowing how math works and how it applies to your daily life, you will be able to have an advantage over co-workers. You're paid for two things in this world, who you know and what you know. Unless your dad or uncle is the big boss at a big corporation, you fall in to the latter of those two options. In this lesson, we used our skills to graph linear equations and to solve a linear system.

Now, as the final task on this project, summarize your thoughts on the project. It is to be typed and turned in two days after the project is due. It is to be no longer than one page. Answer these questions:

  • Did you enjoy this webquest? Why or why not?
  • What was the most difficult part?
  • Was the information easy to find?
  • Approximately how much time did you spend on the webquest.

 

Teacher Page

Purpose:

The purpose of this webquest is to allow students to use systems of linear equations to solve a real world problem. It is also to show that the student has an understanding of the concept of systems by having to explain what the graph means.

Rationale:

It is important for students to realize that the problems they are working on and learning have significance for them after this class. They will need to retain the information, not only for future math classes, but for later life skills.

Learner Discription:

This webquest is designed for Algebra I, Algebra II, or Geometry students. Algebra I students can use is after studying systems of linear equations. Geometry and Algebra II students can use it prior to a section that requires knowledge of systems. The project can be adapted for each grade level (i.e. Algebra II could collect information from 3 companies and solve that system)

Prerequisites:

The learner should:

  • Have basic computer skills
  • Be able to navigate the internet
  • Have a basic understanding of graphing linear equations
  • Have a basic understanding of graphing systems of linear equations
  • Be able to write a paper using a word processing program

Instructional Objectives:

The purpose of this webquest is to show students the real world applications of graphing linear equations and graphing linear systems.

Standards Addressed:

State Performance Indicator

  • SPI 3102.3.8       Determine the equation of a line and/or graph a linear equation.
  • SPI 3102.3.9       Solve systems of linear equation/inequalities in two variables.

Course Level Expectations

  • CLE 3102.1.1     Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
  • CLE 3102.1.2     Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.
  • CLE 3102.1.4     Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.
  • CLE 3102.1.6     Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
  • CLE 3102.1.7     Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.

Subject Matter Description:

  • Introduction: This is a basic overview of our webquest
  • Task: This is the task that you are responsible for completing
  • Process: The process is the basic steps that you will do to complete the task
  • Evaluation: The evaluation explains how you will be graded
  • Conclusion: Discussion and additional information

Assessment:

The webquest will be graded according to the rubric listed above