# Systems of Equations

Introduction

Teacher: Mr. Anthony Spina

Title: Solving Systems of Equations

Subject: Algebra 1

NJSLS.MATH.CONTENT.HSA.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

NJSLS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Objective: Using this webquest activity, students will be able to solve systems of equations and apply these equations to real world experiences by the completion and presentation of word problems.

You just seen and heard how great the newest earbuds sound and you want to buy a pair.  They cost \$400.  You want them badly, so you are working 2 part time jobs that offer different salaries. For each pay week, you are only allowed to work for a total of 25 hours per week. You are only allowed to work at each job for a maximum 15 hours a week.

How will you determine how many weeks you will need to work to buy your ear buds?  Which job would it make more sense to work more hours at and why?

Using this webquest, you will learn and explore the different methods of solving word problems.  You will also develop and solve your own real world equation, which will help you work smarter to obtain your life goals. You will then present your method used to solve your system of equations and discuss your rationale for working hours and job preference.

For this Web Quest, you will be working independently to complete this assignment and its accompanying project. You will be working on this for a total of 3 class periods.

For the first class period, you will be required to follow the provided links to learn about the different methods of how to solve systems of equations.  Your task for this class period is to write down the different examples of how to solve systems of equations with the provided links.

For the second class period,  you will choose two jobs that you may be good at or that you like to do.  You will research these jobs to find the hours pay rate.  Once the hourly pay rates are discovered, you will work to solve how many hours you will have to work at each job in order to make \$400 to pay for your new ear buds.  You will then work on graphing and displaying your data so that you can present it to your peers.

For the third class period, you will present your solution and the methods used to get there. You will be evaluated according to the rubric located in the evaluation tab of this website.

By the end of this Web Quest, you will be able to solve systems of linear equations and apply it to the context of different word problems.

Process

Conclusion

I decided to do this webquest to help model for my students how we use algebra in the real world.  The most difficult part of equations and problem solving is translating the problem into mathematical language.  This lesson builds upon my student’s prior knowledge of solving equations for one variable to solving two or more equations for more than one variable. With solving systems of equations, students needed to learn the four different ways that they can be solved, which are  graphing, elimination, and substitution.

Since this webquest was an actual real world scenario in which the students had control (they got to pick their jobs) and they were able to come to the realization as to which job would be more beneficial to them if they needed to make the most money in a small amount of time.  Students not only had to solve the systems of equations, but they also had to set up their systems of equations. Students were challenged in this assignment to take their learning into the own hands to fully understand the concepts. They were given information that would help them, but it was up to them to ultimately solve their problems. The students also had to critically think on their own, develop a problem and calculate the solution.

For a future webquest on systems of equations, I would like to have the students investigate which cell phone plans are the most beneficial for both themselves and a family member.  By providing instances in which students can use math in everyday life situations, I believe I am help students want to do better and learn more in math class.

Teacher Page

Mr. Spina's  Webquest Sitemap

Conclusion

Evaluation

Introduction

Process