Systems of Equations

Introduction

Teacher: Mr. Anthony Spina 

Title: Solving Systems of Equations

Grade Level: High School

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.  

Task

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

You will use the provided resources to become experts in the different methods of solving systems of equations. These methods will include solving by graphing, elimination, and substitution. Pay close attention to each of these methods to decide which one you like best. You will practice the examples that are demonstrated and apply them to your presentation.  

After you have thoroughly learned the different methods of solving systems of equations, you will apply the methods in the context of a word problem. You will choose two different part time jobs and research the hourly salary rate for each job.  Your goal is to make $400 as quickly as possible so that you can purchase $400 ear buds.  Since you are a student, you can only work a total of 25 hours per week. Each job will only allow you to work a maximum of 15 hours per week.  Your task is to figure out working more hours in which job will get you your ear buds the fastest.  

After you have reached a conclusion based on your word problem, you will create a presentation on the methods and the solution you arrived at to present to the class.

Make sure you understand what you are learning and ask questions if you have any. Work independently or with your peers during p during every process of this assignment. You will be graded based on the rubric in the evaluation section of this site.

 

Day 1

 

Use these links to learn about solving systems of equations. Each method has a very specific process. Make sure you know what each process entails and copy down an example of each in the information organizer attached at the bottom of the page. Do not move on to the next website and method unless you have completed and understand what you have read.

 

Information Organizer

Download this form. This is what you will use to document what you learn and the examples that you see from each website. You may work on the form online, or you may print it out and work on it by hand. It is up to you.

 

Reminder of Solving Equations

This is the first website you should look at to remind yourself how we solved equations for a variable. When we are solving systems of equations, we are doing the same things as we have done before except this time we are given two separate equations with two unknowns.

 

Solving Systems of Equations by Graphing

This should be the next website you visit. Given two equations with two unknowns you graph the equations on the Cartesian coordinate system. The solution will be where the two graphs cross. Watch the videos and the examples to learn the process.

 

Solving Systems of Equations by Substitution

This will be the third website in the WebQuest. Given two equations with two unknowns you will solve one equation for one of the variables. You will substitute the value of that variable in for the same variable in the other equation to solve for the other variable. Watch the videos and examples to learn the process.

 

Solving Systems of Equations by Elimination

This will be the last website that you will visit. Given two equations with two unknowns you will eliminate one variable. This is done by multiplying one of the equations by a value that when added to the other equation will eliminate one of the variables and solve for the other. Watch the videos and the examples to learn the process.

 

Before you leave, review your informational organizer and examples with Mr. Spina. This will ensure that you know how to complete problems with each method correctly and can apply it to your word problems. If you leave without discussing it with him, you will not be permitted to move on to Day 2.

 

Day 2

 

You will begin working on your assigned word problem.  You will solve your word problem detailing how many hours you would have to work at each job to meet the necessary constraints for salary and hours. Ask a peer to look at your work and then have your worked checked by Mr. Spina. 

 

Word Problems

Download this document. You have your jobs picked out and you can input their hourly wages into your word problem.  Your goal is to discover which part time job will make you more money in a shorter amount of time.  You may use any method that you learned during this WebQuest. 

 

Check your work and answers with Mr. Spina before you begin the next portion of this assignment.

 

Once your work has been checked, create a presentation on your word problem and the methods that you used to arrive at your solution. Be very detailed in your presentation so as to make sure that a person who has never solved a system of equations would be able to repeat your process. Your presentation should include:

  1. Your initial word problem
  2. The equations that you created to represent the word problem
  3. The method you chose to use
  4. Your steps to arrive at your solution with a detailed explanation of each part
  5. Opportunities for students to ask questions

You may use any presentation software that you would like as long as it adds value and is not distracting during your presentation. I have included tutorials below for PowerPoint, Movie Maker, and Prezi.

 

PowerPoint Tutorial

Movie Maker Tutorial

Prezi Tutorial

 

Day 3

 

For the last day of this assignment, you will present your solution and the detailed methods that you used. Speak loudly and clearly, do not be nervous, and show the class what you learned during this assignment.

 

 

 

Information Organizer.pdf 

Word Problems for Web Quest.pdf 

 

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

Task