6.+Performance+Task+and+Rubric

= **Performance Task** =



The Quadratic Equation Solver

Your group will be developing a quadratic equation solver. There will be four students in each group. Since we learned four ways to solve quadratic equations, (factoring, the square root property, completing the square, and the quadratic formula) each group will develop algorithms or sets of rules to solve a quadratic equation by each of the four methods. The rules should also include how to determine which method should be used to solve each quadratic equation. Use the methods you learned throughout the lessons to help come up with an algorithm. The groups will come up with a sales pitch to sell their quadratic equation solver to a retail store. The sales pitch will include why their solver is the best and most efficient; it will also show and tell how it works.
 * GOAL **

__The Group__ – The entire group will develop the first part of the solver together. The first part will determine which method is best to use to solve a particular quadratic equation. This can be a list of qualifying questions or flow chart that will lead to one method. For example, “Is this quadratic equation factorable? If yes, move on to the factoring section.” The more specific the algorithm is the better. __The Group Members__ – Each group member will be given a particular method (factoring, the square root property, completing the square, or the quadratic formula) that they need to develop an algorithm for. This can be structured the same way as the first part of the algorithm, or in another way that the group member sees fit. __The Group__ – The group will come together again in the end to go over what each member has done individually. Then everyone will work together to come up with a sales pitch to try to sell their quadratic equation solver to a retail store. The sales pitch should include why their solver is the best and most efficient. It should also include an overview of how the solver works and why they chose to set it up the way they did. Demonstrate how the solver works by solving four quadratic equations, one by each method, using the algorithms you developed. This will prove that your solver works. Also, what will your quadratic equation solver look like? A calculator? A computer? Throughout your group and individual work, I will be meeting with all of you to check on your progress and see what you are coming up with.
 * ROLE **

The intended audience is a retail store manager. You are trying to sell your product to the store so be sure to use professional language and provide a quality product that you are proud of. Try to persuade the manager that your product is best and tell them why it is the best. The manager will be more likely to choose your product if he or she has a full understanding of how it works and why it is the best. You can choose what kind of store you want to try to sell your product to. Be sure to explain why you chose that store and why your solver will sell there. You will develop and sell a quadratic equation solver. There are no quadratic equation solvers on the market and you and your group members are going to develop an efficient solver. The solver will help algebra students just like you with their homework and test problems. The set of rules you develop as part of your quadratic equation solver will serve as a guide to solving quadratic equations. You are going to sell this solver to a retail store. In order to do this, you will have to tell the manager of the store why your solver is the best and most efficient and why it is necessary to sell it in the store. Everyone in the group will conduct research on solving quadratic equations to gain more understanding of the methods you will be using. This can be done online using the provided list of mathematics websites. You may also use any notes or handouts that we had in class. The research you do will help you make algorithms for solving quadratic equations. Pay attention to the way the steps are explained as a quadratic equation is solved. You will need to make copies of any research you use while making the quadratic equation solver. Websites: [|http://www.purplemath.com] [|http://www.mathsisfun.com] [] Pennsylvania Standards: 2.8.8.B - Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships. 2.8.8.C - Create and interpret expressions, equations or inequalities that model problem situations. 2.8.8.E - Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. 2.8.8.G - Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules. 2.8.8.J - Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship. __Explain__ – Students will explain throughout the performance task for example, when they are developing algorithms to solve quadratic equations by four different methods. They will also be explaining how their solver works and why it is the best and most efficient. __Interpret__ – The students will interpret the algorithms they developed for the retail store manager who may or may not know about solving quadratic equations. The group will have to know their product inside and out and how it works in order to sell it to a retail store. __Apply__ – The students will have to use what they know about solving quadratic equations and apply the information to develop a set of rules to explain their steps. They will be using their knowledge and applying it to a different representation of the information. __Have Perspective__ – The group members will each develop an individual algorithm to solve a quadratic using one of the methods. Therefore, the other members will have to be critical of each other’s work. The group members will have to make sure that each algorithm is correct. They will also have to make sure that the algorithms are the most efficient. All of the algorithms will have to fit together and work with the first part of the solver that the group developed together. __Empathize__ – The group members will have to listen to each other’s ideas and determine which is best. They will have to see the good and bad in each idea. One person may find a particular method the best, but others in the group may not be in agreement. __Have Self-Knowledge__ – If a group member is explaining their algorithm, and another group member does not understand, the non-understanding group member will determine what they do not understand so it can be clarified. There will be a constant question and answer between group members so an appropriate solver can be created.
 * AUDIENCE **
 * SITUATION **
 * RESEARCH **
 * If you find another website you would like to use, check with me for approval.
 * PRODUCT **
 * 1) A group algorithm for choosing which method is best for solving a quadratic equation.
 * 2) Individual algorithms for solving a quadratic using a particular method.
 * 3) A list of works sited that you used when doing research.
 * 4) A group sales pitch with a description of how the quadratic equation solver works, why it is the best and most efficient, why the manager of the retail store should choose your solver.
 * These four things should be turned in as one complete product at the end of the assignment. Throughout the assignment, individual parts will be evaluated, but one final product will be turned in at the end.
 * STANDARDS AND CRITERIA **
 * SIX FACETS OF UNDERSTANDING **

**Rubric**



 * =Quadratic Equation Solver Rubric= ||  ||
 * || **4** || **3** || **2** || **1** || **Points Earned** ||
 * **Group Algorithm Creativity** || Completely creative and well thought out. Students have worked together to develop an algorithm that is set up in a interesting way. It is not simply a list of steps to get to the solution. || Mostly creative and well thought out || Somewhat creative and well thought out || Not creative nor well thought out ||  ||
 * **Group Algorithm Accuracy** || Completely accurate and free of errors. Students have worked together to create an algorithm that is bug free and chooses the best method. || Mostly accurate with few errors || Somewhat accurate with some errors || Not accurate with many errors ||  ||
 * **Individual Algorithm Creativity** || Completely creative and well thought out. The student created an algorithm that fits in with the groups algorithm. The algorithm is not just a list of steps; it is set up in an interesting way. || Mostly creative and well thought out || Somewhat creative and well thought out || Not creative nor well thought out ||  ||
 * **Individual Algorithm Accuracy** || Completely accurate and free of errors. The student created an algorithm that is free of errors and obtains the correct solution. || Mostly accurate with few errors || Somewhat accurate with some errors || Not accurate with many errors ||  ||
 * **Group Sales Pitch** || Completely creative and convincing. The sales pitch tells how the solver works, explains why the group chose a particular retail store to sell it to, and why their solver is the best. || Mostly creative and convincing || Somewhat creative and convincing || Not creative nor convincing ||  ||
 * **Research** || All information used and referenced was provided. All of the research was cited and relevant to the assignment. || Most information used and referenced was provided || Some information used and referenced was provided || None of the information used and referenced was provided ||  ||
 * **Group Contribution** || Contributed equally and benefited the group as a whole. This will be determined by the conferences I have with the group members individually and as a whole. || Contributed somewhat equally and mostly benefited the group || Did not contribute equally and sometimes benefited the group || Did not contribute or benefit the group ||  ||
 * **Comments:** ||
 * **Total:** ||  ||