Assessments

Performance Assessment ** Performance Tasks: **

The standings for the local softball teams are posted in the dugouts every week. This week’s standings showed that “Team Red” is in first place.  · The points columns is a method to determine team standings. Each win is assigned x points, each loss is assigned y points, and each tie is assigned z points. The points listed in the table above are the sum of these three products. Unfortunately, whoever put the division standings together must have forgotten to include the total points for “Team Yellow”. How many points does “Team Yellow” have? Use algebra to support your answer. Be sure to show all of your work.
 * Part A:**
 *  ** Team ** ||  ** Wins **  ||  ** Losses **  ||  ** Ties **  ||  ** Points **  ||
 *  Team R Red ||  10  ||  4  ||  10  ||  82  ||
 *  Team B Blue || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 12  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 8  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 4  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 68  ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Team Y Yellow || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 6  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 8  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 10  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Team G Green || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 8  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 12  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 4  || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 36  ||

Do you think this division is the only division in the softball league? Why or why not? Use the standings in part A to support your decision. Be sure to show all of your work. I guess you're asking about the possible combinations of teams playing each other....like is it possible to have 10 ties (that's quite a bit) with just these 4 teams.
 * Part B: **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">The questions in parts A and B involve a real world situation that can be modeled using linear equations with three unknowns. Now, it's your turn. Identify a real world situation and then develop the system of equations which describes the situation. Then proceed as in part A and solve the system of equations. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Be sure to show all of your work. will the students have had enough time prior to this performance task to think through creating systems of equations? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">
 * Part C: **

** Part D: ** For parts A, B, and C, check your solution by answering the question “Does my answer make sense?” Explain your answer to the question.

Present an oral report of your solution to either parts A and B or part C. Submit a written report fully documenting your work for parts A, B, C, and D.
 * Part E: **

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif;"> <span style="color: #0000ff; font-family: Arial,Helvetica,sans-serif;"> The performance task was selected as an overall assessment of solving systems of linear equations in multiple unknowns. The problem represents a real world situation that most students can relate to and provides a clear example of how algebra can be used to solve every day problems. The overall task would be categorized as a summative assessment.
 * Comments**

Part A of the performance task is a simply a matter of solving a system of linear equations. However, the challenge is to identify the equations to be solved, and then to use an appropriate technique to do so.

Part B really calls for thinking outside of “the mathematics box”. Students are required to think about the information provided. They are required to use prior knowledge and logic to answer these questions that may not typically be discussed in a math class.

Part C is an extension of part A. A real world problem was presented in part A and the students were required to solve problems associated with the situation. In this part, students must move two steps backward. They must first identify a real world situation that can be modeled using systems of linear equations. They then must create the model. Having the model, they select a solution methodology and determine the solutions to their problem. This activity permits students to participate in the entire cycle of defining a problem to solving that problem. Part D addresses a concept that may not be covered in many math classes. Specifically, once a solution has been determined, we should evaluate whether or not the solution makes sense. For example, if a student solves the equation x+2=10, and determines that x=25, they should realize that the answer is in error, since adding 2 to 25 would result in a number larger than 25, and 10 is not larger than 25.

Part E summarizes all of the work for this project, and allows students to use verbal and written skills obtained in other classes to document their efforts.

All of the assessments other than part E would be formative in nature. The first four items would be assessed by reviewing homework and class work. These informal assessments done in a non-threatening informal environment, would provide the teacher with information about how each student is progressing and should help to identify students who may require additional help. The last three items would probably be categorized as participation behaviors. While I do believe that participation needs to account for a portion of a student’s grade, it is important to remember that some students will remain silent, either because they are shy or because they are afraid to make a mistake in public, not because they do not understand the material**.** <span style="color: #0000ff; font-family: Arial,Helvetica,sans-serif;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">**GRASPS** Analysis


 * G**oal states the purpose of the task -- The goal of this performance task is for the students to be able to model real world situations with systems of linear equations, and then solve those systems. Part A concentrates on solving the system, while part C concentrates on developing a model which then needs to be solved.


 * R**ole explains student involvement in the scenario --- Students are involved in all aspects of this performance task. They should be able to solve the original system of equations with minimal assistance. However, they may require help in modeling a real world situation. In this case, they would be responsible for identifying a source of assistance, and then working with that source on modeling a situation interest.


 * A**udience identifies the people the students address --- The audience for this performance task is classmates, teachers, and possibly the source of assistance detailed in the "role" description above.


 * S**ituation explains the scenario --- The scenario of this performance tasks is detailed in the problem description above.


 * P**roduct is the tangible evidence of student understanding --- The product is the solution and solution methodology for part A, as well as the model, solution, and solution methodology for part C.


 * S**tandards/criteria describes how students can complete the task successfully --- A rubric is presented on the "Rubric" page of this wiki.

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**SIX FACETS OF UNDERSTANDING** The six facets of understanding include explain, interpret, apply, have perspective, empathize, and have self knowledge. I believe that each of these items is addressed in this performance task, particularly in part C, where the students are required to bring the real world into the math classroom. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif;">