SUBDOMAIN 212.1 – NUMERACY, ALGEBRA, & GEOMETRYSUBDOMAIN 212.2 – PROBABILITY, STATISTICS, & QUANTITATIVE PROBLEMSOLVINGCompetency 212.1.2: Solving Algebraic Equations – The graduate solves algebraicequations and constructs equations to solve real-world problems.Competency 212.2.1: Applying Probability and Statistics – The graduate understandsand applies elementary probability and statistics concepts and knows the relationshipbetween them and sampling and inference.Competency 212.2.3: Interpreting and Communicating Quantitative Information -The graduate interprets documents and materials containing quantitative information andeffectively communicates mathematical arguments and quantitative results.Competency 212.2.4: Applying Technology to Quantitative Problems – The graduateuses appropriate technological tools, including regular and graphing calculators, databases,and/or statistical analysis programs, to solve problems involving computation, graphicalinformation, and informational technology in a wide range of areas.Introduction:“Mathematical literacy is an individual’s capacity to identify and understand the role thatmathematics plays in the world, to make well-founded judgments, and to use and engagewith mathematics in ways that meet the needs of that individual’s life as a constructive,concerned, and reflective citizen” (2003).Individuals encounter countless situations in day-to-day life that require a strongmathematical foundation in order to make informed decisions.Shown below are four real-world scenarios that one might encounter in day-to-day life. Forthis task you will choose one of the scenarios below. Each situation requires a mathematicalcomparison of cost options in order to determine which is best for a consumer (e.g.,customer or person).Scenario 1:A parent is looking for the best option for daycare for a child. A home-based option chargesa flat rate per hour. A center-based option charges a fixed fee per week for a certainnumber of hours and then a fixed rate per hour for any hour provided over the set amount.Determine which option is most advantageous for the parent based upon the parents’needs.Scenario 2:A downtown employee is looking for the best option for parking a car during a 5 day workweek. One parking garage offers unlimited parking at a flat rate per month. Another garageoffers an hourly rate for parking. Which option is best for the employee on a monthly basis?Scenario 3:A family is looking for the best option for moving the family’s belongings into a new home.Moving company A charges its customers a flat rate per mile. Moving company B charges itscustomers a fixed amount for a certain number of miles and then a fixed rate per mile forany miles over the set amount. Determine which company would best serve the needs ofthe family.Scenario 4:A student is looking to secure a hardcopy textbook for an upcoming course. Compare aweekly textbook rental option with a purchase option to determine which option is mostadvantageous for the student based upon the student’s needs.Task:Note: Part A, B, and D of this task should be completed in a word-processing program;hand-written artifacts are not acceptable for this task. Part C should be completed inapproved graphing software; hand-drawn graphs and graphs crafted as art within acomputer program are not acceptable for this taskA. Develop a story problem using the real-world scenario you have selected from the fourprovided above by doing the following:1. Develop a cost comparison problem that can be solved according to the taskinstructions that follow by supplementing your chosen scenario with additionalinformation.2. Explain all needs (e.g., financial, non-financial, situational) of the hypotheticalconsumer.3. Discuss two cost options that are being considered.B. Analyze the cost of each option algebraically by doing the following:1. Develop an algebraic equation(s) with clearly defined variables to represent the costof each option.Note: In some circumstances, a single cost option may require two equations2. Explain the reasoning process used to translate the written description of each costoption into algebraic equations.3. Solve the system of equations algebraically to determine where the two cost options areequivalent, showing all work.a. Explain each step used to solve the system of equations. Include the following inyour explanation:• All mathematical operations used to solve the system of equations• The solution(s) of the system of equations in ordered-pair notationC. Depict the real-world problem on a single graph, within a spreadsheet application usingintegrated graphing tools (e.g., Microsoft Excel, OpenOffice Calc, LibreOffice Calc).Include the following details in your graphical representation of the real-world problem:• Label each axis of the coordinate plane with descriptive labels.• Label all graphical solution(s) of the system of equations as “solution” and includethe ordered pair.• In a legend, indicate which cost option corresponds with each line.• Save and submit your spreadsheet as an *.xls, *.xlsx, or *.ods file.D. Discuss a decision-making process that is based on both mathematical reasoning andnon-financial, or situational, considerations. Your discussion should include thefollowing:• How financial information gleaned from your algebraic and graphical analyses canbe used to determine the conditions for choosing cost option A over cost option Band vice versa• How non-financial, or situational, considerations can impact the decision-makingprocess1. Discuss a final recommendation that states the option that most closely meets theconsumer’s financial needs and non-financial considerations.E. When you use sources, include all in-text citations and references in APA format.Note: When bulleted points are present in the task prompt, the level of detail or supportcalled for in the rubric refers to those bulleted points.Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web linkincluded in the Evaluation Procedures section.Note: When using sources to support ideas and elements in a paper or project, thesubmission MUST include APA formatted in-text citations with a corresponding reference listfor any direct quotes or paraphrasing. It is not necessary to list sources that were consultedif they have not been quoted or paraphrased in the text of the paper or project.Note: No more than a combined total of 30% of a submission can be directly quoted orclosely paraphrased from sources, even if cited correctly. For tips on using APA style, pleaserefer to the APA Handout web link included in the General Instructions section.Reference List:Note: This reference list refers only to direct citations in the task above and may bedifferent from those you need to complete the task. Consult your course of study for a list ofsuggested learning resources.(2003). Mathematical Literacy. Retrieved March 19, 2009, from OECD Programme forInternational Student Assessment (PISA) website:http://www.oecd.org/pages/0,3417,en_32252351_32235968_1_1_1_1_1,00.htMLqlt1_task_5.docxEvaluation Report.docxRubric.doc
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