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Instructional Task Implementation GuideSeason PassTransitional Math Course: Quantitative LiteracyTransitional Math Unit: Math in Decision-MakingUnit Learning Segment: U4A3 What is the best deal? How can I maximize my profit/income?Recommended Length of Task: 2 days/90 minutesTask ObjectivesTask TitleSeason PassTask SummaryYour school is trying to increase interest in its athletic program. It has decided to sell a season pass that will allow the holder to attend all athletic events at the school. The school surveyed families in the community and asked, “What is the most you would pay for an all-sports season pass?” The survey results are shown in the table below.This task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue. Students may use various methods to determine a quadratic function that fits the mathematical model and helps answer the questions.Materials NeededGraphing calculator or DesmosKey Performance IndicatorsQL-A1.A. Use variables to accurately represent quantities or attributes in a variety of authentic tasks.QL-A1.B. Predict and then confirm the effect that changes in variable values have in an algebraic relationship.QL-A1.C. Interpret parts of expressions such as terms, factors, and coefficients.QL-A3.A. Create equations and inequalities that describe numbers or relationships.QL-FM1.B. Predict and then confirm the effect that changes in variable values have in an algebraic relationship.QL-FM2.D. Construct and compare models such as linear and nonlinear models and use them to solve problems.QL-FM2.E. Interpret expressions for functions in terms of the situation they model.Standards of Mathematical PracticeMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoningChecking for UnderstandingDescription of ProductIn doing this task, students analyze data sets, create scatter plots, determine the most appropriate mathematical model, and justify their model selection.Formative Check Points Have small groups share out their work with the class at specified points and ask clarifying questions to expose students to varying methods of analyzation and check for understanding.At the end of day 1 check with each group to make sure they are progressing through multiple methods of analyzing the data and understand what is being asked of them.Task RubricCompetency and IndicatorsLevel 1 – No EvidenceLevel 2 – Partially MeetsLevel 3 - ApproachesLevel 4 - MeetsLevel 5 - ExceedsQL-A1. Students can demonstrate understanding of the characteristics of variables and expressions and apply this knowledge in authentic modeling and problem solving situations. Student does not meet prerequisite skills.Student demonstrates prerequisite skills.Student demonstrates understanding of simple indicators.Student demonstrates understanding of complex indicators in an authentic task.Student demonstrates understanding of indicators that goes beyond expectations.QL-A1.A. Use variables to accurately represent quantities or attributes in a variety of authentic tasks.A. Not yet able to apply vocabulary to identify parts of an expression or define the variables needed in an authentic taskA. Define the variables needed in an authentic taskANDA. Given an authentic task student can identify the variableA. Match correct expression to given taskA. Create an expression from an authentic task. Including naming the variableA. Analyze authentic tasks to interpret variables and quantitiesQL-A1.B. Predict and then confirm the effect that changes in variable values have in an algebraic relationship.B. Not yet able to predict or confirm what changes in an authentic task would do to an expressionB. Can complete one of the following: confirm what changes in an authentic task would do to an expressionB. Predict what changes in an authentic task would do to an expressionB. Mathematically confirm predictions to authentic task changesB. Predict and confirm, with support, the effect of changes in a variable on an algebraic relationshipQL-A1.C. Interpret parts of expressions such as terms, factors, and coefficients.C. Not yet able to identify the parts of an expression C. Group types of expressions discussing similarities C. Identify the parts of an expression needed for an authentic taskC. Interpret parts of an expression in relation to an authentic taskC. Interpret and communicate the parts of an expression in relation to an authentic taskQL-A3. Students can create, solve, and reason with equations and inequalities in the context of authentic modeling and problem solving situations. Student does not meet prerequisite skills.Student demonstrates prerequisite skills.Student demonstrates understanding of simple indicators.Student demonstrates understanding of complex indicators in an authentic task.Student demonstrates understanding of indicators that goes beyond expectations.QL-A3.A. Create equations and inequalities that describe numbers or relationships.A. Not yet able to describe a relationship or a systemA. Explain if an authentic task would be set-up as an equation or inequalityA. Match the appropriate equation or inequality given an authentic taskA. Create an appropriate equation or inequality given an authentic taskA. Create and solve their own authentic task for equationsQL-FM1. Students can apply, analyze and evaluate the characteristics of functions in authentic modeling and problem solving situations. Student does not meet prerequisite skills.Student demonstrates prerequisite skills.Student demonstrates understanding of simple indicators.Student demonstrates understanding of complex indicators in an authentic task.Student demonstrates understanding of indicators that goes beyond expectations.QL-FM1.B. Predict and then confirm the effect that changes in variable values have in an algebraic relationship.B. Not yet able to make a prediction about the algebraic relationshipB. Not yet able to make a correct prediction about the algebraic relationshipB. Make a correct prediction about the algebraic relationship and confirm the answer mathematicallyB. Make a correct prediction, confirm the answer mathematically, and can interpret that answer in an authentic taskB. Analyze and correct others’ predictions including what may have led them to that predictionQL-FM2. Students can build and use functions, including linear, nonlinear, and geometric models in authentic modeling and problem solving situations.Student does not meet prerequisite skills.Student demonstrates prerequisite skills.Student demonstrates understanding of simple indicators.Student demonstrates understanding of complex indicators in an authentic task.Student demonstrates understanding of indicators that goes beyond expectations.QL-FM2.D. Construct and compare models such as linear and nonlinear models and use them to solve problems.D. Not yet able to construct or compare different modelsD. Construct models in a few different representationsD. Construct a variety of modelsANDD. Students can draw some useful conclusions from comparing modelsD. Construct a variety of modelsAND D. Students can draw useful conclusions from comparing modelsAND D. Students can use models and comparisons to solve authentic tasksD. Analyze problems and construct an appropriate model in an authentic taskQL-FM2.E. Interpret expressions for functions in terms of the situation they model.E. Not yet able to mathematically solve situationsE. Solve situations mathematically but are not yet able to interpret pieces of the expressionE. Solve situations and provide an interpretation for individual pieces of the function/expressionE. Solve situations mathematically and provide an interpretation of the function as a whole as well as what the answer means in the context of the situationE. Defend and analyze interpretations of function and what the answer means in the context of an authentic textTask ImplementationTask Launch: Ask students to discuss and/or research online charity fundraiser efforts they have seen or been a part of. Could even turn this into a more in-depth social impact project by having groups of students identify a cause and develop their own charity game to help raise money for their cause.Task Steps/ProceduresResourcesSolution Paths & Potential MisconceptionsParticipationSee page 1, and 3-6 of Equal Salaries Student Resource Page and KeySeason Pass ResourcesThis task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue. Students may use various methods to determine a quadratic function that fits the mathematical model and helps answer the questions.Students may need to quadratic equations after deciding on the key elements (x and y intercepts, other key points, etc.) of their modelPartner task, but can also be done individually based on needs of your studentsAccess & Differentiation to Promote LearningConsiderations for Multiple Means of ExpressionConsiderations for Multiple Means of EngagementConsiderations for Multiple Means of RepresentationStudents can present their findings using a variety of forms: oral presentation with PPT, executive summary on a word doc, or a flyer/brochure to distribute promoting the “season pass” and benefits of it.In addition to the parameters described in the task, students can interview school faculty that deals with fundraising scenarios and design a task that is more applicable to factors present at your school.Students can represent their findings as an in-class presentation, through a pre-recorded video, or even as a presentation with the support of school stakeholders in support of their analysis.Opportunities for ExtensionThis task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue. Students may use various methods to determine a quadratic function that fits the mathematical model and helps answer the questions.Extensions could include further analysis of other elements of comparing quantitative variables (correlation, residuals, linear regression, etc.). Further extensions could include other business scenarios requiring revenue maximization.Opportunities for RemediationMay need to provide additional practice on constructing and analyzing scatterplots: for Additional Skill PracticeMVP Math Modeling Data PracticePractice with further analyzation of comparing quantitative variables in different contexts that relate to students (amount of time spent studying vs. performance on test). This relates well to the Equal Pay task that came previously.Further analysis of other elements of comparing quantitative variables (correlation, residuals, linear regression, etc.) ................
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