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Instructional Task Implementation GuideTeen Policy CostsTransitional Math Course: Quantitative LiteracyTransitional Math Unit: Personal FinanceUnit Learning Segment: U1C3 - SpendingRecommended Length of Task: 3 – 4 days (135 – 180 minutes)Task ObjectivesTask TitleTeen Policy CostsTask SummaryStudents create linear equations and compare/contrast slope of car insurance policies for male vs female teen drivers.Materials Needed? Calculator or device for each student? Insurance rate tables for male and female teens? ISU Real Numbers? 1 sheet of graph paperKey Performance IndicatorsQL-A3.A Create equations and inequalities that describe numbers or relationships. QL-FM2.A: Translate problems from a variety of contexts into mathematical representations and vice versa.QL-FM2.B ?Build a function that models a relationship between two quantitiesQL-FM2.D Construct and compare models such as linear and nonlinear models and use them to solve problems. Standards of Mathematical PracticeMake sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematics Use appropriate tools strategicallyAttend to precisionLook for and make use of structureLook for and express regularity in repeated reasoningChecking for UnderstandingDescription of ProductStudents create scatter plots and then create a line of best-fit equation, first for high and low temperatures in Arizona, and then for insurance policies for teen drivers.Formative Check Points Check scatterplots for temperatures; discuss line of best fit. Check axes for appropriate spacing for insurance graphs.Task RubricCompetency and IndicatorLevel 1 – No EvidenceLevel 2 – Partially MeetsLevel 3 - ApproachesLevel 4 - MeetsLevel 5 - ExceedsQL-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-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.A. Translate problems from a variety of contexts into mathematical representations and vice versa.A. Not yet able to translate problems into any other form of representationA. Translate between tables and graphs (between two visual representations) and sometimes equationA. Translate between visual representations (tables/graphs), equations, and sometimes written descriptionsA. Translate between tables, graphs, equations, and written descriptions in a variety of authentic tasksA. Choose an efficient model to analyze problems in a variety of contextQL-FM2.B. Build a function that models a relationship between two quantities.B. Identify a relationship between two quantities but not yet able to build a function to represent itB. Identify the relationship between two quantities and build a linear function to represent itB. Identify the relationship between two quantities in both linear and quadratic functions and build the corresponding functions to represent itB. Identify and model the relationship between two quantities in linear, quadratic, and exponential functionsANDB. Students can build needed additional functions from these existing functions, and use those functions to solve authentic tasksB. Identify and model relationships between two quantities in a variety of functions, build new functions, and justify their choice of functionQL-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 taskTask ImplementationTask Launch: Discuss how graphs provide a visual representation of related quantities. Lines can be helpful in showing trends, but are all graphs straight lines?Task Steps/ProceduresResource LinkSolution Paths & Potential MisconceptionsParticipationStudents will create a scatterplot of high/low temperatures in Arizona, and then find a line of best fit (not linear regression, just by observation)Teen Policy Costs (ISU Real Numbers)Students may need assistance in creating accurate tick marks on each axis.Students may need assistance in creating line of best fit.Small GroupIndividualStudents will create a scatterplot of insurance premium costs for male and female teen drivers.Teen Policy Costs (ISU Real Numbers)Small GroupIndividualAccess & Differentiation to Promote LearningConsiderations for Multiple Means of ExpressionConsiderations for Multiple Means of EngagementConsiderations for Multiple Means of RepresentationStudents can use graph paper and/or graphing calculators or Desmos.To engage students more effectively in discourse around the lines of best fit, the teacher could use technology (such as ClassPad or Desmos) to show all the different lines of best fit the students have identified layered on the scatterplot. The class can then compare and contrast.Some students may benefit from being provided templates with labeled axes. Or students could be given different examples of scatterplots with lines of best fit for them to analyze in context before creating their own to solidify vocabulary.Opportunities for ExtensionStudents can research local insurance company premium charts and create graphs for comparison.Opportunities for RemediationHelp students with creating graphsLine of best fit for Additional Skill PracticeGraphing points/graphing lines/Practice reading graphs writing equations of lines ................
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