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ICLE Standards:
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Mathematics as Problem Solving: Apply process of
mathematical modeling to real-world situations.
Algebra: Represent situations that involve variable quantities with expression,
equations, inequalities and matrices.
Functions: Represent and analyze relationships
using tables, verbal rules, equations and graphs.
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Performance Task:
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Karen's boss does a considerable amount of travel
in his job. He uses a rental car, and it is Karen's responsibility to secure the rental car for him. She is able to rent from
three different companies. Their costs are:
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U RENT IT COMPANY $50 per day + $0.15 per mile driven
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GOOD DEAL CAR RENTAL CO. $15 per day + $0.20 per mile driven
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WE TRY HARDER CAR RENTAL CO. $100 per day flat rate - no cost per mile
driven
Karen has to choose the company that will be most cost effective for her
boss. She realizes the cost depends upon the miles driven per day. Your task is to help Karen. Express each
company's cost as a function of the number of miles driven per day. Graph the three functions on the same set
of axes and recommend to Karen which company her boss should use when.
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Knowledge / Skills:
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Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. (m7)
Know the components and properties of the rectangular coordinate system, (i.e., x - y axis, origin, quadrants, abscissa (x-coordinate) and ordinate (y-coordinate), and the general representation of a point (x,y)). (m23)
Know how to find the graphic solution of systems of linear equations (e.g., find the point(s) common to a quadratic-linear pair). (m71)
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Rubric:
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4 Points = The student is able to complete the entire task independently. He/she can translate the problem into algebraic equations, graph the equations and make correct inferences from the graphs.
3 Points = The student needs assistance to complete the task. He/she has some difficulty expressing the facts of the problem as algebraic equations. The student makes some minor errors in graphing the equations and has difficulty answering the question based on his/her graphs.
2 Points = The student, even with assistance, is unable to complete the task. He/she shows some understanding of how to write a function, but needs considerable assistance to graph the equations. The student’s response to Karen concerning which company her boss should use and when is vague and confusing.
1 Point = The student is unable to do the task. He/she shows no understanding of functions and cannot graph linear equations. Therefore, he/she cannot do any analysis of the graphs and is unable to make any recommendation.
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