Payless vs. Enterprise
Overview
This task explores the real world topic of building light rails. Throughout the implementation of this task the students will learn about the cost of building railways and how to implement them within a budget. This task explores such mathematical concepts of using coordinates to find the distance between points, using coordinates to build polygons and find the area and length of sides, and writing equations of parallel lines.
Instructor Directions
Payless vs. Enterprise
Submitted by James O'Neal
CharlotteMecklenburg Schools
Driving Question / Scenario  When would it be best to rent from Payless or Enterprise? Do your family members have enough money to rent from either car rental companies? 
Project Summary  This task explores the real world concepts of renting a car and choosing the best deal. Throughout the task students will learn how to successfully present different representations for one the given scenario. This task explores mathematical concepts such as graphing systems of equations and inequalities, understanding their solutions, functions, scatter plots, and linear regression. 
Estimated Time  34 days 
Materials / Resources  Rulers, protractor, color pencils, graphing calculators, to make this all digital, use Desmos. BBB reports Payless Video: http://abcnews.go.com/US/bbbissuesnationwidewarningpaylesscarrental/story?id=47585004 Car Rental Article for Under 25 drivers: https://www.smartertravel.com/2015/07/02/rentingacarunderage25ispossiblebutpricey/ 
Grade  810th grade 
Subject(s)  Math 1 
Educational Standards  NC.M1.FBF.1aBuild a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities.a. Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table).NC.M1.FBF.1aBuild a function that models a relationship between two quantities.Write a function that describes a relationship between two quantities.a. Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table).NC.M1.AREI.10Represent and solve equations and inequalities graphicallyUnderstand that the graph of a twovariable equation represents the set of all solutions to the equation.NC.M1.SID.8Interpret linear models.Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plot, correlation coefficient, and a residual plot to determine the appropriateness of using a linear function to model a relationship between two variables. 
Project Outline  
Ask 

Imagine  Imagine that you want to show your family how much it will cost one of them to rent a compact car over a 7day period from either Enterprise or . You reveal to them the equation of both situations, a graph, and a table so that they will fully be convinced to go with your suggestion. At What point do the prices break even? When would you advise your family to rent from either company? Don’t forget to name and label your graph. Use as much of the graph as possible. 
Plan  Tell the students that they will be provided with rulers and the use of Desmos graphing calculator for computing costs and graphing lines. Students can annotate on the worksheet or if you want to be fully digital, students can copy their graphs and points from desmos. 
Create  Have students use straight edge rulers or protractors and have erasers and extra copies handy. The process of drawing lines and erasing them can become really messy. To avoid all of this, students who may want to do the same graphs digitally can do so in Desmos. You may have students who prefer paper and so have that handy. Encourage the use of colored pencils for shading and creating lines. Again, this can be done in Desmos by students changing the color of lines and even their shades when they get to inequalities. 
Improve  Have students continually refer back to understanding what the axes mean and the words that imply a different graph as the matriculate through each assignment. Language is so important to this task. Have students finetune their language and make sure they understand what the yintercept and the slope/rate of change means in these situations. When students offer advice to their family members, encourage the stretching of vocabulary in their sentences to fully let their family members know why they may or may not have enough money for their rental car during their vacation. 
Closure / Student Reflections  Students can reflect on their family and see who would show up to a family trip not having enough money. Students who may have never heard of the BBB, can reflect on why it would be smart for consumers to know these ratings. Since we live in a ratings culture, ask students do they or their parents look at ratings before they go into restaurants. What happens if you visit a restaurant and their grade is an 85? Many students would take an 85 on an assignment, why is that not good for a restaurant? You could also bring in correlations as to why when something may look cheap up front, that it’s important to read the “fine print”. 
Possible Modifications / Extensions  You may want to modify the budget each family member has. You can ask students about family members that would have more than enough money and would fall out of the threshold of the system of inequalities represented on the graphs. You can ask students what it means to be above the Enterprise line, since in math we say the solution is the shaded region where both inequalities meet. You could also use the line of best fit tasks as an extension since it is more related to data and interpreting it. It may not be a direct flow with this project. 