The number of people who purchase a ticket must not exceed the number of people in the class or the maximum occupancy of the theater. The cost per person will range from $500 to whatever the value is for The fourth step in the modeling cycle is to interpret results in terms of the original situation, the fifth step is validating conclusions, and the sixth step is reporting conclusions and the reasoning behind them. By answering the following questions students will engage in these steps of the modeling cycle. Ask is the cost of a ticket if: “What 100 people purchase a ticket? $5.00 250 people purchase a ticket? $2.50 500 people purchase a ticket? $1.00 1000 people purchase a ticket? $.0.50 Ask As more and more people purchase a ticket what is happening to the cost per “ ticket? The cost decreases. Ask Will the cost per person ever reach zero The ticket sales “ dollars? Explain” No, must always raise $500 so if the cost went to $0/person no money would be raised. Ask is the lowest cost per ticket? There is no lowest possible price if you “What Explain” think about this as a mathematics problem only. In reality, a theater is going to have occupancy limits for safety reasons. Say this theater has a maximum occupancy of 500 people, then the lowest cost per ticket would be $500/500= $1.00 Ask have an algebraic and numeric representation of the situation, what does a “We graph of this situation The graph of this situation would be a series of dots look like?” in the first quadrant because the x-coordinates and the y-coordinates of the points would both be positive. The x-coordinates would all be positive integers while the would be numbers rounded up to the nearest hundredth. Ask does the graph of the situation differ from the graph of produced by your “How The calculator produces a graph that has a section in the first and third calculator?” quadrants. The points in each quadrant are connected and the graph has a vertical break at x=0 and a horizontal break at y=0.
The number of people who purchase a ticket must not exceed the number of people in the class or the maximum occupancy of the theater. The cost per person will range from $500 to whatever the value is for The fourth step in the modeling cycle is to interpret results in terms of the original situation, the fifth step is validating conclusions, and the sixth step is reporting conclusions and the reasoning behind them. By answering the following questions students will engage in these steps of the modeling cycle. Ask “What is the cost of a ticket if: 100 people purchase a ticket? $5.00 250 people purchase a ticket? $2.50 500 people purchase a ticket? $1.00 1000 people purchase a ticket? $.0.50 Ask “ As more and more people purchase a ticket what is happening to the cost per ticket? The cost decreases. Ask “ Will the cost per person ever reach zero dollars? Explain” No, The ticket sales must always raise $500 so if the cost went to $0/person no money would be raised. Ask “What is the lowest cost per ticket? Explain” There is no lowest possible price if you think about this as a mathematics problem only. In reality, a theater is going to have occupancy limits for safety reasons. Say this theater has a maximum occupancy of 500 people, then the lowest cost per ticket would be $500/500= $1.00 Ask “We have an algebraic and numeric representation of the situation, what does a graph of this situation look like?” The graph of this situation would be a series of dots in the first quadrant because the x-coordinates and the y-coordinates of the points would both be positive. The x-coordinates would all be positive integers while the would be numbers rounded up to the nearest hundredth. Ask “How does the graph of the situation differ from the graph of produced by your calculator?” The calculator produces a graph that has a section in the first and third quadrants. The points in each quadrant are connected and the graph has a vertical break at x=0 and a horizontal break at y=0.
A2_U3_LP_Introduction_to_rational_functions.docx