ABSTRACT
For a project in a Year I Integrated Mathematics class, Mr. James asked his students to think of an authentic example of a linear function that they have encountered in their lives. He asked his students to describe the function in words, to determine the independent and dependent variables, to generate a table of values, to write an equation based on the table, and to create a graph of the function. Finally, students were asked to present their functions to the class and were graded on their written papers and on the quality of their presentations. Mr. James listened to the presentations and read the papers enthusiastically because he was able to see his students applying their understanding of functions to their lives. However, the projects submitted by Francis and Joyce were different from those of the others in the class, and Mr. James immediately faced a decision about how to handle their examples. Francis’s function was worded as follows:
The monthly fee for phone calls at my house is $10, which includes the first four outgoing calls. After that, every additional outgoing call costs another 50¢. The total cost for a month is a function of the number of outgoing calls.
