Polynomial Functions and Mathematical Modeling

Procedure

Time: Approximately 60 minutes

Materials: (Optional) Statistics utility program or graphing calculator.

Prerequisites: This activity is designed for students who have a good understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function. They should also be familiar with graphical representations of these functions.

Implementation: This RWLO can be used either in the classroom to demonstrate goodness of fit of a model or provided as an activity / homework assignment for students. Students can work individually or in small groups but it is recommended that each student answer the questions individually.

Steps:
 Read and/or distribute Background Information for the Global Sun - Temperature Project.   Review and/or distribute Part A: Latitude vs. Daylight. You can review this part together with students in class or assign it as an in-class or out-of-class activity. If assigned as an out-of-class activity, there should be a follow-up class discussion that includes why a certain model was chosen, whether another function might also work, what restrictions are placed on the domain and range by the problem situation, and whether the model could be used to predict future values. Although no one answer is correct, some answers may be better than others.    Review and/or distribute Part B: Latitude vs. Temperature. Students should complete this activity as an independent assignment.

Optional Activity:

In lieu of viewing the data plots provided in this RWLO, students can download archived data from other runs of the Global Sun - Temperature project and create their own models using a statistical utility program. Note that all of the models and charts created in this RWLO were done using EXCEL but other programs may be more appropriate. To create the residual plots, insert two additional columns into the spreadsheet; one for predicted values (y) using the equation for each model (x=latitude) and the other column for the residual calculation (residual = observed - predicted). You can then create plots of the residuals for each value of latitude.

(NOTE: this RWLO is based on the Global Sun Temperature Project)