Yesterday while searching for information on the math used by the CDC, I came across a great 72 page pdf on math modeling . It's eight sections cover it all from the general introduction to putting everything together. Every chapter has a summery and an activity at the end. The activities are set up so by the end the student has completed their own mathematical model.
Each chapter focuses on a specific aspect of mathematical modeling. Chapter two is solely on defining the problem statement including the types of problem statements and possible interpretations of those questions. The authors use quite a few mind maps to illustrate the process used to help define the problem.
Chapter three looks at the process of making assumptions for the topic. This chapter puts the material from the previous chapter into focus and helps create a clearer view of the topic. It gives some great information and shows step by step how the assumptions fit together.
Chapter four focuses on what aspects are the variables in the problem, both independent and dependent. The authors provide three different examples so students can see how independent and dependent variables are designated. The authors explain that the problem determines which is the independent and dependent variables. By this point, students have created their initial mathematical model.
Chapter five concentrates on approaches to using model to create initial data. The authors give a set of questions to help the student proceed with this step. Again, there are three examples and each example is shown with two or three different approaches so they can see how this works. The examples include any math and graphs to show results using these specific approaches.
Chapter six examines analyzing the data in two ways. The first is does the answer make sense and the second looks at ways to look at a more detailed analysis of the data. Again using examples the authors show how to analysis the data in both ways and provide a list of things to check for. They even state that students might want to refine the model and run it again if there is time.
Chapter seven ties everything thing together to complete the process including how to write the results up. It includes do's and don'ts for writing the results, and the recommended structure. At the very end, there is a final write-up of a model done on recycling so students can see what the end results should be.
This is a well done guide put out by the Society of Industrial and Applied Math. Check it out, download it, use it. Tomorrow, I'll talk about sites with suggested lesson plans on mathematical modeling.