## Introduction

“Mathematical modeling is the link between mathematics and the rest of the world.” Meerschaert, M., Mathematical Modeling, Elsevier Science, 2010

The process of beginning with a situation and gaining understanding about that situation is generally referred to as “modeling”. If the understanding comes about through the use of mathematics, the process is known as mathematical modeling

Step 1. Identify a situation.

Read and ask questions about the problem. Identify issues you wish to understand so that your questions are focused on exactly what you want to know.

*Teacher Notes: Spend enough time discussing the problem so that all students are aware of all aspects of the problem. This could take up to a full class period.

Step 2. Simplify the situation.

Make assumptions and note the features that you will ignore at first. List the key features of the problem. These are your assumptions that you will use to build the model.

*Teacher Notes: List all assumptions that students generated in Step 1. As a whole group, narrow the list to the most relevant assumptions, no more than two or three. Don’t attempt to use all assumptions listed! However, keep the list of unused assumptions.

Step 3. Build the model and solve the problem.

Describe in mathematical terms the relationships among the parts of the problem, and find an answer to the problem. Some ways to describe the features mathematically include:

• define variables
• write equations
• draw shapes
• measure objects
• calculate probabilities
• gather data, and organize into tables
• make graphs
*Teacher Notes: This is the step where the context becomes mathematized.

Step 4. Evaluate and revise the model.

Check whether the answer makes sense, and test your model. Return to the original context. If the results of the mathematical work make sense, use them until new information becomes available or assumptions change. If not, reconsider the assumptions made in Step 2 and revise them to be more realistic.

*Teacher Notes: Be sure that the computation is correct, and that the solution is reasonable within the context of the problem.

Choices, assumptions, and approximations are present throughout the cycle.