## 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.