The Modeling Process

Dr. Holly Hirst
Appalachian State University
The Shodor Education Foundation
June 1998

Everyone who has ever attempted to solve a word problem has dabbled in modeling. Consider the situation in which pal Joey finds himself:

I asked my dad for some money. He gave me 24 coins (nickels, dimes and quarters) with three times as many dimes as quarters, for a total of $2.95. How many of each coin do I have?

With no experience under his belt, Joey may very well have no idea of where to start. If Joey had some general process to follow (which he could eventually figure out with experience) he could solve this problem to get the answer: 4 nickels, 15 dimes and 5 quarters.

The modeling process is nothing more than a flowchart to follow when taking a real world problem and systematically attacking it to get "an answer."

1. Identify the Problem
   • What is the question?
   • What is the purpose of the solution?
     • The accuracy needed in the solutions
     • The kinds of assumptions that make sense
2. Formulate the Model
   • List the relevant factors
     • Parameters and variables -- which are which?
     • What units should be used? Are they consistent?
   • List any assumptions
     • What are we assuming?
     • What can we neglect?
   • Find relationships
     • Physical laws - proportionality
     • Equations from the current experts in the field
     • Empirically determined equations
       • data collection
       • data fitting - what equation has the right shape?
     • Parameter values
       • data collection
       • parameter estimation
3. Obtain the Mathematical Solution
   • Can we solve the exact model exactly (aka analytically)?
   • Do we need to approximate the solution?
     • Numerical Method
     • Simulation
   • Think carefully about accuracy and error
4. Interpret the Solution
   • Correct signs and magnitudes?
   • Correct general shape?
   • Correct slope / concavity?
5. Compare with Reality
   • Is the answer sensible?
   • Does the answer agree with predictions?
   • Does the answer fulfill its purpose?
   • Is the accuracy sufficient?
6. Think Again!!!
   • Should we change the assumptions?
   • Did we forget something?

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   Last update on: June 9, 1998
   Author: Holly Hirst
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   © Copyright 1998 The Shodor Education Foundation, Inc.