Finding Modeling Problems

  As part of the information from yesterday's column, I discovered two contest sites and one site with information on how to create a model to work the problem.

One of the universities in California created this wonderful slide show "Using Mathematics to Create Real World Problems." to show students the process step by step.

It begins with the steps from the word problem to the finish before going through the problem step by step so students see how the modeling works.  I know very little about modeling because I got a degree in theoretical mathematics in college and none of the classes I took ever delved into this topic. 

In order to teach modeling, I need this slide show to teach myself before I teach the students. The material is clear, easy to follow and ready to use.

The Consortium for Mathematics and Its Applications runs a yearly mathematical modeling contest filled with past problems you can use in your classroom.  The problem I looked at involved a standard bathtub you fill with water and needing to keep a small stream of hot water added into it to keep it warm.  The student is to create a model to show temperature changes as water is added, etc.

As far as I can tell, they do not post the actual solution but they do have problems dating back to the 1980's  There is a link to the Math model site which has some problems and articles focused on mathematical modeling.  It also provides problems for high school and undergraduate levels.

Another web site is the Math Modeling Challenge who offer modeling problems in a contest format.  This looks like it is made for high school students because the problems see a bit more broken down.  They provide regular practice problems for anyone to use.  This site offers some great resources from a free handbook on mathematical modeling to a teaching modeling video series. 

One last thing in regard to real modeling problems.  If you can remove the context and still solve the problems, then they are contrived problems that are not real modeling problems.  This is an important point since we want students to experience the real thing.

I'll be back in the next couple weeks with places to find mathematical modeling problems one can use in the classroom that are real but good to introduce students to the concept.  There will be messy answers so students get used to not having perfect answers.

Let me know what you think.  Have a great day.