Sample Problems

The Moody's Mega Math Challenge problem will be a realistic, open-ended, challenging modeling problem focused on a real-world issue. In addition to being a contest for the best, brightest and most creative minds, the purpose of the Moody's Mega Math Challenge is to elevate high school students' enthusiasm and excitement about using mathematics to solve real-life problems and to increase students' interests in pursuing math-related studies and careers in college and beyond. Moody's and SIAM are interested in improving the pipeline of young people into studies and careers in applied mathematics, and encourage students to participate in this contest as an educational process.

Provided here are several examples of the type of problem you may be asked to solve on your M3 Challenge Day.

It is highly recommended that you read and work through some problems at each level before moving on to the next group.

Level 1: Modeling Scenarios [PDF, 14K]

This list is intended to give you a taste of some of the scenarios that may be presented as modeling problems to student teams in the M3 Challenge. This can be considered basic training material, designed to prompt targeted brainstorming.

List provided courtesy of William P. Fox, Department of Mathematics, Francis Marion University, Florence, SC.

Level 2: AIM Student Resource Books

These booklets detail modeling problems that remain relevant today, despite being somewhat dated in appearance. These examples also have considerable background data, which gives insight into the types of details that need to be considered when solving the Challenge modeling problem. Remember that creativity and originality are highly valued characteristics of a winning solution—along with good quantitative and qualitative analysis.

Used with the permission of the Mathematical Association of America.

Note: Teacher Guides to each of the problems above are available to coaches upon request. Contact M3 Challenge headquarters to have the PDF files emailed to you.

Level 3: HiMCM Problems

These are formal modeling problems and actual student solutions. Please note that the booklets posted here are the published outstanding solutions from a few High School Mathematical Contest in Modeling (HiMCM) competitions. These are top-tier examples in terms of their unique and coherent solutions to mathematical modeling problems. The solution papers for the M3 Challenge problem are not expected to have quite the polish, detail or completeness as you will see here, because of the fact that the HiMCM, which takes place over an entire weekend, permits the students to develop a much larger body of work.

HiMCM links are approved and content is hosted by COMAP, the Consortium for Mathematics and its Applications, which among other activities sponsors the HiMCM competition. You can find COMAP at www.comap.com. Go direct to http://www.mathmodels.org/ on the COMAP web site to check out more useful sample math modeling problems, resources, other contests, and background information.

Level 4: M3Challenge Archives - Outstanding Solution Papers

M3 Challenge 2008 Problem [PDF, 207KB]

Please note that the papers posted here are the solutions of the top six finishing teams in the 2008 M3 Challenge. The students completed these papers within the 14 hour time period given for the contest and were selected by the judges to receive an award.

Go to the M3 Challenge archive to see the 2006 problem [203KB PDF], the 2007 problem [258KB PDF], and their solution papers.

Additional Resources

Teacher-Coach Guides