Sample Problems

Featured Practice Problems

Check back here for information on live text chats around practice problems.

Modeling Scenarios: Levels 1, 2, and 3  

Several examples of the types of problems you may be asked to solve in the M3 Challenge are presented here.

It is highly recommended that participants read and work through some problems at each level before moving on.

Level 1:

Modeling Scenarios [14K PDF]

This list is intended to give students a taste of some of the scenarios that may be presented as modeling problems 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 Resource Books


A Backwater Curve for the Windsor Locks Canal [1.09MB PDF]

Budgeting Time and Money [382K PDF]

Pricing Auto Insurance [466K PDF]

Volcanic Eruption Fallout [560K PDF]


A Backwater Curve for the Windsor Locks Canal [1.73MB PDF]

Budgeting Time and Money [1.8MB PDF]

Pricing Auto Insurance [1.7MB PDF]

Volcanic Eruption Fallout [1.5MB PDF]

These booklets detail modeling problems that remain relevant today despite being somewhat dated in appearance. These examples have considerable background data, which gives insight into the types of details that need to be considered when solving the Challenge 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.

Level 3: From the 2019 SIAM-MfA Workshop on Math Modeling for Teachers

Math Modeling in High School Classrooms

MathWorks slides and data

Have your own idea for a problem? Suggest it!

Unsure how to format your solution paper? Consider using this solution paper template prepared by M3 Challenge judges to help you organize your work and get to the modeling quicker!

Level 4: M3 Challenge Archives: Past Problems and Outstanding Solution Papers

M3 Challenge 2019 Problem

Please note that the papers posted here are the solutions of the top six teams in the 2019 M3 Challenge. The students completed these papers within the 14-hour time period allowed for the contest and were selected by the judges to receive an award. Papers have been lightly edited by SIAM for posting.

M3 Challenge Champions - High Technology High School

M3 Challenge First Runner Up - Richard Montgomery High School

M3 Challenge Third Place - Nicolet High School

M3 Challenge Finalist - Academy for Science and Design

M3 Challenge Finalist - Adlai E. Stevenson High School

M3 Challenge Finalist - Wayzata High School

Technical Computing Award Winner - North Carolina School of Science-Math

Technical Computing Award Runner Up - Academy for Science and Design

Technical Computing Award Third Place - High Technology High School

Past Problems

2018 Problem

2018 Sample Solution: Using MATLAB to Solve the 2018 M3 Problem

2017 Problem

2016 Problem

2015 Problem 

2014 Problem 

2013 Problem 

2012 Problem 

2011 Problem

2010 Problem 

2009 Problem 

2008 Problem 

2007 Problem

2006 Problem 

Go to the M3 Challenge archive to see these problems and their solutions.