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Consortium for Mathematics and its Applications

COMAP’s Mathematical Modeling Modules

COMAP presents a series of modules designed for teaching mathematics through the modeling of real-world phenomena. Most modules are suitable for use in high school classes, and some can be used in middle school, undergraduate courses, and in teacher education.

These modules are free to download and use in classrooms. Teachers have our permission to copy and distribute the student pages in their classes.

Each module in the series is built around several classroom activities. Each module includes student activity pages, teaching notes, and answers. Teaching notes and answers are in two-column format at the beginning of the module. Student activity pages are in full-page format at the end of the module.

Since technology plays a key role in mathematical modeling, most modules in this series offer opportunities to apply one or more forms of technology, such as graphing calculators and/or online graphing utilities, spreadsheets, and geometric utilities.

We have grouped the modules by primary math topic and included a brief description of each module to aid teachers in module selection. However, be aware that a realistic modeling scenario often involves application of several diverse mathematical concepts.

Since each module includes teaching notes and answers, these modules are available only to teachers. We ask that you first submit a short form to help us identify you as a teacher. We do not share your information with anyone. Shortly after submitting your form, you will receive an email with login information. After your initial login, please check back occasionally—new modules will be posted several times per year.

To further enrich your students' modeling experiences, please consider participating in one of our modeling competitions: MCM, ICM, HiMCM/MidMCM, or IM2C.

Pre-Algebra Modules

Voting Models

This module examines plurality, run-off, ranked-choice, and approval models currently in use in the United States and other countries. Mathematical tools include basic arithmetic, percentages, and preference diagrams.

HiMCM Problem: Storing the Sun

This module is based on a problem from the 2021 High School Mathematical Contest in Modeling (HiMCM).  The problem involves finding a configuration for an energy storage system to support solar panels that power an off-grid house. Mathematical tools include proportional reasoning and unit analysis.

Algebra Modules

Modeling Botpaths with Linear Functions

This module’s modeling concerns locating robot paths (botpaths) in order to avoid collisions. The main mathematical tools used are linear functions, their graphs, and solving systems of linear functions. Concepts of midpoint, perpendicularity, slope, and distance between points also arise.

Modeling Pooled-Sample Testing, Part I

The modeling in this module concerns testing pooled samples for diseases such as COVID in order to reduce costs. The mathematical tools used include linear, quadratic, and exponential functions, linear and quadratic inequalities, weighted averages, regression, and simulation.

Modeling the Kemp’s Ridley Sea Turtle Population

This module’s concern is modeling the population of an endangered species. The mathematical tools used include scatterplots, rules of exponents, linear and exponential functions, logarithms, and solving exponential equations.

Geometry Modules

Modeling Packaging

This module’s context is modeling product packaging and determining measures of efficiency for packaging designs. The mathematical tools used include basic percentages and ratios, area and volume, similar triangles, parallel and perpendicular lines, and regular polygons.

Statistics & Probability Modules

Could These Bones Be Amelia Earhart’s?

The modeling in this module involves using statistical techniques to predict human height from bone lengths. Mathematical tools include unit conversion, slopes of lines, equations of lines from two points, fitting a line to data (least squares), and coefficient of correlation (r2).

Modeling Pooled-Sample Testing, Part II

This module uses probability to develop a theory-driven confirmation for the data-driven modeling in Part I. The mathematical tools used are disjoint, complementary, and independent events, expected value, and tree diagrams.

Trigonometry Modules

Modeling Daylight in the Northern Hemisphere

This module uses sinusoidal functions to model the amount of daylight at locations in the northern hemisphere. Mathematical tools include sinusoidal functions, radian measure, rates of change, and piecewise functions.

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