#### Consortium for Mathematics and its Applications

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April 14, 2023
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Written on . Posted in Math Curriculum, Math Modeling, Fun with Math.

# 10 Interesting Math Modeling Modules to Try Today

As part of the expansive collection of resources we provide to the math community, we have a series of math modeling modules designed for teaching mathematics through real-world phenomena. There are many modules available on our website, but we compiled a sample of 10 diverse modules you might want to try in the classroom with your students.

These math modeling modules are free to download and use in classrooms. In fact, each module is built around several classroom activities, including student activity pages, teaching notes, and answers.

### 1. Math for Poets

This math modeling module explores mathematics related to rhythm in poetry and music, with extensions to mathematical topics such as binary codes and de Bruijn sequences.

### 2. Could These Bones Be Amelia Earhart's?

In this module, students create models for predicting human stature from bone lengths. The goal for the development of these models is to determine whether a set of bones found on Nikumaroro Island might be Amelia Earhart's.

### 3. Competition or Collusion? Game Theory in Sports, Business, and Life

Rock, paper, or scissors? Fastball or curveball? Bluff or fold? Work together or backstab the competition? Game theory offers a computational approach to decision-making in competitive situations between “players” who are each choosing from a variety of possible strategies. This module introduces students to game theory concepts and methods, starting with zero-sum games and then moving on to non-zero-sum games.

### 4. The Mathematical Theory of Elections

This math modeling module illustrates how mathematics can design and analyze election and ranking methods. Preference schedules, fairness criteria, and weighted voting all demonstrate that how votes are counted can affect the outcome of an election.

### 5. Math for Drummers

This module presents musical and mathematical topics including musical meter, rhythmic patterns, and their relationship to modular arithmetic.

### 6. I Will if You Will...A Critical Mass Model

This math module introduces the critical mass model, which is applied to examples in which individuals must decide to cheat or not to cheat, to attend or not to attend, to participate or not participate. Students will see and participate in the process of traveling back and forth between a mathematical model and the real world as they solve problems.

### 7. The Mathematics of Focusing a Camera

This module applies precalculus to photography. It introduces the reader to several photographic concepts, including focal length, f-stop, and depth of field.

### 8. Somewhere Within the Rainbow

This module uses Fermat's least-time principle for the path of light to derive the laws of reflection and refraction, and then analyzes the passage of light through a raindrop to explain quantitatively the phenomenon of the rainbow.

### 9. The Mathematics of Scuba Diving

In this math modeling module, exponential solutions of differential equations are used to construct decompression schedules for dives of various durations to various depths.

### 10. Calculus in a Movie Theater

This module explores the concept of viewing angle as a criterion for determining the best seat in a movie theater. It also addresses the question of the best seat in the theater, converting the layout of the theater from a three-dimensional problem to a two-dimensional one.

Did you enjoy these math modules? This is just a sampling of the many modules we have available. Learn more about our math modeling resources here.

# Written by

### COMAP, Inc.

The Consortium for Mathematics and Its Applications is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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