The Corvette Problem is a nonroutine investigation, one that provides an authentic context to explore many interrelated calculus ideas. In our years of sharing this problem with students and colleagues, we have found additional topics from the calculus curriculum to have rich interpretations in this environment. The Corvette Problem contextualizes…

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

The Ultimatum Game is a two-person, multiple-strategy game widely used in the experimental social sciences to demonstrate the human propensity for costly punishment in response to inequitable treatment. The game serves to provide quantitative evidence for a diversity of fairness norms across cultures. The play of the game and its interpretation…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

This article provides two activities, exploring genetic drift of small breeding populations, highlighting the black-footed ferret ("Mustela nigripes"). According to the U.S. Fish and Wildlife service, all black-footed ferrets are descended from 18 individuals, making them extremely vulnerable to genetic drift. They were thought to be…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

Through a series of explorations, this article will demonstrate how the Kentucky Derby winning times dataset provides various opportunities for introductory and advanced topics, from data processing to model building. Although the final goal may be a prediction interval, the dataset is rich enough for it to appear in several places in an…

One of the unique advantages of electrochemistry is that the relationship between thermodynamics and kinetics is quantitative, which is the basis of voltammetry. Mathematical models of electrochemical systems take advantage of this relationship to predict the effect of changing a system property (e.g., concentration, scan rate, or rate constant)…

Folk wisdom of the state of Montana asserts that Flathead Lake, located in the state's northwest corner, is the largest natural freshwater lake west of the Mississippi. But what does it mean to be the "largest?" And, how does one respond to Californians' claims that Lake Tahoe, located on the California-Nevada border, is the rightful…

People use models every day without even realizing it. Models create a structure for predictions (inferences) that can be used or adapted as situations change. A model is a relational system that highlights aspects of a phenomenon that the modeler deems important and diminishes the rest. Statistical models capture variability of data, enabling…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

Friction is one of the common forces that affect our everyday life and one of the oldest problems studied in physics. An interpretation of its nature is included in all general physics courses, in both high school and college. The desire and need to better understand it guided a long list of scientists who devoted themselves to the study of…

Colorimetry allows every color to be defined as a combination of three values, known as "color coordinates." Color coordinates allow researchers to universalize and standardize their color measurements, and nowadays, determining the color coordinates of samples is a routine method applied by organic and analytical chemists, students, and…