The Hiring Problem
Anew wing has been added to the magnet school for Mathematics, Science, and Technology so that the student populatio...
The Gas Station Problem
Every driver recognizes the fluctuations in gas prices that happen almost on a weekly basis. In many areas, local ra...
Spread of an Infectious Disease
Last spring it was SARS.This winter it's the flu. In the spring it's SARS again and the avian flu.The spread of AIDS...
The Blood Testing Problem
Suppose that you have a large population you wish to test for a certain characteristic in their blood or urine (for ...
The Traffic Flow Problem
Everyone has at some time been on a multi-lane highway and encountered road construction that required the traffic t...
The Hot Dog Stand Location Problem
A map shows the walking paths and dormitories in a section of campus and the approximate distances (in 100 feet) bet...
Apportionment: Measuring Unfairness
Every ten years when the census is taken, the federal government rearranges or reapportions the delegates in the Hou...
Great Lakes Problem
Iteration and difference equations are beginning to play a significant role in high school mathematics. The Great La...
The Suez Canal
In the Suez Canal Problem, we consider the real-world, multimillion dollar question of traffic flow through the Suez...
Evaluating Modeling Solutions: The Art Gallery Problem
Mathematical modeling plays an important role in the high school mathematics program in Australia. As part of the fi...
How Many Taxis?
You are standing in the rain trying to hail a cab in a large city. While waiting, seven cabs pass by that already ha...
The Ferris Wheel Problem
This problem is designed for students in Algebra II and beyond. In order to make a start with this problem, students...
The Michael Jordan Problem
The Michael Jordan Problem is a subtle, but challenging problem for Advanced Algebra or Precalculus students. Every y...
Voting Power
In ordinary elections, each person has a single vote and everyone's vote has the same power. However, in some situat...
Measuring Inequity
The distribution of income in our society is a concept of ongoing interest to economists, politicians, public policy...
The Ladder Problem and Extension
This issue's problem comes from Ron Lancaster, of Saint Paul's School in Ontario, Canada. Ron presented this problem ...
The Irrigation Problem
This article has students imagine a linear irrigation system to uniformly spray water on a rectangular field where th...
The Airplane Problem
This article presents data that describe some characteristics of airplanes presently flying in the United States. St...
The Playoff Problem
The Super Bowl is a one-game playoff for the championship of the National Football League. In baseball, the World Ser...
The Cookie Problem
This semester we used a simple modeling problem as one of the questions on our Precalculus final exam: "The Fresh B...
Data Analysis from Algebra to Calculus
Data analysis is an important modeling tool and one whose principles can be developed along with the student's knowl...
The Elevator Problem
In some buildings, all of the elevators can travel to all of the floors, while in others, the elevators are restrict...
The Computer Problem
The school board has just decided that every mathematics classroom in your school will be able to purchase a compute...
UMAP Journal 28.1 Spring 2007 Edition
Table of Contents: GUEST EDITORIAL The Art of Modeling ARTICLES Child's Play Mystery Circuit in Mathematics Class ...
Photovoltaic Systems Off-Grid (UMAP)
This module introduces photovoltaic systems for use off-grid, including analytical and Mathematica construction of s...
Bridge Analysis (ILAP)
Solving systems of equations has applications in a multitude of disciplines. Once such application is in civil engine...
Child's Play
Many people first see the application of probability in childhood. Games involving rolling dice, tossing a coin, or s...
Mystery Circuit in Mathematics Class
We discuss the introduction, student discovery, and teaching of a system of differential equations that model a circu...
Chaos: Graphical Depiction, Logical Dissection, and Manhattan Analogy
An iterated-function dynamical system is a continuous map F from a metricspace X to itself. The sequence of iterates ...
The Will Rogers Effect
The Will Rogers phenomenon came to our attention in an article presented for discussion at Surgery Journal Club at th...
Decimals Into Fractions
Many years ago, I was a guest at a board meeting. The executive officer of the organization was reporting on a surve...
Misnomers in Mathematics Part I
Misnomers in mathematics often stem from early points of view or actual errors in reasoning. The name "geometry," li...
Barycentric Coordinates
Although much of the work we do in mathematics uses the familiar Cartesian coordinate system, there are other system...
The Mathematics of Medical X-Ray Imaging (UMAP)
Determining the internal structure of an object without having to cut it, or viewing a section of a body without inte...
The Scheduling of Traffic Lights (UMAP)
We consider the problem of scheduling traffic lights optimally, or more generally, the problem of allocating optimall...
A Hands-On Approach to Finding Plantonic Volumes
In my last column, I showed how to find the volume of anti-prisms. After finishing it, it occurred to me that you nev...