In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is…

Revisits and discusses the polar bear problem that was published in the March 1997 issue. The problem concerns a riddle: If you walk one mile south, one mile east, and one mile north, and end up in the same spot as you started, what kind of bear would you see? (ASK)

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Least-squares line fitting is developed without calculus. Its rationale and an example with consumption patterns are provided. (MNS)

Contains explanations and examples of mathematical calculations for a secondary level course on personal finance. How to calculate total monetary cost of an item, monthly payments, different types of interest, annual percentage rates, and unit pricing is explained. (RM)

The article presents and discusses an optimization problem concerned with observing objects from a moving car. (MK)

Methods of determining probabilities of various outcomes of the game Yahtzee are described. (SD)

Three examples illustrate a method for solving word problems: guess a solution, write an expression to check the guess, and substitute a variable for the guess in the expression. (MP)

An algebra problem is analyzed, and several variations are suggested for further student inquiry. Practical applications of the problem are discussed. (DT)

Procedures to help algebra students solve problems more efficiently are discussed, using linear programing graphs. (MNS)

A sample mathematical application problem that can be solved with computer programing is discussed. (MP)

A computer program that uses determinants to solve simultaneous systems of equations is presented. The purpose is to show teachers how to use topics from algebra, geometry, and programing to lead pupils to appreciate the beauty and unity of mathematics. (MP)

A 20-question quiz on the uses of numbers in the real world is presented. (MK)

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)