Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Presents an activity in which the subject is the identity of the team in the greatest jeopardy of becoming the big loser in a basketball tournament. Explores several facts about the big loser, offering them in a hierarchy appropriate for creating various short- and long-term projects for a high school mathematics class. (ASK)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

A geometric model used to teach properties of rational numbers to college students is described. (MK)

Offers a real problem for students with younger siblings that uses a board game and illustrates the use of modeling and simulation. (ASK)

Presents a hands-on modeling experiment that focuses on hyperbolic functions, asymptotes, data analysis, applied statistics, and optimization problems. (ASK)

Included are brief articles on multiplication of negative integers and testing knowledge by asking true-false questions that involve a relatively high level of abstraction. A number of specific examples are included. (MNS)

A programing language called DYNAMO, developed especially for writing simulation models, is promoted. Details of six, self-teaching curriculum packages recently developed for simulation-oriented instruction are provided. (MP)

Using a staircase to introduce the concept of slope is discussed. (DT)

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)

Presents four activities that use graphing calculators, spreadsheets, and graphing software to model population growth. (MKR)

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)