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)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

The action in a British sporting event (bumping races) was used to motivate a simple method of computing the correlation between starting and finishing positions. The method is generalized to other situations. (SD)

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)

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

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

Finding the shortest route between two points can be approached by vector methods. Several types of matrices modelling a map of 6 cities are described. (SD)

Provides a brief synopsis of the development of the National Fire Danger Rating System along with an explanation of how it works and possible ways to use it in a modeling or problem-solving unit in a secondary mathematics classroom. (ASK)

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

Directions are given for making a model of a three-dimensional coordinate graph. (DT)

Discusses the use of scaling test scores for an algebra class. Provides example data, several equations used in scaling, and graphs. (YP)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

Presents an algebra project in which students build a dance club. Reveals how this project motivates students and makes algebra more accessible, dynamic, and relevant to their society. (ASK)