Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (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)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

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

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)

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)

With the Seeing and Thinking Mathematically materials, students learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively constructing their own understandings. In this unit students learn to see probability through a mathematical lens by exploring and creating games and simulations and by applying the…

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

The rational plane, consisting of the points in the Cartesian plane having two rational coordinates, is a model in which certain properties do not hold. Nine theorems are discussed. (MNS)

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 model for directed numbers, using a sentry moving along the number line, is described. (MNS)

A model is offered which can be used for teaching addition, subtraction, multiplication, and division with directed numbers. Illustrations for all operations are given. (MNS)

Methods of constructing polyhedra models are described. (DT)