Presents a variety of activities in which 4th grade students investigate prisms and pyramids by building models from folded paper and drinking straws. (Author/NB)

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Presents new proofs of the Pythagorean theorem while exploring examination questions. Briefly reviews the work of Elisha Scott Loomis, a mathematician who amassed 320 different proofs of the theorem. (DDR)

Presents a secondary classroom investigation into mathematical modeling techniques with the graphing calculator using a match stick puzzle. Geometric models, through their corresponding area formulas, are constructed, tested, and analyzed graphically to fit specified problem conditions. (Author/MKR)

Describes an activity, designed to comply with the National Science Education Standards, that integrates science and mathematics concepts. Mathematical modeling of the moon's phases is employed to show students the role of mathematics in describing scientific phenomena. (DKM)

Presents classroom vignettes in which middle grade students with developmentally different views of geometry stimulate each other's reasoning by externalizing mental images through modeling and discourse. (KHR)

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 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)

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)

Presents a model of rational number using pairs of line segments which can embody ratios of numbers. Actions upon these segments can embody arithmetical operations. Discusses tasks in a computer environment for bringing out diverse algebraic and geometric meanings of rational numbers. (Contains 23 references.) (MKR/Author)

Describes a rugby problem designed to help students understand the maximum-minimum situation. Presents a series of explorations that locate an optimal place for kicking the ball to maximize the angle at the goalposts. Uses interactive geometry software to construct a model of the situation. Includes a sample student activity. (KHR)

Describes a credit-card-debt activity that allows students to increase their awareness of underlying mathematical concepts relevant to the world of commerce and personal finance through learning geometric and arithmetic sequences. (KHR)

Describes an activity in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. Explores a simple case of the isoperimetric inequalities. (KHR)

An activity designed as an introduction to High School geometry empowering students to see relationships and make geometric connections. A list of student generated relationships based on student constructed and manipulated diagrams is included. Discussion guidelines are suggested. (DE)

Discussed are various models proposed for the Moebius strip. Included are a discussion of a smooth flat model and two smooth flat algebraic models, some results concerning the shortest Moebius strip, the Moebius strip of least elastic energy, and some observations on real-world Moebius strips. (KR)