Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

Previous work has identified four areas of difficulty that students seem to have with the topic of similarity: (1) understanding the definition of similarity; (2) proportional reasoning; (3) dimensional growth relationships; and (4) correspondences in right triangle similarity. This paper reports the results of an investigation into high school…

Presents a five lesson unit at the fifth grade level to teach the geometric concept of similarity using manipulative materials and multiple representations. The summary presents rationale for teaching and classroom management decisions. (MDH)

Includes materials in reproducible format designed to help students read and draw distance-time graphs and use the slopes of these graphs to draw conclusions about car speed. (PK)

Describes a method that will easily generate any number of triangles of equal area and perimeter, and also geometrically characterize such triangles. (PK)

Describes and gives patterns for polyhedra other than the Platonic and Archimedean solids. The focus is on the deltahedra, but pyramids, prisms, and antiprisms are discussed first to help describe the deltahedra. (PK)

Presents lesson plans for activities to introduce recursive sequences of polygons: golden triangles, regular pentagons, and pentagrams. The resulting number patterns involve Fibonacci sequences. Includes reproducible student worksheets. (MKR)

Presents a geometry exercise which is designed to help students create three-dimensional clay figures, think in three dimensions, and develop vocabulary. Reproducible worksheets are included. (PK)

Presents a lesson in which students communicate verbally and in writing to create and describe geometric transformations, develop vocabulary, demonstrate ability to give unambiguous instructions to translate a triangle, form and test conjectures, and create extensions of problems. Includes reproducible student worksheets and questions for…

Suggests one possible way to combine the technological facility of the computer with students' natural abilities for concept formation. Describes the software the "Geometric preSupposer." (PK)

Includes patterns for and a brief discussion of the polyhedra: octahedron, tetrahedron, dodecahedron, cuboid, prism, and star. (PK)

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)

Presented is a method of reorganizing a high school geometry course to integrate coordinate geometry together with Euclidean geometry at an earlier stage in the course, thus enabling students to prove subsequent theorems from either perspective. Several examples contrasting different proofs from both perspectives are provided. (MDH)

Describes a geometry course that integrates transformation geometry into traditional high school geometry. Discussion of the scope and sequence of the course includes the topics of proof, congruence, translations, rotations, reflections, dilations, quadrilaterals, parallel lines, and similarity. (MDH)

This document extracts ideas from research on the teaching of algebra and geometry which might prove useful to secondary school teachers. Part I reviews research on algebra; it is divided into sections on classroom instructional practices, cognitive factors, attitudes and affective factors, problem solving, computers and calculators, and testing…