Using the correct materials and manipulatives appropriately allows the richness of geometrical concepts to be fully investigated to enable students to explore and reason about shapes. This article explores some of the key ideas involved in learning about two dimensional shapes and discusses how materials can be used to support learning.

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

A simple way to represent hemihedral faces and to illustrate the relationship between the resulting left-handed and right-handed hemihedra is presented. The illustrations highlight that the chirality corresponds to the absence of reflective symmetry but not necessarily to the absence of a C2 axis of symmetry.

Includes lesson plans and worksheets that deal with transformational geometry, specifically reflections. The lesson for grades three to four focuses on angles of incidence and reflection and that for grades five to six involves mirror images. (MKR)

This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)

Presents five worksheets that contain hands-on geometry activities dealing with the ideas of quadrilateral, trapezoid, parallelogram, isosceles, kite, axis of symmetry, and rhombus. (MKR)

A system of area measurement developed for the isometric geoboard is used to justify some relationships that are often proved using square units of area. (Author/MK)

The relationship between area and perimeter is presented through a series of laboratory-type activities and demonstrations. (SD)

Worksheets on constructing the circumcenter, the centroid, the orthocenter, the incenter, and the Nine-Point Circle in a triangle are provided for duplication. (DT)

Presents activities which use patterns on geoboards or dot paper to develop geometry and measurement concepts. Includes reproducible student worksheets. (MKR)

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)

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. The thrust of this module is to introduce the student to transformations by having the student physically transform sets of points. Heavy use of manipulatives is made to aid the student in the transforming activity. Individual sections…

Presents a cooperative-learning lesson in which high school students visit stations equipped with different tools to establish the midpoint of a Pixy Stix, a brand of candy-filled straw. Provides solutions for two potential stations, suggestions to extend the activity, and two activity worksheets. (MDH)