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Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

Describes an investigation of polygons and their properties in which students apply very basic understandings of geometric properties. (KHR)

Describes an activity connected with mathematical definitions that illustrates the process of gradual refinement as a way to understand and construct knowledge. Presents a gradual construction of a specific geometry concept that was the result of interaction between participants in a mathematical discourse. (KHR)

Looks at the connection between soccer fields and mathematics to help students understand middle school geometry topics. Presents an activity in which students explore relationships among polygons to discover which combinations tessellate and which combinations form polyhedra. (ASK)

Some topics in mathematics are unique because they can be explored by learners from the early grades through the advanced grades. An example of such a topic is polygon rings. Presents activities on polygon rings that integrate problem solving, reasoning, and communication. (Author/ASK)

Describes an activity in which students use geometry, measurement, estimation, and graphs to create mathematical jack-o'-lanterns using pumpkins carved in the shapes of polygons. (ASK)

Determines the theoretical probability that a regular polygon will cross a crack when dropped onto floorboards. By following two special cases, a pattern emerges that enables students to consider the general case. (ASK)

Uses match sticks to construct various polyhedra in the Euclidian space R3. Formalizes the idea of a match-stick construction and characterizes all obtainable points with such constructions algebraically. Specifies all the constructible ones among the uniform polyhedra. (Author/ASK)

Identifies common misconceptions about polygons. Discusses current practices used to teach geometry to search for the source of misconceptions, and describes ways to help students avoid these misconceptions. (ASK)

Presents mathematics activities on tangrams to study geometrical shapes such as polygons, symmetrical shapes, and tangram jigsaws. (ASK)

Examines why a flexible polyhedron must be convex. Discusses the theorems of Cauchy and Euler. (ASK)

Presents an activity involving students in the creation of polyhedra which enables them to understand the characteristics and develop a clear definition of different polyhedra for themselves. This activity helps develop spatial ability by encouraging students to experiment with creating models of polyhedra while using a wide variety of polygons for faces. (ASK)

Presents an activity for eighth-grade students and beyond to explore relationships between and among the areas of various polygons. Emphasizes that students should be given the opportunity to design their own examples. (ASK)

Discusses students' progress through distinct levels in the development of their thinking as described by van Hiele levels. Focuses on the quadrilaterals and suggests some level 3 tasks and construction problems. (ASK)

Discusses the need for a van Hiele test without limitations. Presents the background and main characteristics of a procedure to select items in designing three linked tests on polygons and other related concepts. Contains 15 references. (ASK)

Presents a game designed to help middle school students think about geometric properties and the relationships among them. (ASK)

Describes typical student strategies for counting cubes in cube buildings and explains why these problems are difficult for students. Suggests instructional tasks that can help students develop more powerful ways of thinking about such problems. Lists two action research ideas related to this issue. (ASK)

Presents activities to help students develop the notion of geometric congruence and similarity in a hands-on environment. (ASK)

Describes activities that use geoboards to explore properties of polygons such as the relationship between a polygon's number of sides and the sum of its interior angles. Describes a generalized method for constructing any Pythagorean triangle. (DDR)

Presents three sets of polygons marked so that visually appealing designs emerge when the polygons are assembled into tessellations that cover the plane. Provides ideas for using the different sets of tiles in the classroom and reactions of the students who assembled the patterns. (AIM)

Presents a series of lessons that extend the concrete experiences many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions. (DDR)

Describes an extended investigation of polygons and polyhedra which was conducted in response to a challenge posed in Focus, a newsletter from the Mathematical Association of America (MAA). Students were challenged to construct a polyhedron with faces that measure more than 13 inches to a side. Outlines the process, including the questions posed to and by the students. (DDR)

Presents an extended activity consisting of a sequence of tasks organized so that students can visit several mathematical concepts concurrently and explore connections among them. Students build solids using bendable straws to form the skeletons of various polyhedra. Topics covered include tables and charts, algebraic expressions, surface area, volume, and data analysis through measures of central tendency. Includes activity sheets. (PVD)

Argues that genuine problem solving and investigation on the part of pupils rarely occurs in mathematics classrooms in Hong Kong and other Asian countries. Provides a rationale for drawing problems from the content of a curriculum or syllabus. (DDR)

This illustrated book examines everything having to do with the square. It begins with a basic definition of the square and continues by giving some examples of squares and other interesting historical information. Some ideas addressed include why cities are laid out in square blocks, how buildings are designed from squares and cubes, and how prisms and antiprisms can be used in experiments. Fun activities such as brain-teasers, square mazes, and how to blow a cube-shaped bubble are offered. Additional topics include folding a square, drawing a square, calculating the area of a square, square multiplication, squaring off, square numbers, and constructing cuboctahedrons. (AIM)

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)

Presents an extension of Pick's theorem for simple closed polygonal regions to unions of simple closed polygonal regions. Students are guided to discover Pick's theorem from sets of data including numbers of boundary points and numbers of interior points. (Author/MKR)

Explores areas of polygons by comparing polygon area to the area of the associated midpoint polygon, formed by joining the midpoints of consecutive sides. Considers triangles, quadrilaterals, pentagons, and regular polygons using paper folding, drawings on graph paper, and plexiglass MIRA constructions. (Contains 12 references.) (MKR)

Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book about Logo, but about mathematics and thinking mathematically. Many chapters require no Logo skills. Each chapter may include as many as seven sections: summary box, getting started, instructions, examples, activities, key summary, and worksheets and includes appropriate grade-level designations. The chapters in this book are: (1) DeDot Designer, (2) Spirolatera Designs, (3) Digital Root Patterns, (4) GCF and Line Designs, (5) Two Frogs and a Frisbee, (6) Repeating Decimals, (7) Super Wriggly Worms, and (8) Superpoly. Appendices include a summary of LogoWriter keys (Apple IIe/IIc, IBM, and Macintosh), a quick reference (LogoWriter Primitives and Special Words), and additional primitives for the Macintosh. (MKR)

Describes a lesson plan using a chambered nautilus to connect geometry and poetry which can be easily adapted to a wide range of levels. (YDS)

Presents activities to demonstrate some of the properties and relationships among the Platonic polyhedra. (ASK)

Discusses some questions connected with Cauchy's theorem which states that two convex closed polyhedral surfaces whose corresponding faces are congruent and whose faces adjoin each other in the same way are congruent. Describes how to construct a flexible polyhedron. (ASK)

Describes an activity designed to connect geometry with real life for seventh grade students. This activity centers on an elementary investigation of the rigidity characteristics of triangles. Students also discuss the similarities and differences of polygons. (ASK)

Describes a third-grade class's discoveries when students were asked to develop a method to find the area of a trapezoid on the basis of their prior work with finding the area of rectangles. (ASK)

Presents small group activities and materials to emphasize geometric properties and definitions. Activities are designed to encourage student reasoning, communication, and measurement. (ASK)

Offers a problem for teachers to try with their students. The problem is presented visually as a row of 15 connected squares and the task is to determine the number of rectangles. The goal is to encourage teachers to reflect on students' work and analyze classroom dialogue. (PVD)