While the path to mathematical discovery is often intuitive and not simply reducible to the application of a method, neither is it in most cases entirely haphazard. Certain kinds of questions and certain ways of looking at things tend to produce new and interesting results. To illustrate, this paper tells a story of how someone might discover…

A suitable way for teachers to present science content and foster creativity in less academically inclined students is by getting them to engage in design-based science activities and guiding them along the way. This study illustrates how a design-and-make activity was carried out with the aim of getting students to showcase their creativity while…

Explains a discovery activity using the possible positions of the faces of a cube when represented in two dimensions. Suggests rules which would determine which of the edges would connect if the drawing were folded to form the cube. (RS)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)

Five exploratory activities arising from work by sixth-grade students are described. They concern geometric ideas and number concepts, including fractions. Illustrations are included. (MNS)

The game "Pythagoras" is an adaptation of the tangram puzzle. Describes the process of finding all the possible convex polygons with seven sides to prove that the solution to a given puzzle shape of seven sides difficult to find was not possible. (MDH)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)

Presents activities that utilize representations of the side, front, and top views of three-dimensional configurations of blocks to develop spatial-visualization skills and aspects of the concept of function. Provides worksheets of these open-ended investigations. (MDH)

N:4$2 N:4$N Reported are results of a Technical Education Research Centers (TERC) project describing telecommunication interactions between groups of students using the computer software unit "Connectany." Polygons are formed through repetitive "jumps" between points on a circle. Investigation questions and results are shared…

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

Describes activities that use the geometric construction capabilities of the Geometer's Sketchpad computer software to explore triangles. Topics investigated include angle measurement, the sum of the measures of the angles of a triangle and a five-pointed star, triangle classification, and area and perimeter of a triangle. (MDH)