Some examples for investigating shapes in the environment are given. Circular objects, triangulation, symmetrical designs, and further investigations are listed. (MNS)

A square lattice is used to generate classroom activities, such as counting the number of squares in a lattice of a given size. (MP)

The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP)

This activity unit leads students to discover facts related to the maximum area enclosed by figures with given perimeters. Three worksheets are included. (MP)

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)

Using a geoboard to find polygons with given perimeters presents a problem which refines skills and provides an opportunity to inquire and discover. (MK)

Suggests discovery activities in spatial awareness for elementary math, utilizing home-made geometric shapes and soma cubes. (SJL)

A number of paper-folding activities are described. The activities illustrate geometric concepts, theorems, and construction techniques. (SD)

The algorithms for finding cube roots is approached by slicing a cube. (SD)

The properties of the cube are explored. A set of activities is given that forms the basis of a class project on discovery. (MNS)

An approach is presented that is based on modifying the standard axiomatic system found in high school geometry books. Such changes start with the introduction of a side-angle-side (SAS) postulate for similar triangles. It is shown how the new system can prove existence and uniqueness of parallel lines. (MP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

Activities used with seventh and eighth grade students in Western Australia are described. The instructor guides pupils towards experimental solutions and encourages discovery of solutions for similar and more general problems. Investigations include study and construction of polygons, polyhedra, and one and two-sided surfaces. Commercial kits are…

The activity described helps students develop facility in working with two-dimensional coordinate systems. Many students find the activity fascinating, so it can be used to motivate students to become involved in a number of explorations and to engender positive attitudes toward mathematics. (MP)