A study of activities in mental computation and in paper and pencil enrichment activities for sixth graders showed that both treatments produced increases in achievement test scores. Examples of both types of activities used are included. (DT)

This column discusses problems involving a paper folding game for bicimals, the sum of exterior angles of polygons and polyhedra, solving quadratic equations in finite arithmetics, nomograms, and cube folding patterns. (DT)

A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

The material presented is designed to help students explore geometric patterns involving Fibonnaci numbers and the golden ratio, and to aid in review of basic geometry skills. Worksheet masters intended for duplication are provided. Suggestions are made of possible classroom extensions to the initial activities. (MP)

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)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

A Norman window consists of a semi-circular section mounted surmounting a rectangular section. Modifications to a simple problem are presented that assume parts of the window are made with stained glass. The goal is to maximize the level of light transmission with a fixed perimeter. (MP)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

The Mayan system of numeration, which used 20 as the base, is discussed. The material presented has been used to stir the curiosity of students in different systems of numeration. It has been helpful in promoting a speedier and better understanding of base 10. (MP)

The focus is on graphing activities, in which students locate points on a coordinate system and name points by an ordered pair of numbers. Worksheet masters designed for duplication for classroom use are included. Practice is provided with coordinate grids, and student exploration is promoted within the materials. (MP)

The nature of the corner reflector array left on the moon by the July 1969 Apollo astronauts is described. The array was used to reflect earth-originating laser beams back to earth, and yielded a more accurate determination (to within six inches) of distance from the earth to the moon. (MP)