Presents techniques for involving low achievers with essential mathematics requiring more than computational facility. Demonstrated is the need for students to be able to relate to the subject matter of mathematics - its structure and pattern, and its power - and only then be concerned with the precision, the computational skills, and the rules…

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)

Describes an activity which introduces students to each other while introducing the concept of Cartesian coordinates. Also describes an activity for finding the least common multiple, and computer programs (with listings) for generating shapes resembling windowpanes and for determining amounts wagered in a golf game. (JN)

A simple way to introduce natural logarithms and e is presented. The standard approach is outlined, followed by the approach via differentiating the exponential functions that the student knows about. (MNS)

Several brief articles are included in this section. "Purple Puzzlers" are challenging problems for algebra students. "Linear Invaders" is a game to reinforce concepts of graphing lines. "The Diagonal Method" is used to prove that the real and natural numbers cannot be put into one-to-one correspondence. (MNS)

Ten examples of when the sequences of key presses given in calculator instruction booklets are either inefficient or lead to an incorrect answer are given. (MNS)

Work centered on open-ended problem solving was developed. Activities for students aged 14 focused on measurement of length are described, with problems on pygmies and giants. (MNS)

Several questions related to population and the use of resources are posed and discussed, with suggestions on how they might be used with students. (MNS)

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)