Worksheets designed to help students explore factoring integers are presented. (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)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

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)

The use of a ruler with two parallel Straight edges as a tool in geometric constructions is presented, based on ideas that are fairly standard in high school geometry courses. The constructions are seen as potential challenges that provide opportunities for inventiveness by students. (MP)

Activities for calculating experimental and theoretical probabilities are presented. Worksheets designed for duplication for classroom use are provided. Suggestions are given for additional problems that could be generated from the original simulation, and answers to questions on the worksheets are included. The activities simulate parachute…

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

The Concept Game, which focuses on the attributes of parity, balance, majority, closure, and skip of seven-digit binary numbers, is described. Originally written as a computer program, the game is modified so that pupils can play with construction paper chips of just paper and pencil. (MP)

This article describes "Math Their Way" techniques for experiential learning of math concepts by deaf children. Finding, comparing, and creating patterns are emphasized at conceptual, connecting, and symbolic levels. Graphing, counting, and measuring exercises are described, as well as ways to steer free time and exploratory learning toward math…

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

A problem that is seen to allow room for student discovery and exploration is detailed. A discussion starts with an examination of the generation of a general equation for the sum of a set of consecutive integers, and leads to an exploration of more complex sums. (MP)

The unmarked protractor appears to have been ignored in considerations of construction tools other than the standard straightedge and compass. Some geometric problems are presented which are designed to be done using only the unmarked protractor. They are thought to provide challenges to better students. (MP)