This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (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)

Activities designed to lead pupils through the process of using the basic measuring and drawing devices of geometry are presented and move to the discovery of several surprising generalizations about arbitrary triangles. (MP)

The approach is to fill positions in a star shape with values from a set so that the sum of each line is equal to the sum of every other line. There are four values in each of five lines. Related problems based on other shapes are noted. (MP)

The material is designed to help students build a cone model, visualize how its dimensions change as its shape changes, estimate maximum volume position, and develop problem-solving skills. Worksheets designed for duplication for classroom use are included. Part of the activity involves student analysis of a BASIC program. (MP)

The problem involves randomly breaking a stick into three pieces and using the pieces to form a triangle. The probability of getting a triangle is calculated using four different solution methods. Two unique problem interpretations are noted, and one solution method involves a BASIC program. (MP)

The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)

Rubik's Cube is viewed as a tool to generate student interest in applying rather sophisticated mathematics to generate some solution algorithms. Discussion begins with the creation of a notation method for the cube and develops into applications of permutations and set concepts. A special "cycle notation" is employed. (MP)

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

Calculators are used to compute tables of values in solving problems of maximizing areas. Reproducable worksheets are included. (MP)

This course is designed to review the arithmetic skills used by many Marines in the daily pursuance of their duties. It consists of six study units: (1) number systems and operations; (2) fractions and percents; (3) introduction to algebra; (4) units of measurement (considering both the metric and United States systems); (5) geometric forms; and…

A set of activities designed to help students discover properties about order-3 spirolaterals on square grid paper is presented. The materials are prepared on worksheets designed for easy duplication. The lessons can lead to investigations involving spirolaterals of many other orders and shapes. (MP)

A class of seldom-seen real-world applications of high school mathematics is described. The problems considered are viewed as more substantial than ordinary word problems and thus are thought to require a greater commitment of time and energy. Suggestions for student extensions of the project are made. (MP)

Some methods of proof of traditional algebra problems using geometric methods are explored. The techniques used come from the original Greek approaches to these mathematical questions. (MP)