Study of circular transformation and its associated properties is proposed as review and reinforcement of familiar concepts and for developing broader understanding of transformations. Inversion on a circle is discussed in some detail. (MNS)

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)

An approach to problem solving is described that is based on analysis of how fast model race cars can go. The exercises were used to replace standard time/rate/distance exercises, and were found to be greatly enjoyed by both girls and boys. (MP)

Several mathematical problems designed to provide motivation for the application of mathematics to practical situations in sports and industry are presented. (MP)

Problem-solving activities of one form or another are encouraged at all times, with problem-solving lessons recommended at least every 10 to 12 days throughout the year. A number of ways to carry out such a heavy schedule are outlined. (MP)

An approach to problem solving broader than the traditional one most often used by instructors is described and recommended. Implementation of these ideas has the potential of increasing problem solving ability of students while promoting a fuller appreciation of the value of the process. (MP)

An activity designed as an opening-day lesson for a mathematics class is discussed. In practice, the activity is viewed as partly responsible for improving student and teacher rapport. The information gathered can be used in a variety of mathematical investigations, and suggestions for extensions are made. (MP)

The material is designed for pupil practice in: (1) associating numerals with sets of objects and finding sums of two or three numbers; (2) subtracting, one- and two-digit numbers with some regrouping; (3) mental computation using the basic operations; and (4) using combinations of basic operations with whole numbers and decimals. (MP)

A dialog shows how student-teacher interaction on problems can help students learn. Fifty sample problems are provided as starting points for class discussions from grade three through college. Six purposes such problems can serve are identified. A method of classroom presentation, the mathematical scavenger hunt, is discussed. (MP)

Books published recently that are considered fun, colorful, easy-to-read, and have variety and activities for students from grades three to eight are listed. The examples and ideas are only a few that are possible. A fair is suggested for the social interaction and excitement that can be created. (MP)

A class activity is detailed in which alternative designs for glasses are examined. The goal is to design a glass which is built tilted, so that beer can be poured in without creating a foam problem. The activity is viewed as one leading to interesting questions. (MP)

This section focuses on finding two-dimensional geometric shapes in designs and three-dimensional objects. The material is presented on worksheets designed for duplication for classroom use. (MP)

A plan used successfully in the classroom to introduce pupils in grades one through six to calculators is outlined. It comprises a sequence of activities designed to help teachers have a good start when they take the first steps introducing calculators to students. (MP)

Students were encouraged to explore the concept of one million. A short pretest revealed many pupils could not easily comprehend a million. Research and practical investigations began to find "a million things." All students were reported to come through these experiences with a much better understanding. (MP)

Suggested are sight word activities which will help students recognize both language and mathematical symbols in reading materials. Activities described include context clues, structural analysis, phonic cues, and dictionary skills. (DS)