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Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed is the resource role of the mathematics specialist in diagnosing individual student needs and in planning a program to build sequential understandings and skills. Listed are mathematical facts and concepts (for sets and subsets, numbers and numeration, operations, mathematical sentences, measurement, graphs, and geometric figures) followed by suggested teaching activities such as using graph paper to diagram multiplication facts and using both a yardstick and a meter stick to measure student height. Suggested are games and experiences to help children discover and test mathematical generalizations. Recommended instructional approaches include using magic squares to develop computational skills, adapting the seminar teaching/learning style to encourage higher intellectual skills, and the discovery of alternate problem-solving methods to develop creativity. Noted is the relationship of mathematics to other subjects such as science, geography, and music and the need for coordination between mathematics specialists and teachers of gifted children at the elementary and junior high school levels. (LH)