The California Department of Education (CDE) has put forth the following requirements for elementary school children. As per § 51210, the adopted course of study for grades 1 to 6, inclusive, shall include instruction, beginning in grade 1 and continuing through grade 6, in the following areas of study:
English
Including the knowledge of, and appreciation for literature and the language, as well as the skills of speaking, reading, listening, spelling, handwriting, and composition.
Mathematics
Including concepts, operational skills, and problem solving.
Social Sciences
Drawing upon the disciplines of anthropology, economics, geography, history, political science, psychology, and sociology, designed to fit the maturity of the pupils. Instruction shall provide a foundation for understanding the history, resources, development, and government of California and the United States of America; the development of the American economic system including the role of the entrepreneur and labor; the relations of persons to their human and natural environment; eastern and western cultures and civilizations; contemporary issues; and the wise use of natural resources.
Science
Including the biological and physical aspects, with emphasis on the processes of experimental inquiry and on the place of humans in ecological systems.
Visual and Performing Arts
Including instruction in the subjects of dance, music, theatre, and visual arts, aimed at the development of aesthetic appreciation and the skills of creative expression.
Health
Including instruction in the principles and practices of individual, family, and community health.
Physical Education
With emphasis upon the physical activities for the pupils that may be conducive to health and vigor of body and mind.
Drug Education
Instruction shall be given in the elementary and secondary schools on drug education and the effects of the use of tobacco, alcohol, narcotics, dangerous drugs, and other dangerous substances. (§ 51260)
The complete California Education Code (CEC) can be found online.