The purpose of the article is to develop and to reveal the theoretical framework of the extracurricular activities for primary school (5th to 9th years) in the framework of the general cultural directions. The authors consider the conceptual provisions of the author's program of extracurricular activities on the formation of general cultural competence of students through the development of national culture, the assignment and accumulation of background cultural knowledge, including the case names of prominent figures of the Russian culture, in the process of reading through the educational project - the creation of a dictionary of cultural literacy. The methodological model that contains the basic categories of methodology of the Russian language (basic methodological approaches, principles, learning tools, leading techniques, interactive methods, realized in the exercises), constitute the theoretical basis of the extracurricular program. The content of concepts and methodological categories with the involvement of examples and exercises illustrating the algorithms of work on the project - "Dictionary of cultural literacy" is described. The developed model for the formation and development of general cultural competence of students provides teachers with an effective methodology for the organization of extracurricular activities in the primary school within the General cultural direction. The article is addressed to undergraduate and graduate students of philological faculties, teachers of various educational institutions engaged in the organization and conduct of extracurricular activities in the general cultural direction.