(en) The article is dedicated to the definition of methodological conditions under which the use of the solution and research of the “task series” generated by a given task topic will acquire methodological expediency in the context of developing students' abilities to solve mathematical tasks of a productive nature. The authors suggested a possible way to solve it through the synthesis of integrated knowledge and the formation of the integrated images of the task topics that allowed students to develop knowledge and skills of integrative mathematical activity.