The relevance of this study is determined by the problem of developing various methods and techniques of analytic and synthetic activity with the aim of finding solutions to problems that involve the use of analysis and synthesis processes. Analytic and synthetic activity plays an important role in the process of cognition. The purpose of the study is to single out types of work aimed at forming analytic and synthetic activity skills in teaching the algebra course. The results of the study: the skills included in the analytic and synthetic activity are distinguished: to dismember the whole into its component parts; to establish relationships between parts of the whole (to distinguish the general and the different, the known and the unknown, the essential and the nonessential); to make up the whole from the parts, a new object from the individual elements; to draw up an action plan for solving the problem (task); to find errors and explain their reasons. Appropriate content-related components are revealed which are required for working with concepts, theorems, and tasks, and should be used to form analytic and synthetic activity skills in schoolchildren when studying algebra. The significance of the study: the materials of the article can be useful for heads of educational structures at various levels, school teachers, gymnasiums, lyceums, and parents.