The problem that the research is aimed at is caused by the need to resolve the contradiction between the public demand for the quality of training the future digital school teacher regarding the formation of information culture, creativity, communication skills, the ability to work in a team, readiness for change, and the insufficiently developed methodological base for training graduates that meet these requirements. The purpose of the study is to theoretically substantiate and experimentally test the need to involve students of pedagogical specialties in practical activities to design a system of specially selected tasks as an important condition for training future digital school tutors. The methodology of the research is the analysis and generalization of scientific works on the organization of cognitive activity of students of pedagogical specialties. Learning.apps, interactive worksheets, cloud services, Learnis, etc. are used as software tools for the design of practice results. The results of the study. The types of tasks (situational and motivational; reference; borderline) are identified. The development in the direction of intensification and extension is proposed for the system of tasks. The features of organizing practice and the methodological component are described on the example of studying topics of the theory and methodology of teaching computer science. The conclusion gives findings confirming that involving students in practical activities to develop a system of their own tasks really contribute to the formation of professional competencies of future digital school tutors.