This article discusses the pedagogical features of the organization of students' project work when
teaching the elements of the theory of series at school. The content of the project work of students and guidelines for its
implementation in teaching mathematics in a secondary school are presented. The types of design work of students, tasks
and stages of their implementation are highlighted. Teaching elements of the theory of series by the design method is a
learning system that meets the requirements of the modern system of credit education and is able to meet the tasks set
from the point of view of modernity. The article defines the features of the concepts of "project method", "design method",
"use of the design method in the classroom" and teaching design technologies. limits for finding the sum of an arithmetic
progression. The application of the design method includes a complex of various methods that encourage students to
search and research, the design features of special design work (tasks) that put students in a problem situation, and the
possibility of getting out of this situation. Attention is paid to the development of students' abilities in the curriculum, with
project work. At the same time, project-based learning allows you to evaluate not only the preparatory process, but also
the final result of the work of students. This article presents project assignments that form the design and research
activities of students.