The modern multidimensionally transforming world poses the challenges of a new reality, while the presence of a certain cultural universal, based on the formation of socio-psychological, the so-called “soft skills”, is of particular importance. Mathematics, as a tool for systematic knowledge of the world and critical analysis of objective reality, plays a particularly important role in education, and its potential as a school discipline can be used for the formation and evaluation of such "soft" skills as critical thinking; creativity; communication, coordination and cooperation; empathy, emotional intelligence. The purpose of the article is to design a model for the formation and evaluation of “soft skills” based on open practice-oriented tasks and to present the experience of its implementation in teaching mathematics. We distinguish the following features of open practice-oriented tasks: setting the task outside of mathematics, in real reality, and the possibility of solving it by mathematical means; the lack of a rational condition for achieving a practical goal and its search by creative methods (the method of personal empathy, the method of brainstorming, the method of discussion); the use of the mathematical modeling method in the solution; the use of the group work method and the reflection method. Such a task will allow the teacher to work in several directions: the consistency of the educational space with the challenges of modern reality; co-creation, cooperation, cooperation; involvement in creative, research activities; readiness to solve life problems, production tasks and business tasks. The designed model details the activities of the student and teacher at each stage of the task, specifying the methods and forms of work, as well as the structure and content of the “soft skills” being formed. In addition, the model provides for monitoring the dynamics of development and the procedure for evaluating these skills. In order to test the effectiveness of the designed model, a pilot experiment was conducted among students of the ninth grade in the number of twenty people, and the binomial criterion was used to evaluate its results. It is concluded that the designed model is a fairly effective tool for the development and improvement of “soft skills” in teaching mathematics; it can be used as a tool for measuring the levels of development of “soft skills”, but it is necessary to take into account the fact that teacher assessments are used as a method of measurement, so it is desirable to use additional assessment procedures, such as computer testing.