The aim of the article is to describe the organization of training activities in the man-made environment wherein the problems of didactics with pedagogical, psychological, engineering methods are solved. Methods are based on the system-based analysis of engineering activities, on the models of L. S. Vygotsky’s «zone of proximal development», «developmental education» by L. N. Zankov; the application of pedagogical and psychological patternsand taxonomic methods, didactic engineering, theory of probability and mathematical statistics.Results. The model of training of engineers is constructed in the metric competence-based format, which provides a rapid development of the project and constructive student abilities of students based on their knowledge. The parametersdefining the success of engineering activity are found out. The didactic system with the technology of rapid development of a future engineer is designed.Scientific novelty. The functional model of an engineer is proposed. The parametersfor determining the success probability of an engineer are defined; the scale for quality evaluation of competence acquisition is designed; the model of learning in the metric competence-based format is developed; the methods for assessing the complexity of the tests and training courses are proposed.Practical significance. The textbook «Economic and Mathematical Models in Management» for the training of IT-engineers in the metric competence-based formatis developed. The textbook is introduced into an educational process and implementedin the web-network (www.myknitu.ru).