This paper demonstrates the application of STEM technologies using the example of the problem of a thread with a load. As a training problem, parameter finding of a flexible inextensible thread with a load sliding along it, as well as with a fixed load, is considered. A mathematical model of a thread with a load is created without using simplifying assumptions such as a negligibly small mass of the thread, a thread with a small sag or a parabolic approximation of the thread form. When solving the problem, methods of analysis from various branches of mathematics, theoretical mechanics, physics, history of mathematics, as well as various tools of computer mathematical packages (Mathcad), are used. The reasonability of considering such tasks from the perspective of teaching effectiveness for first-year students in engineering as well as in physics and mathematics is proved. Promising educational tasks based on the investigated problem are considered.