First-year engineering students often complain about their mathematics courses as the significance of the difficult and abstract calculus to their field of study remains unclear. We report on the project "MathePraxis", a feasibility study which was designed as a means to give first-year students some impression about the use of mathematics in real practice. We aim to increase the motivation and retention rates among engineering students by connecting the contents of the first-year mathematics lectures with practical applications. We developed three projects, two of which are described in this article: an inverted pendulum considered as a model for the automated control within a Segway and a study on the optimal design of a ribbed cooler. In this article, we briefly present the mathematical content of the projects and report on their implementation. (Contains 3 boxes, 1 table, and 2 figures.)