The use of innovative approaches capable of stimulating students’ curiosity and that allow them to acquire new skills and competences through experimentation is of great importance in primary and secondary school. Among these approaches, Integrative STEAM should be mentioned. As is well-known this approach seeks to offer students an integrated learning of Science, Technology, Engineering, Art and Mathematics through the resolution of real problems. In this sense, pedagogical kits based on STEAM are aimed to help in the interdisciplinary learning process of all of these areas, developing solid and deep learning which may be later applicable to real life situations. In recent years, a series of mechatronics-based learning kits have appeared on the market. These kits propose the use of project-based learning related to everyday problems but, in general, there are not accompanied with useful didactical material that may favour a learning process more motivating, relevant, collaborative, and engaging for today's students and their varied learning styles. In this work we show a new kit with a notebook of activities for the learning of basic physical and technological concepts related to dynamics, cinematics and simple machines. The proposal for the students is the design, fabrication and automation of an elevator as well as its programming, so that it can accomplish a set of operations. With this case study we want for the students to acquire knowledge in these subjects and to develop a series of skills that allow the having an approach to design in engineering.