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Nowadays, students are digital natives, and they live immersed in technology: however, they use it in a mostly superficial way. Therefore, it is important to educate them to use the technological tools that they have available for educational purposes already from the primary school, both at school and in extra-curricular contexts. Moreover, the digital competence has been included by the European Union among the eight key competences for lifelong learning. This demonstrates that educational institutions should play a fundamental role in this field from the early school years. In this paper, we present the design and the implementation of a vertical path for all five years of primary school within a Digital Learning Environment in the context of Space and Shapes. The goal of the path is to promote the skills development in the Space and Shapes area in a vertical perspective through the methodologies of problem solving and automatic formative assessment. The path was implemented on a Digital Learning Environment, integrated with an Advanced Computing Environment and an Automatic Assessment System suitable for STEM. The path consists in five sections from grade 1 to 5; they are dedicated respectively to plane shapes, solid shapes, perimeter, area, and volume. Each section includes a contextualized problem and one or more questions for the formative assessment. For the planning of the vertical path, reference was made especially to the Italian National Indications and the "INVALSI" (the Italian institute which annually administers standardized learning tests to evaluate the school system) test archive was consulted. Initially, this paper shows the theoretical framework to which reference was made during the design of the vertical path. In particular, we present the theory of the development of geometric thought conceived by Dina and Pierre Van Hiele between 1957 and 1986 and the methodologies of problem solving and automatic formative assessment. Then, the design of the path in a vertical perspective is presented, and the resources used during the design phase are shown. Finally, the implementation of a section of the path is shown as a representative example, and the expected results of a possible experimentation are discussed. [ABSTRACT FROM AUTHOR]