Abstract
In close articulation with Christine Chambris' course, this text presents three complementary studies in the field of the teaching-learning of numbers and arithmetic at school. The first deals with the difficulties encountered in the implementation of a project to teach a technique of subtractive calculation by truncation and the reasons for these difficulties, in relation to the technology of this technique concerning the numeration and the units of this domain. The second is an analysis of the implementation of a teaching project that aims to articulate numeration and the metric system by introducing a mixed table of numeration and conversion. The third study, which is more prospective in nature, deals with poorly highlighted knowledge involved in the teaching or learning of multiplication. These three studies reveal the importance of a common object: relative units. In each of the studies, the potentialities of these units are studied, from both praxeological and ecological points of view, as well as the conditions in which these relative units actually live in the institution.