Material from Mesopotamian scribal schools provides a full description of metrological and numerical systems used in Old-Babylonian period. These documents, when closely observed, reveal the efforts made by ancient scholars in order to shape metrological and numerical systems more and more regular, unified and coherent, and to define different sorts of numbers according to their use (quantifying or computing). They reveal also how these systems were developed in relation with specific techniques for computing surfaces and volumes. These strongly standardized systems were widely used in mathematical texts, as well as, to a large extend, in administrative and commercial texts. However, the coherent system for quantifying and computing magnitudes developed in southern scribal schools was unevenly disseminated in different milieus, or different regions. In the first part of this paper, I describe some aspects of the standardization process. In the second part, I show how mathematical practices with abstract numbers and measures in some southern Mesopotamia schools may break the framework inherited from elementary education.