In Germany, there is increasing interest in language competences in mathematics lessons. Based on national curriculum standards, argumentation should also be strengthened in primary school mathematics classes (KMK, 2005). The reported interdisciplinary (linguistics and mathematics education) study on reasoning presents a model to rate arithmetic reasoning competences at primary level, in which mathematical reasoning and its linguistic realization are separately coded. In a pilot study, 243 third, fourth, and sixth grade students solved a number of arithmetic reasoning tasks. The results support a one-dimensional scale for the model of reasoning; its components identify differentiated requirements, which are formulated concretely in the coding guidelines and may point to didactical potential for language support in mathematical reasoning itself, as well as in mathematics lessons at primary level.