The Programme for International Student Assessment (PISA) has proved that in Germany the impact that socio-economic background has on 15-year-old pupils' achievement is stronger than in other countries. The Progress in International Reading Literacy Study (PIRLS) showed that the correlation is less with 10-year-old children, but is still apparent. Subsequently it was demanded that the early and individual education of all children in nursery schools be improved. Curricula for young children were published, including mathematics as a domain of learning skills. Mathematics is a domain which is influenced by cultural differences less strongly than, e.g., language. The study reported here investigated the mathematical competences of 340 nursery school children from Berlin (Germany) in their final year before their enrolment in elementary school. Moreover, the parents were questioned about the social-economic background of the children. The connection between children's achievements and external conditions is described by a framework model, which we adapted from PIRLS. Mathematical competences are described by a developmental psychological model by Ricken and Fritz. Does socio-economic diversity have an impact on mathematical competences already in early childhood? To answer this question, t-tests, variance analysis (ANOVA), correlations, and a structural equation model were calculated. The most important results of the investigation are that the nursery school children from working-class families and children with deficits in language skills have significantly lower competences in mathematics. Moreover, a correlation with the birth order could be proved. (Contains 8 tables and 2 figures.)