This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early mathematics school achievement. The influence of socioeconomic status and number naming speed, assessed in kindergarten, became especially important at the end of Grade 4. Particularly, a subgroup of mathematically low-achieving children in Grade 4 had already performed more poorly than normal children in tasks assessing preschool QNC, number naming speed, and basic arithmetic fact retrieval, as well as nonverbal intelligence and socioeconomic status. (Contains 4 tables and 3 figures.)