Contributions of domain-general and domain-specific numerical competencies were assessed on first graders’ number combination skill (NC) and word-problem skill (WP). Students (n = 205) between 5 and 7 years of age were assessed on 2 aspects of numerosity, 8 domain-general abilities, NC, and WP. Both aspects of numerosity predicted NC when controlling for domain-general abilities, but domain-general abilities did not account for significant additional variance. By contrast, when controlling for domain-general abilities in predicting WP, only precise representation of small quantities was uniquely predictive, and domain-general measures accounted for significant additional variance; central executive component of working memory and concept formation were uniquely predictive. Results suggest that development of NC and WP depends on different constellations of numerical versus more general cognitive abilities.