This study investigated the relative importance of three subdomains of early number competence (number, number relations, and number operations) in predicting later mathematics achievement in cross-sequential samples of pre-K, kindergarten (K), and first graders (N=150 at each grade). OLS-regression analyses showed that each subdomain predicted mathematics achievement at each grade level, controlling for the other two subdomains as well as background variables. All of the subdomains explained a significant amount of variance in later mathematics achievement. Unconditional quantile regression analyses examined relations between number competencies and mathematics achievement at quantiles representing low (0.2), intermediate (0.5) and high (0.8) achievement. The subdomain of number operations was highly related to mathematics achievement for high achievers. For low achievers, number and number relations abilities were most highly related to future mathematics achievement in the pre-K sample, and number relations abilities in the K and first grade samples. Findings highlight the unique importance of all three subdomains of early number competence for later mathematics achievement, but show some of the relations are contingent upon achievement level. [The paper will be published in "Journal of Experimental Child Psychology."]