We determined the relative importance of the so-called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short-term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero-order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non-significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short-term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school-age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development.