This study examined the extent to which children's cognitive abilities in kindergarten and their mothers' education predict their single-digit and procedural calculation skills and the covariance of these with reading skill in Grade 4. In kindergarten, we assessed children's (N=178) basic number skills, linguistic skills, and visual attention. In Grade 4, we assessed their calculation and reading skills. Data on children's cognitive ability at 5 years of age and their mothers' level of education were also collected. The results showed that both of the core components of calculation, single-digit and procedural calculation, as well as their covariance with reading, were predicted by unique cognitive factors. Fluency in single-digit calculation and text reading shared an underlying cognitive process, that is, the ability to fluently retrieve verbal or visual-verbal associations from long-term memory. In contrast, procedural calculation was predicted not only by single-digit calculation but also by mother's education and conceptual knowledge of numbers. Overall, the results suggest that a multicomponential approach, including a hierarchical relation among various components, is fruitful when trying to understand the development of mathematical skill and its covariation with reading.