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The neural substrates of children's reading and arithmetic skills have long been of great interest to cognitive neuroscientists. However, most previous studies have focused on the contrast between these skills as specific domains. Here, we investigate the potentially shared processes across these domains by focusing on how the neural circuits associated with cognitive control influence reading and arithmetic proficiency in 8-to-10-year-old children. Using a task-free resting state approach, we correlated the intrinsic functional connectivity of the right anterior insula (rAI) network with performance on assessments of Chinese character recognition, reading comprehension, subtraction, and multiplication performance. A common rAI network strengthened for reading and arithmetic skill, including the right middle temporal gyrus (MTG) and superior temporal gyrus (STG) in the lateral temporal cortex, as well as the inferior frontal gyrus (IFG). In addition, performance measures evidenced rAI network specializations. Single character recognition was uniquely associated with connectivity to the right superior parietal lobule (SPL). Reading comprehension only, rather than character recognition, was associated with connectivity to the right IFG, MTG and angular gyrus (AG). Furthermore, subtraction was associated with connectivity to premotor cortex whereas multiplication was associated with the supramarginal gyrus. Only reading comprehension and multiplication were associated with hyper connectivity within local rAI network. These results indicate that during a critical period for children's acquisition of reading and arithmetic, these skills are supported by both intra-network synchronization and inter-network connectivity of rAI circuits. Domain-general intrinsic insular connectivity at rest contained also, functional components that segregated into different sets of skill-related networks. The embedded components of cognitive control may be essential to understanding the interplay of multiple functional circuits necessary to more fully characterize cognitive skill acquisition. [ABSTRACT FROM AUTHOR]