Human childhood is characterized by dramatic changes in the mind and brain. However, little is known about the large-scale intrinsic cortical network changes that occur during childhood due to methodological challenges in scanning young children. Here, we overcome this barrier by using sophisticated acquisition and analysis tools to investigate functional network development in children between the ages of 4 and 10 years (n = 92). At multiple spatial scales, age is positively associated with brain network segregation. At the system level, age was associated with segregation of systems involved in attention from those involved in abstract cognition, and with integration among attentional and perceptual systems. Associations between age and functional connectivity are most pronounced in visual and medial prefrontal cortex, the two ends of a gradient from perceptual, externally oriented cortex to abstract, internally oriented cortex. These findings suggest that both ends of the sensory-association gradient may develop early, in contrast to the classical theories that cortical maturation proceeds from back to front, with sensory areas developing first and association areas developing last. More mature patterns of brain network architecture, controlling for age, were associated with better visuospatial reasoning abilities. Our results suggest that as cortical architecture becomes more specialized, children become more able to reason about the world and their place in it.