Previous research contrasting children and adults suggests that the development of numerical and arithmetic processing is characterized by decreased activation in prefrontal cortex and increased activation in parietal cortex. Yet, little is known about neurodevelopmental changes that occur within early childhood. In a well-matched group of 2nd (n = 45) and 3rd (n = 45) grade children, we examined behavioral and neurodevelopmental changes underlying arithmetic problem solving. 3rd graders were more accurate than 2nd graders in an fMRI task involving verification of simple and complex two-operand addition problems. In both 2nd and 3rd graders, arithmetic complexity was associated with increased responses in right inferior frontal and anterior insula, regions implicated in domain-general cognitive control and in the left intraparietal sulcus (IPS), a region important for numerical and arithmetic processing. Consistent with the proposed frontal to parietal shift in arithmetic activity, 3rd graders showed greater activity in the bilateral superior parietal lobule and bilateral IPS as well as visual stream areas including the bilateral lingual gyrus and the right lateral occipital cortex. Contrary to prediction, 3rd graders also showed greater activation in left dorsal lateral prefrontal cortex (dlPFC). Interestingly, 3rd graders also displayed greater functional connectivity between the left dlPFC and multiple dorsal and ventral visual stream areas, including the IPS and lingual gyrus. Examining a set of 23 adults (age 19-21) revealed that the adults had less activity in the dlPFC than both 2nd and 3rd graders, suggesting that the left dlPFC may come online and then decrease during development. Although children and adults had comparable activity in left IPS to 3rd graders, adults had significantly greater frontal to parietal connectivity than children. These results suggest that the narrow one-year interval spanning grades 2 and 3 is characterized by significant changes in brain response and connectivity, and argue that pooling data across wide age ranges and grades can miss important non-linear neurodevelopmental changes.