It is not currently possible to measure the real-world thought process that a child has while observing an actual school lesson. However, if it could be done, children's neural processes would presumably be predictive of what they know. Such neural measures would shed new light on children's real-world thought. Toward that goal, this study examines neural processes that are evoked naturalistically, during educational television viewing. Children and adults all watched the same Sesame Street video during functional magnetic resonance imaging (fMRI). Whole-brain intersubject correlations between the neural timeseries from each child and a group of adults were used to derive maps of "neural maturity" for children. Neural maturity in the intraparietal sulcus (IPS), a region with a known role in basic numerical cognition, predicted children's formal mathematics abilities. In contrast, neural maturity in Broca's area correlated with children's verbal abilities, consistent with prior language research. Our data show that children's neural responses while watching complex real-world stimuli predict their cognitive abilities in a content-specific manner. This more ecologically natural paradigm, combined with the novel measure of "neural maturity," provides a new method for studying real-world mathematics development in the brain.