Understanding that different number notations – sets (•••), number words (/three/), and Arabic numerals (“3”) – represent the same number is important for math competence. It is proposed that learning the associations between notations may engage overlapping neuronal populations (mapping account). Although some studies observed such neurocognitive integration for set-numeral associations in adults, other studies did not, suggesting that the representations of different notations may become less integrated with experience and skill acquisition as symbols become used more flexibly (estrangement account). Critically, individual and developmental differences in how notations are integrated and their relation to math competence are unknown. We test the hypotheses that the mapping and estrangement accounts may both be valid, but in different age groups, and that the extent of integration may relate to math competency differently with age. In a target sample of 40 adults and 40 kindergarteners, participants will decide whether set-word, set-numeral and word-numeral pairs presented sequentially have the same meaning while being scanned using functional magnetic resonance imaging. We will first isolate regions that are selectively engaged by all three notations. For each participant and within each region-of-interest, neural activation patterns elicited by the same number in different notations will be correlated with one another (e.g., ••• with /three/, /three/ with “3”) to index cross-notation representational similarity (CN-RS). We then fit them with models representing full or partial integration. We predict (1) greater full CN-RS in kindergarteners than in adults, (2) positive relation between full CN-RS and math competence in kindergartners, but a negative relation in adults, and (3) integration involving number words (partial CN-RS) remains high in adults and is a critical mechanism for math competence regardless of age. The predicted outcomes will support an inverted-U developmental trajectory of notational integration and provide insights into how numeral knowledge can be supported in later grades. -- *Darren Yeo* *Graduate student, Numerical Brain LabPeabody College, Vanderbilt University* *http://jiansh.wix.com/darrenyeo <http://jiansh.wix.com/darrenyeo>* *Twitter: @darrenjyeo*