Schemas are knowledge structures that can enable rapid learning. Rodent one-shot learning in a multiple paired association navigation task has been postulated to be schema-dependent. We still only poorly understand how schemas, conceptualized at Marr's computational level, are neurally implemented. Moreover, a biologically plausible computational model of the rodent learning has not been demonstrated. Accordingly, we here compose an agent from schemas with biologically plausible neural implementations. The agent gradually learns a metric representation of its environment using a path integration temporal difference error, allowing it to localize in any environment. Additionally, the agent contains an associative memory that can stably form numerous one-shot associations between sensory cues and goal coordinates, implemented with a feedforward layer or a reservoir of recurrently connected neurons whose plastic output weights are governed by a 4-factor reward-modulated Exploratory Hebbian (EH) rule. A third network performs vector subtraction between the agent's current and goal location to decide the direction of movement. We further show that schemas supplemented by an actor-critic allows the agent to succeed even if an obstacle prevents direct heading, and that temporal-difference learning of a working memory gating mechanism enables one-shot learning despite distractors. Our agent recapitulates learning behavior observed in experiments and provides testable predictions that can be probed in future experiments.