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Modeling a structured, dynamic environment like a video game requires keeping track of the objects and their states declarative knowledge) as well as predicting how objects behave (procedural knowledge). Black-box models with a monolithic hidden state often fail to apply procedural knowledge consistently and uniformly, i.e., they lack systematicity. For example, in a video game, correct prediction of one enemy's trajectory does not ensure correct prediction of another's. We address this issue via an architecture that factorizes declarative and procedural knowledge and that imposes modularity within each form of knowledge. The architecture consists of active modules called object files that maintain the state of a single object and invoke passive external knowledge sources called schemata that prescribe state updates. To use a video game as an illustration, two enemies of the same type will share schemata but will have separate object files to encode their distinct state (e.g., health, position). We propose to use attention to determine which object files to update, the selection of schemata, and the propagation of information between object files. The resulting architecture is a drop-in replacement conforming to the same input-output interface as normal recurrent networks (e.g., LSTM, GRU) yet achieves substantially better generalization on environments that have multiple object tokens of the same type, including a challenging intuitive physics benchmark.