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Modeling is an essential and challenging activity in any engineering environment, and it requires some hard-to-train skills such as abstraction and communication. This makes it difficult for educators to teach or train their students, co-workers, or users. The audience of this paper is both educators and learners who struggle with modeling. To address this challenge, we present PapyGame, a gamified version of a robust modeling environment (Papyrus) that aims to improve the learner's motivation, make the learning process an enjoyable experience, and boost learning outcomes. Gamification is the exploitation of gaming mechanisms for serious purposes, such as promoting behavioral changes, soliciting participation and engagement in activities, and more. The paper presents PapyGame's functionalities, architectures, illustrative scenarios, and its potential impact on both educators and learners.