Game based Learning (GBL) has been promoted as a way to enhance science, technology, engineering and mathematics education, in several aspects. In this paper we aim at conceptualizing the creative, embodied and immersive potentials in the context of teaching geometry in primary school. We review two cases where the concept of "game" is related to the development of pupils' creativity and innovation skills. One intervention is inviting pupils to become designers at a "game factory", by using the digital mathematics tool GeoGebra. The second intervention uses mobile technology to have students participate in a collaborative game requiring them to take part in an embodied activity outside the classroom. In the paper we develop a model that view game based creative learning in as a combination of constructive, immersive, and reflective aspects. We do that by considering different meanings of the word "game" in a mathematics education context. That is game as a medium, game as a framing of educational processes, and games as an object. Considering games as media highlights the similarities with texts and any other means of delivering content. We can ask what message a specific game conveys, and discuss how well suited the game is compared to other mediations of the same content. Games can be described a as "semiotic domains" that allow players to interact with knowledge and make sense of the world (Gee, 2003). Games can act as a framing used to govern and plan educational processes, either as direct motivational driver, aiming at engaging more students in certain planned activities (Hamari, Koivisto, & Sarsa, 2014), or as an established form of process control in which complex situations can be played out. In a game the player act according to rules and the process has a natural direction towards finishing or advancing in the game. Furthermore games can frame educational processes by challenge the learners perspective through narratives and role-playing (Shaffer, 2006). Pupils creative design competencies and motivation to create and develop games have been documented as unusually relevant and high (Kafai, 1995; Tekinbas, Gresalfi, Peppler, & Santo, 2014). Mathematical thinking s can be used to think game scenarios through, to govern the competitive aspects of a game and ensure that the gameplay is fair and balanced in terms of the involved struggle. Game literacy, both in terms of playing, producing and discussing games, does thus relate to mathematical literacy and knowledge.