In urban design mapping is a generative tool that can evoke site conditions and animate design potentials. James Corner has stated that a “map is already a project in the making” (1999b, p.216), and thereby points to the evocative ‘agency’ of mapping in composing a design project. This paper takes Corner’s essay as its starting point. It couples his considerations with non-representational research to elaborate mapping as a ‘more-than-representational’ tool with which to think and work when we seek to understand and evoke design sites in conjunction with the lived world. This coupling is done through a concrete mapping study of a suburban site of lived mobilities and mundane architectures. From this standpoint the paper elaborates three central attentions of mapping as a creative and reflected more-than-representational tool in urban design: the evocations of eventfulness of sites, intricate relations between lived lives and architecture, and the potential yet-to-be of sites.