In this paper, we outline a perspective on participatory designs for computational play as a social and material activity, beyond an understanding of computational activities as an individual “thinking” endeavor. The overall aim of this study is to explore how a participatory design approach including traditional and digital resources trigger children’s computational play. By this, our intention is to contribute to the contemporary debate on the increased use of computational thinking related activities in early childhood education and their potentials for play and learning. Framed by a perspective considering traditional and digital resources as access points to play and learning, the empirical study involves 50 children from 2nd grade, aged 8–9 years from two different primary schools in northern Denmark. The outcomes demonstrates that computational play has the potential to reconfigure learning activities by providing new, previously unthinkable, activities that can support children in early childhood education and their development of computational literacy. At the same time, the analyses show that computational play requires new ways to be scaffolded to not counteract children’s independent experimentation, testing, and creativity. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.