This article shows conditions for how an educational digital tool can open doors to an increasingly playful world -- and address some of the issues with introducing digital maths in early childhood education. Guided by a design-based research approach, the multimodal design of the educational app-based game DigiMat was iteratively created by a multidisciplinary team and introduced to teachers and children. In this study, we focused on transformative processes to illuminate conditions for meaningful "design for learning," based on what teachers reported in interventions. In addition, we considered children's play with the app-based game, which elucidated the conditions for "design in learning." We performed thematic analysis and applied the Learning Design Sequence model to illuminate notions from critical incidents with children and teachers. The findings indicate that, although children "re-design" and create their purpose whilst playing, beyond digital affordances, teachers needed an explicit alignment with the curriculum to integrate meaningful and guided play with the use of DigiMat. This study indicates that designers and innovators wishing to introduce playful apps into educational practice should consider how learning outcomes and playful activities resonate with educational practice. Based on our findings, we argue that digital educational tools should be designed and implemented collaboratively with teachers and children, in a didactic context where the goals of the curriculum are recognised.