One of the key goals for mathematics education around the world is to ensure all children’s proficiency with numbers and more generally to have a flexible and adaptive understanding and knowledge of arithmetic. Game-based learning environments are means to support the development of such competence. In this paper we describe our design-based research on Fingu, an application that targets the understanding and mastering of the basic numbers 1 to 10 as part-whole relations. The aim of this paper is to present the design rationale of Fingu and empirical research conducted in Swedish pre-school and primary school settings.