We describe the design background of the mathematics game Fingu for iPad aimed at 4 to 8 year old children. We first describe how Fingu theoretically can support children's development of fundamental arithmetic skills, focusing on conceptual subitizing, the embodiment of numerosity, and finger gnosis. Then we present the results of an exploratory micro-longitudinal study of the game with 11 5- and 6-year old children playing the game for several weeks and being filmed at three occasions. We discuss how their behavior with the game develops over time and can be related to the development of arithmetic skills. Finally we discuss how we will proceed testing the effectiveness of Fingu in a larger controlled study.