In recent years, scholars have increasingly advocated the importance of cultivating non-cognitive skills (social and emotional skills) in early childhood, and play is useful in acquiring the skills. Simultaneously, young children also need to acquire mathematical cognitive skills as a learning foundation. However, many researchers have indicated that simple direct instruction in mathematics is not useful during early education. Therefore, in early childhood, children need forms of play for mathematics at home because play effectively develops non-cognitive skills; moreover, cognitive skills and non-cognitive skills cross-fertilize each other. Moreover, in kindergartens and nursery schools, it is difficult to deal with many "maths" (both temporally and content-wise). Also, parental engagement and attachment have considerable impact on non-cognitive skills. In this research, we created a form of simple mathematics quiz game (simple mathematics play) that young children can play at home. The main aspect of this play's content is the application of systematic and extensive mathematics in early childhood, without promoting only cognitive skills as a primary objective. And we tried the play for one child as a case study. This case study suggests that certain improvements in cognitive skills regarding mathematics were recognized because of play, while also enabling acquisition of non-cognitive skills.