This chapter describes a study of the informal knowledge of addition and subtraction number sentences that preschool children in Israel bring with them to school. The study continued throughout the first year of schooling in order to follow the development of this knowledge. The chapter covers three main topics: the theoretical framework that we used to construct the research tools and to analyze the data, the study, and the main findings, and raises issues in need of further exploration. The main function of the symbolic arithmetic system is to represent the arithmetic concepts, operations, and relations, to transmit information and to enable students to arrive at the mathematical meaning behind the symbol. The chapter assesses kindergarten and first-grade children's knowledge about these two components of the symbolic arithmetic system, with particular focus on the differences between recognizing and producing addition and subtraction number sentences.