This is the second part of our paper An Approach to Learning and Teaching of Arithmetic. Following and somewhat modifying the Skempian conception of concepts, we consider a concept to be a tripartite entity consisted of corresponding examples, mental image and name (and possibly a symbol labeling it). Then, a detailed building of the structure of the number block up to 10 is considered. In the same way how the idea of a number is preceded by representation of a set, addition and subtraction are preceded by representation of an additive scheme followed by an addition or a subtraction task, respectively. Thus, the meaning of these two operations and all their properties are established on intuition of sets at the sensory level. Each of two numbers from this block are related to the third one, by expressing their interdependence in the form of sums and differences, what makes this block a system of concepts in the sense of Vigotskii.