The purpose of this paper is to present different strategies of addition and subtraction as well as to point out the importance of using different strategies when solving tasks. The selection of strategies is adaptive, it depends on child's knowledge of about specific strategies, as well as on characteristics of the task which is being solved. Moreover, the purpose of the paper is to present cognitive structures, that is, mental images, as an important part of calculating. The way in which children imagine and present smaller numbers contributes to easier presentation of larger numbers and mathematical operations. The materials Rechenschiffchen and Zwanzigerfeld contribute to the construction of those cognitive structures. The research conducted for the purpose of this paper is based on the issue of construction of cognitive models, and it is carried out on the material Das Zwanzigerfeld mit Wendeplättchen. The research was conducted in primary school Mitnica Vukovar, with 37 pupils engaged. The results of the research have shown that the children of the working group are capable to easily II present and recognize the specific number and/or operation structure. Children easily recognize the smaller structures on sight, and the material is particularly suitable for working with children with specific difficulties in mathematics as well as for visual types of pupils. Children use the number presentation and operations in a line more often.