The ability to perceive structures in sets and to use them to determine cardinality is one important basis for arithmetical learning. This study is based on a theoretical model that distinguishes between the two processes of perception and determination. A total of 95 5-year-old children were interviewed individually to find out whether and how children of this age perceive structures in a visually presented set and whether and how they use these structures to determine the cardinality of the set. To gain insights into the invisible process of perception, eye-tracking was used. Known structures, such as the pattern of a dice-four, seem to play a role in these processes. With the help of an analyzing process consisting of three different types of data, final interpretations were generated that suggest that 5-year-old children can already perceive structures and use them to determine cardinalities. There also seem to be children who are already aware of a structure, but cannot use it to determine the cardinality. This leads to the conclusion that perception and use of structures are possible elements for early mathematical education at this age.