In this paper we report on findings from a study of 5-to-6-year-old children's ways of structuring part-part-whole relations using finger patterns. We focused our analysis on data from interviews with 28 children who during their last year of preschool learned to enact a structural approach. We used this data set to analyze their different ways of structuring a task with one part unknown, and what constitutes the ability to structure the task in a conceptually powerful way. The way children structure number relations was interpreted as being related to how they experience the task at hand. We identified some ways of structuring as being more powerful for future learning, particularly those that facilitate the child in experiencing parts and the whole simultaneously. We suggest that there are three aspects that children need to discern in order to structure the task successfully in both the short and the long term: what constitutes the whole, the parts within the whole, and finger patterns as a representation of the cardinality of a set. The pedagogical implications are that attention to children's ways of experiencing the number relations in arithmetic tasks gives clues to why some children develop powerful strategies, and how to support children in their learning to solve arithmetic tasks.