This study investigates how the graph representation creates opportunities for young students to develop an understanding of functional relationships in pattern generalizations. The empirical data is from an educational teacher-focused classroom design research focusing on generalizations in arithmetical growing patterns in Grade 1. The results show that the students in Grade 1 are given an opportunity to reason mathematically in both recursive-and covariational thinking. The results also show how the teaching provided opportunities for the students to use multiple representations of functional thinking and how oral language is a common representation to describe relationships. However, using a well-thought-out terminology to exploit the potential of the graph representation when discussing functional relationships and generalizations appears to be important.