This study explores the generalization process of fourth-grade students within a functional thinking context, as part of a broader research project on algebraic thinking in elementary education. Specifically, the study investigates how students reason and construct generalizations when solving a functional task based on the linear function f(n) = 2n + 1, embedded in a familiar real-world context (an amusement park scenario). Data were collected from a classroom session involving 25 students, and qualitative analysis focused on verbal and written representations across three reasoning phases: abduction, induction, and generalization. Findings reveal that the abduction phase—where students explored concrete, close cases and generated initial conjectures—was the most prominent. Induction emerged as students extended these conjectures to distant numerical cases, validating structural patterns. Generalization, however, was less frequently observed and presented more difficulty, as it required students to express abstract relationships using variables. Only a few students attempted to formulate general rules using letters such as “B” or “Z,” often showing conceptual confusion. The study emphasizes the importance of using contextualized functional tasks to support the transition from arithmetic to algebraic reasoning in early grades. It also underscores the critical role of teacher guidance and classroom discussion in fostering the development of functional thinking and algebraic generalization. The results contribute to understanding how young learners engage with algebraic structures and highlight the need for further research into individual generalization processes through interviews and individual assessments.