A theoretical model describing young students' (Grade 3) arithmetic-algebraic structure sense was formulated and validated empirically (n = 130), hypothesizing that young students' arithmetic-algebraic structure sense consists of five distinct but correlated factors; structure in numerical equivalence and word-problem modeling, structure in arithmetic, mathematical structure in number sequences, varying quantities and number correspondences, structure in patterns, and structure in functions. Data analysis suggested that arithmetic and arithmetic-algebraic tasks can be categorized based on the proposed model. Analysis traced three categories of students that represent different profiles of students. Students of the "basic arithmetic structure" sense profile approach flexibly simple arithmetic and patterning tasks that do not require generalization; students of the "advanced arithmetic structure" profile exhibit an awareness of local relations by describing the underlined relations in a variety of numerical situations. Students of the "emergent arithmetic-algebraic" profile utilize the awareness of mathematical structural relations to symbolize functional relations. A structural model showed the importance of grasping structure in patterns and describing the mathematical structure in numerical situations to develop structure in functions.