Abstract Three experiments investigated the role of length, density, and number dimensions in children's numerosity judgments of linear arrays of beads. The number dimension is physically defined by a length × density rule. Judgments based, even in part, on the number dimension would show signs of a length × density rule. Experiment 1 examined numerosity judgments of large arrays. Results showed that judgments by 3- and 4-year-olds obeyed a length + density rule, providing cogent evidence for a general adding strategy in young children's judgments of quantity. The physical length × density rule emerged gradually with increasing age. Experiment 2 showed that numerosity judgments of small arrays by 3- and 4-year-olds obeyed a length × density rule, indicating response to the number dimension. This result was expected and thereby validated the linearity of the response scale at the youngest ages. Experiment 3 verified the integration rules for individual 3- and 4-year-olds. The integration rules were interpreted in terms of Piaget's stages of the development of quantification. No evidence for Piaget's initial stage was found. This leads to a new view of early quantification which grants young children the ability to integrate stimulus dimensions.