The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet (i.e., letter sequence) and the calendar year (i.e., month sequence). The representation of non-numerical order showed the same developmental pattern previously observed for numerical representation, with a logarithmic mapping in the youngest children and a shift to linear mapping in older children. Although the individual ability to position non-numerical items was related to the child's knowledge of the sequence, a significant amount of unique variance was explained by her type of number-line representation. These results suggest that the child's conception of numerical order is generalized to non-numerical sequences and that the concept of linearity is acquired in the numerical domain first and progressively extended to all ordinal sequences. (Contains 3 figures and 5 tables.)