In order to describe developments in children's conceptions of numbers and numerical relations, judgments of similarities between numbers were solicited from adults and from children in kindergarten and grades 3 and 6. A nonmetric multidimensional scaling analysis suggested that children gradually become sensitive to an expanding set of numerical relationships during this period, although even kindergartners appear to understand the importance of magnitude as a basis for judging similarity between numbers. A second study further probed the basis for kindergartners' number-similarity judgments, using the first 10 letters of the alphabet as stimuli and providing subjects with an explicit criterion for making judgments (distance between letters in the alphabet). These results suggest that the number-similarity judgments of kindergartners, and to a lesser extent of third-graders, are based upon counting distance. Results implicate the acquisition of numerical skills and operations such as counting, addition, and multiplication in a gradual broadening of the concept of number. (Author)