Sixty-five preschoolers (5:7-6:7) carried out two kinds of task: In one, they were asked to judge the relations among number, length, and crowdedness; in the other, to identify the same number, length, or crowdedness. Three distinct groups of the participants were found. In the first group, the participants were able considerably to identify the same number, length, and crowdedness and to judge correctly the direct relations both between number and length and between number and crowdedness. However, they did not understand at all the inverse relation between length and crowdedness. For the participants in the second group, crowdedness did not seem to be clearly discriminated from both number and length yet. The participants in the third group could not clearly understand even the meaning of "crowded-sparse." Although the participants in the first group seemed to develop better than those in the second who that seemed to develop better than those in the third one, there were no differences in the mean age among the three groups.