The Give a Number (GaN) task is used to characterize the initial acquisition of symbolic numbers. Recent observations may imply that the assumptions of the original description about the development of initial symbolic numbers acquisition can be inaccurate. First, there may be children who know larger numbers than 4 and, still, they do not know all other numbers from their counting list. Second, the knowledge about these first numbers may not be all-or-nothing but it may be a more gradual knowledge. Here, a modified version of the GaN task was used to directly investigate these two properties of the development. Measuring 3- and 4-year-old children it was found that there are large-number-subset-knowers, and the knowledge about numbers is not all-or-nothing around the edge of children’s known number range. These results suggest that a modified version of the GaN task would be more suitable to capture a detailed pattern of numerical development: Instead of the titration method all numbers of interest should be used, and numbers larger than 5 should also be measured. Because subset-knowers may know numbers beyond 4, these results may also challenge the Object Tracking System account of the initial symbolic number learning.