Children's understanding of the cardinal significance of counting is often assessed by the ‘give x’ task, in which they are categorized as ‘counters’ or ‘grabbers’. Previous research indicates a sudden stage‐like shift, implying insight into a principle. Employing a microgenetic approach, the present study was designed to explore whether this dichotomy masks a more subtle pattern. Fifty‐five 39‐ to 58‐month‐olds received five ‘give x’ trials, involving 4, 5, 6, 7, and 10 objects, within a single session counterbalanced across individuals, each child participating in two similar sessions one week apart. Children's spontaneous strategies were recorded. They also completed a simple verbal counting test. Participants seldom simply ‘grabbed’; even those who never counted gave items one‐by‐one. Some gave correct amounts by starting off counting then taking the remainder silently, suggesting internal counting. There was also evidence of children taking correct non‐subitizable quantities without overtly counting. Individuals' strategy choice and the way they employed particular strategies varied, both within and between sessions. Furthermore, after achieving procedural mastery, children continued to refine their use of strategies. The results are discussed in relation to Karmiloff‐Smith's RR model and Siegler's overlapping waves model. Copyright © 2007 John Wiley & Sons, Ltd.