Tasks based on the function concept (y = f(x)) were used in a study charting the development of anticipation in children from 5 through 7 years of age. In each task a desired outcome was a function of a combination of specific, rule-constrained, antecedent conditions. Subjects' behavior was scored according to criteria differentiating six levels of cognitive performance. Level 5 indicated consistent use of anticipation; Level 4 indicated partial use of anticipation, and Levels 3 through 0 referred to the use of trial-and-error strategies. Trial-and-error was defined as pausing to figure out what to do before each step in the solution, whereas anticipation was defined as pausing before the first step and then proceeding with the other steps without pause. Age trends in the data for these tasks indicated that (1) 5-year-olds generally find some solutions by trial-and-error; (2) 7-year-olds generally find most solutions by trial-and-error; and (3) solutions by operational anticipation become common only among 7-year-olds on the easiest task. Age trends for solutions termed "efficient,""repetitive," or "rambling" illustrated an "intuitive" form of anticipation in which trial-and-error behavior involved strategic searching at each step. Such intuitive anticipation was found to increase between 5 and 7 years of age. Correlations between functional composition ability and several concrete operational abilities support Piagetian theory. (RH)