Past research showed that Indian children average information about motivation and ability in prediction of performance. However, a multiplying-type rule develops from an adding-type rule in American children. The present research tested the hypothesis that integration rule depends upon age and culture of children and nature of task. Consistent with the hypothesis, Experiment 1 (n = 96) obtained evidence for no difference between children of fourth and eighth grades in prediction of performance in puzzle contest but for development of an adding-type rule from a multiplying-type rule in prediction of performance in singing contest. As the latter finding was surprising, Experiment 2 (n = 144) studied kindergarten through eleventh grade children. Results indicated that a multiplying-type rule evolves out of an adding-type rule but gets replaced by the adding-type rule during sixth and seventh grades. Of the three interpretations, namely, changes in weight of information, changes in integration rule, and changes in response reproduction processes, of the age differences, the first one seemed to be the most parsimonious.