This paper, the first in a 2-part series, proposes a Model-of-Knowledge for the social analysis of intergenerational encounters between older adults and children and discusses professional intervention. The model is based on the findings of a pilot counseling activity at a primary school in Israel. It sets forth 4 types of encounters between children and older adults. The encounters included an estimation of the relative advantage of knowledge on both sides, a mutual estimation of equal knowledge, and a mutual estimation of equal lack of knowledge. Beyond the presentation of each type's content, the paper deals with this question: How does the proposed Model-of-Knowledge reflect the intergenerational gap between children and older adults and mediate between them? Gerontologists and educational professionals are invited to explore the psychosocial insights that the model brings to the fore.