In this study, based on the analysis of a teaching experiment with middle school students, we propose a framework for describing meanings of a point represented on a plane in terms of multiplicative objects in the context of graphing. We classify those meanings as representing: (1) non-multiplicative objects; (2) quantitative multiplicative objects (Type-1 and Type 2); and (3) spatial multiplicative objects. We then discuss implications of these meanings with respect to students' graphing activities. [For the complete proceedings, see ED629884.]