We examine the meanings students give to points when they are graphing relationships between quantities in dynamic, experiential contexts. Using data from teaching experiments with middle-grades students, we illustrate two main categories of meanings: iconic and quantitative. We then introduce four distinct subcategories of meanings: (a) iconic and transformed iconic translations (a point represents an object or location), (b) nonunited points (a point represents a single quantity's magnitude), (c) spatial-quantitative multiplicative objects (a point is an object or location with quantitative properties), and (d) quantitative multiplicative objects in conventional and nonconventional planes (a point represents two quantities' magnitudes). We discuss the implications of these meanings for research, teaching, and curriculum development.