In a series of publications, we have employed ontological theories and principles used to evaluate and improve the quality of conceptual modeling grammars and models. In this article, we continue this work by providing an ontological interpretation and sound modeling guidelines for a traditionally neglected notion in the conceptual modeling literature, namely, the representation of types whose instances are quantities (amounts of matter, masses). Here, we analyze different alternatives for the adequate representation of quantities as well as their parts in conceptual models. Moreover, we advance a number of metamodeling constraints that can be incorporated in a UML 2.0 metamodel extension, thus, allowing for the suitable representation of these notions.