This study examined how a child constructed a scheme (abbreviated QRE) for producing mathematical equivalence via operations on composite units between two multiplicative situations consisting of singletons and composite units. Within the context of a teaching experiment, the work of one child, Joe, was analyzed over the course of 14 teaching episodes. Joe made the conceptual advance from a Relational Equivalence Scheme (RE) and absence of a Quantitative Relational Equivalence Scheme (QRE), through the participatory stage, to an anticipatory stage of a QRE scheme. Joe's progression distinguished between creating equivalence with an RE via operations on singletons and a QRE--a conceptual root for fundamental algebraic concepts such as the distributive property, solving linear equations, and a relational understanding of the equal sign. [For the complete proceedings, see ED583608.]