Dataspace management systems (DSMSs) hold the promise of pay-asyou-go data integration. We describe a comprehensive model of DSMS functionality using an algebraic style. We begin by characterizing a dataspace life cycle and highlighting opportunities for both automation and user-driven improvement techniques. Building on the observation that many of the techniques developed in model management are of use in data integration contexts as well, we briefly introduce the model management area and explain how previous work on both data integration and model management needs extending if the full dataspace life cycle is to be supported. We show that many model management operators already enable important functionality (e.g., the merging of schemas, the composition of mappings, etc.) and formulate these capabilities in an algebraic structure, thereby giving rise to the notion of the core functionality of a DSMS as a many-sorted algebra. Given this view, we show how core tasks in the dataspace life cycle can be enacted by means of algebraic programs. An extended case study illustrates how such algebraic programs capture a challenging, practical scenario.