Systems for processing continuous monitoring queries over data streams must be adaptive because data streams are often bursty and data characteristics may vary over time. In this paper, we focus on one particular type of adaptivity: the ability to gracefully degrade performance via "load shedding" (dropping unprocessed tuples to reduce system load) when the demands placed on the system cannot be met in full given available resources. Focusing on aggregation queries, we present algorithms that determine at what points in a query plan should load shedding be performed and what amount of load should be shed at each point in order to minimize the degree of inaccuracy introduced into query answers. We report the results of experiments that validate our analytical conclusions.