This study explores changes in students' strategies as they solve different types of volume problems. Fifth graders were presented with pictures showing 3D objects and a unit cube; they determined how many cubes made up the object and explained their responses. We examined whether children transferred strategies across problem types, varying in terms of (a) availability of grids that divided objects into individual unit cubes, (b) order of items, (c) object shape, and (d) availability of the unit cube. Children's strategy choices varied systematically with object and task characteristics. They were more likely to use conceptually appropriate strategies when presented with grids. With non-gridded objects, they were more likely to treat a 3D object as a collection of 2D faces. Presenting gridded items first increased the use of conceptually appropriate strategies on the non-gridded items. We discuss findings in the context of Siegler's theory of strategy choice and address educational implications. (Contains 3 figures and 12 tables.)