This paper describes a design research study with ten second-grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked how they counted in multiple bases, specifically how they knew when to go to a new place value and why it was necessary to do so. All ten students showed skillfulness in counting and representing the numbers, but analysis of their responses showed different levels of generalization of method and explanation of underlying ideas. [For complete proceedings, see ED489597.]