The main thesis of this paper is that the construction and coordination of abstract units is central to mathematical activity in both numerical and geometric settings. Data were gathered from students in grade three through six, with four students being observed over a three year period. A consistent parallel was found in the sophistication of the types of units constructed in a geometric setting (tiling the plane) with their numeric activity. The tiling activity of the students was analyzed for evidence of the construction and coordination of units. Some students constructed rather sophisticated abstract composite units to facilitate their tiling with a particular shape while others had difficulty making a covering. Students who constructed abstract composite units in tiling did so also in adding and subtracting whole numbers. Evidence of unitizing and coordinating the units constructed was associated with advances in mathematical thinking. Unitizing seems to be a fundamental mental operation in coming to act mathematically. As mathematics activities are planned, it is important to provide opportunities for students to construct abstract composite units in both geometric and numeric settings. Emphasis on prescribed procedures such as subtracting with two-digit numerals may inhibit this construction process.