With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This paper reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials are broadened to include new forms of materials such as virtual manipulatives. Manipulatives are in a broader network of learning tools. Applying a theoretical lens to a specific material, the polynomial tile, the paper demonstrates the following (a) a complementary relationships between virtual and concrete manipulatives; (b) two or more theories can appropriately justify the same material and (c) exploration of a specific manipulative may generate novel theoretical rationales. This exploration is helpful in the process of designing, selecting, categorizing and evaluating learning tools. (Contains 1 table, 7 figures and 9 notes.)