The appropriateness of guess and check as a problem-solving strategy has been debated. This qualitative study examines the use of guess and check by middle-grades students to solve linear systems of equations. Students' reasoning is examined within the number sequences framework, which is based in part on students' units coordination. Only students at the fourth and fifth stages (out of five) correctly solved systems of equations algebraically; this is attributed to their operations on two- and three-level unit structures, and to a disembedding operation. Students at the third stage applied strategic guess and check methods, which is attributed to assimilating with composite units (i.e., units of units), but these students could not correctly use an algebraic method. For students at the second stage, guess and check was non-strategic, which is attributed to their construction of composite units in activity. Implications for instruction are discussed. [For the complete proceedings, see ED630060.]