This study is focused on the structure of equivalence problem to probe the evolution from operational to relational view of students' understanding of the equals sign. We propose a modified construct map which incorporates the intermediate levels in such a transition which were previously ignored. Our findings suggest that the structure of number sentences (place value and the position of answer box) has an undeniably significant role in developing students' conception of equivalence. In addition, the designed and validated example presented here could potentially serve as a tool for better assessment of understanding of equivalence. [For complete proceedings, see ED581294.]