In this study, the authors wanted to examine whether success on items testing basic equivalence knowledge, such as the meaning of the equal sign and ability to solve problems such as 3 + 5 = 4 + _, predicted success on items testing more advanced algebraic thinking (i.e. principles of equality and solving equations that use letter variables). This investigation is a follow up study to their initial efforts to design an instrument to measure children's understanding of equivalence (Rittle-Johnson, et. al. under review). This replication and extension with a new sample also provides evidence for the validity and generalizability of our instrument. They had two specific predictions about the relations between basic-level and advanced-level knowledge items. First, they expected that the relative difficulty of the two types of knowledge would be born out on the Rasch model. That is, they expected that their empirically derived difficulty scores would be higher for the advanced-level items than for the basic-level item. Second, they expected that performance on basic-level items could be used to predict performance on advanced-level items. (Contains 1 table and 1 figure.)