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Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students' formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is known about the factors influencing students' understanding of mathematical equivalence particularly across different countries. We have conducted the first large-scale study to explore the factors associated with primary school students' understanding of mathematical equivalence across six countries (China, England, New Zealand, South Korea, Turkiye, and the United States). Participants were 2,760 primary school students and their teachers (N = 108). Using multilevel structural equation modeling, we found that students' knowledge of definitions of the equals sign relates to their equation-solving performance. We also found that while teachers' knowledge of students' relational strategies does relate to students' understanding of equivalence, teachers' knowledge of students' operational strategies, and the format of arithmetic practice presented in the students' current year textbooks do not. Using England as the reference country, we found that this pattern was similar across the samples from all the participating countries. Taken together, our findings have important theoretical and practical implications, providing a more complete picture of the individual and classroom-level factors associated with students' understanding of equivalence. Educational Impact and Implications Statement: Students' poor performance on mathematical equivalence problems is well-established, yet the potential factors involved remain unclear. Research suggests that the format of arithmetic practice offered to students could be a factor associated with students' formal understanding of equivalence. We conducted a large-scale study, which revealed that teachers' knowledge of students' relational strategies relates to students' understanding of equivalence across six countries. However, the format of arithmetic practice presented in students' current year textbooks did not relate to students' understanding of equivalence. Our results suggest that students' understanding of mathematical equivalence is more reflective of their current teachers' knowledge than it is of the way arithmetic practice is presented in textbooks in students' current school year. [ABSTRACT FROM AUTHOR]