Equity is a concept that is often measured in terms of test scores, with educators looking for equal test scores among students of different cultural groups, social classes or sexes. In this article the term 'relational equity' is proposed to describe equitable relations in classrooms; relations that include students treating each other with respect and responsibility. This concept will be illustrated through the results of a four-year study of different mathematics teaching approaches, conducted in three Californian high schools. In one of the schools—a diverse, urban high school—students achieved at higher levels, learned good behaviour, and learned to respect students from different cultural groups, social classes, ability levels and sexes. In addition, differences in attainment between different cultural groups were eliminated in some cases and reduced in all others. Importantly, the goals of high achievement and equity were achieved in tandem through a mixed-ability mathematics approach that is not used or well known in the UK.