Research on young children’s development of executive function (EF) and early mathematics has established relationships between the two, but studies have not investigated whether these relations differ for children with different outcomes in mathematics and EF, especially in the context of interventions. To examine the homogeneity of those relations and the intervention effects, we conducted quantile regression analyses on data from a large study of two prekindergarten interventions: the Building Blocks math curriculum alone (BB), or BB with scaffolding of play to promote executive function (BBSEF). Results revealed that EF competencies have a larger positive relationship to mathematics for children with low math competence compared to children with medium or high competence. The significant predictive relationship of mathematical competencies on EF did not vary for children with different levels of EF abilities at prekindergarten and varied only slightly at kindergarten. Also, interventions had similar immediate effects on math and EF for children with various abilities. The BB intervention had a larger positive delayed effect on math and EF competencies for children with low scores relative to children with high scores. The delayed effect of the BBSEF intervention was similar for children with different levels of EF and math competencies. (author abstract)