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The participation of about 150 Flemish primary schools in TIMSS 2015 (grade 4) was used to test the Klieme model on instructional quality. Next to the effect of instructional quality on achievement, we explored whether instructional quality mediated socio-cultural group composition effects and whether it was mediated by the school emphasis on academic success. Two level CFA and SEM (students within classes) were used. Our results indicate that instructional quality affects math achievement and that school climate mediates this relationship for the supportive climate dimension. A negative relation between cognitive activation and math was found. Different results support the assumption of reversed causality, amongst others the results of the mediation analyses in which lower SES-classes receive higher cognitive activation.