On various international tests of achievement Finnish, Flemish and Hungarian students have been amongst the more successful in Europe. Linear equations, a topic students traditionally find difficult, is a key topic in the transition from mathematics as inductive and concrete to deductive and abstract. This paper, by means of an analysis of video-taped lessons taught by case study teachers, one from each of Finland, Flanders and Hungary, examines comparatively how teachers defined locally as effective construct opportunities for their students to learn the mathematics of linear equations. The findings show that all three teachers acted in ways contrary to received research wisdom, exploiting the balance scale as the key metaphor for inducting students into the solution processes of algebraic equations.