This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics for (relational) understanding' is evident in both documents. Distinctions are drawn between strategy, representation and procedure, and the progression towards efficient calculation strategies is emphasised (neither of which is clear in the CAPS). The suggestion made in the TMU framework is that teachers can shift from bundling concrete manipulatives for multi-digit numbers to the standard written algorithm in Grades R-3, which contradicts both the CAPS and insights gleaned from mathematics education literature and two learning programmes that have shown positive results at large scale. In particular, the justifications for delaying teacher introduction of 'break up both numbers' strategies are discussed. Further, when the 'break up both numbers' strategy is used, alternatives to the standard written algorithm which have been found to be more accessible to learners -- expanded notation, write all totals, and new groups below -- are offered. Ways of using empty number lines and 'drawing numbers' to show the 5-wise and 10-wise structure are suggested. These alternative representations for breaking up both numbers are expected to be accessible to teachers for whom the standard written algorithm is a familiar calculation strategy.