This article presents the translation and adaptation process of a mathematics test for the acquisition of key mathematical (arithmetic) concepts by children from four to eight years of age. The origin of this test was in Germany, whence it was sourced by researchers at the University of Johannesburg. A conceptual model of hierarchical mathematics competence development forms the theoretical foundation of the test. This notion of hierarchical competence was tested in a one-dimensional Rasch analysis, which confirmed the hierarchical structure of the test with five levels of ability. In the translation process, it was imperative to ascertain whether the items of the translation had retained the conceptual content of the original test and had been allocated to the same conceptual levels as in the original test. In a number of pilot studies with a total of 1 600 South African children, we focused on the items that had been allocated to a different level, aiming to find out whether this was the result of translation errors. In analyses of different samples, discussing and reflecting on the model fit, and especially on items that did not fit well, 'misfitting' items could mostly be attributed to translation difficulties and differences in the children's strategies, and not to a generally altered model. The final model was established after the rephrasing of critical items. This model has already been tested with 500 additional South African children. Results are presented and discussed, with the focus on the Sesotho test results.