From 2012 through 2017 the Australian Council for Educational Research (ACER) in co-operation with the Afghanistan Ministry of Education undertook a program of national assessment in Afghanistan: the Monitoring Trends in Educational Growth (MTEG). The assessment program measures mathematical, reading and writing literacy in the national population at the end of grade 3 and grade 6. An aim that emerged later in the assessment program was to be able to locate grade 3 students and grade 6 students on the same learning metric and to describe growth not only within the same grade cohort, but between them in the long-term. This study comprises of, in grade 6, 5 979 students, in grade 3, 4 936 students, and in a grade 4 and 5 link sample, 1200 students. This paper addresses the methodological approaches used to meet this challenge. The measurement approach had to control for variations in modality - Grade 6 was a paper- based assessment while grade 3 was computer-based to accommodate the relatively low levels of literacy in the grade 3 population. This linking study also had to implement a novel design, with neither common-students or items, an intermediate sample of grade 4 and 5 students was drawn. Novel approaches to assessing the quality of link-items was needed, and both model-oriented approaches (e.g., iterative comparisons of nested model deviance) sensitivity analysis (e.g., rank-order association of item parameters between samples) were implemented with the relatively sparse data.