We draw on our work with designed instructional sequence on Fractions as Measures across three international contexts and explore the functions of the design features related to the stories embedded within the sequence. We discuss functions that relate to how stories support students' meaningful engagement in classroom mathematical activities, focusing, in particular, on students from under-resourced environments. While doing so, we highlight the mediating role of teachers who adapt designed resources to the specific needs of their classrooms. We clarify how instructional sequences can provide guidance for teachers' adaptations by making design rationales for mathematics and functions of the story explicit.