Movable partitions and partition systems include a sheet of interconnected panels configured to fold in an accordion fashion. At least two of the interconnected panels have first and second lateral ends extending between a top edge and a bottom edge of the panels. The lateral ends may comprise generally cylindrical structures having openings comprising gaps between lateral edges of the respective panel and a first major surface of the respective panel. The first lateral end of one panel may be engaged with the second lateral end of another panel of the at least two panels. The lateral edges may be enlarged. The at least two panels can extend to a fully extended state in which they are coplanar. Methods of forming movable partitions and partition systems include forming and interconnecting such panels. Methods of repairing movable partitions and partition systems include disengaging such panels by applying lateral forces therebetween.