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Can the hangers that the masses are hung from, be movable? For example, can the loops of the given masses, be attached to movable ringed hooks that the students slide along the two arms of their weighing device?

Yes, as long as the hooks are only used for attachment and the entire device only uses the Law of the Lever for calculating the unknown mass. General rule #2 applies: http://www.soinc.org/ethics_rules