Hi Everyone - I work as a trainer and facilitator and as a translator. There isn't a translation for "Moderationskarte" - it's not a prompt card or cue card. Prompt or cue cards would be if the person was giving a presentation and reading from the cards or using the cards to remind him/her what they were planning to say. This is a bit different.

Trainers and facilitators in Germany use rectangular or circular cards to collect ideas from the participants/answer questions/direct discussions (among other things). These cards get pinned on pin boards that are at the front of the room or placed on the floor. They have nothing to do with preparing for a speech or presentation. Index cards are Karteikarten - not the same thing. Facilitation card might be ok, but it's not something in common use in US English (I think it's because we simply don't use these cards when leading trainings - the closest method I've seen to using "Moderationskarten" in US trainings would be sticky notes or Post-It notes).