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Wiktionary
flannelgraph

n. A board covered with flannel fabric used as a backdrop when telling stories to children, the characters in the story being placed and moved on the backdrop.

Wikipedia
Flannelgraph

Flannelgraph (also called flannel board or flannelgram) is a storytelling system that uses a board covered with flannel fabric, usually resting on an easel. It is very similar to Fuzzy Felt, although its primary use is as a storytelling medium, rather than as a toy.