Make fun of straw as cattle feed (5)

I believe the answer is:

chaff

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'make fun' is the definition.
'chaff' can be an answer for 'fun' (thesaurus). I am unsure of the 'make' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for chaff that I've seen before include "It's separated from wheat during threshing" , "Tease in good-humoured way" , "shells" , "Refuse from threshing" , "Winnowed husks of grain" .)

I've seen this clue in The Times.

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