"hack" noun = tips or advice
"hack" verb = apply tips or advice
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It's an ugly word which came from a sense of hacking something (as in with a blunt instrument) rather than cutting accurately with an appropriate tool, somethign sharp.
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In this misuse, it has retained a meaning of unusual, or unexpected. Though the tips offered are usually very obvious click bait, these days.
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"Life hacks" purport to be things to change to make you life better.
A "teacher hack", would presumably be an idea that makes teaching easier, or more effective in some way. An example might be a novel incentive to get students to turn up on time.