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It is about a young teacher who was at first very enthusiastic about working with children, but now her exhilaration is beginning to "fray around the edges".

"This was her first year of flaking poster paint from her eyebrows, going to sleep at night with the salty taste of paste in her gums, and exiling so many children at a shot for a 'time-out' that there was no longer any activity to take a time out from."

Can you explain or rephrase?

Thanks!

Diana
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At a shot = at one time
A 'time-out' is a sort of gentle punishment for an unruly child; s/he is told to 'take a time-out' (take a short break or recess) from the current activity and move to another area or activity for a while.
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Thank you MrM!

Diana