Meaning
To cut someone some slack / To give a break
Example
Professor, me dá uma colher de chá, eu estudei muito mas fiquei nervoso na prova!
Professor, cut me some slack, I studied a lot but got nervous during the test!
Origin
The image comes from old sickroom care: tea was thought to be a gentle, restorative drink, so it was fed to the ill and the recovering one small spoonful at a time. To "give someone a teaspoon of tea" (dar uma colher de chá) therefore meant to ease the way for someone who was struggling.
Sources: Espírito do Chá, Mexido de Ideias.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity