Meaning
To play dumb / To act clueless
Example
Não adianta dar uma de João sem braço, eu sei que foi você que comeu meu bolo!
Don't play dumb, I know it was you who ate my cake!
Origin
The image is of a man hiding an arm to seem unable. The common account traces it to people who feigned a missing limb — beggars simulating mutilation for alms, or men dodging labour and military service — pretending to be incapable rather than admit they simply would not do the work. João, the most ordinary Portuguese name, stands in for "any man".
Source: Ciberdúvidas da Língua Portuguesa.
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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