At the end of "K-ON!
" episode 11 aired on June 11th, the next episode was called "The final episode 'Keion!'".
Screenshot of the preview
The preview caused a turmoil on the internet and a news website reported that K-ON! series was cut down to 12 episodes, even accelerated the confusion.
Getnews, reporting the turmoil
However, all the major anime magazines released this month announced that the episode 13 will be aired on June 25. The chances are quite slim that K-ON! was shortened by one episode.
The synopsis of episode 13 indicates it's an extra story after the school festival.
According to the official BBS of K-ON!, the TBS staff denied the rumor of shortening. She said "The airing continues until episode 13. Ep12 is the final episode, and Ep13 is a Bangaihen
Source: TBS K-ON! BBS