Middle-grade book about a boy who falls in a puddle with his dog & they both become invisible (except the dog's tail). They solve a mystery involving anagrams

[Abby]

Probably read this in 2003 or so. The story starts by telling readers the boy & his dog fell in a puddle over the summer and are invisible (except the tip of the dog's tail). His friends are pretty accepting of this and are trying to help him become visible again.

There's also a mystery involving their teacher (I think she's missing) and a librarian, and they keep finding clues in anagrams and library books.

[Becca]

The Invisible Inc. books by Elizabeth Levy. The first book is The Schoolyard Mystery.