Here are three great mystery series for those of you who are just starting to read books which are a little longer than the basic early reader.
Nate the Great [Book One]
Nate the Great solves the mystery of the missing picture.
Series:Nate the Great 
The Clue of the Left-Handed Envelope  [Book One]
Everyone loves the new teacher, Mr. Merlin. Mr. Merlin used to be a spy, and he knows all about secret codes and the strange and gross ways the police solve mysteries. Now there's a mystery in their very own class! Noelle and Todd want to solve the mystery before anyone else. But first they have to figure out Mr. Merlin's clues. How can a bunch of envelopes tell them who sent the letter?
Series: Third-Grade Detectives by George Edward Stanley 
January Joker [Book One]
Seven-year-olds Bradley, Brian, Nate, and Lucy make observations and gather clues that convince them that their older siblings, cousin, and animals have been captured by hungry space aliens.
Series: Calendar Mysteries