Lori and Max by Catherine O'Flynn
Lori wants to be a detective, but so far the most exciting mystery she has solved is the disappearance of her nan's specs down the side of the sofa. Max is the new girl at school and Lori is asked to look after her. Max is odd. She doesn't fit in - but then, Lori realises, she doesn't really fit in either. When some charity money goes missing and Max disappears, Lori seems to be the only person who doesn't think Max has stolen it and run away. Even the police don't want to investigate and suddenly Lori finds she has a real crime on her hands.