In addition to the leveled readings available through the 朝読 collections, there are many publishers offering books aimed at children reading at a Japanese grade 3-6 level.
One series that is ranked as grade 5-6 but falls at the lower end of mid-level would be the 怪談レストラン（童心社), which is a set of ghost/monster short stories by well known authors.
You may have luck reading ショート・ショート stories by 星新一 and his successor 阿刀田高. These stories might be a little more difficult but because they are very short, it is possible to read them without losing interest. They work very well for reading in class.
I am interested in learning more about this series 声に出すことばえほん and whether it would work for our students.
Somewhere in between mid-level and upper-level are the collected sets such as the now out of print 少年少女日本文学館 or this new version