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.
Authors like 松谷みよ子, さとうさとる are now somewhat dated but still worth reading. Newer authors like 柏葉幸子 and 岡田淳 offer a range of topics at a good level to keep language learners reading.
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