Hi there,
I could develop this for you, it wouldn't be an android app but an accessible website which can be accessed using an android phone or any phone that has a web browser. Would use bootstrap for the layout and would code in PHP (CodeIgniter framework). Ready to start today!
Admin can manage the teachers, students and classes/groups of students
Teachers can log in using their account and can log a missing student, they can select a class/group and have a list of students from that class, and they can search by student name/last name
You'll probably require some sort of reports for this too available for admin (and teachers?), as the budget is pretty low I could build a textual/table report for a selected class.
Another problem I see coming up is when the school year is done, and the new one starts, we'll probably want a start a new school year option as well, I'll probably have to slightly increase the price if you want this included.
Regards,
Julijan