Pairprep is a free site that has a number of “courses” (a series of multiple choice questions on a particular topic – like “ESL”) where students can compete against a friend, a random opponent, or themselves as they choose answers. Teachers can monitor student progress through a virtual classroom.
Teachers can create that classroom by choosing an existing courses through first clicking on the course name and then clicking the big read “Contribute” button on the upper right of the page. Or teachers can create their own course from scratch.
In addition, I’m adding it to The Best Online Games Students Can Play In Private Virtual “Rooms.” Even though the other sites on that list let students compete against all their classmates instead of just one, Pairprep is close enough to fit.