Assuming the quiz is mostly reading/writing, maybe you could use some games to assess them, too? Like 'Simon Says' with 3rd-grade phrases and vocab for listening comprehension, nunchi for numbers/anything sequential, that sort of thing. An action reading game could be good, too-- 4th graders tend to love TPR games and you'd be able to test how well they can recognise and pronounce certain words or phrases. You could also do calmer activities like showing them a video and asking them about details they saw/heard, like colours of stuff, numbers of objects/people, animals, weather, etc, to check how well they can understand those questions/express themselves in English.

I hope some of these ideas are useful, and best of luck!