This sentence is sort of ridiculous in English--it should be classroom, not class. A class in English is composed of students, not their materials. So, does класс in Russian also mean the room?
Then really Duo should have offered a 'classroom' button instead of, or as well as, 'class'. Because in English, the word 'class' here is wrong.
there are pencils in his grade.
Почему не принимает?
"There are some pencils in his class" - it's also right, isn't it?
I think it should be accepted
Contrary to his impassioned assertions.
Is есть necessary here?
More than likely not, it seems to ebb and flow on this course.