It is a grammatical sentence.
It is an imperative for the child's parents.

It means that you (dad, mom, grandma....) do not have to take the place of the child and write the number for him. He has to write the number himself.

Have your child to write = let him write, don't write for him
have your child write = direct him so that he writes
make him write = direct with authority (force, maybe) so that he writes

There's no different meaning to distinguish between "have your child to write" (incorrect) and "have your child write." (correct)

I'd give the teacher the benefit of the doubt. The teacher accidentally included the word "to," making it incorrect English.