Surviving the quiz onslaught by lazy teaching

Hello everyone. Here is something I have started doing this semester to cut down on the number of small quizzes I have to grade.
1. I give a reading assignment with a paragraph or two written response required.
2. At the beginning of the next class, I quickly check to make sure that all of the students have done the required writing. With 27 students, it takes about 5 minutes. If they have done it, I give them credit for that part of the quiz.
3. I then put the students into groups, assign a notetaker, and make the students report their work to group.
4. Then a spokesperson from each group reports the group work to the class at large. If each group can make a good report, I give each member of the group credit for that part of the quiz. At this point, we can open things up for deeper class discusssions.

It has been working for me so far this semester. I like it because it holds the students accountable, improves the quality of my class discussions, and cuts down on my grading.