Extra credit questions sometimes motivate students to study more. Occasionally I find several valuable questions which are all good as extra credit question choices but I have to limit the number of points that a student can possible receive from doing extra credit work. Say the full mark of a homework set is $10$ and there are $n$ questions which are suitable as extra credit questions.
Here my goal is:
- Encourage students to try as many of them as possible.
- Do not give a student more than $1$ point for all the extra credit work.
Here I am asking if the following is a good strategy:
If the student attempted $k$ out of the $n$ extra credit questions, the student will receive up to $1/2$ points for his best finished question, up to $1/4$ points for his second best finished question, etc. In general, I will give the student up to $1/2^m$ points for the $m$-th best answered question. So a motivated student can try most extra credit questions out of the set of $n$ questions and no student can receive more than one point for his extra credit work.