Should I present my boss with a weekly productivity log?

I usually help various co-workers on assignments around the office. Should I submit a log to my boss every week, listing my input around the office? I just want him to know that I am being productive or should I just continue to keep quiet and do my work? When my boss comes over to my desk, it’s obvious that I am working on something and I am being productive, this is not high school. Why should I provide him with a weekly log? My boss did not request a weekly log. However, my performance review mentioned a problem with prioritizing assignments and meeting deadlines and I don’t think he realize how much work I have and why I can’t meet deadlines. I think If I presented a weekly productivity log will just give him another reason to be bossy, annoying and nag the h*ll out of me. I already feel like I am being watched CAREFULLY, something like a fish in a fish bowl.