OP I have been working out in gyms for years and have always carried a small notebook and pen with me. It's very common and no one will think its odd or strange. It really motivates me to stay on track and I get a lot of satisfaction out of putting a check mark next to each exercise as I complete it. There are actually a few women in my gym that bring their iPads with them so that they can follow along with their favorite exercise video - primarily floor exercises though.
Do what works for you - otherwise you'll never be successful. I also wear headphones as music totally motivates me, and it keeps gym creeps from talking to me. I'm at the gym to accomplish something, not get chatted up....although it is flattering
