While I was in elementary school, my art teacher used to teach me how to paper cut. It's really easy to practice paper cut. You just need to learn how to fold them properly and knowing the specific place to cut. Moreover, if you do not expect any specific shapes out of your paper cut, you can just fold the an uncut paper several times and cut it freely as you want, it will turn out to be some interesting shapes that you wouldn't even expect.
Crochet would also be an interesting workshop to do at the nursing home. Moreover, I found several variable workshop that are applicable. Here are some pictures I found on internet.