Hello Grambeau,
I see that this is your first ever post, so I wish you welcome to the forum.
As my mother is living at home with us, I cannot answer your question. However I look forward to seeing what answers you get from those who do have people in care homes.
I do all I can to keep Mum nimble, fit and active. She is 86, has pretty advanced Alzheimers, and I try to get her to take a walk with her dog (15 to 20 mins or four rounds of the block) morning and evening. Also she does 'bum and tum' exercises which are her variation of pelvic floor exercises, a bit of gymnastics while lying on her bed. She likes this and I think it boosts her mood and helps her sleep at night. After all she can't spend all her time indoors sitting about.
When the sun shines, Mum goes into her garden and potters about. I am amazed at how physical she can sometimes be there, lots of weeding, and on other days she just carries a gardening hand fork around.
Mum is getting to the stage where she would prefer not to walk at all, but I stick to my guns and so there can sometimes be arguments or she sabotages my efforts by walking very slowly or nipping indoors after a few minutes. This is the Alzheimers at work, because she has always been a committed walker.
I heard from a friend in Australia that the favorite passtime in a care home for dementia patients was 'balloon tennis', a large balloon is hit with a rolled up newspaper, and the residents simply adore it, and roar with laughter.
Anyway, these are my thoughts on exercise. I look forward to seeing what others say to you. Keep posting and keep asking questions, lots of very lovely, experienced people here. All the best, BE