I know you don't want to hear it, but as others have said, playing by themselves is completely normal and necessary for their development. If she's happy playing by herself feel free to do something else
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I think watching kids play is much more interesting/rewarding if you know what to look for, so maybe get a child development or child psychology book and read up. It's then quite interesting/exciting when you see them do something for the first time, little things that you might miss if you didn't know to watch out for it.
With regards to ideas for play;
role play - try new things doctors/shops/parents/post office/cafe/dentist anything you haven't done before. Also try expanding games you have played before. For example, if she brings you a tea cup instead of drinking, spill it and see if she clears it up or tells you off
. This can be an extension of/or extended by a real visit or a book.
Take anything you play with a lot into a different context, duplo is great in the bath or tub of water, diggers are great with mud/stones/sand, plastic food/tea set also good in the bath/with water or give her dried pasta to play with.
Fill tubs with jelly, cooked pasta, shaving foam, sand, stones etc (not all at once!) and then add animals/dinosaurs/cars. Hours of fun.
Bubbles of different colours, sizes etc are great.
Painting the wall/floor with water keeps mine busy for ages.
Slatdough is a good alternative to playdough, once she's made something you can cook it, paint it and keep it (or send to Granny if you don't want it cluttering up the house!).
Sticky-back plastic is great as an alternative to glueing. You can take some to the park and stick leaves/twigs etc on to make a nature collage, or tissue paper to make a stained glass window, or things of all one colour (how many green things can we find?) or rubbish to make a recycled picture.
Library for different books is essential I find.
Things like pairing socks is a job done and helps pre-reading skills
. Sorting pegs/cotton reels/buttons by colour is good. Threading beads onto string to make a necklace or 'sewing' also fun.
Fridge magnets are also very popular here. Things like tap-tap art and fuzzy felt are good as well (it says 5+ or something on the box, but it's fine as long as you supervise closely and make sure she doesn't eat any pieces), you could try very basic board games. Maybe see if you have a local toy library?
The Imagination Tree is a lovely website with great ideas for art/craft stuff on. It's a tad sickly-sweet, but fantastic ideas.