If you can muster up the patience, DIY is popular with kids that age because they love to be useful and competent. Put up shelves, use polyfilla to patch up the hole in the wall from your last DIY attempt, sand and refinish the dining table. Once done, it is there to be admired for years! This is why I prefer DIY to cookery.
Recently I grumpily consented to cut out the bits so dd2 could make a teddy bear, fully expecting that I would be doing the lion's share of the sewing myself. I dislike sewing and am not very good at it. But she managed nearly everything herself. It is a charming bear with a wonky demented smile which I find both appealing and sinister.
Has your child worked on a Halloween costume and some decorations yet? We are gearing up for that.
Some kids love to plan parties. That could involve anything from menu planning and cooking to selecting music and activities, decorating, considering the guest list, and producing invitations.
You could offer machines, either broken or intact, to be disassembled: a wind-up alarm clock, a derelict bicycle, a lock and key.
My partner's family always enjoyed making rag rugs together at this time of year.
Map reading. Once on a long road trip, my mum put my sister and me in charge of reading the map and telling her where to go. We were four and six. She had to obey our every order so long as it was safe and legal to do so. Utterly fantastic. We got lost many times. It was a great success from our point of view. You could do this in a car if you drive, or on foot in a town centre if you don't.
Today a friend's child showed me one of these guides: www.ispymichelin.com/i-spy-16-c.asp He was all fired up to look out for the different items pictured in the book and tick them off.