My family always loved projects that involved challenge, physical manipulation of objects, or educational value of some sort. We loved them in any combination of the three, as single elements or combinations of them. We liked things that we could do individually (like reading, in which individually doing it was often a requirement, in a sense, but could be done as a group all reading their own stuff, or someone reading things aloud to the rest).
Puzzles of all kinds were a favorite of us all. Word games. Number games. Logic puzzles. Riddles. Drawing/art-type puzzles. But one of the things we often did as a family project were jigsaw puzzles. The best thing about a jigsaw puzzle is that you can work on it as a group project all at once and together, or individually as you have time, with no one else being present.
I can remember times, when I was growing up, we had a table in the spare room that often had a jigsaw puzzle in progress sitting it. Sometimes, if the weather was bad and there were few options for outside activity, and there was nothing on television that captivated our attention, we would all head to the spare room and work on the puzzle as a group, each taking different sorts of pieces. One of us would work with all the straight-edged pieces, putting the edges of the puzzle together. Others of us would choose colors to focus on, like all the green or red or blue pieces, trying to begin filling in some of the pattern to start seeing the picture. Sometimes one of us would work on one section of the puzzle, pulling out pieces that looked as if they could be part of "the lake" or "the house" in the picture.
We sometimes made things more challenging by trying to work the puzzle without referring back to the picture on the top of the box, other than the first look when we started a session. Or, sometimes not looking at the box at all after the first opening of the box. THAT was the most challenging of all.
During the time of the construction of the puzzle, it was worked on every day, even if we were not doing it as a group, even if we were not kept inside by the weather. Every time we passed by that table, filled with little puzzle pieces and a growing, recognizable picture, we would stop (an uncontrollable urge) and spend five or ten minutes attaching a few more pieces to that picture.
It was always interesting if we started a puzzle on the kitchen table during times that we did not have a table in the spare room, or did not have a spare room in which to put a table. Mealtimes were a challenge. We had to eat around the puzzle, trying not to spill any of our food on the makeshift centerpiece! It was tempting to work on the puzzle while eating our sandwiches or soup or pasta. Sometimes we succeeded in waiting until dinner was over. Sometimes we were not successful in getting through the meal without working on the puzzle.
Jigsaw puzzles. They were great fun in our family. Every time we had one in progress, it was a family project that we all enjoyed. Once one was done and pulled back apart (after allowing it pride of place for a while for us to admire our finished work), we would go for a time without starting one. Then one of us would find a great picture of a place we had visited or lived, of an animal or house or castle or other intriguing scene, bring it home, open the box, and start the process all over again.