One of the most important joys I would like to impart to my child is the joy of solving. I mean that I want my kids to feel adequate at solving problems and accomplished when they get the answer. I looked at algebra like a puzzle--knowing that I was given the tools during instruction, it was just a matter of figuring out how to use them. I can't say for sure why I have a joy of working on a problem. Why I might want to keep trying until I get the right answer.
I think one of the main reasons why I enjoyed it so much was because I was fairly certain I could actually solve it. When it came to math, the problems were based on that day's lesson, but not the exact same as the ones presented in class. At that time, in school, I hated being given problems that I hadn't been taught. It seemed pointless to flounder without knowing if there was a hope of finding the solution. My older daughter is the same way. She hated Spelling Power because she felt it was unfair to be tested on words before she knew them. (Spelling Power has an option for a pre-test or diagnostic test so children do not need to study words they already know how to spell. I could not make this differentiation to my daughter.) I would not give my children a math problem that they hadn't been given the tools to solve.
Another reason I think I enjoy the 'thrill of the hunt' when solving problems is puzzle books. I remember my mom spending a lot of time on those variety puzzle books and buying me my own copies. I still pick up books when I make my way to a book store or the magazine stand in the drugstore. These books are great for 7th or 8th graders and up. The reason why I wouldn't recommend them for most younger kids is because they assume a significant amount of prior knowledge and context, and many puzzles start at a high level. I would especially concentrate on logic problems--and by logic problems, I mean all of the many different types of problems that appear in the logic problem variety books. Those types of problems have less to do with generic information (unlike crossword puzzles) and more about the puzzling out of the answer. Some of the problems in the regular books would be OK for younger kids, but certainly not all. And keeping my experience above in mind, I would edit the content presented to the kids and assure that they have the basic skills necessary.
There are a number of fun puzzle books for available for younger kids. I found some cute puzzle books that were just the thing, though a little easy, for my 7 year-old. They're called My First Puzzles and there's a number of them. They are mini-books, about 3" square with a number of different activities. The front of the book recommends them for three and four year-olds, but I think that they are great for a beginning reader level. There are some easy crosswords, mazes, connect-the-dots and some other interesting puzzles. Another book I got for my older daughter (10) has a nice flip-book format, but only includes sudoku, word searches, and word finds. The sudoku is nice logic practice and word finds are good for spatial development.
So I'm trying to help my kids understand the joy of solving a problem for fun and I hope they bring that joy to solving other problems they come across in their schoolwork.