"Living Math" is an approach that uses real books (not textbooks), to build or supplement a math curriculum. The best resource for doing this is the Living Math website. There's a fantastic yahoo group associated with the site, called the Living Math Forum. It's a pretty high traffic group with tons of friendly and knowledgeable members who respond eagerly to questions. If you have a particular problem you're trying to solve or a more general question comparing various approaches, you will get detailed responses from that group!
If you click on "reader lists" you'll find hundreds of living math books, arranged by math topic. Unless you have the money and space for a huge library at home, you'll want to check most of these books out of the library. I do buy a lot of books, but I try to only purchase books that I can see having a long useful life, usually they have a lot of math content presented through an engaging story, and often they can be enjoyed by young children without touching on the math content at all.
For the youngest children, there are zillions of picture books that illustrate math concepts for young children. Some are designed just to get a math-concept across to kids with a little sugar-coating, like the Stuart Murphy MathStart books. Others are really stories, like One Grain of Rice and Math Curse, where the math comes along for the ride. There are some nice ones for teaching children about big numbers, like How Much is a Million, and Big Numbers. Most of these books have engaging pictures and stories with a bit of math slipped in. Some can easily be read to toddlers, and they'll begin to understand the math part over time.
For elementary age children, I love the Sir Cumference series. These books have great stories, set in the time of knights, and feature ridiculous wordplay, like Sir Cumference and the Sword in the Cone, or Sir Cumference and the Dragon of Pi. If it's not obvious from the titles, these books have quite a bit of real geometry going on, and it's well integrated into the storylines. Another favorite at my house is The Cat in Numberland, a story about Hotel Infinity where all the counting numbers live (one to a room) and how they find space for Zero when he shows up one day. The video "The Story of One" is a fun introduction to how humans started using numbers in the first place (it's available from Netflix).
Once your child enjoys reading novels (or if you'd like to read some novel-length books aloud), the Number Devil is a great story that introduces lots of interesting math concepts. I forgot to mention them at the meeting, but over the past few days my 8 year old has been devouring Murderous Maths, a series about math "with all the mean and ugly bits left in" that is published for audiences in the UK. You can order them from Horrible Books (along with Horrible Histories and Horrible Science - it's a British sense of humour thing, I guess). If you'd like to look at them first, let me know and you can come see mine.
For something completely different, check out James Tanton's Math Without Words. It's a series of visual math puzzles presented, well, without any words. It's hard to describe, but there is a review here, and it includes a few of the puzzles. James' books are available on Lulu.com, and there are many that I'd like to own someday. I bought the PDF of Math Without Words and had the whole thing printed so I could hang a few puzzles in the house for my kids to look at, and then get them down and work on them when we think we've figured them out. The first step for each puzzle is figuring out what you're trying to figure out!
If you're looking for something just a little more, well, "mathy," Living Math won't let you down! Ed Zacarro has many books that were designed for supplemental use in the classroom. Last year we used Primary Grade Challenge Math as the spine for our math explorations. It consists entirely of word problems, presented by a funny cartoon Einstein and a little mouse. Einstein and the mouse walk you through each type of problem, and then present four sets of five problems, increasing in difficulty. It worked great for us.
Life of Fred Math will provide you with a complete curriculum in story form. The author is a former teacher, and every math concept that he presents is motivated by the story he is telling. His books now start in elementary school and go through Calculus. The main critique of Life of Fred is that it doesn't have enough practice problems for kids to really get the concepts, but it would be easy to supplement that if your children enjoy the story.
I keep thinking this post should be over, then I remember some other resource that I shouldn't leave out. Math clubs or math circles can be a great way to get your kids talking about math and solving problems with their peers. A couple of books to help you set up a group math experience, even just with all of your kids, are Family Math and Get it Together, Math Problems for Groups.
I hope you have gotten a taste of just how wide ranging the resources are for doing math in a non-traditional way. Whether you want to use Living Math as your entire math program or just pull in the most interesting bits to supplement what you've chosen, Living Math can liven up your math routine.
