It's not a textbook, but it's not really a storybook either.
I had utterly forgotten about it until I saw your question and started thinking. When I was a kid, I really liked reading a set of childrens' encyclopedias that we had.
Thanks to Google, I think it was Childcraft Annual's Mathemagics.
From what I remember it was filled with short-story-type things illustrating various math and logic puzzles. I enjoyed reading and re-reading them and thinking through the logic puzzles.
This website has a review of the book and a few photos.
Two relevant quotes from there:
Mathemagic is laid out brilliantly. It baits the hook by opening with things kids love – puzzles, tricks and games. The first chapter, if read sequentially, takes readers by the hand and welcomes them into the world of math, logic, and the beauty of rational thought.
Because we read through Mathemagic as an evolving story, we noticed how each chapter got a little richer, a little more mathematical, but always practical, vibrant, and accessible. After puzzles and riddles, we got the history of numbers, counting, and math.
I'll also mention "Lockhart's Lament", not as something to read to your kids, but as something that is a good read for anyone interested in math. It illustrates how the "math" that is taught in schools really eliminates all that is fun in math: thinking, puzzling and coming up with solutions. Although, based on you asking this, I suspect that you probably already know that ;)