Anno's Mysterious Multiplying Jar, Demi's One Grain of Rice
I was reading Anno's Mysterious Multiplying Jar again tonight with my girls, followed up with One Grain of Rice by Demi. I thought to myself, these are concepts that most people wouldn't dream of attempting to expose a 4 and a 6 y/old to. One of the things I love about some of these books is the fact that you can get mileage out of them for years. Every time we read them we get something more out of them.
With the Anno book, the artwork and at least the first series of factorials are comprehensible even for younger kids. For example, if there are three mountains on two countries, both girls get that this is 2 sets of 3 = 6, and my 6 y/o could even go so far as the four kingdoms being 6 sets of 4 - skip count by 4's six times to get 24. Then my girls lose track of the sheer size of the number until we get to the dots, but even then, they can't track it well (the factorial multiplication is different than the doubling of course, and these two books are a great way to contrast that). My 8 y/o can comprehend the progression of 10! = (10x9x8x7x6x5x4x3x2x1), however.
From LivingMathForum, July 14, 2004