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.
The Demi book is interesting for me. I find the geometrical display of the Anno book more comprehensible, but the kids seem to grasp the exponential growth of the numbers in the Demi story better, I'm sure in part because doubling exponentially is more understandable than factorials. The illustrations are also somewhat geometrically displayed as you get on into the story, but not so obviously so.
Every time I read it, my 6 y/o asks more questions. Tonight it was about the raja, what that meant, why was he selfish, etc. Then, in the back, there is a number table that shows how many grains of rice were delivered day by day. Tonight they made me read each and every number out! When I got to the 30th day, I read the number - 536,870,912. My 6 y/o asked me the question, "If you took one grain of rice away from that, how many would that be?" I showed her it would be the same number with the "2" less 1 = 1, because that was the units place, and she got that 12 - 1 would equal 11, and 912 - 1 would equal 911, etc.
This is a really fun website for doubling inquiry:
I just really enjoyed these tonight with my girls and felt like writing! Hope you all are having a relaxing summer reading math :o)
PS: You know, this is one of the better examples of how you can deeply learn all your elementary math from picture books.
Just in one evening, with three books read with my 4, 6 and 8 y/o (we also read the Anne Geddes "Ten In the Bed," that book is gorgeous btw!), we covered concepts of:
Counting backward and forwards by ones, twos, threes, fours, fives and tens;
Skip counting and multiplication
Spacial concepts (how *would* you fit 3 million plus jars in one jar :o?)
Along with a bit of geography, history, social studies, science and art. I'm not kidding, all of these were verbally and actively explored in the space of an hour.
Not bad for a bit of bedtime reading.
> How can you cover so many concepts in so short a time? My children > get confused with too many new topics. How much depth is presented? In one hour I would imagine you would hit upon each topic. If I do this with my daughter she is lost. >
I don't know if this helps, but because I am not going for mastery of the concepts until they are ready, there is no pressure. I am not "teaching", I'm being led by the books and by the questions the kids ask. If I ask a question and my kids don't respond, I just move on, rather than trying to push it. Last night for instance in the Anno book when we got to the fourth page of dots and their interest was obviously waning, I shut the book and moved on to the Demi book without feeling like I to finish it.
It's the repetition of the exposure that seems to do it. We do this virtually every day/night (and usually we also read some Spanish and story books besides, we do spend at least a couple hours reading a day). I have been talking about place value for over a year with my 6 y/o. So last night as reinforcement and new application, there just wasn't some formal intro from a book. Now, today I was thinking about pulling out the Math U See blocks and drawing decimal street to review those ideas for her since *she* brought it up through her question last night.
Again, my best comparison is learning language. How do children pick up the new words, grammar, etc.? They are constantly exposed to it from birth. This is really teaching math like language. It is second nature now for my 4 y/o to have three tomatoes on her plate at dinner, to ask for one more, and
*say* "Three plus one more makes four!" with joy and confidence. In the Anno book one page had five boxes and one had four; my 6 y/o silently calculated 10 thinking there were 5 and 5, and I showed her that there were only 4 on the other page, so it was 5 and 5 less 1 = ? She easily realized it was 9 .
. . In the new I Love Math book we have that we were reading they mentioned a dozen plus 2 "How much is a dozen?" "Twelve" (complete with a discussion about Hacker from Cyberspace, apparently a dozen was covered recently!) and I asked, then, how much is a dozen plus 2? "Fourteen." We have done this for over a year. She used to come up with a lot of wrong answers, but since it was play, that was okay, we'd just find out how she got her answer and think / write / or build the idea to get the right answer. Of course the 4 y/o is intently listening in to all of this, not comprehending it all, but when she is ready, these ideas will come easily to her because she has been exposed to them for so long.
From LivingMathForum, July 14, 2004