Anno's Magic Seeds
I have read this picture book several times since we got it, but it has been put away for a few months. My 7 y/old daughter pulled it out last night and was trying to read it herself, and asked me to read it to her today. I recalled the last time we had sat down with it, she could only comprehend the first few pages of the math ideas. Today she astounded me with her progress in such a short time.
The story starts with a man giving Jack 2 magic seeds. The seeds are so satisfying that if you bake and eat one, you will not be hungry for a year. He was told to plant the other. This plant always bears 2 more seeds for each seed planted. So he eats one, plants one, year after year and he's a pretty happy and contented guy. But one year it occurs to him that this will go on forever. So he decides to find another way of getting food for one year, and plant 2 seeds instead of 1.
Of course, from that point, a doubling pattern emerges, but it has a twist, because each year Jack eats one before planting the rest. Then, as his store of seeds grows, he marries and has a child, so he feeds them, and they sell seeds, so keeping track of the math at the very end becomes very challenging.
The illustrations are delightful, clean, and orderly enough to facilitate skip counting, but not so symmetrical that it is contrived and obvious.
Now to go back to my daughter's progress. When he starts planting after the first doubling, we followed the book in asking the questions, how many seeds will he grow next year? This will always be double what was *planted* the year before, not what was grown. She got this easily, when months ago it was befuddling to her. In year 1, he grows 4 seeds plants, 3, in year 2 he grew 6 seeds planted 5, and in year 3 he grew 10, planted 9, year 4 grew 18, planted 17 . . . all this she got easily, she enjoys and understands doubling, we've read books and played with this idea for so long. Year 5 got to some numbers that she wasn't quite as proficient in, doubling 17, so she looked at the graphic to count. It was arrayed in 3 long rows, with 3 left over, and one seed in Jack's pocket.
I expected her to skip count by 3's, but she told me she was going to multiply. I said, wow, show me how. She counted the 3, then the row length of 10, and got 30, added the 3 and the 1, and correctly got 34.
I asked her how she knew to do this, I have not taught her this. She said that that was how she counted the tiles in the kitchen, she counted one side, then the other, and multiplied. We have read books like Amanda Bean's Amazing Dream that explain the step of going from skip counting to multiplication, but I had not seen her "get" this before, so it was fun hearing her tell me she had learned it while I was sleeping.
Here's where the versatility of the book comes on. On the next page (which has 66 seeds arrayed – 34, less the one he ate, doubled next year). It is arrayed in rows of 10 DOUBLES. So, she counted 2, 4, 6, . to 20. Then she skip counted "20, 40, 60 plus 6 = 66".
After taking his own seed, he also gave a seed to Alice who helped him, so he planted 64. From this point forward the math was stretching for her, but she kept it up for about 20 more minutes. In some cases, the math is broken down, so she couldn't figure out the big numbers, but if they said, "Each of the 5 guests got 2 seeds (at Jack and Alice's wedding :o)" she could compute the 10. Funny thing was, I saw that in 2 places, but she solved each differently. One she got that 5 doubled is 10. The other she skip counted 2, 4, 6, 8, 10. She asked me again if 5 times 2 is the same as 2 times 5 and verified it - this is a question she has asked a lot lately, so it is trying to stick in her mind, and thinking of the numbers as objects, like seeds per person, is helping her learn an algebraic property.
Just when I thought she was tiring from the math as the numbers were getting quite large, Jack, his wife and their child get hit with a hurricane. This was an interesting thing to read about after Katrina & Rita! He manages to save his house and 10 seeds. If you can get a copy of the book and read it, it is very poignant after the recent disasters
experienced for real, but Jack cheerfully starts all over, grateful they have food and planting seeds, because he knows how little he started with to begin with - one little seed.
My 5 y/old who had wandered over half-way through the reading pipes up "Ten seeds minus three seeds they ate is 6 seeds!" and then she of course counts the seeds in the picture one by one to see if she is right, finding that whoops, it's 7, but it's something to laugh about. This is the kind of book she practices skip counting by 2s and 10s. There are lots of groupings in the illustrations for a younger child to enjoy and count while you skim over the more complicated math.
My oldest son who recently finished a chapter on functions in algebra was sitting next to me reading it with us. At 13 he still enjoys books like this. He and I figured out a formula to account for the pattern of the seeds based on a table. This was very fun to relate this picture book to his algebra, LOL.
So that's kind of a review and a method example wrapped in one. I am an unabashed Anno math book fan. Some are better than others, but this one really is exceptional in that the age range of applicability is very wide.
Julie Brennan, 10/5/05