Anno's Mysterious Multiplying Jar

I saw this book as I walked past  the children's  books at the library.  I picked it up because I had seen it when Tom and I stayed at a bed and breakfast on Russian Hill in San Francisco thirty years ago. 

I am not a believer in my ability to understand Math. I took College Algebra and College Trig because I didn't like it when people told me I couldn't understand Math because I was a girl.  I passed both courses. I hate to have someone tell me I can't do anything.
I've learned that I can memorize Math formulas but they don't stick with me.  I learned when I memorized the multiplication facts in fourth grade that I don't believe what people tell me about numbers.  I especially dislike people saying,   "Just memorize it.  Don't worry about understanding it.  Just accept it."  

1 X 2 was easy to see.  7 X 8 was not.  Periodically, I would make seven rows of eight dots or eight rows of seven dots and count them one by one to see that there were really 56 dots total.  It is clear that I am visual when it comes to Math.  (And also, that I am a skeptic about what I am told.)

And that is what appeals to me about this PICTURE BOOK.  It explains the math concept, Factorials,  through pictures. 

First there is the Mysterious Multiplying Jar.  In it is water which becomes the sea and in the sea is an island. And then the fun begins.

On the island are two countries.

In each of the two countries are three mountains.

By now you have probably noticed that although there are two countries and three mountains in each country, the pictures of each item is different.  Different-looking countries, different-looking mountains. That is one of the aspects that I find fascinating.  So much to notice besides the numbers.  A small child and I could sit and just look at the pictures and notice what is on one mountain that is the same on another mountain.  Then we could notice what was on one mountain and NOT on the other mountain.  We could count things.

Eventually there are nine boxes in eight cupboards in seven rooms in six houses in five villages in four walled kingdoms on each of the three mountains...lots and lots and lots of items.  And guess what.  There are ten of these Mysterious multiplying jars in each of those nine boxes. 

And then the Annos explain the same concept with dots. Here is the page showing dots rather than the houses in the villages.  6! = 6x5x4x3x2x1= 720.

They continue with the dots until they fill up two complete pages with dots to represent the eight cupboards in each room.  It becomes quite clear why mathematicians use the factorial, 8!, to represent that number of things.

Anno's Mysterious Multipying Jar was written by Masaichiro and Mitsumasa Anno in 1981.  It is fun as a picture book and I think it would be helpful to any student encountering factorials for the first time, especially if they think like I do.

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