Blog 3 -- Two of Everything: A Chinese Folktale -- By: Lily Toy Hong -- August Turner

1)                  One day, while digging in his garden, a poor Chinese farmer unearths a brass pot.  He takes the pot back to his home to show to his wife.  On the way home, he drops his coin purse that held 5 coins.  He puts the coin purse in the pot so he wouldn't lose it again on the way home.  He gets home and shows the pot to his wife, who bends over the pot while inspecting it.  Her one and only hair-pin falls into the pot.  She searches around for it in the pot, and instead of finding 1 hair-pin and 1 coin purse, she finds 2 hair-pins and 2 coin purses!  The couple quickly realize the magical properties of the pot and double everything they have!  However, that is not enough, they want meat and cake and fresh fruit to double as well, but cannot afford these items.  The wife devises a clever plan to come up with sufficient funds to buy these items.  She adds the 5 additional coins from the second coin purse to the original coin purse, which now holds 10 coins.  She puts the purse into the pot, and now they have 20 coins!  They stop there, but if they continued doing the same procedure, they would’ve grown their wealth exponentially.

2)                  The mathematical concept in Two of Everything is: doubling or exponential growth.  Although the farmers only double their coins twice (from 5 to 10, and then 10 to 20), the story demonstrates the concept of exponential growth.  They start with 5 coins, which doubled to 10 after placing the purse in the pot.  They then double the purse that has 10 coins, so they have 20 coins.  They could then (the story doesn’t go in this direction, but easily could) double the 20 coins to get 40 coins, and then double the 40 coins to get 80, 80 to 160, 160 to 320, 320 to 640, 640 to 1280, 1280 to 2560, and so on.  The expression for this growth is 5 * 2^n, when n is greater than or equal to zero.  Although this book does not go beyond 5 * 2^2, and primarily focuses on multiplying by 2, the concept of exponential growth is briefly introduced and lays forth the foundation of this by describing how doubling works.

3)                  Everyone enjoys a story where the protagonist(s) end(s) up better off than where they started.  Most mathematical concepts that demonstrate an increase or growth of some kind are a great/easy way to create a story that elevates the main character’s position.  I think children, in fact most people, would rather learn or be taught subliminally.  I know I’d prefer to read and analyze a children’s book rather than sit in front of a text book and figure out why, for some random reason, Sally has 5 watermelons one day and then 160 watermelons 5 days later.