Fair sharing folktale.
In my writing about fractions, I call situations where some quantity is shared equally among some number of people “equal sharing.” Many other people call these same kinds of situations “fair sharing.” But, as Elizabeth Fennema once pointed out to me, “fair” does not always mean “equal.”
Just a couple of days ago, I ran across a folktale called “A Fair Division” in the October 2003 issue of Highlights for Children. It shows very cleverly why “fair” is not always “equal” and it makes a good math problem too. Here’s my paraphrase of it (or you can view a jpg of the entire text, minus the hints the author gave for figuring it out. Yes, that’s right. I took out the hints!).
Two farmers, Ram and Shyam were eating chapatis. Ram had 3 pieces of the flat, round bread and Shyam had 5. A traveller who looked hungry and tired rode up to the two men. Ram and Shyam decided to share their chapatis with him. The 3 men stacked the 8 chapatis (like pancakes) and cut the stack into 3 equal parts. They shared the pieces equally and ate until nothing was left. The traveller, who was a nobleman, was so grateful that he gave the two farmers 8 gold coins for his share of the food.
After the traveller left, Ram and Shyam wondered how they should share the 8 gold coins. Ram said that there were 8 coins and only 2 people, so each person should get an equal share of 4 coins. “But that’s not fair,” said Shyam, “since I had 5 chapatis to begin with.” Ram could see his point, but he didn’t really want to give 5 of the coins to Shyam. So he suggested they go see Maulvi, who was very wise. Shyam agreed.
Ram and Shyam told the whole story to Maulvi. After thinking for a long time, he said that the fairest way to share the coins was to give Shyam 7 coins and Ram only 1 coin. Both men were surprised. But when they asked Maulvi to explain his reasoning, they were satisfied that it was a fair division of the 8 coins.
What do you think Maulvi’ reasoning could have been? What makes it fair?
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