The Kings Chessboard

One of the first stories I read in grade school was the story "The Kings Chessboard". While this is essentially the same story as "One Grain of Rice", the day we read that in class I remembered the Kings Chessboard and it was one of my favorite stores in grade school.

1) "The Kings Chessboard"by David Birch starts off in Ancient India. A wise man who performed many good services for the King is summoned before him and granted a reward. The Wise man refuses to accept a reward from the King until the King gets angry. Eventually, the Wise Man decides to ask for a piece of grain per square on a chessboard and for each day that passes, so 64 days, with the amount of rice doubling per day. The court laughed at his request and everyone thought he was insane. Is the Wise man insane however? And will his request lead to just a simple small amount of rice, or so much more?

2) The King demands that the Wise Man accept a reward from him, so after some quick thinking the Wise Man decides that the King will grant him a grain of rice for every piece on a chessboard but for every next piece on the board the amount from the previous square will double. For the first square of the the chessboard, the wise man will receive one, for the second square two, the third square four, and so on. Eventually, the King stopped keeping track of the rice, but the servant and the royal weigher, who were in charge of bringing the rice to the Wise man noticed that the amount of rice was getting out of hand quite quickly. The Weigher was too scared to tell anyone about the imminent problem and the rice continued. As each day passed, the amount of rice grew and grew, until "one grain became two, then one ounce became two ounces, a pound became a pound, and so on". The final number came to 549,755,830,887 tons of rice. The King realized that there was not enough rice in India to fulfill this wish and eventually summoned the Wise Man to ask him to release him from the debt. The two converse and the Wise Man releases the King from the rice debt.

The story of the "Kings Chessboard" shows the power of exponential growth. The rice grows from the second day on by 2^x.
Day
1- 2^0= 1
2- 2^1= 2
3- 2^2= 4
4- 2^3= 8

and so on until 2^63, which is 18,446,744,073,709,551,615 grains of rice. This is a fun and creative way to introduce kids and even adults to the power of exponents. Using the board helps show that as you move to the next square, the number is doubled from the previous one.

3) Literature is a great way to teach math because it puts everything in an easy and straight forward way to think about it. Exponents for example can be hard to follow since it is figuring out the difference of doing math 2 times 3 versus the exponent 2^3 and doing 2 x 2 x 2. The Chessboard puts it into an easy to understand representation of how exponents work. Literature and visuals offer an alternative to dense math lecture and can break it down using real world concepts that we all live with to help us understand.