The children’s book I decided to read was the King’s Chessboard by David Birch. When the wise man refuses to accept a reward for his service to the king, the King insists and so the wise man asks for a payment of rice for each square of the King’s chessboard, and for the amount to be doubled each day. He then reaches to the end of the board in 64 days. The wise man asks for one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before. The emperor agreed. This becomes tons of rice, and the King realizes his error. This book has a clever plot to it, and is a great way to teach kids about exponents and exponential growth.
This book is a great way to show and teach exponential growth. With the plot you are able to understand the the effects of exponential growth in a pattern and able to to describe this pattern with a algebraic expression. In the story you have to find the number of grains for the 64th day. By the end of the period the King would have given out 274,877,906,944 tons of rice.
The exercise of working through this problem is used to explain exponents and exponential growth because with 64 squares on a chessboard, if the total number of grains doubles on successive squares, then the sum of the grains on all 64 squares is 1+ 2+4+8..and so forth for the 64 squares. The number of grains on the second half of the chessboard is 232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice (the square of the number of grains on the first half of the board plus itself).This story helps show how fast exponents like doubling, and how they are shown everywhere around us.
The exercise of working through this problem is used to explain exponents and exponential growth because with 64 squares on a chessboard, if the total number of grains doubles on successive squares, then the sum of the grains on all 64 squares is 1+ 2+4+8..and so forth for the 64 squares. The number of grains on the second half of the chessboard is 232 + 233 + 234 ... + 263, for a total of 264 − 232 grains of rice (the square of the number of grains on the first half of the board plus itself).This story helps show how fast exponents like doubling, and how they are shown everywhere around us.
you gave a great summary of the book and it sounds like a useful, cute book
ReplyDeleteThis sounds like an extension of the book Professor Little read to us about exponential growth, but sounds like it takes it to a higher level. Instead of just doubling the rice for a month, this book takes to the power of 64.......that would certainly be a lot of rice
ReplyDeletecatherine,
ReplyDeletegood post! this is another one of my favorite books for talking about exponential growth. you did a nice job of showing the calculations and how exponential growth works. you could have included a little bit more of an explanation on the effectiveness of literature in mathematics. but still good job.
professor little