Blog #3 Jeff Greenberg

Jeff Greenberg 

Blog #3 

“The King’s Chessboard” by David Birch tells a story about a wise man whose service for the King needs to be rewarded. In the beginning of the story, the wise man insists that he doesn’t want a reward because it is a reward for him to serve the King. However, the King, frustrated, demands the wise man pick a reward or else face consequence. So, the wise man glances at the King’s chessboard and decides upon a reward. He decides for every square on the chessboard, the King should give twice the number of grains of rice for each square before it. The King doesn’t understand the math behind the agreement but agrees to it anyway to avoid embarrassment.

Towards the middle of the book, the agreement begins to take its course. On the first day, the king gave him one grain of rice. On the second day, the king gave him two grains of rice. On the third day, the King gave him four grains of rice. On the fourth day, the King gave him eight grains of rice, and so on.

Near the end of the book, the King’s helpers realize a problem. They couldn’t supply enough rice for the agreement. The 30^th day, the wise man accumulated so much rice that the King’s helpers and even the King’s wife needed to tell the King to stop the agreement. So, after much thought, the King met with the wise man. They both decided to stop the agreement. The King would also let the wise man continue to work for him, and from that day on the King used the agreement as a lesson to teach people not to let their pride get the best of them.

The mathematical concept presented in “The King’s Chessboard” by David Birch was exponential functions. The wise man gets twice the number of grains of rice for each square on the chessboard before it. There are 64 squares on a chessboard. So, on the first day, he got one grain. On the second day, he got two grains of rice. On the fifth day, he got sixty-four grains of rice. On the Thirty-first day, he got around two billion grains of rice. The exponential equation is represented by f (x)= 2^x, with the number 0 counting as the first day. The book does a great job of involving a moral around the mathematical concept. Since the King didn’t want others to know that he didn’t fully understand the math behind the agreement, he agreed to it anyway which resulted in his demise essentially. Thus, the King learned not to let his pride get the best of him.

I believe this story is an effective way of teaching exponential functions because they use a very simple concept of doubling each number before each square on the chessboard. Kids know what a chessboard is and they know what grains of rice are. They also know how to double numbers. This story emphasized that exponential functions have an output of larger numbers. The book also helped demonstrate this concept through its pictures of grains of rice multiplying on the chessboard.