One Grain of Rice: Power of Doubling (9.23.10 Kindergarten)

Many years ago, there lived a selfish raja in India. He ruled that all

the people should give him almost all of their rice for safekeeping,

so that in a time of need there would be rice to eat. One year, a

famine hit and no one had any rice to eat, but the raja would not

give the stored rice to the people because he wanted to save it for

himself. One day a clever girl named Rani created a plan to help

the starving people of India. She asked the raja for one grain of

rice and for each day for thirty days she asked the raja to double

the amount of rice given the day before. The raja did not realize

how much one grain of rice would amount to if it were doubled

every day for one month. The raja learned a valuable lesson about

selfishness and Rani saved the people of India from starvation

through her cunningness and her understanding of math.

Start with one grain of rice on day one and two on day two, four on day three and so on.  Let's see how far they can go.  I am more interested in the children understanding the power of doubling.  I would be very happy if they understood 1,2,4,8.  Also, if you look at the numbers with them on each day, help them to recite the numbers using the ones, thousands, millions.  The children were surprisingly adept at reciting the numbers during class.

This is a list of the first thirty powers of two, the numbers of grains of rice Rani received on the 1st through 30th day.  Actually, she received 536,870,912 on the 30th day. The actual amount she received in total for the 30 days is the next double, 1,073,741,824 plus one.

2^0 1

2^1 2

2^2 4

2^3 8

2^4 16

2^5 32

2^6 64

2^7 128

2^8 256

2^9 512

2^10  1,024

2^11  2,048

2^12  4,096

2^13  8,192

2^14  16,384

2^15  32,768

2^16  65,536

2^17  131,072

2^18  262,144

2^19  524,288

2^20 1,048,576

2^21  2,097,152

2^22 4,194,304

2^23 8,388,608

2^24 16,777,216

2^25 33,554,432

2^26 67,108,864

2^27 134,217,728

2^28 268,435,456

2^29 536,870,912

2^30 1,073,741,824