Doubling Numbers: One Grain of Rice

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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 rescued falling rice from a damaged basket and returned it to the raja. When the raja offered her a reward, she 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.

The children watched as one grain of rice grew to 1,073,741,824 after 30 days. They built blocks that double from 1 to 2 to 4 to 8 to 16 to 32. This almost hit the ceiling. We then counted the height of these blocks after the 30th double, and calculated that it would reach over 33,000 miles. Twelve more doubles and we reach the Sun.

I had the children use their fingers to count powers of two starting with 2 to 4 to 8 to 16 to 32 to 64 to 128 to 256 to 512 to 1,024. Please have them practice their powers of two by reciting these 10 numbers. I use a stop watch to time myself and then retime myself watching my time improve every time. This can be a fun exercise. If they are a little uncomfortable with the last 5 powers, just focus on 2,4,8,16 and 32.

If your child can add comfortably with carrying, have them fill out the attached pdf by doubling 30 times. If they are not adding with carrys yet, just have them write the 30 numbers using the below list of powers of 2.

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 1024

2^11 2048

2^12 4096

2^13 8192

2^14 16384

2^15 32768

2^16 65536

2^17 131072

2^18 262144

2^19 524288

2^20 1048576

2^21 2097152

2^22 4194304

2^23 8388608

2^24 16777216

2^25 33554432

2^26 67108864

2^27 134217728

2^28 268435456

2^29 536870912

2^30 1073741824

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.

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