# One Grain of Rice (K and 1st Grade) Doubling with the first 30 powers of 2 -- Exponential Growth

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.

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.

I taught the children a method of doubling where I start with 1, 2, 4, 8, and on the 10th day I am at 512. Then I estimate that 512 is close to 500. When I perform the 11th double, I achieve 1,000 or 1K (K is used to represent 1000 because one kilo is 1000). If this is done with a 3 by 10 grid, they quickly see that the next double is 2K, then 4K, 8K and so on until they reach 512K (estimate to 500,000); then double again to 1,000,000 or 1 million or 1M, then 2M, then 4M, then 8M, then 16M and so on until 512M on the 30th day. This method of doubling by estimating every 10th is an underestimation but gets us very close to the correct answer in a matter of seconds.

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 carries yet, just have them write the 30 numbers using the below list of powers of 2:

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 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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One_Grain_of_Rice_30_Doubles_to_1_Billoin.pdf | 564.86 KB |