Appendix C
Anno's Magic Seeds by Mitsumasa Anno
One Grain of Rice: A Mathematical Folktale by Demi
1. A group of planted seeds grows by 35% every hour. If Anno begins with 100 seeds, how many are there after 6 hours?
2. In his first year Jack produced 2 seeds. In his second year he produced three-times as many seeds. In his third year he produced 5 times as many seeds as the first year. How many seeds will Jack have produced in his first 3 years? If he sells the seeds for $200.00 each, how much will he have made?
3. From his earnings of seed sales, Jack saved $2.00 on January 1, $4.00 on February 1, $8.00 on March 1, $16.00 on April 1, and so on. How much money would he save in one year?
4. Jack sold 100 seeds in five days. Each day he sold 6 more than the day before. How many seeds did he sell on the first day?
5. The amount of money Rani received for the grains of rice she sold was $1,000. On January 1, 2002 she put the money in an interest yielding savings account. It grows at a constant rate of 2% per year. In what year does the amount first exceed $1,500?
6. Rani passed around a basket of cooked grains of rice to the girls at her party. Before the party she ate 5 grains and gave a friend 3. Eight girls arrived at the party. The first girl took a grain, the second girl took 3 grains, the third girl took 5 grains and so on, each girl taking two more than the girl before. After the last girl took her grains, the basket was empty. How many grains were in the basket at the beginning?
7. One bowl holds four thousand ninety-six grains of rice. How many grains would it take to fill 14 bowls? If there are 93,814 grains, how many bowls will it take to hold them all?
8. One deer can carry one basket of rice containing 8,388,608 grains. One Brahma bull can carry two baskets of rice containing 2,097,152 total grains. Which team of animals can carry more grains: 4 deer or 15 Brahma bulls? How many more grains can that animal carry? How many more bulls are needed to carry the same amount as four deer?
9. How many grains of rice did Rani get on the 5th day? How many grains of rice did she get on the 10th day? How many grains of rice did Rani get on the 15th day?
10. What if, on the 10th day some rice fell out of the bag before it was delivered to Rani, and she only got 500 grains, and then this amount kept getting doubled. How many grains of rice would she get on the 15th day? On the 20th day? Do you have to compute this out, or is there some way you could have predicted the answer more easily?
Appendix C Answer Key
1. 605
2. 18 seeds; $3600
3. $8,190
4. 8
5. halfway through the year 2022
6. 72
7. 57,344; 23
8. deer team = 33,554,432 bull team = 31,457,280; 2,097,152; 1; (Again, we see a pattern with the numbers. The amount of difference with these two teams is the same amount as one Brahma bull can carry.)
9. 512; 1,024; 32,768
10. 16,000; 512,000; answers will vary
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