# One Girl, One Grain of Rice, and One Surprising Mathematical Sequence

Recently, I was thrilled to hear that One Grain of Rice was the “book of the week” in my son’s 2nd grade class.  When I started this blog in July, I planned to write about this book, but forgot all about it. So I was happy for the reminder.

The Book

One Grain of Rice is a mathematical folktale based on the Indian tale Sissa and the Troublesome Trifles recorded in Trickster Tales by I. G. Edmonds.

In the story, a young girl Rani, returns some spilled rice to the raja (another name for Indian king). The raja had been hoarding all the rice in his land which led to famine for the villagers.  Obligated to reward Rani for returning the rice, the raja tells Rani to name her price. When Rani asks for a single grain of rice, the raja convinces her to ask for more. In addition to the one grain, Rani asks that the raja double that amount for each of 30 days: 1 grain of rice on day one, 2 grains on day two, 4 on day three, 8 on day four and so on.  The raja agrees, certain Rani has once again asked for too little.

The tale is beautifully accompanied by Demi’s intricate, gilded illustrations. Inspired by traditional Indian miniature paintings of the sixteenth and seventeenth centuries, Demi created the artwork using Chinese brushes and a variety of paints and inks.

For more of Demi’s books go here . Even if you’re not in the market for a picture book,  click the link for some amazing cover art!

The Math

One Grain of Sand introduces children to the power of exponential growth.

An exponential growth pattern is a pattern that grows by a factor greater than 1. The growth factor for Rani’s rice reward is 2 because each successive term in the sequence can be obtained by multiplying the previous term by 2 (i.e., doubling).

In the original tale, Sissa and the Troublesome Trifles, the main character is an inventor  of a new game called chess. The inventor convinces the raja to give him a grain of rice on the first square on the chess board and to double that amount successively for each of the 64 squares on the board.

This problem is often referred to as the rice and/or wheat and chessboard problem:

If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?

My introduction to the wheat and chessboard problem was as a graduate student working for the middle school curriculum project Connected Mathematics.  Specifically, the problem below.

My experience working for Connected Mathematics was key in shaping my vision of learning/teaching mathematics.   I was inspired by their presentation of mathematical concepts (e.g., exponential growth and fractions) often in context, their attention to sense-making, and connection-noticing/seeking.

It was also the first time I realized the power of anchoring mathematical ideas to story.

The Magic

My children LOVE this book.

And while the mathematical surprise and wonder that comes with exponential patterns is magic enough, there is one more reason this book was magical.

Rani is a female character. A clever female character in a book that my son adores. A front and center character in a book for my daughter to read.  I say this for two reasons.

1. After watching this Rebel Girls  video ,  I’ve thought a lot about the types of books my children read and the characters to which they are drawn/exposed . And I’m more cognizant of what characters are in the kidslit books on our shelves.
2. The fact that Rani is a girl did not phase my son. Maybe this was particular to this story or because he is too young to care. And perhaps this will always be the case. But as my children grow, I hope to guide them to read stories that they may not consider at first. For example,  I will encourage my son to read a book The Girl that Drank the Moon by Kelly Barnhill (the main character is a girl). Because Boys should read “girl” books and vice versa.

So, I thank you Demi for adding mathematically-minded Rani to our list of picture book characters.

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Thanks and see you next Monday! #mathbookmagic