The Rajah's Rice: A Mathematical Folktale from India adapted by David Barry
Students will experience large numbers and learn exponential representation and understand patterns and relations, powers of 2
Lesson Created by:
Joe Gelroth, Eugene Field Elementary, Manhattan, KS
- Book (The Rajah's Rice: A Mathematical Folktale from India, by David Barry), pencils, prepared chart of a chessboard and a four column chart, with columns labeled: "square", "grains of rice", "expressed as factors of 2", and "notation".
1. Launching the lesson (engage):
- Read the story and stop at an appropriate place to allow the students to work with the pattern that is beginning to emerge.
- Discuss the story up to this point. Is the Rajah foolish or wise? Is Chandra foolish, wise or is she trying to trick the Rajah?
2. Developing the lesson:
- Provide the students with a prepared chessboard chart and encourage them to continue the pattern. Be prepared to stop them well before they have reached the final square on the chessboard.
- A point of frustration will be reached because the numbers have become so large that is nearly impossible to fit them into the chessboard square. This is a good time to discuss how the numbers are calculated (successive multiplication of 2).
- Provide the students with a chart and have them rewrite the numbers of grain of rice as factors of 2. (64 = 2x2x2x2x2x2) Again, be prepared to stop them before frustration sets in.
- Finish reading the story and discover how the author "solved" the problem of dealing with large numbers.
- Discuss how it might be possible to write large numbers more easily. Guide the discussion to exponential notation. (Powers of 2). An additional column on the chart, will allow the students to easily write these large numbers as powers of 2. 21 22 23 24, etc.
- The students should come to understand that in the equation 2n every time n increase by 1, the number represented by 2n doubles. (24 is twice as large as 23).