Blogpost #3
Ana Maria Lopez
Topic: Exponential
functions
Book title: The Kings chessboard
Author: David Birch and Illustrator:
Devis Grebu
1.
Summary: In a
far away land, the amazing King of India orders to his kingdom that the wise
man should be rewarded for his useful services. The wise man strongly insists
that he is just rewarded with just having the honor to serve the king. Yet,
this was not enough for this king. After insisting, the wise man says: “Tomorrow,
for the first square of your chessboard, give me one grain of rice; the next
day, for the second square, two grains of rice; the next day after that, four
grains of rice; then, the following day, eight grains for the next square of
your chessboard. Thus for each square give me twice the number of grains for
the square before it, and so on for every square of the chessboard”. Not
knowing the real trick the King agrees. The wise man begins to receive large
amount of bags of rice. At the end, they both end agreeing to end the rice deal
but yet the wise man continued to serve the king.
2.
The
mathematical concept presented in this story is the exponential function. In
this case, the chessboard has 64 squares; in this case it would be 64 days. In
this case, as the wise man descried, he received 1 grain on day 1, 2 grains on
day 2, 4 grains on day 3, 8 days on day 4, 16 grains on day 5, 32 on day 6 and
so on. In this case, the number of rice grains doubled every day for 64 days.
At the beginning, it might have seemed, to the king and to many others who read
the story, that the number of grans of rice was small. But as the numbers
became bigger and they kept doubling the number of grains of rice, the amount
of rice became really big. This situation can be modeled by the function 2^n.
3.
In this case,
the use of a simple pictures and a very straightforward plot, facilitates the
understanding of the exponential function. In this case, the author does a
really effective job on, very clearly and basically (with simple rice grains),
explaining such a complex topic. In this case, this situation of “ the King’s
Chessboard” illustrates the effect of doubling. Additionally, when applying a
mathematical concept to a real life situation, students in general can
understand the concept even better.
This story seems really similar to the one in class, and you did a great job of relating it to exponential functions. Your point about using a simple and straightforward plot to help understanding difficult concepts was a very good one. Also writing out the function was a really great idea!
ReplyDeleteI like how you chose to talk about a book that explains more challenging math, instead of the basic math skills like most math books do. You clearly understood the purpose of the book and it might even be a useful tool for us when studying for the exams!
ReplyDeleteOh this book is similar to the one in class. I agree with the previous comments above. This shows a cool new way of seeing exponential functions. Hopefully this helps, because I'm struggling in this chapter.
ReplyDeleteana,
ReplyDeletemuy excellente!! wonderful job of explaining this book and discussing in detail how it relates to exponential functions! i also agree with your comment that picture books can help understand a concept even better.
professor little