Power Play
NCERT Class 8 Mathematics Chapter 2: Power Play (Pages 19–47)
Summary of Power Play
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Power Play at a Glance
CBSE
Class 8
Mathematics
Ganita Prakash Part I
2
19–47
7 study resources
Power Play Summary
In this chapter, students are introduced to the fascinating idea of folding a sheet of paper and how its thickness increases dramatically with each fold. It begins with an engaging challenge: how many times can you fold a large sheet of paper? Many commonly believe that you can only fold a paper a maximum of seven times. However, the chapter encourages students to experiment with different types of paper, like thinner newspaper or tissue paper, to see if that changes the number of folds possible. The chapter then delves into the concept of thickness growth with each fold. By assuming the initial thickness of standard paper is one thousandth of a centimeter, students are prompted to make guesses about the thickness after thirty folds and then after forty-six folds. Surprisingly, they learn that after just thirty folds, the thickness can reach over ten kilometers, reminiscent of the height at which airplanes typically fly. The concept of multidimensional growth is vividly illustrated, as the thickness roughly doubles with each fold. By the end, students will find it astonishing to realize that after forty-six folds, the thickness of the paper surpasses seven hundred thousand kilometers, even stretching out to reach the vicinity of the Moon! Next, the chapter provides a table showcasing the thickness of the paper as it is folded from one to seventeen times. This visual representation aids in understanding the substantial changes in thickness. For example, after ten folds, it measures a little over one centimeter, and after seventeen folds, it becomes about one hundred thirty centimeters, or slightly over four feet tall. The chapter emphasizes the power of multiplicative growth, often called exponential growth, showing how the thickness grows significantly at each step. For example, students are asked to analyze the increase in thickness after every group of folds, such as from ten to twenty folds, where the thickness increases by one thousand twenty-four times. This exploration introduces the fundamental ideas of exponential notation and operations, explaining how we can represent growth mathematically. By understanding that each fold doubles the thickness, students also encounter the concept of exponents. The chapter explains how a single fold of paper could be represented succinctly as a multiplication of twos, leading to an expression of thickness that relies on exponential notation. The transition from simple multiplication to exponential forms not only enriches their understanding of math but also illustrates how large numbers can emerge from simple concepts. Overall, this chapter serves as an engaging introduction to exponential growth through a practical and relatable activity - folding paper, turning what seems like a simple exercise into a profound exploration of mathematical concepts.
