Power Play

About this chapter

Power Play is the second chapter of Class 8 Ganita Prakash Part 1. It opens with an impossible-looking task — Estu, Roxie and friends folding a 0.001 cm sheet of paper. After 10 folds it crosses 1 cm, after 17 folds it is about 131 cm, after 30 folds it is about 10.7 km (the height at which planes fly) and after 46 folds it can reach the Moon. This 'doubling each time' is multiplicative or exponential growth, and the chapter shows that it is best written using powers — 0.001 × 2^n. From this opener the chapter builds six big ideas — multiplicative or exponential growth and how it differs from linear growth; exponential notation with base and exponent (5^4 = 625, the Stones that Shine poem and Magical Pond doubling); the three laws of exponents for counting numbers (n^a × n^b = n^(a+b), (n^a)^b = n^(ab), n^a ÷ n^b = n^(a−b)) along with m^a × n^a = (mn)^a and combinations (Estu's 4 dresses × 3 caps); zero and negative exponents (n^0 = 1, n^(−a) = 1/n^a) and Power Lines; powers of 10 to read big numbers and scientific or standard form x × 10^y; and finally 'Did You Ever Wonder?' — estimation using powers, Tulābhāra, pādayātra and a tour of populations from one northern white rhino to 10^25 drops of water on Earth. CTET Paper 2 Mathematics tests this chapter through laws-of-exponent simplifications, prime factorisation in exponential form, expanded-form questions on numbers like 47561, scientific-notation conversions and 'why does multiplying by a number greater than 1 make it grow so fast?' pedagogy items. The four tests — Practice 15, Quiz 15, Hard 15, Mastery 30 — cover all six ideas at CTET depth.