Number Play

About this chapter

Number Play is the fifth chapter of Class 8 Ganita Prakash Part 1. It revisits factors, multiples, parity and remainders from earlier classes, but now uses algebra and visual block models to prove why divisibility shortcuts work — not just how to use them. The chapter moves through six big ideas. First, sums of consecutive numbers and the parity of expressions like a ± b ± c ± d, where switching one sign changes the value by an even number. Second, when adding two even numbers gives a multiple of 4, using the forms 4p and 4q + 2. Third, the Always/Sometimes/Never test for divisibility statements — if a divides M and N, then a divides M + N and M − N; if A is divisible by both k and m, then A is divisible by the LCM of k and m. Fourth, the divisibility shortcuts for 9, 3, and 11 derived from place-value remainders (each digit equals the remainder its place value leaves when divided by 9; alternating + and − signs for 11). Fifth, digital roots — repeated digit-sum to a single digit — and Aryabhata II's Mahasiddhanta link. Sixth, cryptarithms where letters stand for digits. CTET Paper 2 tests the chapter through divisibility-rule MCQs, parity reasoning, statement-based always/sometimes/never items, digital-root applications and pedagogy items on the 'why' behind shortcuts. The four tests — Practice 15, Quiz 15, Hard 15, Mastery 30 — cover all six ideas at CTET depth.