Chapter 13 — Algebra Play

Chapter 13 of the Class 8 Maths NCERT textbook (Ganita Prakash), "Algebra Play", uses algebra to explain and create mathematical tricks, puzzles, and numerical patterns such as 'Think of a Number' tricks, number pyramids, calendar grids, and divisibility tricks.

• Algebra behind the magic — The chapter models 'Think of a Number' tricks with an unknown, showing why the outcome is fixed no matter the starting number — revealing that the 'magic' is simply an algebraic identity in disguise.
• Structured number puzzles — Number pyramids, calendar-grid sums and shape-based grids are all solved by writing and solving equations, so puzzles become a training ground for setting up and manipulating expressions.
• Proving why tricks work — Algebra justifies patterns rigorously — why reversing a two-digit number and subtracting always gives a multiple of 9, or why abcabc is divisible by 7, 11 and 13 — alongside optimisation and word problems.

1. 01"Think of a Number" tricks always yield the same final result regardless of starting number (e.g., doubling, adding 4, dividing by 2, subtracting original = 2)
2. 02Number pyramids: each number is the sum of the two directly below it; unknown values can be found using algebraic equations
3. 03Calendar magic: finding which date was chosen from the sum of a 2×2 grid (sum = 4a + 16, where a is top-left number)
4. 04Largest product strategy: to maximize a 2-digit × 1-digit product using 3 given digits, use the largest digit as the multiplier and arrange the other two in decreasing order
5. 05Divisibility tricks work via algebra: reversing a 2-digit number and finding the difference gives 9(b – a), always divisible by 9
6. 06Algebra justifies mathematical statements: any 3-digit number abcabc is divisible by 7, 11, and 13 (their product is 1001)