Number Play – Class 6 Maths Chapter 3 Notes & NCERT PDF

Introduction

Numbers do much more than count. In Number Play we use numbers to convey information, find patterns, estimate, solve puzzles and even win games. The chapter also shows that some number questions are easy to ask but still unsolved by mathematicians!

Key Ideas

3.1 Numbers can Tell us Things

Children stand in a line and each says a number. The rule: each child says how many of their neighbours are taller (0, 1 or 2). Children at the ends have only one neighbour, so they can never say 2. With 5 children of different heights, 1, 1, 1, 1, 1 is impossible — the tallest child always says 0.

3.2 Supercells

A cell is a supercell if its number is larger than the numbers in all its neighbouring cells.

In a row, neighbours are left and right; in a grid, neighbours are left, right, top and bottom (e.g. 8632 beats 4580, 8280, 4795 and 1944). Key facts: the largest number is always a supercell; the smallest can never be one; so a table can never have zero supercells. To get the most supercells in a row, make every other cell a supercell.

3.3 Patterns of Numbers on the Number Line

Place numbers like 2180, 2754, 9950 and 9590 between the right thousands on a number line, and fill in missing marks by finding the step between labelled points.

3.4 Playing with Digits

3.5 Pretty Palindromic Patterns

A palindrome reads the same both ways: 66, 848, 575, 1111. With digits 1, 2, 3 there are 9 three-digit palindromes (111, 121, 131, 212, 222, 232, 313, 323, 333). Reverse-and-add: start with a 2-digit number, add its reverse, repeat until you get a palindrome. For 2-digit starts this always works; for 196 nobody knows!

3.6 The Magic Number of Kaprekar

D. R. Kaprekar, a school teacher from Devlali, Maharashtra, discovered in 1949: take a 4-digit number (at least two different digits), subtract the smallest arrangement of its digits from the largest, and repeat. You always reach 6174, the Kaprekar constant.

3.7 Clock and Calendar Numbers

Clock patterns: 4:44, 10:10, 12:21. Manish's birthday 20/12/2012 repeats "2012"; Meghana's 11/02/2011 is a palindrome date. Can a year's calendar be reused? Yes — after some years the days and dates match again.

3.8 Mental Math

Build big numbers from a few "middle" numbers: 38,800 = 25,000 + 400 × 2 + 13,000; 39,800 = 40,000 − 800 + 300 + 300. Always, sometimes, never: 4-digit + 2-digit can never give a 6-digit number (9,999 + 99 = 10,098); 5-digit + 5-digit can't be 18,500 (the smallest sum is 10,000 + 10,000 = 20,000); 5-digit − 5-digit can't be 91,500 (the biggest difference is 99,999 − 10,000 = 89,999).

3.9 Playing with Number Patterns

Grids like eight 32s in 4 rows are summed fastest by multiplication and grouping, not one-by-one adding.

3.10 The Collatz Conjecture — an unsolved mystery

Rule: if the number is even, halve it; if odd, multiply by 3 and add 1; repeat. 12 → 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. In 1937 Lothar Collatz conjectured every start reaches 1. It is still unproven today!

3.11 Simple Estimation

Paromita estimates ~100 children in her class (sections of 32, 29, 35) and ~500 in the school. Estimate steps, breaths, distances and hours sensibly.

3.12 Games and Winning Strategies

Game of 21: players add 1, 2 or 3; first to 21 wins. Say 1, 5, 9, 13, 17, 21 (jumps of 4) — the first player can always win by starting with 1.

Worked Examples

Figure it Out — Hints

Maths Words

Common Mistakes

Maths in Daily Life

Estimation for shopping, travel time and crowd size; palindromic dates and times; strategy games like 21 with family.