NCERT Ganita Prakash, Class 6, textbook pages 55–73

How to teach Class 6 Maths Chapter 3, Number Play, at home

Number puzzles, palindromes, estimation and mental maths, taught with things you already have at home: a 20-minute activity, a game for the week, a 5-day plan and the mistakes to watch for.

3524 → 3087 → 8352→ 6174 → 6174Kaprekar’s magic number

NCERT Class 6 Maths Chapter 3 Number Play: what it teaches

A playful chapter: numbers that tell things (supercells), palindromes, Kaprekar’s magic number 6174, the Collatz conjecture, clock and calendar patterns, mental maths tricks and estimation, and games with winning strategies.

Why it matters later. Number play builds number sense, estimation and reasoning used across all of mathematics.

See it: this chapter in pictures

47 + 74 = 12156 + 65 = 121reverse and add → palindrome
Palindromes read the same both ways.
Collatz from 6:6 → 3 → 10 → 5 → 16→ 8 → 4 → 2 → 1even: halve odd: ×3 + 1
Nobody has proved it always reaches 1.
21 game: say 3, 6, 9… 18 to win
Games have winning strategies to discover.

You need

  • paper and pencil
  • a calendar
  • a calculator for checking

Tonight’s 20 minutes

  1. Pick a 4-digit number (not all digits the same). Arrange digits largest-to-smallest minus smallest-to-largest. Repeat: you reach 6174.
  2. Reverse-and-add: 47 + 74 = 121, a palindrome. Try 56, 87.
  3. Collatz: start with any number; if even halve it, if odd ×3 +1. Do you always reach 1?
  4. Estimate: how many steps from home to school? Then count.

Words to use

  • palindrome
  • Kaprekar constant
  • conjecture
  • estimate
  • strategy
  • mental maths

Watch for

  • Errors in long subtractions for Kaprekar. Keep leading zeros: 1000 − 0001 needs care.
  • Treating estimates as wild guesses. Base estimates on something measured: count 10 steps, then scale up.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouTry Kaprekar with 3524.

Your child5432 − 2345 = 3087.

YouKeep going.

Your child8730 − 0378 = 8352… then 6174!

YouAnd again?

Your child7641 − 1467 = 6174. It’s stuck!

A game for this week: 21 game

  1. Players take turns counting on 1 or 2 numbers from 1.
  2. Whoever says 21 wins.
  3. Play several rounds and find the winning numbers (3, 6, 9, 12, 15, 18).
  4. Change the target and find the new strategy.

A 5-day plan, 20 minutes a day

  1. Day 1Kaprekar’s 6174.
  2. Day 2Reverse-and-add palindromes.
  3. Day 3Collatz sequences.
  4. Day 4Estimation challenges.
  5. Day 521 game.

Everyday moments to practise

  • Car number palindromes.
  • Estimating crowd sizes.
  • Calendar date patterns.
  • Game strategies.

Quick check

Ask these at the end of the week. Tap to see the answer.

Is 12321 a palindrome?

Yes.

Kaprekar’s constant?

6174.

Collatz from 6: what comes next?

3 (6 is even, so halve it).

Ready for the next chapter when your child…

  • Explores number puzzles with persistence.
  • Estimates sensibly.
  • Explains a winning strategy.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Prakash (Class 6). See the full Class 6 parent guide for every chapter.

Questions parents ask

What is Kaprekar’s constant?

6174: the number you reach by repeatedly subtracting a 4-digit number’s smallest arrangement from its largest.

What is the Collatz conjecture?

A still-unproved idea that repeated halving or ×3+1 always reaches 1.

Why is this chapter in maths?

It builds curiosity, number sense and reasoning.