Grade 6 • Maths • Ganita Prakash
Number Play
~ patterns, puzzles & the magic of numbers ~
🔢 ✏️ 🧩 🔍 📐 ✨
💡 Big Idea:
Numbers aren't just for counting — we can play with them to spot
patterns, make estimates,
solve puzzles, and win games!
This whole way of thinking is called computational thinking.
Children stand in a line. Each says a number = the count of taller neighbours they have.
- 0 → no taller neighbour 1 → one taller neighbour 2 → both neighbours taller
- End children can never say '2' — they only have one neighbour!
- All children of same height → everyone says 0
Rule
A cell is a supercell if its number is greater than all its neighbouring cells
(left, right — and top/bottom too, in a grid).
- The largest number in a table is ALWAYS a supercell ✔
- The smallest number can NEVER be a supercell ✘ (neighbours are always bigger)
- To get max supercells: fill alternately — high, low, high, low...
- Numbers are placed by estimating their position between two marked points
- Always check the gap/interval between marked numbers first, then divide equally
- Circle the smallest & box the largest in any sequence given
| 1-digit | 2-digit | 3-digit | 4-digit | 5-digit |
|---|
| 9 | 90 | 900 | 9,000 | 90,000 |
Digit Sum
Add up all digits of a number → e.g. 68 → 6+8 = 14.
Numbers like 176, 545 also have digit sum 14!
- Digit '7' appears 20 times from 1–100, and 300 times from 1–1000
- 3-digit numbers with consecutive digits (like 345) → digit sum is always a multiple of 3
Meaning
A palindrome reads the same forwards and backwards →
66, 121, 575, 1111
Reverse-and-Add trick: take a number, add it to its reverse, repeat till you get a palindrome!
34 + 43
➜
77 ✔ palindrome!
29 + 92 = 121
➜
✔ palindrome!
- Every 2-digit start number eventually reaches a palindrome ✔
- For 3-digit numbers → still unsolved! (196 is suspected to never reach one 👀)
6 Kaprekar's Magic Number
By D.R. Kaprekar (Devlali, Maharashtra) — discovered in 1949.
Take any 4-digit number (≥2 different digits)
↓
A = largest arrangement B = smallest arrangement
↓
C = A − B → repeat with C
↓
You ALWAYS land on 6174 !!
Example
6382 → 8632−2368=6264 → 6642−2466=4176 → 7641−1467=6174 ✨
- 6174 = the "Kaprekar constant" for 4-digit numbers
- For 3-digit numbers, the repeating number is 495
7 Clock & Calendar Numbers
- Special clock patterns: 4:44, 10:10, 12:21 — try finding more!
- Palindromic dates: digits read same both ways → e.g. 11/02/2011
- Calendars repeat: after 6 years (with 1 leap year) or 5 years (with 2 leap years) in between
8 Mental Math & Estimation
Adding smartly
Use middle numbers more than once:
3400 = 1500+1500+400
Estimation
Don't need the exact count — a reasonable guess is enough!
e.g. students in school ≈ 500
Always / Sometimes / Never? — test digit-count rules with real examples before deciding!
9 Number Patterns in Shapes
Instead of adding one-by-one, look for repeating groups and multiply — much quicker!
e.g. 8 boxes of 40 + 10 boxes of 50 = (8×40) + (10×50) = 320 + 500 = 820
10 The Collatz Conjecture 🧩
Rule
Start with any number →
if even: divide by 2 |
if odd: multiply by 3, add 1 → repeat!
12
➜
6
➜
3
➜
10
➜
5
➜
16
➜
8
➜
4
➜
2
➜
1 🎉
Proposed by Lothar Collatz in 1937 — believed to always reach 1, but
still unproven for every number! One of maths' great mysteries.
11 Games & Winning Strategies 🎮
Game "21"
Take turns adding 1, 2 or 3 to a running total. First to reach 21 wins!
Winning trick: always land on multiples of 4 → 5, 9, 13, 17, 21
Try your own versions — change the target number or the amount you can add, and find the new pattern!
✅ Quick Revision Checklist
- Meaning of a supercell + why smallest number can never be one
- Placing numbers correctly on a number line
- Digit sums & counting digit occurrences
- Palindrome meaning + reverse-and-add trick
- Kaprekar's steps → constant is 6174
- Palindromic clock times & calendar repeat rule
- Mental addition using repeated middle numbers
- Quick pattern-based summation (groups, not one-by-one)
- Collatz rule: even→÷2, odd→×3+1
- Winning strategy for the game "21"