NCERT Class 6 Maths Chapter 3 – Number Play
NCERT Class 6 Maths Chapter 3 – Number Play
Introduction
Numbers are used everywhere in daily life. We use them for:
counting objects
measuring quantities
telling time
identifying patterns
solving puzzles
In Chapter 3 – Number Play, students explore numbers in creative ways. The chapter focuses on patterns, logical thinking, and interesting mathematical puzzles.
Instead of just performing calculations, students learn how numbers behave in different situations.
Where Do We Use Numbers?
Examples of real-life use of numbers:
Time on a clock
Calendar dates
Marks in exams
Height and weight measurements
Money transactions
Numbers help us organise our daily life.
Q. Think about various situations where we use numbers. List five different situations in
which numbers are used. See what your classmates have listed, share, and discuss.
Ans. Five different possible situations in which numbers are used -
1. Time
2. Calendar
3. Counting objects/Marks
4. Measurement of height & weight
5. Money
Section 3.1
Page No. 56
Q1. Can the children rearrange themselves so that the children standing at the ends say
‘2’?
Ans. No; There will be no one standing on the other side of the child standing at the end.
Q2. Can we arrange the children in a line so that all would say only 0s?
Ans. Yes; All the children in the line should be of same height.
Q3. Can two children standing next to each other say the same number?
Ans. Yes; Refer picture on page 55.
Q4. There are 5 children in a group, all of different heights. Can they stand such that four
of them say ‘1’ and the last one says ‘0’? Why or why not?
Ans. Yes, they can, if they are standing in ascending order of height.
Q5. For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?
Section 3.1 Numbers Can Tell Us Things
In this activity, children stand in a line and say numbers based on how many taller neighbours they have.
Rule:
A child says 1 if one neighbour is taller.
A child says 2 if both neighbours are taller.
A child says 0 if none are taller.
Question 1
Can the children at the ends say “2”?
Solution
No.
Reason:
Children at the ends have only one neighbour, not two.
So they cannot have two taller neighbours.
Question 2
Can all children say 0?
Solution
Yes.
If all children have equal height, then none of them will have taller neighbours.
Therefore every child says 0.
Question 3
Can two children standing together say the same number?
Solution
Yes.
Example:
Two children may both have exactly one taller neighbour, so both say 1.
Section 3.2 Supercells
A supercell is a cell that contains a number larger than its neighbouring cells.
Example:
In the table
200 577 626
The number 626 is a supercell because it is larger than its neighbours.
Question
Will the largest number in the table always be a supercell?
Solution
Yes.
The largest number must be greater than all neighbouring numbers.
Therefore it will always be a supercell.
Question
Can the smallest number be a supercell?
Solution
No.
A supercell must be larger than its neighbours.
Since the smallest number is smaller than other numbers, it cannot be a supercell.
Section 3.3 Patterns on the Number Line
Example numbers:
1050
1500
2180
2754
3600
5030
5300
8400
9590
9950
These numbers must be placed correctly between 1000 and 10,000 on the number line.
Learning Idea
Students understand:
number order
number magnitude
spacing between numbers
Digit Sum Activity
Example:
68 → 6 + 8 = 14
176 → 1 + 7 + 6 = 14
Both have digit sum 14.
Smallest number with digit sum 14
Digits must add to 14.
Example:
5 + 9 = 14
Smallest number = 59
Largest 5-digit number with digit sum 14
Largest arrangement:
95000
Because
9 + 5 = 14
Digit Detective Puzzle
How many times does digit 7 appear from 1 to 100?
Solution
Numbers containing 7:
7
17
27
37
47
57
67
77
87
97
70
71
72
73
74
75
76
78
79
Total occurrences = 20
Section 3.5 Palindromic Numbers
A palindrome reads the same forward and backward.
Examples:
66
575
848
1111
Example:
121 → same both directions.
3-digit palindromes using digits 1,2,3
111
121
131
212
222
232
313
323
333
Reverse and Add Method
Example
12 + 21 = 33
33 is a palindrome.
Sometimes we repeat the process until a palindrome appears.
Section 3.6 Kaprekar Constant
Steps:
1 Choose a 4-digit number (example 6382)
2 Arrange digits in descending order
3 Arrange digits in ascending order
4 Subtract
Example:
8632
2368
8632 − 2368 = 6264
Repeat process.
Eventually the number becomes
6174
This is called the Kaprekar Constant.
Section 3.7 Clock Number Patterns
Examples of interesting clock times:
4:44
11:11
12:21
10:10
These show patterns or palindromes.
Section 3.8 Mental Math
Students learn to combine numbers mentally to reach target values.
Example
1500 + 1500 + 400 = 3400
This improves mental calculation skills.
Section 3.9 Number Patterns
Students observe patterns in grids of numbers and find faster ways to calculate sums.
Instead of adding numbers one by one, students identify repeating structures.
Section 3.10 Collatz Conjecture
If number is even → divide by 2
If number is odd → multiply by 3 and add 1
Example starting from 12:
12 → 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Mathematicians believe every number eventually reaches 1, but it has not been fully proven.
Section 3.11 Estimation
Estimation means guessing a reasonable value without exact calculation.
Examples:
students in school
steps to classroom
distance between cities
Estimation helps in real-life decision making.
Section 3.12 Games with Numbers
Example game: Reach 21
Rules:
Players add 1, 2, or 3 to the previous number.
Goal: reach 21.
Winning strategy:
Say numbers in pattern
4 → 8 → 12 → 16 → 20 → 21
Chapter Summary
In this chapter students learned:
number patterns
digit sums
palindromes
Kaprekar constant
estimation
mathematical puzzles
number games
These activities develop logical thinking and problem solving skills.
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