PW Class 7 Maths Notes Chapter 6: Number Play
Neha Tanna9 Sept, 2026
Numbers may seem simple when you use them for counting, but understanding the patterns and rules behind them can become confusing. In Number Play, you explore even and odd numbers, number patterns, magic squares, the Virahāṅka–Fibonacci sequence, and alphametics. Identifying these patterns and applying the right rules may require careful practice.
PW Class 7 Maths Chapter 6 Notes help you understand these concepts through simple explanations, important rules, and examples. They bring the key ideas together in one place, making it easier to revise number patterns, practise logical problems, and strengthen your understanding of the chapter.
Why Do Numbers Follow Patterns?
Many mathematical problems become easier when you recognise patterns instead of calculating every answer separately. Number Play introduces relationships that help explain how numbers behave.
Even Numbers
Even numbers can be divided into pairs without any object being left over.
Examples: 2, 4, 6, 8, 10, 12…
Odd Numbers
Odd numbers always leave one object unpaired.
Examples: 1, 3, 5, 7, 9, 11…
These two groups of numbers are called parity, and they help us predict the result of many calculations.
Understanding the Rules of Even and Odd Numbers
The parity of numbers follows fixed mathematical rules.
|
Operation |
Result |
|
Even + Even |
Even |
|
Odd + Odd |
Even |
|
Even + Odd |
Odd |
Formulas for Even and Odd Numbers
-
nᵗʰ Even Number: 2n2n2n
-
nᵗʰ Odd Number: 2n−12n-12n−1
Example
|
n |
2n |
2n − 1 |
|
1 |
2 |
1 |
|
2 |
4 |
3 |
|
3 |
6 |
5 |
|
4 |
8 |
7 |
These formulas generate every even and odd number in order.
Exploring the Magic of Magic Squares
A magic square is a square arrangement of numbers where the sum of every row, column, and diagonal is the same.
Example of a 3 × 3 Magic Square
|
8 |
1 |
6 |
|
3 |
5 |
7 |
|
4 |
9 |
2 |
Every row, column, and diagonal adds up to 15.
Important Terms
-
Magic Square: A number grid with equal sums.
-
Magic Sum (Magic Constant): The common total of every row, column, and diagonal.
Magic Constant Formula
For an n × n magic square:
M=n(n2+1)2M=\frac{n(n^2+1)}{2}M=2n(n2+1)
This formula helps determine the magic sum for any square of order n.
The Virahāṅka–Fibonacci Number Pattern
One of the most famous number patterns begins with:
1, 2, 3, 5, 8, 13, 21, 34, …1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;\dots1,2,3,5,8,13,21,34,…
Each new number is obtained by adding the previous two numbers.
Rule
Next Term=Previous Term+Current Term
Continuing the Pattern
|
Previous Two Numbers |
Next Number |
|
1, 2 |
3 |
|
2, 3 |
5 |
|
3, 5 |
8 |
|
5, 8 |
13 |
|
8, 13 |
21 |
This sequence appears in mathematics, art, nature, and many interesting patterns.
A Brief Journey of the Virahāṅka–Fibonacci Sequence
The sequence was studied by several mathematicians long before it became widely known in Europe.
|
Mathematician |
Contribution |
|
Pingala (c. 300 BCE) |
Earliest reference to the pattern |
|
Virahāṅka (c. 700 CE) |
First explicit mathematical rule |
|
Gopala (c. 1135 CE) |
Continued the study of the sequence |
|
Hemachandra (c. 1150 CE) |
Further developed the pattern |
|
Fibonacci (1202 CE) |
Introduced the sequence to Europe |
This history shows how mathematical ideas developed across different cultures and time periods.
Decoding Alphametics: When Letters Represent Digits
Alphametics are number puzzles where letters replace digits.
Rules of Alphametics
-
Each letter represents one unique digit.
-
The same letter always has the same value.
-
Different letters represent different digits.
Example
T+T+T=UTT+T+T=UTT+T+T=UT
If:
5+5+5=155+5+5=155+5+5=15
Then:
-
T = 5
-
U = 1
The goal is to identify the correct digit represented by each letter using logical reasoning.
Class 7 Maths Chapter 6 Notes PDF
Use the Number Play Chapter 6 Notes PDF to revise parity rules, magic squares, the Virahāṅka–Fibonacci sequence, and alphametics before practising questions.
Class 7 Maths Chapter 6 Notes PDF
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How PW Notes for Class 7 Maths Chapter 6 Can Help You
PW Class 7 Maths Chapter 6 Notes cover the key concepts of Number Play in a simple and easy-to-revise format. They help you understand number patterns, remember important rules, and practise different types of mathematical problems.
-
Understand Even and Odd Numbers: Learn how even and odd numbers are identified and how they behave during addition.
-
Revise Number Rules: Quickly recall important parity rules and the formulas for finding the nth even and odd numbers.
-
Learn Magic Squares: Understand magic sums and how numbers are arranged so that rows, columns, and diagonals have the same total.
-
Understand the Virahāṅka–Fibonacci Sequence: Learn the pattern behind the sequence and how each term is formed from the previous two terms.
-
Solve Alphametic Puzzles: Understand how letters represent unique digits and use logical thinking to find the missing values.
-
Recall Key Concepts: Revise important definitions, formulas, rules, and examples in one place.
-
Strengthen Problem-Solving Skills: Use the notes to build confidence before attempting NCERT exercises and school-level questions.
Understanding number patterns can make mathematics more interesting and help you approach problems with better reasoning. Number Play introduces concepts such as even and odd numbers, magic squares, the Virahāṅka–Fibonacci sequence, and alphametics through different patterns and puzzles. PW Class 7 Maths Chapter 6 Notes help you revisit these concepts easily and build confidence before solving questions and preparing for school exams.
Related Resources
-
CBSE Class 7 Maths Sample Papers
CBSE Class 7 Maths Notes Chapter 6 FAQs
What are even numbers?
What is a magic square?
What is the main rule for letters in Alphametics?
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