NCERT Solutions for Class 7 Mathematics Chapter 6 Number Play
NCERT Solutions for Class 7 Mathematics Chapter 6 Number Play
NCERT Solutions for Class 7 Mathematics Chapter 6 Number Play
This worksheet provides complete and accurate NCERT Solutions for Class 7 Mathematics Chapter Number Play. This chapter helps students understand how numbers behave in patterns, arrangements, and logical reasoning situations. It develops analytical thinking and introduces concepts like parity (even-odd), sequences, grids, and magic squares. These solutions follow NCERT guidelines and ensure clear understanding for students and parents.
Chapter summary: concepts & themes
This chapter is activity-based and focuses on exploring number patterns through real-life and visual situations. Students learn how numbers convey information, how even and odd numbers behave, and how patterns form in grids and sequences. It also introduces fascinating mathematical ideas like magic squares and Fibonacci (Virahanka) numbers.
What this NCERT chapter covers?
• Understanding number patterns and arrangements
• Concept of parity (even and odd numbers)
• Properties of addition and subtraction of numbers
• Parity in grids and expressions
• Magic squares and their properties
• Introduction to Fibonacci sequence (Virahanka numbers)
How to use these NCERT solutions?
Students should first observe patterns and attempt questions independently. Then, they can refer to these solutions for correct reasoning and step-by-step answers. Teachers and parents can guide students in understanding logic rather than memorizing answers.
Student tips & learning tricks
• Focus on patterns rather than calculations
• Remember parity rules (even/odd behavior)
• Use logical thinking for grid and arrangement questions
• Practice drawing diagrams for better clarity
• Observe relationships between numbers carefully
Why NCERT solutions are important?
NCERT Solutions help students build strong reasoning and logical thinking skills. They improve problem-solving ability and prepare students for higher-level mathematics and competitive exams.
Complete answer key – NCERT solutions
Numbers Tell Us Things (Page 128)
Explanation: Each number represents how many taller children are standing in front of that child.
Answer (given arrangement):
0, 0, 1, 0, 3, 0, 3
Figure it Out (Page 128)
1. (a) Possible arrangement exists
(b) All zeros → heights increase left to right
(c) Strictly decreasing heights
(d) Alternating tall-short pattern
(e) First person tallest
(f) First 3 increasing, last 4 shorter
2. (a) Only Sometimes True
(b) Always True
(c) Always True
(d) Only Sometimes True
(e) Only Sometimes True
(f) 7 (maximum possible)
Picking Parity (Page 131)
Explanation: Parity means whether a number is even or odd.
1. (a) Even
(b) Even
(c) Even
(d) Even
2. Lakpa made a mistake
Reason:
odd + odd = even
even + even = even
Total cannot be odd (₹205 is odd)
3. (d) even – even = even
(e) odd – odd = even
(f) even – odd = odd
(g) odd – even = odd
Small Squares in Grids
Rule:
odd × odd = odd
otherwise = even
Examples:
(a) 27 × 13 → Odd
(b) 42 × 78 → Even
(c) 135 × 654 → Even
Parity of Expressions
Always even:
2n, 4n, 6k + 2
Always odd:
2n + 1, 4n + 3
Sometimes even/odd:
3n + 4, n + 5
Even & Odd Number Formulas
nth even number = 2n
nth odd number = 2n − 1
100th even number = 200
100th odd number = 199
Grids and Magic Squares (Page 133–136)
Explanation:
Numbers in circles represent sums of rows and columns.
Grid Solution Example:
9 1 3
8 2 4
7 6 5
Magic Square:
8 1 6
3 5 7
4 9 2
Magic sum = 15
Key Concepts:
• Sum of numbers 1–9 = 45
• Row sum = Column sum = 15
• Centre number = 5
• Numbers 1 and 9 cannot be at corners
• They are placed in middle positions
Important Observations:
• Minimum row sum = 6
• Maximum row sum = 24
• If sums fall outside this range → grid not possible
Fibonacci (Virahanka) Concept
Sequence:
1, 2, 3, 5, 8, 13…
Each number = sum of previous two
This sequence appears in patterns, nature, and mathematics
Summary
This chapter helps students understand number patterns, parity rules, and logical arrangements. It introduces important mathematical thinking skills through activities like grids and magic squares. It also connects mathematics with real-life patterns and sequences.
Build strong reasoning skills with these structured NCERT Solutions and enjoy learning mathematics in a fun and logical way.