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Class 7 Mathematics Chapter 6 Number Play

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I. Chapter Summary:

This chapter explores interesting properties and patterns in numbers. It introduces students to concepts such as divisibility rules, prime and composite numbers, and interesting number tricks. The chapter encourages logical thinking and number sense by uncovering how numbers behave in different operations and sequences.

II. Key Concepts Covered:

• Divisibility Rules: Guidelines to quickly determine whether a number is divisible by 2, 3, 5, 9, etc.

• Prime Numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.

• Composite Numbers: Numbers having more than two divisors.

• Factors and Multiples: Understanding factors as numbers that divide a given number exactly and multiples as numbers obtained by multiplying the given number by integers.

• Odd and Even Numbers: Characteristics and properties.

• Patterns in Numbers: Observing sequences and special properties (e.g., squares, cubes).

• Number Tricks: Mathematical shortcuts and interesting observations for quick calculations.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which of the following numbers is prime?
   a) 15
   b) 17
   c) 21
   d) 27
   Answer: b) 17
   (PYQ 2021)

2. A number is divisible by 9 if:
   a) Sum of digits is divisible by 3
   b) Sum of digits is divisible by 9
   c) Number ends with 0
   d) Number is even
   Answer: b) Sum of digits is divisible by 9
   (PYQ 2020)

3. Which number is both even and prime?
   a) 2
   b) 4
   c) 6
   d) 8
   Answer: a) 2
   (PYQ 2019)

4. The factors of 12 are:
   a) 1, 2, 3, 4, 6, 12
   b) 1, 2, 6, 12
   c) 2, 3, 6
   d) 1, 3, 6, 12
   Answer: a) 1, 2, 3, 4, 6, 12
   (PYQ 2018)

(B) Short Answer Questions (2/3 Marks):

1. Define prime and composite numbers with examples.

2. State the divisibility rule for 5 and illustrate it with two examples.

3. List the factors of 24.

4. Explain the difference between multiples and factors.

(C) Long Answer Questions (5 Marks):

1. Explain the divisibility rules for 2, 3, 5, and 9 with examples.

2. Find all prime numbers between 1 and 50.

3. Prove that every composite number has at least one prime factor less than or equal to its square root.

4. Use number patterns to find the next three numbers in the sequence: 1, 4, 9, 16, …

(D) HOTS (Higher Order Thinking Skills) Questions:

1. If a number is divisible by both 2 and 3, is it divisible by 6? Explain with examples.

2. Find the smallest composite number that has exactly three factors.

IV. Key Formulas/Concepts:

• Divisibility Rules:

  • Divisible by 2 → Last digit even

  • Divisible by 3 → Sum of digits divisible by 3

  • Divisible by 5 → Last digit 0 or 5

  • Divisible by 9 → Sum of digits divisible by 9

• Prime numbers have exactly two factors: 1 and the number itself.

• Composite numbers have more than two factors.

• Factorization is expressing a number as a product of its factors.

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

• 1 Mark: Definitions and divisibility rules (2018, 2020)

• 2/3 Marks: Listing factors, prime and composite numbers (2019, 2021)

• 5 Marks: Prime factorization and number pattern problems (2018, 2022)

VIII. Real-World Application Examples to Connect with Topics:

• Cryptography and security systems use prime numbers.

• Divisibility rules simplify checks in everyday calculations like sharing items equally.

• Factors and multiples help in scheduling, resource allocation, and design layouts.

• Patterns in numbers are foundational for computer algorithms and programming.

IX. Student Tips & Strategies for Success (Class-Specific):

• Practice divisibility tests regularly to improve calculation speed.

• Memorize prime numbers up to 50 for quick reference.

• Understand factorization as a method to solve complex problems easily.

• Attempt varied problems involving number properties to strengthen logical thinking.

X. Career Guidance & Exploration (Class-Specific):

• For Classes 9–10:

  • Builds foundation for algebra and number theory useful in engineering and computer science.

  • Important for Olympiad preparation and NTSE exams.

• For Classes 11–12:

  • Essential in higher mathematics, cryptography, data science, and analytics.

  • Useful for competitive exams like JEE and other entrance tests.

XI. Important Notes:

• Always cross-check with the latest NCERT and CBSE updates for syllabus changes.

• Consistent practice with number properties enhances speed and accuracy.

• Focus on understanding concepts deeply rather than memorizing formulas.