Number Play - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Number Play is the chapter where students learn to experiment like mathematicians. Instead of only applying known rules, they observe patterns, test examples, make guesses, and then explain why the pattern works. It strengthens mental maths and logical confidence.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Patterns need testing

A pattern seen in three examples may or may not always work. Good mathematics asks: does it always work, and why?

Factors and multiples

A factor divides a number exactly. A multiple is obtained by multiplying a number by whole numbers. These ideas support divisibility and later LCM/HCF.

Divisibility tricks

Divisibility tests are shortcuts based on place value. They are not magic; they come from how numbers are built.

3. Rules and formulas to remember

• Even number: 2n. Any number divisible by 2.
• Odd number: 2n + 1. One more than an even number.
• Divisible by 9: Sum of digits is divisible by 9. A place-value shortcut.
• Multiple of a: a x n. Where n is a whole number.

4. Worked examples

Example 1: Is 7,326 divisible by 9?

Digit sum = 7 + 3 + 2 + 6 = 18. Since 18 is divisible by 9, 7,326 is divisible by 9.

Example 2: Find the first five multiples of 12.

12, 24, 36, 48, 60.

Example 3: Write three factors of 36 greater than 4.

6, 9, 12, 18, or 36. Any three are acceptable.

Example 4: Show why the sum of two odd numbers is even.

Let odd numbers be 2a + 1 and 2b + 1. Sum = 2a + 2b + 2 = 2(a + b + 1), which is even.

5. Activity corner

Choose a two-digit number, reverse its digits, subtract the smaller from the larger, and study the result. Students notice multiples of 9, then explain using place value.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Calling every observed pattern a rule Fix: Test many cases and try to explain the reason.
• Mistake: Mixing up factor and multiple Fix: Factor divides; multiple is produced by multiplying.
• Mistake: Using divisibility tests without checking the full condition Fix: For 6, the number must be divisible by both 2 and 3.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Is 4,815 divisible by 3?
2. List all factors of 24.
3. Find the 8th multiple of 7.
4. Is 2,730 divisible by 6?
5. What is the form of an odd number?
6. Give one reason number puzzles are useful.

9. Answer key

1. Is 4,815 divisible by 3? Answer: Yes, digit sum is 18.

2. List all factors of 24. Answer: 1, 2, 3, 4, 6, 8, 12, 24.

3. Find the 8th multiple of 7. Answer: 56.

4. Is 2,730 divisible by 6? Answer: Yes, it is even and digit sum 12 is divisible by 3.

5. What is the form of an odd number? Answer: 2n + 1.

6. Give one reason number puzzles are useful. Answer: They build pattern recognition and proof thinking.

10. Quick revision

• Main themes: number patterns, divisibility, factors, multiples, puzzles.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.