Number Play
Numbers hide surprising patterns and puzzles. This Class 7 Ganita Prakash chapter plays with numbers — spotting and continuing patterns, exploring palindromes and digit puzzles, and reasoning about number properties — to sharpen number sense and logical thinking rather than rote calculation.
Learning objectives
- Spot and extend number patterns.
- Explore palindromes and digit puzzles.
- Reason about properties of numbers.
- Use logic to solve number games.
Key concepts
Patterns in numbers
Many number sequences follow a rule we can discover and continue. Some grow by adding a fixed amount (2, 5, 8, 11…), others by multiplying (1, 2, 4, 8…), and some come from shapes, like the square numbers 1, 4, 9, 16. Finding the rule lets us predict any term.
Palindromes and digit puzzles
A palindrome reads the same forwards and backwards, like 121 or 1331. Reversing a number and adding it to the original, repeated a few times, often produces a palindrome. Such digit puzzles reveal how the positions of digits affect a number.
Properties of numbers
Numbers can be even or odd, and patterns appear in how they behave: the sum of two odd numbers is even, an even number times any number is even, and the digits of multiples of 9 add up to a multiple of 9. Noticing such properties helps in quick checking.
Reasoning and number games
Number play is really about reasoning. Puzzles like 'find the missing number' or 'make the target using these digits' are solved by thinking logically about what must be true, not by guessing. This kind of thinking is the heart of mathematics.
Important formulas
Even + even / odd + odd
= even; odd + even = odd
Divisibility by 9
digit sum is a multiple of 9
Key definitions
- Pattern
- An arrangement of numbers following a rule.
- Palindrome
- A number that reads the same forwards and backwards.
- Even number
- A whole number exactly divisible by 2.
- Digit sum
- The sum of all digits of a number.
Solved examples
Q1. Is 1331 a palindrome?
Solution: Yes, it reads the same forwards and backwards.
Q2. Find the next number: 2, 6, 12, 20, ___.
Solution: Differences grow 4, 6, 8…, so add 10: 30.
Q3. Is the sum of two odd numbers even or odd?
Solution: Even (e.g. 3 + 5 = 8).
Common mistakes to avoid
- Guessing the next term instead of finding the rule.
- Thinking every number reversed is a palindrome.
- Assuming odd + odd is odd (it is even).
- Forgetting the order of digits changes a number's value.
Number Play — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
A number that reads the same both ways is a:
Practice questions
Short answer
What is a palindrome?
A number that reads the same forwards and backwards, like 121.
Is the sum of two even numbers even or odd?
Even.
How do you find the rule of a pattern?
Compare each term with the previous one to see how it changes.
Long answer
Explain how to discover the rule of a number pattern, using 2, 6, 12, 20.
To find a pattern's rule, we look at how each term relates to the one before it. In 2, 6, 12, 20, the differences between terms are 4, 6 and 8 — themselves increasing by 2 each time. So the next difference should be 10, giving 20 + 10 = 30, and the one after that 12, giving 42. By describing how the terms change rather than guessing, we can extend the pattern reliably and even predict far-off terms.
Describe some properties of even and odd numbers with examples.
Even numbers are exactly divisible by 2 (like 2, 4, 6), while odd numbers are not (like 1, 3, 5). These behave in predictable ways when combined: the sum of two even numbers is even (4 + 6 = 10), the sum of two odd numbers is also even (3 + 5 = 8), but the sum of an odd and an even number is odd (3 + 4 = 7). Also, an even number multiplied by any whole number stays even. Noticing such properties lets us quickly check whether an answer is reasonable without full calculation.
HOTS (Higher Order Thinking)
Using the digits 1, 2 and 3 once each, what is the largest 3-digit palindrome you can make? Explain.
None — a palindrome needs its first and last digits equal, but 1, 2, 3 are all different, so no palindrome is possible.
Without adding, is 23 + 19 odd or even? Why?
Even, because the sum of two odd numbers is always even.
Quick revision
Revision notes
- Find a pattern's rule, then extend it.
- Palindrome: reads the same both ways (121, 1331).
- odd + odd = even; even + even = even; odd + even = odd.
- Digit sum of a multiple of 9 is a multiple of 9.
Key takeaways
- Number play builds reasoning, not just calculation.
- Patterns and properties make numbers predictable.
- Logic beats guessing in number puzzles.
Frequently asked questions
What is a palindrome number?
A number that reads the same forwards and backwards.
Is odd plus odd even?
Yes, the sum of two odd numbers is always even.
How do I continue a number pattern?
Find the rule connecting the terms, then apply it.