Patterns in Mathematics Notes, Class 6th
NCERT • Class 6 • Mathematics • Chapter 1
Patterns in Mathematics
Easy notes | Examples | Solved questions | Practice quiz
What will you learn?
- Recognise and describe patterns.
- Find the rule behind a number sequence.
- Explore even numbers, odd numbers, and triangular and square numbers.
- Use patterns to predict what comes next.
Big idea: Mathematics is not only about calculations. It is also about noticing patterns and discovering rules.
1. What is a Pattern?
A pattern is an arrangement of numbers, shapes, colours, or objects that follows a rule or repeats in a predictable way.
Shape pattern
Rule: Circle, square, circle, square…
Growing pattern
Rule: Add one star each time.
Number pattern
Rule: Add 2 each time.
Remember: To continue a pattern, first identify its rule.
2. Number Sequences
A number sequence is a list of numbers arranged according to a rule. Each number is called a term.
The difference between consecutive terms is 5. Therefore, the next term is 30.
How to find the rule
- Compare the first two terms.
- Check how the number changes: addition, subtraction, multiplication, or another rule.
- Test the same rule on the next terms.
- Use the rule to find the missing or next term.
| Sequence | Rule | Next term |
|---|---|---|
| 3, 6, 9, 12, … | Add 3 | 15 |
| 20, 18, 16, 14, … | Subtract 2 | 12 |
| 2, 4, 8, 16, … | Multiply by 2 | 32 |
| 1, 4, 7, 10, … | Add 3 | 13 |
Note: A sequence can sometimes follow more than one possible rule. Use the rule that best fits the information given.
3. Even and Odd Numbers
Even numbers
Numbers that can be grouped into pairs with no object left over.
Examples: 14, 28, 100
Odd numbers
Numbers that leave one object unpaired when grouped into pairs.
Examples: 15, 27, 101
Quick check: A whole number ending in 0, 2, 4, 6, or 8 is even. A whole number ending in 1, 3, 5, 7, or 9 is odd.
4. Triangular Numbers
Triangular numbers can be represented by dots arranged in a triangle. Each new term adds one more dot than the previous row.
1 dot
1
3 dots
● ●
1 + 2 = 3
6 dots
● ●
● ● ●
1 + 2 + 3 = 6
10 dots
Four rows contain:
The triangular number sequence is:
Rule: Add the next counting number each time: +2, +3, +4, +5, …
After 10, add 5: 10 + 5 = 15.
5. Square Numbers
A square number is the number of objects arranged in a square with the same number of rows and columns.
| Arrangement | Calculation | Square number |
|---|---|---|
| 1 row × 1 column | 1 × 1 | 1 |
| 2 rows × 2 columns | 2 × 2 | 4 |
| 3 rows × 3 columns | 3 × 3 | 9 |
| 4 rows × 4 columns | 4 × 4 | 16 |
| 5 rows × 5 columns | 5 × 5 | 25 |
The square number sequence begins:
We can write these as \(1^2, 2^2, 3^2, 4^2, 5^2,\ldots\). For example, \(6^2 = 6 \times 6 = 36\).
The next one is \(6 \times 6 = \mathbf{36}\).
6. Other Interesting Number Patterns
Counting numbers
Start at 1 and add 1 each time.
Numbers ending in zero
Add 10 each time. These are multiples of 10.
Numbers that double
Multiply each term by 2 to get the next term.
Descending pattern
Subtract 5 each time.
7. Patterns in Everyday Life
- Calendar: Dates in a column usually increase by 7 from one week to the next.
- Tiles: Floor tiles may repeat a colour or shape pattern.
- Nature: Petals, leaves, and some seed arrangements show patterns.
- Music: Rhythms often repeat in a predictable order.
- Daily routine: A timetable repeats activities on particular days.
Mathematics helps us describe these patterns clearly and predict what may happen next.
8. Solved Questions
9. Practice Worksheet
Try these questions before checking the answers below.
- Complete: 4, 8, 12, 16, __, __.
- Complete: 30, 27, 24, 21, __.
- Complete: 1, 2, 4, 8, __, __.
- Write the first six even numbers greater than zero.
- Write the first six odd numbers.
- What is the next triangular number after 21?
- What is \(7 \times 7\)? Is the answer a square number?
- Explain the rule in this sequence: 100, 90, 80, 70, …
- Make your own number sequence with at least six terms and write its rule.
- Find a repeating pattern at home and describe it in words or symbols.
Show answer key
- 20, 24 (add 4).
- 18 (subtract 3).
- 16, 32 (multiply by 2).
- 2, 4, 6, 8, 10, 12.
- 1, 3, 5, 7, 9, 11.
- 28 (add 7).
- 49; yes, \(7^2 = 49\).
- Subtract 10 each time.
- Answers will vary. Example: 2, 4, 6, 8, 10, 12; add 2.
- Answers will vary.
10. Quiz
Test your understanding of Patterns in Mathematics. Select one answer for each question, then click Check My Answers.
11. Quick Revision
- A pattern follows a rule.
- A sequence is an ordered list of terms.
- Even numbers are divisible by 2 with no remainder; odd numbers are not.
- Triangular numbers begin: 1, 3, 6, 10, 15, 21, …
- Square numbers begin: 1, 4, 9, 16, 25, 36, …
- Compare terms carefully to discover the rule before predicting the next term.
Exit question: Can you explain a number pattern to a friend without simply giving the next number?