CBSE Class 6 Maths Revision Notes Chapter 1 Patterns in Mathematics
Patterns in Mathematics help students recognise rules in numbers, shapes and visual arrangements. For CBSE Class 6 Maths, this chapter covers number sequences, shape sequences, square numbers, triangular numbers, cube numbers and links between numbers and shapes.
Mathematics is not only about calculations. It is also about finding patterns and understanding why they exist. Patterns appear in numbers, shapes, nature, games, buildings, calendars, clocks and technology. When students learn to recognise patterns, they can predict what comes next and understand mathematical ideas more clearly.
Use these CBSE Class 6 Maths Revision Notes Chapter 1 for the 2026–27 academic year to revise Patterns in Mathematics. These notes explain number patterns, shape patterns, visual sequences and relationships between different sequences in a simple, exam-ready format.
Key Takeaways
- Mathematics: It can be understood as the study of patterns and their explanations.
- Number sequences: Counting numbers, odd numbers, even numbers, squares, cubes and triangular numbers follow fixed rules.
- Visual patterns: Dots, grids and shapes make number patterns easier to understand.
- Shape sequences: Regular polygons, stacked squares, stacked triangles and Koch snowflake patterns connect geometry with numbers.
Need help revising Patterns in Mathematics?
Access interactive practice, chapter-wise notes and doubt-solving support on the Extramarks Learning App. Sign Up Free
Access Class 6 Maths Chapter 1 Patterns in Mathematics Notes in 30 Minutes
Revise this chapter as a pattern journey.
Numbers → Pictures → Relationships → Shapes → Number-shape links
| Revision Area | What to Revise |
| Meaning of Mathematics | Search for patterns and explanations |
| Number Patterns | Counting, odd, even, square, cube and triangular numbers |
| Visualising Sequences | Using dots, grids and shapes |
| Relations Among Sequences | How one sequence forms another |
| Shape Patterns | Polygons, stacked shapes and snowflake patterns |
| Number-Shape Links | How shapes produce number sequences |
| Quick Rules | Rules used to find the next term |
Patterns in Mathematics Class 6 Notes: What This Chapter Covers
Patterns in Mathematics Class 6 Notes introduce students to a new way of looking at maths. Instead of only solving sums, students learn to observe, compare, predict and explain.
This chapter mainly covers:
- What mathematics means
- Patterns in numbers
- Common number sequences
- Visualising number sequences
- Relations among number sequences
- Patterns in shapes
- Relation between shape sequences and number sequences
What Is Mathematics?
Mathematics is the study of patterns and the reasons behind those patterns.
Patterns are found everywhere. They appear in days of the week, seasons, rangoli designs, building tiles, games, music beats, calendars and nature.
For example:
| Place | Pattern Example |
| Calendar | Days repeat in a fixed order |
| Nature | Petals, leaves and shells show patterns |
| Games | Scores and moves may follow rules |
| Buildings | Tiles and designs repeat |
| Technology | Codes and algorithms use patterns |
Mathematics helps us understand these patterns and use them to solve problems.
Patterns in Numbers
A number pattern is a sequence of numbers arranged according to a rule.
Once we know the rule, we can find the next numbers in the sequence.
What Is a Number Sequence?
A number sequence is a list of numbers written in a particular order.
Example:
2, 4, 6, 8, 10
This is a sequence of even numbers.
The rule is:
Add 2 each time.
Common Number Sequences in Class 6 Maths Chapter 1
| Sequence | Numbers | Rule |
| All 1’s | 1, 1, 1, 1, 1 | Same number repeats |
| Counting Numbers | 1, 2, 3, 4, 5 | Add 1 each time |
| Odd Numbers | 1, 3, 5, 7, 9 | Add 2 each time |
| Even Numbers | 2, 4, 6, 8, 10 | Add 2 each time |
| Triangular Numbers | 1, 3, 6, 10, 15 | Add 2, then 3, then 4 and so on |
| Square Numbers | 1, 4, 9, 16, 25 | 1², 2², 3², 4², 5² |
| Cube Numbers | 1, 8, 27, 64, 125 | 1³, 2³, 3³, 4³, 5³ |
| Virahānka Numbers | 1, 2, 3, 5, 8, 13 | Add previous two numbers |
| Powers of 2 | 1, 2, 4, 8, 16 | Multiply by 2 each time |
| Powers of 3 | 1, 3, 9, 27, 81 | Multiply by 3 each time |
Important Number Patterns in Class 6 Mathematics Chapter 1 Notes
Each number sequence has a different rule. Students should first observe the terms, then find what changes from one term to the next.
Counting Numbers
Counting numbers begin from 1 and increase by 1 each time.
Sequence:
1, 2, 3, 4, 5, 6, 7, ...
Rule:
Add 1 to get the next number.
Odd Numbers
Odd numbers are numbers that are not divisible by 2.
Sequence:
1, 3, 5, 7, 9, 11, ...
Rule:
Add 2 to get the next number.
Even Numbers
Even numbers are numbers that are divisible by 2.
Sequence:
2, 4, 6, 8, 10, 12, ...
Rule:
Add 2 to get the next number.
Triangular Numbers
Triangular numbers can be arranged in the shape of a triangle.
Sequence:
1, 3, 6, 10, 15, 21, ...
Rule:
Add the next counting number each time.
| Step | Addition | Triangular Number |
| 1 | 1 | 1 |
| 2 | 1 + 2 | 3 |
| 3 | 1 + 2 + 3 | 6 |
| 4 | 1 + 2 + 3 + 4 | 10 |
| 5 | 1 + 2 + 3 + 4 + 5 | 15 |
Square Numbers
Square numbers can be arranged as dots in a square grid.
Sequence:
1, 4, 9, 16, 25, 36, ...
Rule:
Multiply a number by itself.
| Number | Square Number |
| 1 × 1 | 1 |
| 2 × 2 | 4 |
| 3 × 3 | 9 |
| 4 × 4 | 16 |
| 5 × 5 | 25 |
| 6 × 6 | 36 |
Cube Numbers
Cube numbers can be represented using cube-shaped arrangements.
Sequence:
1, 8, 27, 64, 125, ...
Rule:
Multiply a number by itself three times.
| Number | Cube Number |
| 1 × 1 × 1 | 1 |
| 2 × 2 × 2 | 8 |
| 3 × 3 × 3 | 27 |
| 4 × 4 × 4 | 64 |
| 5 × 5 × 5 | 125 |
Virahānka Numbers
Virahānka numbers are formed by adding the previous two numbers.
Sequence:
1, 2, 3, 5, 8, 13, 21, ...
Rule:
Next number = Previous number + Number before it
Examples:
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
Powers of 2
Powers of 2 are formed by multiplying by 2 each time.
Sequence:
1, 2, 4, 8, 16, 32, 64, ...
Rule:
Multiply the previous number by 2.
Powers of 3
Powers of 3 are formed by multiplying by 3 each time.
Sequence:
1, 3, 9, 27, 81, 243, ...
Rule:
Multiply the previous number by 3.
Visualising Number Sequences
Visualising means representing numbers using pictures, dots, grids or shapes.
Pictures make patterns easier to understand. They also help students see why a pattern works.
Why Visualisation Helps
| Without Visualisation | With Visualisation |
| Students only memorise numbers | Students see the rule |
| Pattern may look difficult | Pattern becomes easier |
| Relation is hidden | Relation becomes visible |
| Hard to explain why | Easier to explain why |
Visualising Square Numbers
Square numbers can be shown using dots in square grids.
Examples:
1 dot = 1
2 × 2 dots = 4
3 × 3 dots = 9
4 × 4 dots = 16
This is why 1, 4, 9, 16 and 25 are called square numbers.
Visualising Triangular Numbers
Triangular numbers can be shown using dots arranged in triangles.
Examples:
1 dot = 1
1 + 2 dots = 3
1 + 2 + 3 dots = 6
1 + 2 + 3 + 4 dots = 10
This is why 1, 3, 6, 10 and 15 are called triangular numbers.
Visualising Cube Numbers
Cube numbers can be imagined as cubes made of smaller unit cubes.
Examples:
1³ = 1
2³ = 8
3³ = 27
4³ = 64
This is why 1, 8, 27, 64 and 125 are called cube numbers.
Relations Among Number Sequences
Number sequences are often connected. A new sequence can be formed by adding or combining another sequence.
Sum of Odd Numbers Gives Square Numbers
When we add odd numbers from 1, we get square numbers.
| Addition | Result |
| 1 | 1 |
| 1 + 3 | 4 |
| 1 + 3 + 5 | 9 |
| 1 + 3 + 5 + 7 | 16 |
| 1 + 3 + 5 + 7 + 9 | 25 |
| 1 + 3 + 5 + 7 + 9 + 11 | 36 |
So:
1 + 3 + 5 + 7 + 9 = 25
This is the same as:
5² = 25
Why Does This Happen?
A square grid can be built by adding layers of odd numbers.
Start with 1 dot.
Add 3 dots to make a 2 × 2 square.
Add 5 dots to make a 3 × 3 square.
Add 7 dots to make a 4 × 4 square.
So, adding odd numbers creates larger and larger squares.
Sum of First 10 Odd Numbers
The sum of the first 10 odd numbers is:
10² = 100
So:
1 + 3 + 5 + ... + 19 = 100
Sum of First 100 Odd Numbers
The sum of the first 100 odd numbers is:
100² = 10,000
Adding Numbers Up and Down
Another way to form square numbers is by adding counting numbers up and then down.
| Addition Pattern | Result |
| 1 | 1 |
| 1 + 2 + 1 | 4 |
| 1 + 2 + 3 + 2 + 1 | 9 |
| 1 + 2 + 3 + 4 + 3 + 2 + 1 | 16 |
| 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 | 25 |
The result is always a square number.
Quick Rule
If the highest number in the up-and-down pattern is n, the result is n².
Example:
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 5² = 25
So:
1 + 2 + 3 + ... + 100 + 99 + ... + 3 + 2 + 1 = 100² = 10,000
More Relations Among Sequences
Adding Counting Numbers Gives Triangular Numbers
When we add counting numbers from 1, we get triangular numbers.
| Addition | Result |
| 1 | 1 |
| 1 + 2 | 3 |
| 1 + 2 + 3 | 6 |
| 1 + 2 + 3 + 4 | 10 |
| 1 + 2 + 3 + 4 + 5 | 15 |
So, counting numbers added step by step form triangular numbers.
Adding Consecutive Triangular Numbers Gives Square Numbers
When we add two consecutive triangular numbers, we get square numbers.
| Addition | Result |
| 1 + 3 | 4 |
| 3 + 6 | 9 |
| 6 + 10 | 16 |
| 10 + 15 | 25 |
This gives:
4, 9, 16, 25, ...
These are square numbers.
Adding Powers of 2 and Then Adding 1
Take powers of 2:
1, 2, 4, 8, 16, ...
Now start adding them:
| Addition | Result | Add 1 |
| 1 | 1 | 2 |
| 1 + 2 | 3 | 4 |
| 1 + 2 + 4 | 7 | 8 |
| 1 + 2 + 4 + 8 | 15 | 16 |
| 1 + 2 + 4 + 8 + 16 | 31 | 32 |
After adding 1, we again get powers of 2.
Patterns in Shapes
Patterns are not limited to numbers. Shapes can also follow rules.
A shape pattern is a sequence of shapes arranged according to a rule.
Examples include:
- Regular polygons
- Stacked squares
- Stacked triangles
- Complete graphs
- Koch snowflake patterns
Regular Polygons
A regular polygon has equal sides and equal angles.
The sequence of regular polygons begins with:
| Shape | Number of Sides |
| Triangle | 3 |
| Quadrilateral or Square | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Heptagon | 7 |
| Octagon | 8 |
| Nonagon | 9 |
| Decagon | 10 |
The number of sides follows the counting numbers starting from 3.
Sequence:
3, 4, 5, 6, 7, 8, 9, 10, ...
The number of corners is also the same as the number of sides.
Stacked Squares
Stacked squares are shape patterns made by arranging smaller squares.
The number of small squares follows square numbers.
Sequence:
1, 4, 9, 16, 25, ...
This happens because each shape forms a square arrangement.
| Shape Size | Number of Small Squares |
| 1 × 1 | 1 |
| 2 × 2 | 4 |
| 3 × 3 | 9 |
| 4 × 4 | 16 |
| 5 × 5 | 25 |
Stacked Triangles
Stacked triangles are shape patterns made using smaller triangles.
In the chapter, these patterns can also connect to square numbers through the adding-up-and-down pattern.
Sequence:
1, 4, 9, 16, 25, ...
This can be understood as:
1
1 + 2 + 1
1 + 2 + 3 + 2 + 1
These totals form square numbers.
Complete Graphs
A complete graph is a shape where every point is connected to every other point.
The number of lines in complete graphs follows triangular numbers.
Sequence:
1, 3, 6, 10, 15, ...
This happens because every new point connects to all earlier points.
Koch Snowflake Pattern
The Koch snowflake is a shape pattern where each line segment is replaced by a smaller pattern.
The number of line segments follows:
3, 12, 48, 192, ...
This is:
3 × powers of 4
| Step | Number of Segments |
| 1 | 3 |
| 2 | 12 |
| 3 | 48 |
| 4 | 192 |
| 5 | 768 |
The rule is:
Multiply by 4 each time.
Relation Between Number and Shape Sequences
Shape sequences often produce number sequences.
This is one of the main ideas in Class 6 Maths Chapter 1 Patterns in Mathematics.
| Shape Pattern | Related Number Sequence |
| Regular polygons | Counting numbers from 3 |
| Stacked squares | Square numbers |
| Stacked triangles | Square numbers |
| Complete graphs | Triangular numbers |
| Koch snowflake | 3 × powers of 4 |
| Dot triangles | Triangular numbers |
| Dot squares | Square numbers |
| Cubes | Cube numbers |
Solved Examples for Class 6 Maths Chapter 1 Patterns in Mathematics
Example 1: Find the next three numbers
Sequence:
1, 4, 9, 16, 25, ...
These are square numbers.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
Next three numbers:
6² = 36
7² = 49
8² = 64
Answer:
36, 49, 64
Example 2: Identify the pattern
Sequence:
1, 2, 3, 5, 8, 13, ...
Each number is formed by adding the previous two numbers.
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
Next number:
8 + 13 = 21
Answer:
This is the Virahānka number sequence. The next number is 21.
Example 3: Find the sum
Find:
1 + 3 + 5 + 7 + 9 + 11 + 13
There are 7 odd numbers.
The sum of the first n odd numbers is n².
So:
7² = 49
Answer:
49
Example 4: Find the result of an up-and-down pattern
Find:
1 + 2 + 3 + 4 + 3 + 2 + 1
The highest number is 4.
So, the result is:
4² = 16
Answer:
16
Example 5: Identify the shape-number relation
A sequence of regular polygons has 3 sides, 4 sides, 5 sides and 6 sides.
The number sequence is:
3, 4, 5, 6, ...
This follows counting numbers starting from 3.
Answer:
The shape pattern is related to counting numbers.
Quick Revision Tables for Patterns in Mathematics
Number Sequence Rule Table
| Sequence | First Few Terms | Rule |
| Counting Numbers | 1, 2, 3, 4 | Add 1 |
| Odd Numbers | 1, 3, 5, 7 | Add 2 |
| Even Numbers | 2, 4, 6, 8 | Add 2 |
| Triangular Numbers | 1, 3, 6, 10 | Add next counting number |
| Square Numbers | 1, 4, 9, 16 | n² |
| Cube Numbers | 1, 8, 27, 64 | n³ |
| Virahānka Numbers | 1, 2, 3, 5 | Add previous two numbers |
| Powers of 2 | 1, 2, 4, 8 | Multiply by 2 |
| Powers of 3 | 1, 3, 9, 27 | Multiply by 3 |
Pattern Relationship Table
| Pattern | Result |
| Sum of odd numbers | Square numbers |
| Counting numbers added step by step | Triangular numbers |
| Counting numbers added up and down | Square numbers |
| Consecutive triangular numbers added | Square numbers |
| Powers of 2 added and then 1 added | Powers of 2 |
| Hexagonal numbers added | Cube numbers |
Shape Pattern Table
| Shape Sequence | Number Pattern |
| Regular polygons | 3, 4, 5, 6, ... |
| Stacked squares | 1, 4, 9, 16, ... |
| Stacked triangles | 1, 4, 9, 16, ... |
| Complete graphs | 1, 3, 6, 10, ... |
| Koch snowflake | 3, 12, 48, 192, ... |
Important Terms in Class 6 Maths Chapter 1
| Term | Meaning |
| Pattern | Arrangement that follows a rule |
| Number Sequence | List of numbers in a particular order |
| Counting Numbers | 1, 2, 3, 4 and so on |
| Odd Numbers | Numbers not divisible by 2 |
| Even Numbers | Numbers divisible by 2 |
| Triangular Numbers | Numbers that can be arranged as triangles |
| Square Numbers | Numbers that can be arranged as squares |
| Cube Numbers | Numbers formed as n³ |
| Virahānka Numbers | Numbers formed by adding previous two terms |
| Shape Pattern | Sequence of shapes following a rule |
| Regular Polygon | Shape with equal sides and equal angles |
Common Mistakes in Patterns in Mathematics Class 6 Notes
| Mistake | Correct Point |
| Looking only at one number | Study the change between terms |
| Confusing odd and even patterns | Odd numbers start from 1, even numbers start from 2 |
| Calling all repeated sequences square numbers | Square numbers follow n² |
| Forgetting visual patterns | Pictures help explain why patterns work |
| Mixing triangular and square numbers | Triangular numbers form triangles, square numbers form squares |
| Thinking shape patterns are separate from numbers | Shape patterns often create number sequences |
| Memorising without rule | Always write the rule for the sequence |
Useful Links for Class 6 Maths
| Section | Useful Links |
| Syllabus | CBSE Class 6 Maths Syllabus |
| Revision Notes | CBSE Class 6 Maths Revision Notes |
| NCERT Solutions | NCERT Solutions for Class 6 Maths |
| Sample Papers | CBSE Sample Papers for Class 6 Maths |
| Important Questions | Important Questions Class 6 Maths |
| NCERT Books | NCERT Books for Class 6 Maths |
| Class 6 Support | CBSE Class 6 Syllabus |
FAQs (Frequently Asked Questions)
The main idea is to understand mathematics as the study of patterns. Students learn number sequences, shape sequences, visual patterns and relationships between numbers and shapes.
Compare one term with the next. Check whether numbers are added, subtracted, multiplied or formed using squares, cubes or previous terms. Once the rule is clear, the next terms can be found.
Odd numbers form square numbers because each new odd number can be added as a new layer around a square grid. For example, 1 + 3 + 5 + 7 = 16, which is 4².
Triangular numbers are numbers that can be arranged in the shape of a triangle. The sequence is 1, 3, 6, 10, 15 and so on. They are formed by adding counting numbers step by step.
Shape patterns often create number sequences. For example, regular polygons follow counting numbers from 3, stacked squares follow square numbers, and complete graphs follow triangular numbers.