Maths

Patterns

Class 3

🎯 Learning Objectives

Understand what a pattern is and identify the rule behind it.
Identify, extend, and create shape patterns (repeating and rotating).
Recognise and continue number patterns (addition, subtraction, multiplication).
Understand growing patterns where amounts increase step by step.
Identify symmetry patterns and mirror images in shapes and designs.
Spot patterns in multiplication tables.
Relate patterns to Indian art forms — rangoli, kolam, mehndi, and saree borders.

📖 Introduction

Have you ever looked closely at a rangoli design during Diwali? Or noticed the beautiful border on your mother's saree? These designs have something special — they follow a pattern!

A pattern is an arrangement of shapes, numbers, or colours that repeats following a fixed rule. Once you know the rule, you can predict what comes next. Patterns are everywhere — in nature (petals of a sunflower), in music (rhythm of a tabla), in art (mehndi designs), and in mathematics (multiplication tables).

In Class 3, we will explore different types of patterns — shape patterns, colour patterns, number patterns, growing patterns, and symmetry patterns. We will also discover how Indian art uses mathematical patterns beautifully!

What is a Pattern?

A pattern is something that repeats in the same order, following a fixed rule. The part that repeats is called the core (or unit) of the pattern.

Example: 🔴🔵🟡🔴🔵🟡🔴🔵🟡 — The core is "Red, Blue, Yellow". It repeats 3 times.
Example: Clap, Clap, Stomp, Clap, Clap, Stomp — The core is "Clap, Clap, Stomp".
Example: 5, 10, 15, 20, 25 — The rule is "Add 5 each time".

How to find the rule:

Look at what repeats or what changes from one step to the next.
Ask: "What is the same? What is different?"
Check if your rule works for every part of the pattern.

Think about it: The days of the week follow a pattern — Monday, Tuesday, Wednesday... After Sunday, it starts again from Monday. That's a repeating pattern with a core of 7 days!

Shape Patterns (Repeating Patterns)

In a shape pattern, shapes repeat in the same order again and again. The group of shapes that repeats is called the core.

Example 1: ○ □ △ ○ □ △ ○ □ △ ...
Core: Circle, Square, Triangle (3 shapes repeat). Next shape: Circle

Example 2: □ □ ○ □ □ ○ □ □ ○ ...
Core: Square, Square, Circle (group of 3 repeats). Next: Square, Square

Example 3: △ ○ ○ △ ○ ○ △ ○ ○ ...
Core: Triangle, Circle, Circle. Next: Triangle

Tips to identify shape patterns:

Count how many shapes are in the repeating group (core).
Check if the same group appears again and again.
Use the core to predict what comes next.

Colour Patterns

In a colour pattern, colours repeat in a fixed order. These are very common in Indian art!

Example 1: Red, Blue, Red, Blue, Red, Blue ...
Core: Red, Blue (AB pattern). Next colour: Red

Example 2: Red, Yellow, Green, Red, Yellow, Green ...
Core: Red, Yellow, Green (ABC pattern). Next: Red

Example 3: Orange, Orange, White, Green, Orange, Orange, White, Green ...
Core: Orange, Orange, White, Green (AABC pattern — like the Indian flag colours!). Next: Orange

Real-life colour patterns:

Bangles: Red, Green, Red, Green — alternating colours on a bangle set.
Rangoli: White, Red, Yellow, White, Red, Yellow — colours in rangoli powder designs.
Saree borders: Gold, Maroon, Gold, Maroon — repeating border patterns.
Traffic lights: Red, Yellow, Green — a fixed colour sequence.

Number Patterns

In a number pattern, numbers follow a rule. The rule tells us what operation to do to get the next number.

Adding Patterns (Increasing)

Pattern	Rule	Next 3 Numbers
2, 4, 6, 8, 10, ...	Add 2	12, 14, 16
5, 10, 15, 20, 25, ...	Add 5	30, 35, 40
3, 6, 9, 12, 15, ...	Add 3	18, 21, 24
7, 14, 21, 28, 35, ...	Add 7	42, 49, 56
10, 20, 30, 40, 50, ...	Add 10	60, 70, 80
4, 8, 12, 16, 20, ...	Add 4	24, 28, 32

Subtracting Patterns (Decreasing)

Pattern	Rule	Next 3 Numbers
50, 45, 40, 35, 30, ...	Subtract 5	25, 20, 15
100, 90, 80, 70, 60, ...	Subtract 10	50, 40, 30
30, 27, 24, 21, 18, ...	Subtract 3	15, 12, 9
40, 36, 32, 28, 24, ...	Subtract 4	20, 16, 12

How to find the rule:
Pattern: 8, 15, 22, 29, 36, ...
Step 1: Find the difference: 15 − 8 = 7, 22 − 15 = 7, 29 − 22 = 7
Step 2: The difference is always 7. Rule: Add 7
Step 3: Next number: 36 + 7 = 43

Growing Patterns

A growing pattern is a pattern where the amount increases (grows) at each step. Unlike repeating patterns, growing patterns do not repeat the same group — they get bigger!

Example 1 — Dot Pattern:
Step 1: ● (1 dot)
Step 2: ● ● ● (3 dots)
Step 3: ● ● ● ● ● (5 dots)
Step 4: ● ● ● ● ● ● ● (7 dots)
Rule: Add 2 more dots each time. Numbers: 1, 3, 5, 7, 9, ...

Example 2 — Square Pattern:
Step 1: 1 square
Step 2: 4 squares (2×2)
Step 3: 9 squares (3×3)
Step 4: 16 squares (4×4)
Rule: Square numbers! 1, 4, 9, 16, 25, ...

Example 3 — Staircase Pattern:
Step 1: 1 block
Step 2: 1 + 2 = 3 blocks
Step 3: 1 + 2 + 3 = 6 blocks
Step 4: 1 + 2 + 3 + 4 = 10 blocks
Rule: Add one more row each time. Numbers: 1, 3, 6, 10, 15, ...

Think about it: When you stack blocks to make a staircase, each step has one more block than the step before. That's a growing pattern! Can you find growing patterns in a rangoli design?

Symmetry Patterns (Mirror Images)

A symmetry pattern is when one half of a design is the mirror image of the other half. If you fold the design along the middle line (called the line of symmetry), both halves match exactly.

Examples of symmetry:
• A butterfly — left wing mirrors the right wing.
• The letter "A" — left side mirrors the right side.
• A rangoli design — all four sides are mirror images of each other.
• A kolam design — the pattern is the same on all sides.

Symmetry in Indian art:

Rangoli: Most rangoli designs have 4-fold symmetry — they look the same from all four sides.
Kolam: South Indian kolam designs are drawn with dots and loops, creating perfect symmetry.
Mehndi: Mehndi patterns on both hands are often mirror images of each other.
Taj Mahal: The building is perfectly symmetrical — left side mirrors the right side.

Letters with symmetry: A, H, I, M, O, T, U, V, W, X, Y (vertical line of symmetry)

Letters with horizontal symmetry: B, C, D, E, H, I, K, O, X

Patterns in Multiplication Tables

Multiplication tables are full of patterns! Let's discover some:

Table	Pattern in Last Digit	Other Patterns
Table of 2	2, 4, 6, 8, 0, 2, 4, 6, 8, 0	All answers are even numbers
Table of 5	5, 0, 5, 0, 5, 0, 5, 0, 5, 0	Answers end in 5 or 0 only
Table of 9	9, 8, 7, 6, 5, 4, 3, 2, 1, 0	Digits add up to 9 (e.g., 18→1+8=9)
Table of 10	0, 0, 0, 0, 0, 0, 0, 0, 0, 0	Just add a zero to the number
Table of 11	1, 2, 3, 4, 5, 6, 7, 8, 9, 0	Up to 9×11, both digits are the same (11, 22, 33...)

The magic of 9:
9 × 1 = 09 → 0 + 9 = 9
9 × 2 = 18 → 1 + 8 = 9
9 × 3 = 27 → 2 + 7 = 9
9 × 4 = 36 → 3 + 6 = 9
9 × 5 = 45 → 4 + 5 = 9
The digits of every answer in the 9 times table add up to 9!

Think about it: In the table of 9, the tens digit goes up (0, 1, 2, 3, 4...) and the units digit goes down (9, 8, 7, 6, 5...). Two patterns in one!

Patterns in Indian Art and Culture

India has a rich tradition of using mathematical patterns in art. Let's explore some:

🪷 Rangoli Patterns

Rangoli is drawn during festivals like Diwali, Pongal, and Onam. Rangoli designs use:

Repeating patterns: The same motif (flower, leaf, diya) repeats around a centre.
Symmetry: The design looks the same from all sides (rotational symmetry).
Colour patterns: Colours alternate in a fixed order.

🌀 Kolam Designs (South India)

Kolam is drawn with rice flour every morning in front of homes in Tamil Nadu, Karnataka, and Andhra Pradesh. Kolam uses:

Dot patterns: Dots are placed in a grid, then connected with curves.
Loop patterns: A single continuous line loops around all dots without lifting.
Growing patterns: Simple kolams grow into complex ones by adding more dots.

✋ Mehndi Patterns

Mehndi (henna) designs on hands use repeating patterns:

Paisley shapes repeating in a row.
Flower petals arranged in a circle (rotational pattern).
Leaf patterns along fingers (repeating with size change — growing pattern).

🧵 Saree Border Designs

The border of a saree has a repeating pattern that goes all along the edge:

Geometric shapes (triangles, diamonds) repeating.
Flower-vine patterns that repeat every few centimetres.
Colour patterns in the weave (gold, red, gold, red).

Rangoli design with repeating geometric shapes and colours

Shape pattern sequence with what comes next challenge

📝 Key Words

Word	Meaning
Pattern	An arrangement that repeats or follows a fixed rule
Core	The smallest part of a pattern that repeats
Rule	The instruction that tells how the pattern works (e.g., "Add 3")
Repeating pattern	A pattern where the same group repeats again and again
Growing pattern	A pattern where the amount increases at each step
Number pattern	A sequence of numbers that follows a rule
Shape pattern	A sequence of shapes that repeats in a fixed order
Symmetry	When one half is the mirror image of the other half
Line of symmetry	The line along which a shape can be folded to get matching halves
Sequence	An ordered list of numbers or objects following a pattern

⭐ Key Points to Remember

A pattern is an arrangement that repeats or follows a fixed rule.
The core is the smallest repeating unit of a pattern.
In number patterns, find the difference between consecutive numbers to discover the rule.
In shape patterns, identify the group of shapes that keeps repeating.
Growing patterns increase at each step — they do not repeat the same group.
Symmetry means one half mirrors the other half exactly.
Multiplication tables have many patterns (e.g., table of 9: digits always add to 9).
Indian art forms like rangoli, kolam, and mehndi are based on mathematical patterns.
To extend a pattern: find the rule → apply it → predict the next items.

✏️ Practice Questions

A. Find the Rule and Write the Next 3 Numbers (10 marks)

1. 4, 8, 12, 16, 20, , , (Rule: )

2. 7, 14, 21, 28, 35, , , (Rule: )

3. 6, 12, 18, 24, 30, , , (Rule: )

4. 9, 18, 27, 36, 45, , , (Rule: )

5. 100, 90, 80, 70, 60, , , (Rule: )

6. 50, 45, 40, 35, 30, , , (Rule: )

7. 11, 22, 33, 44, 55, , , (Rule: )

8. 8, 16, 24, 32, 40, , , (Rule: )

9. 15, 30, 45, 60, 75, , , (Rule: )

10. 99, 88, 77, 66, 55, , , (Rule: )

B. Fill in the Missing Numbers (5 marks)

1. 3, 6, , 12, , 18, 21

2. 20, 25, , 35, , 45, 50

3. 80, , 60, 50, , 30, 20

4. 12, 16, , 24, , 32, 36

5. 45, 40, , 30, , 20, 15

C. Multiple Choice Questions (5 marks)

1. What is the rule for: 5, 10, 15, 20, 25?

(a) Add 3(b) Add 5(c) Add 10(d) Add 2

2. In the pattern ○ □ △ ○ □ △ ○ □ △ ..., what is the core?

(a) ○ □(b) ○ □ △(c) □ △ ○(d) ○ ○ ○

3. Which is a growing pattern?

(a) 2, 2, 2, 2(b) 1, 3, 5, 7, 9(c) A, B, A, B(d) Red, Blue, Red, Blue

4. In the table of 9, the digits of each answer add up to:

(a) 10(b) 8(c) 9(d) 7

5. Which letter has a vertical line of symmetry?

(a) F(b) A(c) J(d) R

D. Short Answer Questions (5 marks)

1. Write the first 10 numbers in the table of 6. What pattern do you see in the last digits?

2. Draw the next 3 shapes in this pattern: □ △ △ □ △ △ □ ...

3. A growing pattern starts with 2, 5, 8, 11, 14. What is the rule? What are the next 3 numbers?

4. Name 3 things in your home that have a symmetry pattern.

5. Meena is making a rangoli with this colour pattern: Red, Yellow, Blue, Red, Yellow, Blue. What is the 10th colour she will use?

E. Think and Solve (5 marks)

1. Arjun arranges 1 block in row 1, 3 blocks in row 2, 5 blocks in row 3, and 7 blocks in row 4. How many blocks will be in row 5 and row 6?

2. Create your own number pattern using the rule "Subtract 6". Start from 60 and write 8 numbers.

3. Sita is making a bead necklace with this pattern: 2 red, 1 blue, 3 green, 2 red, 1 blue, 3 green. If she uses 30 beads in total, how many green beads will she use?

4. Look at this pattern: 1, 4, 9, 16, 25, ___. What is the rule? (Hint: Think of square numbers!) What comes next?

5. Draw a simple rangoli design that shows both a repeating pattern and symmetry. Label the core and the line of symmetry.

🎨 Fun Activity — Pattern Detective!

Activity 1: Pattern Hunt at Home

Walk around your home and find 5 patterns. Write them down:

Pattern on a bedsheet or curtain: ___________________________
Pattern on floor tiles: ___________________________
Pattern on a plate or cup: ___________________________
Pattern on clothing: ___________________________
Pattern in nature (leaves, flowers): ___________________________

Activity 2: Create Your Own Rangoli Pattern

Using coloured pencils, create a rangoli design in the space below. Your design must have:

At least one repeating pattern (shapes or colours)
At least one line of symmetry
At least 3 different colours

Write the rule of your repeating pattern: ___________________________

How many lines of symmetry does your design have? ___________

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Mathematics

Patterns

Class 3 | CBSE / NCERT / ICSE

Name: Class: Date:

What is a Pattern?

A pattern is an arrangement of shapes, numbers, or colours that repeats following a fixed rule. The part that repeats is called the core. Patterns are everywhere — in rangoli designs, saree borders, mehndi, kolam, multiplication tables, and nature.

Shape Patterns (Repeating Patterns)

In a shape pattern, shapes repeat in the same order. The repeating group is the core.

Examples:

○ □ △ ○ □ △ ○ □ △ ... → Core: Circle, Square, Triangle. Next: Circle

□ □ ○ □ □ ○ □ □ ○ ... → Core: Square, Square, Circle. Next: Square, Square

Colour Patterns

Colours repeat in a fixed order. Examples from Indian art:

Red, Blue, Red, Blue ... (AB pattern) | Red, Yellow, Green, Red, Yellow, Green ... (ABC pattern)

Bangles, rangoli powder, saree borders — all use colour patterns!

Number Patterns

Pattern	Rule	Next 3
2, 4, 6, 8, 10	Add 2	12, 14, 16
5, 10, 15, 20, 25	Add 5	30, 35, 40
7, 14, 21, 28, 35	Add 7	42, 49, 56
50, 45, 40, 35, 30	Subtract 5	25, 20, 15
100, 90, 80, 70, 60	Subtract 10	50, 40, 30

How to find the rule: Find the difference between consecutive numbers. If it's the same each time, that's your rule!

Growing Patterns

A growing pattern increases at each step (does not repeat the same group).

Example: 1, 3, 5, 7, 9 ... (add 2 more each time) | 1, 4, 9, 16, 25 ... (square numbers)

Staircase: 1, 3, 6, 10, 15 ... (add 1 more row each time)

Symmetry Patterns

A symmetry pattern has one half that mirrors the other. The fold line is the line of symmetry.

Examples: Butterfly wings, letter A, rangoli designs, kolam, Taj Mahal.

Letters with vertical symmetry: A, H, I, M, O, T, U, V, W, X, Y

Patterns in Multiplication Tables

Table	Pattern
Table of 2	All answers are even; last digits: 2, 4, 6, 8, 0 (repeats)
Table of 5	Answers end in 5 or 0 only
Table of 9	Digits add up to 9 (e.g., 18→1+8=9, 27→2+7=9)
Table of 10	Just add a zero to the number

Patterns in Indian Art

Rangoli: Repeating motifs + symmetry + colour patterns. Drawn during Diwali, Pongal, Onam.

Kolam: Dot grids with loops. Growing patterns (more dots = bigger design). South India tradition.

Mehndi: Paisley, flowers, leaves repeating. Mirror patterns on both hands.

Saree borders: Geometric shapes (triangles, diamonds) repeating along the edge.

Key Points:

A pattern repeats or follows a fixed rule. The repeating unit is the core.
Number patterns: find the difference between consecutive numbers to discover the rule.
Shape patterns: identify the repeating group of shapes.
Growing patterns increase at each step — they don't repeat.
Symmetry means one half mirrors the other half exactly.
Table of 9: digits always add to 9. Table of 5: ends in 0 or 5.
Indian art (rangoli, kolam, mehndi, saree borders) uses mathematical patterns.

Patterns — Practice Questions

Class 3 | Mathematics

A. Find the Rule and Write the Next 3 Numbers

1. 4, 8, 12, 16, 20, , , (Rule: )

2. 7, 14, 21, 28, 35, , , (Rule: )

3. 6, 12, 18, 24, 30, , , (Rule: )

4. 9, 18, 27, 36, 45, , , (Rule: )

5. 100, 90, 80, 70, 60, , , (Rule: )

6. 50, 45, 40, 35, 30, , , (Rule: )

7. 11, 22, 33, 44, 55, , , (Rule: )

8. 8, 16, 24, 32, 40, , , (Rule: )

9. 15, 30, 45, 60, 75, , , (Rule: )

10. 99, 88, 77, 66, 55, , , (Rule: )

B. Fill in the Missing Numbers

1. 3, 6, , 12, , 18, 21

2. 20, 25, , 35, , 45, 50

3. 80, , 60, 50, , 30, 20

4. 12, 16, , 24, , 32, 36

5. 45, 40, , 30, , 20, 15

C. Multiple Choice Questions

1. What is the rule for: 5, 10, 15, 20, 25?

(a) Add 3(b) Add 5(c) Add 10(d) Add 2

2. In the pattern ○ □ △ ○ □ △ ○ □ △ ..., what is the core?

(a) ○ □(b) ○ □ △(c) □ △ ○(d) ○ ○ ○

3. Which is a growing pattern?

(a) 2, 2, 2, 2(b) 1, 3, 5, 7, 9(c) A, B, A, B(d) Red, Blue, Red, Blue

4. In the table of 9, the digits of each answer add up to:

(a) 10(b) 8(c) 9(d) 7

5. Which letter has a vertical line of symmetry?

(a) F(b) A(c) J(d) R

D. Short Answer Questions

1. Write the first 10 numbers in the table of 6. What pattern do you see in the last digits?

2. Draw the next 3 shapes: □ △ △ □ △ △ □ ...

3. A growing pattern starts with 2, 5, 8, 11, 14. What is the rule? Next 3 numbers?

4. Name 3 things in your home that have a symmetry pattern.

5. Meena makes a rangoli: Red, Yellow, Blue, Red, Yellow, Blue. What is the 10th colour?

E. Think and Solve

1. Arjun arranges 1 block in row 1, 3 in row 2, 5 in row 3, 7 in row 4. How many in rows 5 and 6?

2. Create a number pattern: rule "Subtract 6", start from 60. Write 8 numbers.

3. Sita's bead necklace: 2 red, 1 blue, 3 green (repeats). With 30 beads total, how many green?

4. Pattern: 1, 4, 9, 16, 25, ___. What is the rule? What comes next?

5. Draw a simple rangoli with a repeating pattern and symmetry. Label the core and symmetry line.

🎨 Fun Activity — Pattern Detective!

Pattern Hunt: Find 5 patterns at home and write them:

1. Bedsheet/curtain: ___________________________ 2. Floor tiles: ___________________________

3. Plate/cup: ___________________________ 4. Clothing: ___________________________

5. Nature (leaves/flowers): ___________________________

Create a Rangoli: Draw a rangoli with a repeating pattern, symmetry, and 3+ colours below:

Rule of your pattern: ___________________________ Lines of symmetry: ___________

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