Geometric Patterns (Grade 4)
Patterns are everywhere — in floor tiles, fabric designs, rangoli, and nature. A geometric pattern is a pattern made using shapes. The shapes repeat, rotate, flip, or grow in a regular way.
In Class 4, you will learn to identify, extend, and create geometric patterns using shapes like triangles, squares, circles, and hexagons. You will also discover the rule behind each pattern.
What is Geometric Patterns - Class 4 Maths (Patterns)?
A geometric pattern is an arrangement of shapes that follows a rule. The rule tells you how the shapes change from one step to the next.
Types of geometric patterns:
- Repeating pattern: A set of shapes repeats over and over. Example: circle, square, circle, square, ...
- Growing pattern: The number of shapes increases at each step. Example: 1 triangle, 3 triangles, 5 triangles, ...
- Rotating pattern: A shape turns by a fixed angle at each step.
- Symmetry pattern: Shapes are arranged to create mirror images.
Solved Examples
Example 1: Example 1: Identifying a repeating pattern
Problem: What comes next? Triangle, Circle, Square, Triangle, Circle, Square, Triangle, Circle, ?
Solution:
Step 1: The repeating unit is: Triangle, Circle, Square.
Step 2: After Circle, the next shape is Square.
Answer: The next shape is a Square.
Example 2: Example 2: Growing pattern with squares
Problem: Step 1 has 1 square, Step 2 has 4 squares (2×2), Step 3 has 9 squares (3×3). How many squares in Step 5?
Solution:
Step 1: The pattern is: 1, 4, 9, ... These are perfect squares: 1², 2², 3²
Step 2: Step 4 = 4² = 16 squares
Step 3: Step 5 = 5² = 25 squares
Answer: Step 5 has 25 squares.
Example 3: Example 3: Shape and colour pattern
Problem: Red circle, Blue triangle, Green square, Red circle, Blue triangle, Green square, Red circle, ? What comes next?
Solution:
Step 1: The repeating unit has 3 elements: Red circle, Blue triangle, Green square.
Step 2: After Red circle, the next element is Blue triangle.
Answer: The next shape is a Blue triangle.
Example 4: Example 4: Growing pattern — adding triangles
Problem: Ria draws: Step 1 — 2 triangles, Step 2 — 5 triangles, Step 3 — 8 triangles. How many triangles in Step 6?
Solution:
Step 1: Find the rule: 2, 5, 8, ... Each step adds 3 triangles.
Step 2: Step 4 = 8 + 3 = 11, Step 5 = 11 + 3 = 14, Step 6 = 14 + 3 = 17
Answer: Step 6 has 17 triangles.
Example 5: Example 5: Pattern with rotation
Problem: An arrow points: Right → Down → Left → Up → Right → Down → ? What direction is next?
Solution:
Step 1: The arrow rotates 90° clockwise each time.
Step 2: After Down, the next direction is Left.
Answer: The next direction is Left.
Example 6: Example 6: Mirror pattern (symmetry)
Problem: Aman draws: Triangle, Square, Circle, | Circle, Square, Triangle. What type of pattern is this?
Solution:
Step 1: The line "|" is the line of symmetry.
Step 2: The shapes on the right are a mirror image of the shapes on the left.
Answer: This is a symmetry (mirror) pattern.
Example 7: Example 7: Rangoli pattern
Problem: In a rangoli design, each ring adds 6 more dots than the previous ring. Ring 1 has 6 dots, Ring 2 has 12 dots. How many dots in Ring 4?
Solution:
Step 1: Rule: add 6 each ring. 6, 12, 18, 24, ...
Step 2: Ring 3 = 18, Ring 4 = 24
Answer: Ring 4 has 24 dots.
Example 8: Example 8: Predicting the 10th shape
Problem: Pattern: Star, Heart, Diamond, Star, Heart, Diamond, ... What is the 10th shape?
Solution:
Step 1: The repeating unit has 3 shapes: Star, Heart, Diamond.
Step 2: Divide 10 by 3: 10 ÷ 3 = 3 remainder 1.
Step 3: Remainder 1 → the 1st shape in the unit = Star.
Answer: The 10th shape is a Star.
Example 9: Example 9: Creating a pattern
Problem: Create a geometric pattern using only triangles and circles with the rule "add one more triangle each step."
Solution:
Step 1: Start: 1 triangle, 1 circle
Step 2: 2 triangles, 1 circle
Step 3: 3 triangles, 1 circle
Step 4: 4 triangles, 1 circle
Answer: The pattern grows by adding one triangle per step while keeping one circle constant.
Example 10: Example 10: Matchstick pattern
Problem: Dev makes shapes with matchsticks. 1 square = 4 matchsticks. 2 joined squares = 7 matchsticks. 3 joined squares = 10 matchsticks. How many for 6 joined squares?
Solution:
Step 1: Pattern: 4, 7, 10, ... (add 3 each time)
Step 2: 4 squares = 13, 5 squares = 16, 6 squares = 19
Step 3: Rule: Matchsticks = 3 × number of squares + 1
Step 4: 3 × 6 + 1 = 19 ✓
Answer: 6 joined squares need 19 matchsticks.
Key Points to Remember
- A geometric pattern is an arrangement of shapes following a rule.
- Repeating patterns have a unit that repeats. Use division to find any position.
- Growing patterns have shapes that increase by a fixed amount each step.
- Rotating patterns involve shapes turning by a fixed angle.
- Symmetry patterns are mirror images across a line.
- To extend a pattern, first identify the rule, then apply it.
- Matchstick patterns, rangoli designs, and floor tiles are real-life geometric patterns.
Practice Problems
- What comes next? Square, Triangle, Triangle, Square, Triangle, Triangle, Square, Triangle, ?
- A growing pattern has 3 circles in Step 1, 6 in Step 2, 9 in Step 3. How many circles in Step 7?
- A pattern repeats every 4 shapes: Star, Circle, Triangle, Heart. What is the 15th shape?
- Draw a mirror pattern using squares and circles with a vertical line of symmetry.
- How many matchsticks are needed for 10 joined triangles if 1 triangle needs 3 and each added triangle needs 2 more?
- An arrow rotates 90° clockwise each step. If it starts pointing up, where does it point after 7 steps?
- Create a growing pattern where each step adds 2 more hexagons than the previous step. Write the first 5 steps.
Frequently Asked Questions
Q1. What is a geometric pattern?
A geometric pattern is an arrangement of shapes that follows a specific rule. The shapes may repeat, grow in number, rotate, or reflect to form the pattern.
Q2. How do you find the rule of a pattern?
Look at how the shapes change from one step to the next. Check if shapes are repeating, increasing in number, rotating, or forming mirror images. The consistent change is the rule.
Q3. What is the difference between a repeating and growing pattern?
A repeating pattern has a fixed group of shapes that cycles over and over (e.g., A, B, C, A, B, C). A growing pattern changes size at each step, usually by adding more shapes.
Q4. How do you find the 20th shape in a repeating pattern?
Count the number of shapes in one repeating unit. Divide 20 by that number. The remainder tells you the position within the unit. For example, with a unit of 3 shapes: 20 ÷ 3 = 6 remainder 2, so the 20th shape is the 2nd shape in the unit.
Q5. What are some real-life examples of geometric patterns?
Floor tiles, rangoli designs, fabric prints, wallpaper borders, brick arrangements, and honeycomb structures all use geometric patterns.
Q6. What is a symmetry pattern?
A symmetry pattern has shapes arranged so that one half is a mirror image of the other half. The line dividing the two halves is called the line of symmetry.
Q7. Can a pattern have both shapes and colours?
Yes. Many patterns combine shape changes with colour changes. For example, Red circle, Blue square, Red circle, Blue square uses both shape and colour in the repeating unit.
Q8. How are geometric patterns different from number patterns?
Geometric patterns use shapes (visual), while number patterns use numbers. However, many geometric patterns can be described with numbers. For example, a growing triangle pattern with 1, 3, 5, 7 triangles follows the number rule "add 2."
