Shape Patterns (Grade 3)
Shape patterns are arrangements of shapes that follow a rule and repeat. In Class 3, students learn to identify the repeating unit in a shape pattern, extend the pattern, and create their own.
Shape patterns are found in floor tiles, fabric designs, rangoli, and wallpaper borders. They combine geometry with logical thinking.
What is Shape Patterns - Class 3 Maths (Patterns)?
A shape pattern is a sequence of shapes arranged according to a repeating rule. The group of shapes that repeats is called the core or repeating unit.
Types of shape patterns:
- Repeating pattern: The same group of shapes repeats. Example: circle, square, circle, square, ...
- Growing pattern: The number of shapes increases in each step. Example: 1 triangle, 2 triangles, 3 triangles, ...
- Rotating/flipping pattern: Shapes change direction or position in each step.
Solved Examples
Example 1: Simple Repeating Pattern
Question: Find the next 2 shapes: circle, triangle, circle, triangle, circle, ___, ___
Think:
- The core = circle, triangle
- It keeps repeating.
- After circle → triangle, then circle.
Answer: triangle, circle.
Example 2: Three-Shape Repeating Pattern
Question: Find the next shape: square, circle, triangle, square, circle, triangle, square, ___
Think:
- Core = square, circle, triangle
- After square comes → circle.
Answer: The next shape is circle.
Example 3: Colour and Shape Pattern
Question: Ria makes a pattern with colour and shape: red circle, blue square, red circle, blue square, ___
Think:
- Core = red circle, blue square
- Next = red circle
Answer: The next shape is a red circle.
Example 4: Growing Shape Pattern
Question: Aman builds with matchsticks: Step 1 = 1 square (4 sticks), Step 2 = 2 squares (7 sticks), Step 3 = 3 squares (10 sticks). How many sticks for Step 4?
Think:
- Sticks: 4, 7, 10, ...
- Rule: add 3 each time
- Step 4 = 10 + 3 = 13 sticks
Answer: Step 4 needs 13 matchsticks.
Example 5: Identifying the Core
Question: What is the core of this pattern: triangle, triangle, square, triangle, triangle, square, triangle, triangle, square?
Think:
- Look for the smallest group that repeats.
- Core = triangle, triangle, square
Answer: The core is triangle, triangle, square.
Example 6: Finding the Position of a Shape
Question: In the pattern circle, square, triangle (repeating), what is the 10th shape?
Think:
- Core has 3 shapes.
- 10 ÷ 3 = 3 remainder 1
- Remainder 1 → 1st shape in core = circle
Answer: The 10th shape is a circle.
Example 7: Pattern with Size Change
Question: Priya draws circles: small, medium, large, small, medium, large, ___
Think:
- Core = small, medium, large
- Next = small
Answer: The next circle is small.
Example 8: Creating a Shape Pattern
Question: Dev wants to make a pattern using rectangles and triangles with a core of 4 shapes. Create one.
Think:
- Core could be: rectangle, triangle, triangle, rectangle
- Pattern: rectangle, triangle, triangle, rectangle, rectangle, triangle, triangle, rectangle, ...
Answer: One possible pattern: rectangle, triangle, triangle, rectangle (repeating).
Example 9: Counting Shapes in a Pattern
Question: A border pattern has 6 repetitions of the core: star, heart. How many shapes are there in total?
Think:
- Core has 2 shapes.
- 6 repetitions = 6 × 2 = 12 shapes.
Answer: There are 12 shapes in total.
Key Points to Remember
- A shape pattern follows a repeating or growing rule.
- The core is the smallest repeating unit of the pattern.
- Repeating patterns use the same core over and over.
- Growing patterns add more shapes at each step.
- Patterns can involve shape, colour, size, or direction.
- To find a shape at a specific position, divide the position by the core length and check the remainder.
- Shape patterns build logical reasoning and connect maths to art.
Practice Problems
- Find the next 3 shapes: square, circle, circle, square, circle, circle, ___, ___, ___
- What is the core of: triangle, circle, square, triangle, circle, square?
- In the pattern hexagon, star (repeating), what is the 15th shape?
- Aman makes a growing pattern: 1 triangle in row 1, 3 triangles in row 2, 5 triangles in row 3. How many in row 4?
- Create a shape pattern with a core of 3 shapes using circles and squares.
- A pattern has 5 repetitions of the core: circle, triangle, rectangle. How many shapes in total?
- Draw the next step in this growing pattern: Step 1 = 1 dot, Step 2 = 3 dots, Step 3 = 6 dots.
Frequently Asked Questions
Q1. What is a shape pattern?
A shape pattern is a sequence of shapes that follows a rule. The same group of shapes repeats (repeating pattern) or the number of shapes grows (growing pattern).
Q2. What is the core of a pattern?
The core is the smallest group of shapes that repeats to form the full pattern. For example, in circle-square-circle-square, the core is circle-square.
Q3. How do you find the next shape in a pattern?
Identify the core and see where you are in the cycle. The next shape follows the core's sequence.
Q4. What is the difference between a repeating and a growing pattern?
A repeating pattern uses the same core over and over. A growing pattern adds more shapes at each step, like 1 triangle, then 2 triangles, then 3.
Q5. How do you find which shape is at the 20th position?
Divide 20 by the number of shapes in the core. The remainder tells the position within the core. If remainder is 0, it is the last shape of the core.
Q6. Can patterns involve more than shape?
Yes. Patterns can combine shape with colour (red circle, blue square), size (small, medium, large), or direction (up arrow, down arrow).
Q7. Where do we see shape patterns in daily life?
Shape patterns are found in floor tiles, fabric prints, wallpaper borders, rangoli designs, jewellery, and architecture.
Q8. Are shape patterns covered in NCERT Class 3?
Yes. Shape patterns are part of the Patterns chapter in NCERT Class 3 Maths. Students identify, extend, and create patterns using shapes.
