Rotational Symmetry

Content Standards

In this lesson, students will be able to Understand the concept of rotational symmetry in two-dimensional shapes. Learn about centre of rotation, angle of rotation, and order of rotation.
Apply these ideas to identify rotational symmetry in real-world objects.

Performance Standards

Students will be able to:

Define rotational symmetry and locate the centre of rotation in a figure.
Determine the angle of rotation and order of rotation for common shapes.
Recognise rotational symmetry in objects from daily life.

Alignment Standards

Reference: NCERT Book Alignment

The lesson is aligned with the NCERT Grade 6 Mathematics Textbook: Ganita Prakash, Chapter 9: Symmetry, Section 2 – Rotational Symmetry.

Learning Objectives

By the end of the lesson, students will be able to:

Explain what rotational symmetry means in simple terms.
Identify the centre of rotation in a shape.
Calculate the angle of rotation and order of rotation for basic geometric figures.
Relate rotational symmetry to objects and patterns found in nature, art, and design.

Prerequisites (Prior Knowledge)

Basic 2D shapes and their lines of symmetry.
Concept of rotation/turn (quarter turn, half turn, full turn).
Folding and matching halves from the earlier Line of Symmetry lesson.

Introduction

This lesson introduces students to the concept of rotational symmetry, an important extension of the symmetry they have already explored through lines of symmetry. Students will learn that some figures can be turned around a fixed point and still look exactly the same. They will understand the terms centre of rotation (the fixed point about which a figure rotates), angle of rotation (the smallest turn needed for the figure to look the same), and order of rotation (how many times a figure matches itself in one full turn). The lesson uses simple, hands-on activities with shape cut-outs and familiar real-world objects such as fans, wheels, and logos to make the concept clear and engaging. By connecting geometry to patterns in art, design, and nature, the lesson helps students see symmetry as both a mathematical property and a visual feature of the world around them.

Timeline (40 Minutes)

Title	Approximate Duration	Procedure	Reference Material
Engage	5	Show everyday items with rotational symmetry (fan, steering wheel, clock). Ask students: “When I rotate this, does it look different or the same?” Materials: Real objects or slides.	Slides
Explore	10	Hands-on Activity: Students use Rotational Symmetry Virtual Lab to have a handson experience about rotational symmetry in everyday objects.	Slides + Virtual Lab
Explain	10	Teacher explains, Rotational Symmetry: A figure has rotational symmetry if it matches itself after turning around a fixed point. Centre of Rotation: The fixed point about which the figure is rotated. Angle of Rotation: The smallest angle the figure must be turned to look the same. Order of Rotation: Number of times a figure fits onto itself in one full 360° turn. Examples: Square → Centre: middle point, Order = 4, Angle = 90°. Rectangle → Centre: middle point, Order = 2, Angle = 180°. Equilateral Triangle → Centre: centroid, Order = 3, Angle = 120°. Circle → Centre: centre point, Order = infinite.	Slides
Evaluate	10	Challenge: “Find 3 objects at home with rotational symmetry. Note their centre of rotation and order.”	Slides
Extend	5	Challenge: “Find 3 objects at home with rotational symmetry. Note their centre of rotation and order.” Discuss how logos (Mercedes, recycling symbol), designs, and mandalas use rotational symmetry.	Slides

Rotational Symmetry

Introduction

Have you ever seen a ceiling fan or a wheel turning? Even after it turns a little, it still looks the same! Some shapes and objects can be turned (rotated) around a fixed point and still look exactly as they did before. This special property is called rotational symmetry.

Rotational symmetry is all around us. The blades of a fan, the hands of a clock, the pattern on a rangoli, a bicycle wheel, and even some logos you see on TV all have rotational symmetry. Learning about rotational symmetry helps us understand patterns, designs, and how shapes behave when they are turned. In this lesson, you will learn what rotational symmetry is, what the centre of rotation is, and how to find the angle of rotation and the order of rotation for different shapes.

Theory

1. What is Rotational Symmetry?

A shape is said to have rotational symmetry if it looks exactly the same after being turned (rotated) around a fixed point by a certain angle.

If you rotate the shape less than a full turn (less than 360°) and it still looks unchanged, the shape has rotational symmetry.
If you have to turn it a full 360° before it looks the same, then it does not have rotational symmetry.

Example:

A square looks the same after a turn of 90°, 180°, 270°, and 360°.
A rectangle looks the same after a turn of 180° and 360°.
A scalene triangle does not look the same until it completes a full 360° turn, so it has no rotational symmetry.

2. Centre of Rotation

The centre of rotation is the fixed point about which the shape is turned.

For most regular shapes (like squares, rectangles, and circles), the centre of rotation is the middle point of the shape.
Imagine putting a pin through the middle of a paper shape and spinning it — the pin is the centre of rotation.

3. Angle of Rotation

If a square matches itself every time you turn it by 90°, then its angle of rotation is 90°.
For a rectangle, the angle of rotation is 180° because it only matches itself halfway through a turn.
A circle can match itself at any tiny turn, so its angle of rotation can be any angle.

4. Order of Rotation

The order of rotation tells us how many times a shape looks exactly the same in one full 360° turn.

Square → Order 4 (it looks the same 4 times in one full turn).
Rectangle → Order 2 (it looks the same 2 times).
Equilateral Triangle → Order 3.
Circle → Infinite order (it matches itself at every possible turn).

5. Real-Life Examples of Rotational Symmetry

Nature: Flowers, starfish, snowflakes.
Objects: Fans, wheels, clock hands, coins.
Designs & Art: Rangoli patterns, mandalas, logos like the recycling symbol or Mercedes Benz logo.
Games: Spinner wheels, pinwheels, and some board game pieces.

Understanding rotational symmetry helps in art, engineering, logo design, and even architecture. It makes designs look balanced, beautiful, and interesting.

Vocabulary

This is the list of vocabulary terms used throughout the lesson.

Rotation – Turning a shape around a fixed point.
Rotational Symmetry – When a shape looks exactly the same after being rotated (turned) by some angle.
Centre of Rotation – The fixed point around which a shape is turned.
Angle of Rotation – The smallest angle you rotate a shape so that it looks the same.
Order of Rotation – The number of times a shape matches itself during one full 360° turn.
Full Turn – A rotation of 360°.
Regular Polygon – A shape with all sides and angles equal (e.g., square, equilateral triangle) that usually has high rotational symmetry.
Pattern – A design or arrangement that repeats or stays the same after a transformation such as rotation.

Rotational Symmetry

Introduction

This VR lab helps students discover and practise rotational symmetry by interacting with 3-D/2-D objects in a safe, hands-on virtual environment. Through guided exploration and built-in tools, students will: identify the centre of rotation, measure the angle of rotation, compute the order of rotation, and experiment with making shapes rotationally symmetric (for example by removing a block). The lab uses familiar items (fans, wheels, logos, lego-style blocks, parallelograms) so concepts link directly to real life. Immediate visual feedback and an end-of-lab quiz let students check understanding while the teacher monitors progress.

Key Features

Interactive introduction: Short guided demo explaining rotational symmetry, centre, angle and order.
Rotate & snap controls: Manual rotate with controller + an interactive slider to set specific rotation angles (with numeric display).
Parallelogram activity: Special module with an interactive slider to discover its angle of rotation and order.
Drag-and-drop object library: Wide set of shapes and everyday objects (starfish, wheel etc) students can place on the stage and test for rotational symmetry.
Editable lego object: Blocky object made of lego-style blocks; students can delete or add blocks to create rotational symmetry.
MCQs are integrated at the end of each module for engagement.

Step-by-Step Procedure for VR Experience

Step 1: Introduction to Rotational Symmetry

Students learn the definition of Rotational Symmetry

Step 2: Angle and Centre of Rotation through Flower

They observe a rotating flower and see how it is symmetric even when it is rotated.
Get knowledge of the technical terms like centre of rotation and angle of rotation

Step 3: Order Of Rotational Symmetry Through Parallelogram

Rotate a parallelogram using a slider and figure out order of rotation and angle of rotation.

Step 4: Drag and Drop Activity and Angle Of Rotation

Drag and Drop different objects and measure their angle of rotation.

Step 4: Delete the Lego Block Activity

Delete a lego block from the object by clicking on it to make it rotationally symmetric.

Step 5: Evaluation

After interaction, students proceed to the quiz:
- 2 MCQs