Chapter 10 — Symmetrical Designs

Chapter 10 of the Class 5 Mathematics NCERT textbook (Maths Mela), "Symmetrical Designs", explores reflection symmetry and rotational symmetry through hands-on activities like alphabet cutouts, windmill (firki) making, and block printing patterns — download the PDF to find step-by-step craft activities and design exercises that make symmetry concepts concrete for Class 5 students.

• Reflection Symmetry and Lines of Symmetry — Students use lines of symmetry to make paper cutouts of letters and shapes. A letter like A has one vertical line of symmetry, while H has both vertical and horizontal lines, so it can be cut from a quarter-folded sheet.
• Rotational Symmetry — A shape has rotational symmetry if it looks the same after being turned by a fraction of a full rotation. The letter H looks the same after a half turn; a firki (windmill) looks the same after quarter, half, and three-quarter turns.
• Making a Windmill (Firki) — A step-by-step activity guides students to fold a square sheet diagonally twice, cut along the four lines of the X-shape halfway to the centre, fold alternate corners to the middle, and fix with a pin to create a spinning firki — which itself demonstrates rotational symmetry.
• Designing with Both Symmetries — Students sort designs into three categories: those with only reflection symmetry, only rotational symmetry, or both. They also modify designs by adding shapes so the result looks the same after a quarter or half turn.
• Block Printing and Cultural Connection — The chapter introduces Rajasthan's traditional block printing craft, where artisans use carved wooden blocks to print repeating patterns on fabric. Students match wooden blocks to their prints and observe how a block used four times produces a design with quarter-turn rotational symmetry.

1. 01Letters with a vertical line of symmetry (like A) can be cut from paper folded in half; letters with two lines of symmetry (like H) can be cut from paper folded into quarters.
2. 02A firki (windmill) made from a square sheet looks the same after a quarter turn, half turn, and three-quarter turn — it has rotational symmetry.
3. 03The letter H has rotational symmetry because it looks the same when rotated by half a turn.
4. 04Students explore which digits (0-9) have reflection symmetry, rotational symmetry, or both, and find multi-digit numbers with these properties.
5. 05Designs can be modified by adding shapes to achieve quarter-turn or half-turn rotational symmetry, and such designs may also carry reflection symmetry.
6. 06Block printing from Rajasthan is used as a real-world example: a block stamped four times creates a pattern that looks the same after every quarter turn.
7. 07Square and equilateral triangle cutouts with equal side lengths are used to build different symmetrical designs, which are then sorted by their type of symmetry.