Symmetrical Designs 5 MathsChapter 10 CBSE Notes 2025-26

Symmetry is an important idea in mathematics and our daily life. In this chapter, we learn about different types of symmetry—like reflection symmetry and rotational symmetry—by exploring alphabets, numbers, shapes, and Indian traditional patterns. Understanding symmetry helps us easily make beautiful designs, cut-outs, and recognize balance in various objects. When Prem and Manu wanted to make “Happy Birthday” cutouts for their friend, they remembered their earlier lessons about lines of symmetry and reflections in letters.

Symmetry in Alphabets and Cutouts Some letters such as A and H have vertical or horizontal lines of symmetry. For example, the letter A has a vertical line of symmetry. To make a cutout, you can fold a paper in half, draw half of 'A' along the fold, cut along the outline, and open the paper to get the full letter, perfectly symmetrical. Similarly, the letter H has two lines of symmetry—one vertical and one horizontal, so you can fold the paper into one-fourth and draw only a quarter of the letter for the same result.

You can practice by identifying which of the letters (E, N, X, T, K, V, O) have vertical, horizontal, or both lines of symmetry. For example, 'O' and 'X' have both vertical and horizontal lines of symmetry, while 'E' and 'T' only have vertical or horizontal symmetry. These tricks make creating cutouts faster and more accurate.

Paper Activities: Designs with Symmetry Students are encouraged to use their understanding of symmetry to make paper cutouts not just of letters, but also objects like diyas, boats, and other simple designs. By folding paper along lines of symmetry and cutting along outlines, one can create beautiful, balanced shapes easily.

Rotational Symmetry with Firki (Windmill) Symmetry is not only about folding. It is also how a shape looks when turned or rotated. Lali teaches how to make a firki (windmill) using a square paper. By folding diagonally, cutting along the ‘X’ lines till halfway, and folding alternate corners to the centre, you create a basic windmill. Fix it with a pin and see it spin! When rotated by a quarter turn (1/4), half turn (1/2), three-quarter turn (3/4), and complete turn, the windmill looks the same. This is called rotational symmetry.

Assessing Symmetry in Letters and Numbers Many capital letters and digits have symmetry. Rotational symmetry means turning a shape around a point, and it still looks the same. Reflection symmetry (or mirror symmetry) means folding along a line and each side matches. For instance, the letter H and some numbers (like 0 and 8) have both types of symmetry. You can test letters and digits for reflection and rotational symmetry using tracing paper, cutouts, and nails to fix the centre.

• A vertical line of symmetry divides a shape into two equal, mirror-image parts.
• A horizontal line of symmetry does the same from top to bottom.
• Some shapes, like a square or a circle, have more than one line of symmetry.

Students check for symmetry in different numbers and create their own examples with two, three, or four digits that have either form of symmetry or both. For example, the number 88 has both vertical and horizontal symmetry, while 69 has rotational symmetry.

Activities and Exploration To understand symmetry better, students perform several hands-on activities:

• Colouring squares with two colours to make designs that look the same after turning them by a quarter turn or half turn.
• Changing or adding shapes so that designs have required symmetry after certain turns, and identifying the lines of symmetry.

Making designs with cut-out squares and equilateral triangles also helps. Try arranging these shapes in different patterns and check if the designs have reflection or rotational symmetry—or even both! This practical approach builds a stronger understanding compared to only reading.

Sorting Designs by Symmetry After making several designs, students can sort them into three groups:

• Designs with only rotational symmetry (look the same only after turning).
• Designs with only reflection symmetry (look the same on both sides of a line).
• Designs with both types of symmetry.

Sorting helps you easily see and compare the properties of each design and solidifies the concept of the types of symmetry.

Symmetry in Traditional Indian Art: Block Printing Symmetry is not just found in letters and shapes. Traditional arts of India, such as block printing in Rajasthan, use symmetrical designs. Artisans carve wooden blocks and use them to print patterns on cloth. These patterns often have both rotational and reflection symmetry, making them look pleasing and balanced. Noticing symmetry in such art deepens your appreciation for maths in culture.

Students are encouraged to match block prints with their blocks and observe how each print appears after multiple turns, checking for quarter turn (1/4), half turn (1/2), and full turn symmetries. Students also identify which block print designs have lines of symmetry.

Another fun project is to make your own symmetrical design using vegetable blocks, such as half-cut potatoes or ladies fingers dipped in paint. Observing if the pattern repeats after set turns and deciding whether it has rotational, reflection, or both symmetries is part of this creative activity.

Key Questions and Hands-on Practice Several questions or activities are suggested:

• Which letters and numbers have horizontal, vertical, or both lines of symmetry?
• Which digits or numbers have rotational symmetry?
• Can you find examples of 2-, 3-, or 4-digit numbers that have both symmetries?
• Colour or draw designs that look the same after certain turns or reflections.
• Observe traditional block prints and match designs with their printing blocks.

By performing these activities and reflecting on which designs fit which type of symmetry, students come to understand symmetry as an idea that unifies art, mathematics, language, and our daily lives.

Summary Table: Symmetry in Letters and Numbers

Conclusion Through this chapter, children learn to see symmetry all around them. By engaging with letters, shapes, and patterns, especially traditional block prints, they gain a deeper appreciation for both maths and culture. Hands-on activities encourage observation and creativity, making symmetry a fun and useful concept in daily life.

Class 5 Maths Chapter 10 Notes – Symmetry: Key Points for Quick Revision

These Class 5 Maths Chapter 10 Symmetry revision notes help you quickly understand lines of symmetry, reflection, and rotational symmetry in shapes, alphabets, and numbers. They highlight step-by-step activities for easy practice. Mastering symmetry prepares you for creative art and math tasks in school.

Our Class 5 Maths Symmetry notes summarize the NCERT chapter with clear examples, tables, and questions. With these notes, you’ll easily recognize different types of symmetry in both classroom and real-life situations, making revision simple and effective.