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Symmetrical Designs – Class 5 Maths Chapter 10 Notes & NCERT PDF

Class 5MathematicsChapter 10NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 10 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 10: Symmetrical Designs

Introduction

Prem and Manu are making "Happy Birthday" letter cut-outs for Lali's birthday. They remember reflection symmetry from Grade 4 and discover a clever trick: letters with a line of symmetry can be cut by drawing only half or a quarter of the letter on folded paper. Then Lali makes firkis (paper windmills), which teach us a new idea — rotational symmetry. The chapter ends with symmetrical designs, digits, and the wooden block printing of Rajasthan.

Key Ideas

1. Reflection Symmetry (Line Symmetry)

A shape has reflection symmetry if one half is the mirror image of the other half along a line of symmetry.

  • A has a vertical line of symmetry → fold paper in half, draw half of A along the fold, cut, open.
  • H has two lines of symmetry (vertical and horizontal) → fold the paper into a quarter, draw one-fourth of H, cut, open.

    • Among E, N, X, T, K, V, O:

  • Vertical line of symmetry: T, V (and X, O)
  • Horizontal line of symmetry: E, K (and X, O)
  • Both: X, O
  • No line of symmetry: N

    • 2. Rotational Symmetry

    A shape has rotational symmetry if it looks exactly the same before one full turn is completed.
  • A firki looks the same after a ¼ turn, ½ turn, ¾ turn and a full turn.
  • The letter H looks the same after a ½ turn.
  • The letter N also looks the same after a ½ turn (though it has no line of symmetry).

    • Every shape looks the same after a full turn, so that alone does not count.

    3. Symmetry in Digits and Numbers

    Look at the digits carefully:

  • 0 and 8 have reflection symmetry and also look the same after a ½ turn.
  • 3 has a horizontal line of symmetry.
  • Numbers can be symmetrical too — for example || and |00| look the same in a mirror and after a ½ turn.

    • 4. Making Symmetrical Designs

  • Add shapes to a design so it looks the same after a ½ turn, then after a ¼ turn.
  • Cut out squares and equilateral triangles of the same side length and build designs.
  • Sort designs into three groups: only rotational, only reflection, both.

    • 5. Wooden Block Printing

    Artisans of Rajasthan carve wooden blocks and print them again and again on cloth. When one block is printed 4 times by turning it, the final print looks the same after every ¼ turn — it has rotational symmetry.

    Worked Examples

    Example 1 — Cutting the letter H:

  • Fold the paper once vertically and once horizontally (into a quarter).
  • Draw one-fourth of H touching both folds.
  • Cut along the outline.
  • Open — the full H appears because H has two lines of symmetry.

    • Example 2 — Firki turns: Mark a dot on one blade. After a ¼ turn the firki looks the same (only the dot has moved). So it has rotational symmetry at ¼, ½ and ¾ turns.

    Example 3 — Does N have symmetry? No mirror line works for N, so it has no reflection symmetry. But turn it upside down (½ turn) and it looks the same, so it has rotational symmetry.

    Example 4 — Colouring a square: Colour a square divided into 4 parts using two colours in opposite corners. It looks the same after every ½ turn.

    Maths Words

  • Symmetry (सममिति)
  • Line of symmetry (सममिति रेखा)
  • Reflection symmetry (परावर्तन सममिति)
  • Rotational symmetry (घूर्णन सममिति)
  • Vertical (ऊर्ध्वाधर), Horizontal (क्षैतिज)
  • Turn: ¼, ½, ¾, full (चौथाई, आधा, तीन-चौथाई, पूरा चक्कर)
  • Mirror image (दर्पण प्रतिबिंब)

    • Maths in Daily Life

    Rangoli, kites, windmills, fan blades, flowers, logos, block-printed fabric, tiles, and many letters on signboards use symmetry.

    Common Mistakes

  • Thinking a shape has rotational symmetry just because it looks the same after a full turn — every shape does.
  • Mixing up reflection and rotation: N has rotation but no reflection.
  • Drawing the half-letter away from the fold, so the cut-out falls apart.
  • Assuming all letters with one line of symmetry also have rotational symmetry (A and T do not).

    • Practice Tips

  • Use a small mirror to test lines of symmetry.
  • Trace a shape on tracing paper, pin the centre, and turn it to test rotational symmetry.
  • Mark a dot on the shape to keep track of turns.
  • Make your own vegetable-block prints and check their symmetry.

    • 💡 Key Learning Points

    • ✓A shape has reflection symmetry when one half is the mirror image of the other along a line of symmetry.
    • ✓Letters with one line of symmetry (like A) can be cut from paper folded in half; letters with two (like H) from paper folded into quarters.
    • ✓A shape has rotational symmetry if it looks the same before completing a full turn (a firki at ¼, ½, ¾ turn; H at ½ turn).
    • ✓Some shapes have only rotational symmetry (N), some only reflection symmetry (A, T), and some both (H, X, O).
    • ✓Symmetry is used in real designs such as Rajasthani wooden block printing, where one block printed 4 times gives a pattern with ¼-turn symmetry.

    👨‍🏫 Teaching Tips

    • →Let children cut the letters A and H exactly as Prem and Manu did, then try E, N, X, T, K, V, O.
    • →Make firkis in class; mark a dot on one blade and count how many times it looks the same in one full turn.
    • →Give tracing paper and a pin so children can test rotational symmetry of letters and digits themselves.
    • →Use small mirrors to check lines of symmetry in letters, digits and the border shapes in the book.
    • →Create a class chart sorting designs into 'only rotational', 'only reflection' and 'both'.
    • →Show real block-printed cloth or pictures and let children match blocks to prints.
    • →Do the vegetable-block printing project (potato or lady's finger stamps) as art-maths integration.

    📋 Assessment Questions

    1. Can the child draw the line(s) of symmetry on letters such as A, E, H and X?
    2. Can the child explain why the letter N has rotational symmetry but no reflection symmetry?
    3. Can the child say at which turns a firki looks the same?
    4. Can the child modify a design so that it looks the same after a ½ turn or a ¼ turn?
    5. Can the child sort given shapes into only rotational, only reflection, or both?

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    Keep learning

    All chapters in Maths Mela - Mathematics Class 5

    1. 1. We the Travellers — I
    2. 2. Fractions
    3. 3. Angles as Turns
    4. 4. We the Travellers — II
    5. 5. Far and Near
    6. 6. The Dairy Farm
    7. 7. Shapes and Patterns
    8. 8. Weight and Capacity
    9. 9. Coconut Farm
    10. 10. Symmetrical Designs
    11. 11. Grandmother’s Quilt
    12. 12. Racing Seconds
    13. 13. Animal Jumps
    14. 14. Maps and Locations
    15. 15. Data Through Pictures