NCERT Class 3 Maths (Maths Mela) · Chapter 14

The Surajkund Fair

Symmetry in malas, rangolis, and masks, mirror images, tiling paths with no gaps, and reading a simple map.

📌 What you’ll learn in this chapter
  • Symmetry: two halves that match exactly
  • Making symmetrical malas, rangolis, and masks
  • Mirror images
  • Tiling: covering a path with no gaps and no overlaps
  • Finding places and following directions on a map

🎪 Let’s Begin: A Trip to the Fair

At the fair, Soni sees a beautiful butterfly kite. Its left wing looks exactly like its right wing, like a mirror! That’s called symmetry.

🦋 Part 1: Symmetry

If you can fold a shape so that one half fits exactly on the other half, the shape is symmetrical. The fold line is the line of symmetry.

  • Symmetrical: butterfly, leaf, heart, face, star, the letter A
  • Not symmetrical: the letter F, a hand with a ring on one finger
💡 Mirror test Place a mirror on the middle line. If the mirror shows the full shape, the shape is symmetrical.

📿 Part 2: Symmetrical Malas

A mala of 8 beads is symmetrical if the colours on the left half are a mirror of the right half. For example: 🔴🔴🔵🔵 | 🔴🔴🔵🔵 is not symmetrical, but 🔴🔴🔵🔵 | 🔵🔵🔴🔴 is!

🧱 Part 3: Tiling Paths

Tiles on a footpath fit together with no gaps (so feet don’t get stuck) and no overlaps. Squares, rectangles, triangles, and hexagons tile well. Circles leave gaps!

🗺️ Part 4: Maps and Directions

A map shows places with small pictures (symbols). Use words like left, right, straight, near, in front of, behind to give directions.

⚠️ Common mistake Left and right change when you turn around! Always imagine yourself walking on the map.

✏️ Practice Time

Try these on your own first, then check your answer below each question.

Q1. Is the letter H symmetrical?
✅ AnswerYes
Q2. Name 2 symmetrical things in nature.
✅ AnswerFor example, a butterfly and a leaf.
Q3. Do circle-shaped tiles leave gaps?
✅ AnswerYes

📘 NCERT Textbook Activity Help

Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!

Page 177 · Fair picture

Things that look the same from left and right

✅ AnswerLook for decorated arches, doors, lanterns, the giant wheel, kites, and pots. These look the same on both sides.
Pages 178–179 · Malas

Symmetrical malas

✅ AnswerA mala is symmetrical when the first 4 beads are a mirror of the last 4. With 4 beads of each colour, each half needs 2 of each colour. There are 6 such symmetrical malas.
With 6 beads of one colour and 2 of another: put 1 of the second colour in each half, in matching places. For example: 🔵🟡🟡🟡 | 🟡🟡🟡🔵 (4 ways in all).
Pages 180–181 · Kolam and rangoli

Symmetry in rangoli

✅ AnswerMost rangolis are symmetrical, and many have more than one line of symmetry. To complete a rangoli, copy each dot and line on the other side at the same distance from the middle line.
Pages 182–183 · Masks and the painter

Why Avi sees with one eye

✅ AnswerAvi’s mask is not symmetrical: its two eye holes are not in matching places, so only one hole lines up with his eye.
The painter’s trick works only for symmetrical things. He can’t trick you if you ask him to paint things that are not symmetrical, like a person looking sideways, a teapot with a spout, or the letter F.
Pages 184–185 · Mirror game and explore

Mirror images

✅ AnswerPlace a mirror on the line and check that each counter on Avi’s side matches the reflection of Soni’s side. For Micy and Catty, move the three balls that are in the wrong places. For the shape cutouts, pick shapes whose edges fit exactly with no gaps.
Pages 186–187 · Tiling

Paths with no gaps

✅ AnswerFill the shapes with squares, triangles, and rhombuses so there are no gaps or overlaps. Make your own tile by joining two shapes, then repeat it to make a path.
Pages 188–191 · Giant wheel and map

Finding places

✅ AnswerGiant wheel: find the kulfi cart, then the blue-flag stall, then count to the second stall from there, in front of the yellow-roofed stall. It’s the stall with the puppets in a basket.
Map: read each symbol from the key in your book (the car is parking, and the ₹ card is the ATM). Count the exit signs to find how many exits there are (2 on this map). Follow the coloured lanes in order to reach the chaupal, then reverse the steps to guide the uncle to the ATM.

👨‍👩‍👧 Tips for Parents

  • Make symmetrical paper masks and ink blot butterflies together.
  • Look for symmetry in leaves, flowers, and buildings.
  • Draw a simple map of your house or street and give directions.
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