Mathematics: Class 3 — Chapter 14: The Surajkund Fair

• Observe the entrance gate, shops, and decorations.
• Identify objects and structures that look exactly the same on both the left and right sides. This balanced proportion is known as symmetry.

Soni and Avi make malas using 8 beads (4 of one colour and 4 of another).

• Symmetrical Mala: A mala where the left and right halves are exactly the same. For example, a pattern of beads arranged as Red-Blue-Blue-Red on both sides.
• Non-Symmetrical Mala: A mala where the two halves do not match.

At the Tamil Nadu stall, Soni and Avi observe kolam (rangoli) patterns made on dot grids.

• A line of symmetry can divide a rangoli into two identical halves. Folding the pattern along this line makes one half lie exactly on top of the other.
• Traditional symmetrical rangolis include Pookalam from Kerala and Aipan from Uttarakhand.

Creating a cat mask step-by-step:

1. Fold a piece of paper in half.
2. Draw half of the cat's face along the fold.
3. Cut along the outline and open the fold to get a perfectly symmetrical mask with two aligned eye holes.

A painter draws only half of Soni's portrait and asks for the full payment of $₹200$, telling her to place a mirror next to it to see the complete picture. Soni plays a trick back by giving him a note of $₹100$ (half the money) and telling him to place a mirror next to it to see the full $₹200$!

• This trick only works for objects that have a mirror line (symmetry).
• Objects like a cup, a flag, or a tree cannot be divided into two similar halves and thus cannot be completed using a mirror.

Placing counters on a grid to create a perfect mirror image across a central dividing line.

Footpaths in the fair are paved with tiles. If there are gaps between tiles, people can trip. Perfectly designed tiles fit together with no gaps and no overlaps, a concept known as tessellation or tiling.

• Soni's tiles use rectangular and square shapes to form a repeating pattern.
• Avi's tiles use hexagons and triangles to create a seamless path.

Using relative positions to locate stalls (e.g., "near the kulfi cart", "second stall from the yellow-roofed stall").

Soni and Avi use a map of the fair to find their grandparents at the chaupal.

• Map Legend: Symbols representing Parking, ATM, Restaurant, Shops, Giant Wheel, Pond, Play Area, and Chaupal.
• Following Directions: Moving along colored lanes (blue, green, red, golden) and making left/right turns to navigate from the entry to specific locations.