The Surajkund Fair

Given: A picture of the Surajkund Fair scene.

In the picture we can see stalls, people in colourful clothes, decorations, flags, handicraft items, food carts, and various fair activities. There are patterns on the floor (tiles), and objects like masks, malas, and rangolis around the fair.

Given: A picture of the Surajkund Fair.

Concept: Objects that look the same from the left and right side are called symmetrical objects.

Things that look the same from the left and right side include:
- The entrance gate of the fair
- Masks worn by people
- Flowers used in decoration
- The giant wheel
- Faces of people

All these objects have a line of symmetry — if you fold them along the middle, both halves match exactly.

Given: Strings of 8 beads each, to be coloured using two colours.

Activity: Use any two colours (for example, red ● and blue ●) to colour the beads on each string.

Example patterns you can make:
- ● ● ● ● ● ● ● ● (all one colour — symmetrical)
- ● ● ● ● ○ ○ ○ ○ (4 of each — symmetrical if arranged as mirror image)
- ● ○ ● ○ ● ○ ● ○ (alternating — symmetrical)
- ● ● ○ ○ ○ ○ ● ● (symmetrical)
- ● ○ ○ ● ● ○ ○ ● (symmetrical)

Note: Colour the beads on the printed strings as per your chosen pattern. Try to make different arrangements each time.

Given: Several malas (bead strings) coloured with two colours.

Concept: A mala is symmetrical if, when you fold it in the middle, both halves look exactly the same (mirror images of each other).

How to check: Fold the mala at the centre bead (or between the two middle beads). If the left half matches the right half exactly, the mala is symmetrical.

Tick ☑ all malas where the pattern on the left side is the mirror image of the pattern on the right side.
Leave unchecked (or cross) the malas where the two halves do not match.

Given: 8 beads, 2 colours.

Concept: We need to count how many symmetrical arrangements are possible with 8 beads using 2 colours.

For a mala of 8 beads to be symmetrical, the first 4 beads (from one end) must mirror the last 4 beads. So we only need to decide the colour of the first 4 beads — the other 4 are fixed.

Number of choices for 4 beads with 2 colours = $2 \times 2 \times 2 \times 2 = 16$

So there are $\mathbf{16}$ symmetrical malas that can be made with 8 beads of 2 colours.

(Note: This includes the cases where all beads are the same colour.)

Given: Several malas shown with bead patterns.

Concept: A mala is symmetrical if its left half is the mirror image of its right half.

Method:
1. Find the centre of the mala.
2. Compare the bead on the 1st position with the bead on the 8th position — they must be the same colour.
3. Compare the 2nd with the 7th, the 3rd with the 6th, and the 4th with the 5th.
4. If all pairs match, the mala is symmetrical → Tick ☑
5. If any pair does not match, the mala is not symmetrical → Cross ☐

Apply this rule to each mala shown in the picture and mark accordingly.

Given: 6 beads of one colour (say red ●) and 2 beads of another colour (say blue ○), total 8 beads.

Concept: For a symmetrical mala, the pattern must be the same on both halves.

Since we have 2 blue beads, they must be placed symmetrically (mirror positions).

Possible symmetrical arrangements:
1. ○ ● ● ● ● ● ● ○ — blue beads at positions 1 and 8
2. ● ○ ● ● ● ● ○ ● — blue beads at positions 2 and 7
3. ● ● ○ ● ● ○ ● ● — blue beads at positions 3 and 6
4. ● ● ● ○ ○ ● ● ● — blue beads at positions 4 and 5

Colour the beads in the given strings using these patterns. Each of these 4 arrangements is symmetrical.

Given: Several rangoli patterns are shown.

Concept: A rangoli is symmetrical if a line can be drawn through it such that both halves are mirror images of each other.

Observation: Most traditional rangolis are symmetrical — they look the same on both sides of a central line. However, not all rangolis shown may be symmetrical.

Answer: No, not all rangolis are symmetrical. Some rangolis have a line of symmetry (they are symmetrical), while others do not have any line that divides them into two identical halves (they are not symmetrical).

To check: Try to draw a line through each rangoli. If both halves match, it is symmetrical.

Given: Rangoli patterns to be traced.

Activity steps:
1. Place a tracing paper over each rangoli and trace it carefully.
2. Try to fold the tracing paper along a line through the centre of the rangoli.
3. If one half lies exactly on the other half after folding, the rangoli is symmetrical.
4. If the halves do not match, the rangoli is not symmetrical.

Observation: The fold line is called the line of symmetry. A rangoli may have one or more lines of symmetry.

Given: Rangoli patterns are shown.

Concept: The line that divides a shape into two identical (mirror image) halves is called the line of symmetry.

Method:
1. Look at each rangoli carefully.
2. Imagine folding it — find the fold line where both halves would match.
3. Draw that line on the rangoli.

Note: Some rangolis may have more than one line of symmetry (e.g., a square rangoli may have 4 lines of symmetry). Draw all such lines you can find.

Given: The concept of symmetry.

Symmetrical things we can find around us:
- Human face (left and right halves are similar)
- Butterfly wings
- Leaves of a plant
- Windows and doors
- The letter 'A', 'H', 'M', 'T', 'V', 'W'
- A kite shape
- Flowers
- Spectacles

All these objects have at least one line of symmetry — a line along which they can be folded so that both halves match exactly.

Given: Half-completed rangoli patterns on dot grids.

Concept: To complete a symmetrical rangoli, the other half must be the mirror image of the given half.

Steps:
1. Identify the line of symmetry (the fold line) — it is usually the vertical or horizontal centre line.
2. For each point or line on the given half, find its mirror position on the other side of the line of symmetry.
3. The mirror position is at the same distance from the line of symmetry but on the opposite side.
4. Connect the mirror points to complete the rangoli.

Result: The completed rangoli will look the same on both sides of the line of symmetry.

Given: A notebook to draw rangolis.

Steps to draw a symmetrical rangoli:
1. Draw a dot grid in your notebook.
2. Draw a vertical (or horizontal) line in the centre — this is your line of symmetry.
3. Draw a pattern on one side of the line using the dots as guides.
4. Mirror the same pattern on the other side.
5. Colour both halves with the same colours in the same positions.

Example: Draw a flower pattern — the petals on the left should match the petals on the right. You can also try a star, a butterfly, or a geometric pattern.

Remember: Both halves must be identical mirror images for the rangoli to be symmetrical.

Given: Soni folded the paper and drew the cat on one side, then cut it out. Avi did not fold the paper correctly or drew on both sides separately without matching.

Reason: When you fold a paper and draw on one side, then cut it out, both halves are exactly the same — the mask is symmetrical. The eye holes on both sides are at the same position, so you can see with both eyes.

Avi's mask is not symmetrical — the eye holes are not at the same position on both sides. So one eye hole does not align with Avi's eye, and Avi can only see with one eye.

Conclusion: A mask must be symmetrical so that both eye holes are at equal distances from the centre, allowing both eyes to see through.

Given: A painter is drawing Soni's picture.

The Trick: The painter is drawing only half of Soni's face/picture and then folding or reflecting it to complete the other half — because a face is symmetrical. The painter uses the symmetry of the face to quickly complete the portrait.

To stop the trick: We need to give the painter things to draw that are NOT symmetrical — things that do not have a line of symmetry.

Three such things (non-symmetrical objects):
1. A hand (the left hand and right hand are mirror images of each other, but a single hand is not symmetrical by itself)
2. The letter 'F' or 'G' or 'R' — these letters are not symmetrical
3. A shoe (left shoe is not symmetrical)
4. A comb with teeth on one side only
5. A flag with a design only on one side

Draw any three non-symmetrical objects in the space provided. The painter cannot use the folding trick for these objects.