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.

Given: Soni places 4 counters on her side of a grid. Avi must place counters on his side to create a mirror image.

Concept: In a mirror image, every counter on Soni's side must have a matching counter on Avi's side at the same distance from the mirror line, but on the opposite side.

How to check:
1. Place a mirror (or a ruler) along the dividing line between Soni's and Avi's sides.
2. Look at the reflection of Soni's counters in the mirror.
3. If Avi's counters match the reflection exactly, Avi has placed them correctly.

Note: Since the actual grid image is not visible, apply the above method to the grid shown in the book. Each counter on Soni's side at position $(r, c)$ from the mirror line should have a matching counter on Avi's side at the same row $r$ and same distance $c$ from the mirror line on the other side.

Given: Four shapes/objects are shown (images not visible in OCR, but the activity involves symmetry).

Concept: In a group of objects, the odd one out is the one that is different from the others based on a property — here, likely symmetry.

Method:
1. Check each object for symmetry.
2. If three objects are symmetrical and one is not, the non-symmetrical one is the odd one out.
3. Alternatively, if three are non-symmetrical and one is symmetrical, the symmetrical one is the odd one out.

Note: Since the actual images are not visible, apply the following reasoning to the shapes shown in your book:
- Identify which shapes have a line of symmetry and which do not.
- The shape that is different from the rest (either the only symmetrical one or the only non-symmetrical one) is the odd one out.

Give your reason clearly, for example: "Shape ___ is the odd one out because it is the only one that is not symmetrical" or "because it is the only one with more than one line of symmetry."

Given: A grid of boxes (7 boxes total — 4 red, 3 blue), to be filled so that one side is the mirror image of the other.

Concept: For mirror symmetry, the arrangement on the left of the centre must match the arrangement on the right.

Note: Since the grid has 7 boxes, the middle box is the centre. The 3 boxes on the left must mirror the 3 boxes on the right, and the centre box has its own colour.

For the arrangement to be symmetrical:
- The centre box can be red or blue.
- The 3 pairs (left-right) must each have the same colour.

Case 1: Centre box is red (uses 1 red). Remaining: 3 red and 3 blue for 3 pairs.
Each pair must be the same colour. We need to choose which pairs are red and which are blue.
Number of ways = $\binom{3}{3} = 1$ way (all pairs red) — but that uses 6 red + 1 red = 7 red, not 4 red.
Let's recalculate: 3 pairs, need 3 red boxes and 3 blue boxes among the 6 paired boxes.
Each pair contributes 2 of the same colour. So we need $\frac{3}{2}$ pairs red — not a whole number. This doesn't work.

Case 2: Centre box is blue (uses 1 blue). Remaining: 4 red and 2 blue for 3 pairs.
Each pair is same colour. Need 4 red in 3 pairs: $\frac{4}{2} = 2$ pairs red, $\frac{2}{2} = 1$ pair blue.
Number of ways to choose which 2 of 3 pairs are red = $\binom{3}{2} = 3$ ways.

So there are $\mathbf{3}$ ways to fill the boxes symmetrically with 4 red and 3 blue.

(Note: The exact answer may vary depending on the grid shape shown in the book. Apply the mirror symmetry rule to the actual grid.)

Given: Catty's side shows a certain arrangement of balls. Micy's side is different. Only 3 balls in Micy's side can be moved.

Concept: We need to find which 3 balls in Micy's arrangement are in the wrong position compared to Catty's arrangement, and move them to the correct positions.

Method:
1. Compare Catty's arrangement with Micy's arrangement ball by ball.
2. Find the positions where they differ.
3. Move exactly 3 balls in Micy's side to make it match Catty's side.

Note: Since the actual images are not visible, apply this method to the arrangements shown in your book. Identify the 3 balls that are out of place in Micy's side and move them to match Catty's side exactly.

Given: A large shape and several smaller shape cutouts are shown.

Concept: Tiling/tessellation — shapes that can fill a larger shape completely without any gaps or overlaps.

Method:
1. Look at the large shape carefully.
2. Try to mentally (or physically) place each cutout shape inside the large shape.
3. The correct cutout(s) will fill the large shape completely — no part of the large shape will be left empty, and no cutout will go outside the boundary.

Note: Since the actual images are not visible, apply the above method to the shapes shown in your book. The answer will be the shape(s) that tile the given large shape perfectly.

Given: Several outline shapes are shown, and rangometry shapes (triangles, squares, hexagons, etc.) are to be used to fill them.

Concept: Tiling — filling a shape completely using smaller shapes with no gaps (empty spaces) and no overlaps (shapes on top of each other).

Steps:
1. Take the rangometry shapes (cut-outs).
2. Place them inside the given outline shape one by one.
3. Arrange them so that they fit together perfectly — edges touching, no space left empty, no two shapes on top of each other.
4. Trace the shapes once you have found the correct arrangement.

Tip: Start from one corner and work your way across. Try rotating or flipping the shapes if needed to make them fit.

Given: Rangometry shapes and a path from Start to End.

Steps:
1. Choose two or more rangometry shapes (e.g., a triangle and a square).
2. Join them together to create your own tile shape.
3. Trace this tile shape repeatedly, placing each tracing next to the previous one with no gaps or overlaps.
4. Continue tracing until the path from Start to End is completely filled.

Note: The tile you create should be able to repeat (tessellate) to fill the path. Try different combinations of shapes to create interesting patterns.

Given: Several path patterns are shown to be filled with tiles.

Steps:
1. Look at each path carefully — note its shape and size.
2. Choose appropriate rangometry shapes that can fill the path.
3. Place the shapes along the path, fitting them together with no gaps and no overlaps.
4. Trace the shapes to record your tiling.

Tip: For a straight path, rectangles or squares work well. For a curved or irregular path, try triangles or combinations of shapes. Rotate the shapes as needed to make them fit.

Given: A fair map with various stalls and places.

This is a fun activity to practise giving and understanding directions and descriptions.

How to play:
1. One player thinks of a stall or place on the map (keep it secret).
2. The other player asks yes/no questions to guess the place.

Example questions:
- Is it near the entrance? (Yes/No)
- Is it on the left side of the map? (Yes/No)
- Is it next to the food stall? (Yes/No)
- Does it have a flag? (Yes/No)
- Is it in the centre of the fair? (Yes/No)

3. The player who is guessing uses the answers to narrow down the location.
4. The player who guesses correctly in the fewest questions wins.

This activity helps us learn to use positional words like left, right, near, far, next to, in front of, behind, etc.

Given: A map of the Surajkund Fair with various signs and symbols.

Method: Look at the map legend (key) to find what the △ sign represents.

Answer: The △ sign shows the location of the First Aid / Medical Centre (or as indicated in the map legend of your book). Check the map key and write the name of the place shown by △.

Given: A map of the Surajkund Fair.

Method: Look at the map for a picture/symbol that represents a play area (it may show swings, slides, or children playing).

Answer: Find the picture on the map that shows children playing or playground equipment, and circle it. (Refer to the actual map in your book to identify and circle the correct picture.)

Given: A map of the Surajkund Fair with a P sign.

Answer: The P sign shows the Parking area. In most maps and public places, P is the universal symbol for parking.

Check the map legend in your book to confirm.

Given: A map of the Surajkund Fair.

Method: Look at the map for all places marked as 'Exit'.

Answer: Count the number of exit signs/routes shown on the map in your book and write the number.

(Based on typical fair maps, there are usually $\mathbf{2}$ exit routes, but refer to the actual map in your book for the correct answer.)

Given: A map of the Surajkund Fair with coloured lanes.

Steps to follow on the map:
1. Start at the entry point.
2. Walk along the blue lane (move forward on the blue-coloured path).
3. When you reach the green lane, turn right and walk along it.
4. You will see a restaurant on your right — do not stop, keep walking.
5. Turn left onto the red lane.
6. Take the first left turn onto the golden lane — you will see stalls on the way.
7. Walk past the stalls and you will reach the chaupal where Dada and Dadi are waiting.

Trace this path on the map in your book with a pencil to find the chaupal.

Given: A map of the Surajkund Fair. Starting point: Chaupal. Destination: ATM.

Method: Look at the map and find the chaupal and the ATM. Then trace a path from the chaupal to the ATM using the coloured lanes.

Sample directions (based on a typical fair map layout — refer to your actual map):
1. Start from the chaupal.
2. Walk back on the golden lane towards the main path.
3. Turn right onto the red lane.
4. Walk straight and turn right onto the green lane.
5. The ATM will be visible on your left/right (as shown on the map).

Note: Write the exact directions based on the map in your book, using the lane colours and landmarks (restaurant, stalls, play area, etc.) as reference points.