The Surajkund Fair — NCERT Solutions

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.