Toy Joy

Given: A picture of Jaya's rocket made of different 3-D shapes (image not visible, so standard rocket model values are used as per NCERT).

A typical rocket model of this type uses:
- Cube: $0$
- Cuboid: $1$
- Cone: $1$
- Cylinder: $2$

(Note: Exact counts depend on the figure. Students should count each shape carefully from their textbook image and fill in accordingly.)

Given: A picture of Jaya's rocket.

By observing the arrangement of shapes in the rocket from bottom to top, the shape that is between the red cuboid and the yellow cuboid is a Cylinder.

(Students should verify by looking at the actual image in their textbook.)

Given: The rocket model built by Jaya.

By observing the image, the shape on top of the orange cylinder is a Cone.

(Students should verify by looking at the actual image in their textbook.)

Given: The rocket model built by Jaya.

By observing the image, the shape under the pink cone is a Cylinder.

(Students should verify by looking at the actual image in their textbook.)

Given: A picture of Devika's toy engine made of different coloured 3-D shapes.

By carefully counting each shape in the toy engine image (standard NCERT answer):
- Red cylinders: $2$
- Yellow cones: $1$
- Grey cuboids: $2$
- Blue cubes: $1$

(Note: Students must count from the actual image in their textbook and fill in the correct numbers.)

Given: Students are asked to look around the classroom and identify real objects that resemble each 3-D shape.

Sample answers for the table:

| Cylinder | Sphere | Cube | Cuboid | Cone |
|---|---|---|---|---|
| Water bottle | Ball | Dice | Chalk box | Birthday cap |
| Drum | Globe | Sugar cube | Brick | Ice cream cone |
| Pencil holder | Marble | Wooden block | Book | Funnel |

(Students should fill in objects they actually find in their own classroom.)

(a) Shape found the most: Cuboid — because books, boxes, chalk boxes, desks, and bricks are all cuboids.

(b) Shape found the least: Cone — cone-shaped objects are not very common in a classroom.

(c) Objects made up of more than one shape:
- A sharpened pencil (cylinder + cone)
- A table (cuboid top + cylindrical or cuboid legs)
- A water bottle with a cap (cylinder + cone or cylinder)

(Students should give examples from their own classroom.)

Given: A set of 3-D shapes shown in the image.

Concept: We identify each shape by its properties:
- Cube – 6 equal square faces, 12 equal edges, 8 corners.
- Cone – 1 circular flat face, 1 curved surface, 1 apex (pointed top).
- Cylinder – 2 circular flat faces, 1 curved surface, no corners.
- Cuboid – 6 rectangular faces (may not all be equal), 12 edges, 8 corners.

Instructions to follow on the image:
- ⭕ Circle all shapes that are cubes.
- ✔ Tick all shapes that are cones.
- ✖ Cross all shapes that are cylinders.
- ☐ Draw a box around all shapes that are cuboids.

(Students should apply these markings directly on the shapes shown in their textbook image, identifying each shape by its properties as described above.)

Given: We need to identify 3-D shapes based on their properties — faces, edges, and surfaces.

Concept: Properties of 3-D shapes:
- Sphere – 0 edges, 0 flat faces, 1 curved surface.
- Cube/Cuboid – all flat (rectangular/square) faces, all straight edges.
- Cylinder – 2 flat circular faces + 1 curved surface; edges are curved circles.
- Cone – 1 flat circular face + 1 curved surface; 1 curved edge at the base.

(a) Shape with no edges:
$$\boxed{\text{Sphere}}$$
A sphere has no edges and no corners — it is perfectly round.

(b) Shape with only flat faces:
$$\boxed{\text{Cube and Cuboid}}$$
All faces of a cube and cuboid are flat (square or rectangular).

(c) Shape with only curved faces:
$$\boxed{\text{Sphere}}$$
A sphere has only one curved surface and no flat face.

(d) Shape with both straight and curved edges:
$$\boxed{\text{Cylinder and Cone}}$$
A cylinder has two circular (curved) edges. A cone has one circular (curved) edge at its base.

(e) Shape with both flat and curved faces:
$$\boxed{\text{Cylinder and Cone}}$$
A cylinder has 2 flat circular faces and 1 curved surface.
A cone has 1 flat circular face and 1 curved surface.

Given: Images of 3-D shapes built using clay balls (as corners/vertices) and sticks (as edges).

Activity-based question — Steps to build shapes with clay and sticks:

To build a Cube:
- You need $8$ clay balls (for 8 corners) and $12$ equal-length sticks (for 12 edges).
- Join 4 sticks in a square for the bottom face, then 4 sticks standing upright at each corner, then 4 sticks joining the tops to form the top face.

To build a Cuboid:
- You need $8$ clay balls and $12$ sticks (4 long, 4 medium, 4 short).
- Arrange similarly to the cube but with sticks of different lengths.

To build a Triangular Pyramid (Tetrahedron):
- You need $4$ clay balls and $6$ equal sticks.

Shapes you can build: Cube, Cuboid, Triangular Pyramid, Square Pyramid.

(Students should try building these shapes using clay and sticks as a hands-on activity.)

Given: Images of structures/shapes made by joining unit cubes together.

Activity: Students are asked to physically arrange unit cubes (like dice or building blocks) to recreate the shapes shown in the images.

Steps:
- Look at each shape in the image carefully.
- Count how many unit cubes are used in each shape.
- Arrange your cubes one by one, matching the pattern shown.
- Check that your arrangement looks the same from the front, side, and top.

Example structures typically shown:
- A straight row of $3$ cubes (like a train).
- An L-shaped arrangement.
- A staircase arrangement.

(Students should use actual cubes/blocks and build the shapes shown in their textbook images.)

Given: Two or more 3-D shapes are shown for comparison (image not fully visible; typical comparison is between a Cube and a Cuboid, or Cylinder and Cone).

Concept: Compare 3-D shapes by their faces, edges, corners, and surfaces.

Example: Comparing a Cube and a Cuboid:

| Property | Cube | Cuboid |
|---|---|---|
| Number of faces | 6 | 6 |
| Number of edges | 12 | 12 |
| Number of corners | 8 | 8 |
| Shape of faces | All square (equal) | Rectangular (may differ) |

Same: Both have 6 flat faces, 12 edges, and 8 corners. Both have only flat faces.

Different: In a cube all faces are equal squares; in a cuboid the faces are rectangles and may not all be equal.

Example: Comparing a Cylinder and a Cone:

Same: Both have a curved surface and a circular flat face at the base.

Different: A cylinder has 2 circular flat faces and no pointed top; a cone has only 1 circular flat face and a pointed apex.

(Students should apply this comparison to the specific shapes shown in their textbook image.)

Given: A standard die (cube) with faces numbered 1 to 6.

Concept: On a standard die, the numbers on opposite faces always add up to $7$.

Working:
$$1 + 6 = 7 \Rightarrow \text{Face opposite to } 1 = 6$$
$$2 + 5 = 7 \Rightarrow \text{Face opposite to } 2 = 5$$
$$3 + 4 = 7 \Rightarrow \text{Face opposite to } 3 = 4$$

Answers:
- Face opposite number $1$ = $\mathbf{6}$
- Face opposite number $2$ = $\mathbf{5}$
- Face opposite number $3$ = $\mathbf{4}$

Pattern noticed: The numbers on opposite faces of a die always add up to $\mathbf{7}$.

Given: An image of a model made by stacking 3-D shapes one on top of another.

Concept: To describe the order of construction, we start from the bottom (base) and move upward.

Standard answer for a typical rocket/tower model:

Step 1: First, place the cuboid at the bottom as the base.

Step 2: Then, place the cylinder on top of the cuboid.

Step 3: Finally, place the cone on top of the cylinder.

Order: Cuboid → Cylinder → Cone (from bottom to top).

(Students should describe the order based on the specific model shown in their textbook image, starting from the shape at the bottom and ending with the shape at the top.)

Given: 3 unit cubes to be joined face-to-face in different ways.

Concept: When joining cubes face-to-face, we count arrangements that look different (different shapes, not just rotations of the same shape).

Working:

With 3 cubes joined face-to-face, there are 2 distinct arrangements:

Arrangement 1 – Straight (I-shape):
All 3 cubes are placed in a straight line.
$$\square\square\square$$

Arrangement 2 – L-shape (bent):
2 cubes are in a row, and the 3rd cube is placed on top of or to the side of one end cube, making an L-shape.

Answer: You can join 3 cubes in $\mathbf{2}$ different ways.

(Students should physically try both arrangements with actual cubes/blocks to verify.)

Given: Images of models made using different 3-D shapes.

Concept: Identify each 3-D shape and describe its position using positional words such as on top of, under, beside, between, etc.

Sample answer (based on a typical house/tower model):

Model 1 (House):
- Shapes used: Cuboid (walls) and Triangular prism or Cone (roof).
- Arrangement: The cuboid is at the bottom. The cone/triangular prism is on top of the cuboid.

Model 2 (Tower/Rocket):
- Shapes used: Cylinder and Cone.
- Arrangement: The cylinder is at the bottom. The cone is on top of the cylinder.

Model 3 (Train/Vehicle):
- Shapes used: Cuboid (body), Cylinders (wheels), Cone (front).
- Arrangement: The cuboid forms the main body. Cylinders are on the sides as wheels. The cone is in front.

(Students should name the shapes and describe the arrangement for the specific models shown in their textbook images.)

Given: 6 dice (each die is a cube) to be arranged into different shapes.

Concept: By joining unit cubes (dice) face-to-face, we can form larger 3-D shapes.

(a) To make a Cuboid:
Arrange the 6 dice in a $2 \times 3 \times 1$ arrangement:
- Place 3 dice in a row.
- Place another 3 dice beside them to form a $2 \times 3$ flat rectangle.
- This forms a cuboid (flat, rectangular block).

Alternatively, arrange them in a $1 \times 2 \times 3$ stack.

(b) To make a Tower:
Stack all 6 dice one on top of the other in a straight vertical column:
$$\text{Die 1 (bottom)} \to \text{Die 2} \to \text{Die 3} \to \text{Die 4} \to \text{Die 5} \to \text{Die 6 (top)}$$
This makes a tall, thin tower (a long cuboid standing upright).

(c) Any other shape of your choice:
Example — Make an L-shape:
- Place 4 dice in a row (horizontal).
- Stack 2 more dice on top of one end.
This creates an L-shaped or staircase structure.

(Students should physically try these arrangements with actual dice and observe the shapes formed.)