Toy Joy — NCERT Solutions

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:

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.)