Class 4 Maths Mela Chapter 1 Shapes Around Us Solutions
Page 1
Try to make a model of the buildings shown here using blocks.
1. What parts of the building have you shown in your model (for example, roof, pillars, base, etc.)?
Answer: The model of India Gate has different parts like the base, arches, pillars and the roof or top structure.
2. Why did you select these parts?
I select these parts because they represent whole structure of the India Gate.
Here’s why each one is important:
The Base is holds up the main structure and pillars help the gate stand tall. The arches give the India Gate its special shape and design. The top structure makes it look complete.
3. What shapes will model these parts well?
We can use simple shapes to make the India Gate model. The base can be a rectangle, like a flat box. The pillars can be tall rectangles or tubes. The arches can be half circles or U-shapes. The top part can be a flat square or rectangle, like a roof. These shapes make it easy to build and understand the model.
4. How is your model similar to the picture of the real building?
My model is like the real India Gate because it has the same main parts. It has a base at the bottom, tall pillars on the sides, round arches in the middle, and a top part like a roof. The shapes and parts look like the real building, just in a smaller and simpler way.
5. How is it different from the real building?
My model is different from the real India Gate because it is much smaller. It is made with easy shapes and materials, not brick. It doesn’t have all the small details or carvings. My model looks like the real structure, but it is just a simple demo version for study and fun.
Discussion:
1. What would happen if you removed one piece of your model? Would the model still look like the original building?
If I remove one piece of my model, it will not look like the real India Gate. For example, if I remove one pillar or an arch, the model may fall down or look very different. All the parts are important to make it look like the real building and stay strong.
2. In what ways could you make the model even better?
I could make the model better by adding more details, like small designs, using color, tiny flags or lights. I could also using better materials to make it look more real.
Page 2
Project Work
1. Do you think it looks like the Qutub Minar?
Yes it looks like the Qutub Minar.
2. What shape would you use if you made a model of the Qutub Minar? Why?
If I made a model of the Qutub Minar, I would use a cylinder shape because the real Qutub Minar is tall, round, and looks like a big tower. A cylinder shape would match it best and help show how it goes up high into the sky!
3. How many such shapes will you use?
I will use five cylindrical shapes because the real Qutub Minar has five levels.
Earlier, people made buildings with clay bricks, stone blocks or wood. Today we also use concrete blocks, hollow blocks, etc.
4. What is common to all of these bricks? ………..
All these bricks have a explained clear shape or geometric shape, straight edges, flat sides. They can be arranged in a pattern to build strong buildings.
Page 3
Craft
1. Make a sphere-like shape with paper strips
This is a fun craft where paper strips are woven in a crisscross way to make a shape that looks like a ball or sphere.
2. Use the nets given at the end of the book to make the models shown (prisms and pyramids).
For prisms
a. What shape of face is common to all the prisms? _________________
Rectangle shape of face is common to all the prisms.
b. What other shapes do these prisms have? _________________
These prisms have triangle, square, or hexagon shapes.
c. How many such faces each? _________________
A triangular prism has 5 faces – 2 triangles and 3 rectangles. A square prism has 6 faces – 2 squares and 4 rectangles. A hexagonal prism has 8 faces – 2 hexagons and 6 rectangles.
For Pyramids
a. What shape of face is common to all the pyramids? _______________
Triangle shape of face is common to all the pyramids.
b. All the triangular faces meet at_________________ point.
All the triangular faces meet at the top point.
c. Identify any other shape in each of the pyramids _________________
Here’s the other shape you can find in each pyramid:
- Triangular pyramid – Has a triangle base
- Square pyramid – Has a square base
- Pentagonal pyramid – Has a pentagon base
Is a cube also a prism?
Yes! a cube also a prism?
What is the difference between a prism and a pyramid? Discuss.
A prism has two same-shaped bases, like two squares or two triangles, and the sides are rectangles. A pyramid has only one base, and all the other sides are triangles that meet at the top point. So, a prism looks like a box, and a pyramid looks like a mountain or a tent.
Page 4
3. Now try to make the above shape using straws and plasticine/ thread and fill in the table.
Identify any relationship that you may find between the number of faces (F), edges (E), and corners (V). Calculate F+V–E in each case. What do you notice?
Here are 3D shapes sorted by the number of flat faces:
- 1 flat face – Cone
- 2 flat faces – Cylinder
- 4 flat faces – Triangular prism
- 5 flat faces – Square pyramid
- 6 flat faces – Cube or Square prism
- 8 flat faces – Hexagonal prism
There’s a special rule called Euler’s Formula that helps us find a relationship between faces (F), edges (E), and corners (V) (also called vertices).
The Euler’s formula is: 𝐹+𝑉−𝐸 = 2
a. Cone
Cone faces F = 2
Cone edges E =1
Cone Vertices V = 1
F + V – E = 2 + 1 – 1 = 2 ✅ (but curved, not a polyhedron)
b. Cylinder
Cylinder faces F = 3 (2 flat, 1 curved)
Cylinder edges E = 2
Cylinder vertices = 0
F + V – E = 3 + 0 – 2 = 1 ❌ (not a polyhedron)
c. Triangular Prism
Triangular Prism faces F= 5
Triangular Prism edges E= 9
Triangular Prism vertices V= 6
F + V – E = 5 + 6 – 9 = 2 ✅
d. Square Pyramid
Square Pyramid faces= 5
Square Pyramid edges= 8
Square Pyramid vertices= 5
F + V – E = 5 + 5 – 8 = 2 ✅
e. Cube
Cube faces F= 6
Cube edges E= 12
Cube vertices V= 8
F + V – E = 6 + 8 – 12 = 2 ✅
f. Hexagonal Prism
Hexagonal Prism faces F= 8
Hexagonal Prism edges E= 18
Hexagonal Prism vertices V= 12
F + V – E = 8 + 12 – 18 = 2 ✅
What we notice:
uler’s formula F + V – E = 2 works for solid shapes with flat faces. It does not work for shapes with curved faces because they are not polyhedrons.
Can you construct a 3D shape with 3 flat faces?
Answer: Yes, we can make a 3D shape with 3 flat faces.
Name of the shape
Here are 3D shapes sorted by the number of straight edges:
- 6 straight edges : Triangular pyramid (also called a tetrahedron)
- 8 straight edges: Square pyramid
- 9 straight edges: Triangular prism
- 12 straight edges: Cube, Square prism
Page 5
Let Us Observe
1. Take a die. Look at the face that has number 1. The face numbered 6 is opposite to the face numbered 1.
What is the face opposite to the
a) face numbered 2? …..…
b) face numbered 3? ……..
c) face numbered 4? ……..
Answer:
a) Face numbered 2 is opposite to 5
b) Face numbered 3 is opposite to 4
c) Face numbered 4 is opposite to 3
2. a) Which faces have common edges with the face
numbered 1? ……………………….
b) Which face has no common edge with the face
numbered 1? ………………………
Answer:
a) 2, 3, 4, and 5 faces have common edges with the face numbered 1.
b) 6 face has no common edge with the face numbered 1.
3. Look at three different views of the same cube.
a) What colour is the face that is opposite to the red face?
Answer: Blue colour is the face that is opposite to the red face.
b) What colour is the face that is opposite to the yellow
face? …………………..…………..
Answer: Green colour is the face that is opposite to the yellow face.
Page 6
Sorting 3D shapes
Write the names of 3D shapes in the correct places.
3D shapes:
(1) A. All faces look the same
Cube, Sphere
(1) B. All faces do not look the same
- Cuboid
- Cylinder
- Cone
- Square pyramid
- Triangular prism
(2) A. Shapes with curved edges
- Cylinder
- Cone
- Sphere
(2) B. Shapes with straight edges
- Cube
- Cuboid
- Square pyramid
- Triangular prism
- Hexagonal prism
(3) A. Shapes with rectangular faces
- Cube
- Cuboid
- Triangular prism
- Hexagonal prism
✅ Shapes with both rectangular and triangular faces
- Triangular prism
- Square pyramid
(3) B.Shapes with triangular faces
- Triangular prism
- Square pyramid
- Triangular pyramid
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Page 7
In which circle did you write triangular prism and rectangular pyramid?
Answer:
Triangular prism and rectangular (square) pyramid go in the intersection of Sets A and B in Venn diagram (3), as they have both rectangular and triangular faces.
Cube Towers
How many cubes are there in each of these cube towers?
Answer:
- In first tower (rectangular tower) there are 30 cubes.
- In Second tower, there are 66 cubes.
Page 8
Drawing Cubes on a Triangular Dot Paper
Can you complete the following cubes?
Answer:
1. Match the pictures to the descriptions and name the shapes.
a) I have 5 faces and 5 corners. I have 8 edges. 1 of my faces is a square and 4 of my faces are triangles.
Answer: Square Pyramid
b) I have 1 flat face, 1 curved face, and 1 edge.
Answer: Cone
c) I have 1 curved face. I have no edges or corners.
Answer: Sphere
d) I have 2 flat faces, 1 curved face, and 2 edges. I have no corners.
Answer: Cylinder
e) I have 5 faces, 6 corners, and 9 edges, and 2 of my faces are triangles.
Answer: Triangular Prism
f) I have 6 faces, 12 edges, and 8 corners.
Answer: Cube or Cuboid
2. Each one is different. How? Discuss.
Answer:
1. Red sphere: This is a perfectly round 3D shape with no edges or vertices. Every point on its surface is equidistant from its center.
2. Gold cone: This shape has a circular base that tapers to a single point (vertex) at the top. It has one curved surface and one flat circular surface.
3. Blue triangular pyramid (tetrahedron): This has four triangular faces, four vertices, and six edges. All faces are flat.
4. Green cube: This has six equal square faces, eight vertices and twelve edges. All faces are flat and meet at right angles.
5. Purple rectangular prism: Similar to the cube but with rectangular faces instead of squares. It has six rectangular faces, eight vertices and twelve edges.
Page 9
3. Match the following nets to the appropriate solids given below.
Answer:
Net (a) matches with solid (3) – Triangular Prism
Net (b) matches with solid (4) – Cube
Net (c) matches with solid (1) – Triangular Pyramid
Net (d) matches with solid (2) – Square Pyramid
4. Which of these nets can be folded to make a solid of the kind given below?
Answer:
Nets (a), (c) and (d) can be folded to make a cube.
5. Nitesh cuts up a net on the folds. Here are its pieces.
Answer:
The pieces shown (a, b, c, d) form the net of a triangular prism.
Page 10
Let Us Do
1. Mark the angles in the following pictures.
Answer:
a) Scissors: The angle is formed between the two blades of the scissors. When open, they form an acute angle (less than 90°).
b) Clothes hanger: The main angle is at the top/peak of the hanger where the two sides meet, forming an acute angle. There are also angles where the sides meet the bottom horizontal part.
c) Hand gesture: The fingers form an acute angle between them.
d) Seesaw: The angle changes depending on which side is up. When balanced, it would form a straight angle (180°) with the horizontal. When tilted, it forms obtuse and acute angles with the horizontal.
e) Playground slide: There are several angles here:
- An acute angle between the slide and the ground
- An acute angle between the ladder and the ground
- Various angles where different components connect
2. Where do you see angles in the classroom? Give a few examples.
Answer:
Angles can be seen in corners of the room, edges of desks and tables, corners of books and notebooks, corners of blackboard/whiteboard, in scissor blades, in the hands of a clock, etc.
Page 11
Right Angles
(a) Let’s make a right angle with a piece of paper as shown.
Answer: Do this task in your classroom.
(b) Identify the angles that you think are right angles and circle them in the dot grid given below. Check using your right angle checker.
Answer:
(c) Check for right angles in a book, window and any other object. Write the names of object where you find right angles.
Answer: I found right angles in many things around me. A book has right angles at its corners. A window has right angles in the frame. I also saw right angles in a door, a table, and the tiles on the floor.
Page 12
Let Us Do
1. Draw some right angles on the dot grid.
Answer:
Acute and Obtuse Angles
Name some objects from your classroom which have an acute angle.
Answer:
- Open scissors,
- slant of a pen stand, s
- ome chair designs.
- clock hands at certain times (e.g., 11:30),
Name some objects from your classroom which have an obtuse angle.
Answer:
- certain roof designs,
- certain chair positions,
- Open compass,
- partially open doors.
Identify all angles in the following letters.
Answer:
Letter V:
Contains 1 angle at the bottom point where the two lines meet (marked with a small curved line in the image)
Letter A:
Contains 2 angles:
- The top point where the two slanted lines meet
- The interior angle where the horizontal crossbar meets the left slanted line (marked with a small curved line in the image)
Letter Z:
Contains 2 angles:
- The upper right angle where the top horizontal line meets the diagonal line (marked with a small curved line in the image)
- The lower left angle where the diagonal line meets the bottom horizontal line
Page 13
Let Us Do
1.
Answer:
2. In the figures given below, mark the acute angles in red, right angles in green and obtuse angles in blue.
Answer:
First Figure (Leftmost):
- Right Arm and Body: Forms an acute angle (marked in red).
- Right Leg and Body: Forms an obtuse angle (marked in blue).
- Left Arm and Body: Forms a right angle (marked in green).
Second Figure:
- Right Leg and Body: Forms a right angle (marked in green).
- Both Arms: Form acute angles with the body (marked in red).
Third Figure:
- Left Arm and Body: Forms an acute angle (marked in red).
- Right Arm and Body: Forms a right angle (marked in green).
- Both Arms and Legs: Appear to form acute angles (marked in red).
Fourth Figure (Rightmost):
Page 14
Shapes with Straws
Make a triangle with straws of different sizes and clay/plasticine.
1. Does the shape of the triangle change if we gently push one of its sides?
Answer: No, triangles are rigid shapes.
2. What kinds of angles does a triangle have?
Answer: A triangle can have acute, obtuse or right angles, depending on the specific triangle.
3. What kinds of angles do you see in the rectangle?
Answer: Four right angles (90°).
4. Does the shape of the rectangle change if we gently push one of its sides?
Answer: Yes, it changes to a parallelogram.
5. What has happened to the angles of the new shape? Are they still right angles? What types of angles have been formed?
Answer: The angles are no longer right angles. Two acute angles and two obtuse angles have been formed.
6. Similarly, push one side of a square. Are they still right angles? What types of angles have been formed?
Answer: No longer right angles. Two acute angles and two obtuse angles have been formed.
7. How are the angles of triangles and rectangles similar or different?
Answer: Triangles maintain their shape when pushed (rigid), while rectangles deform. A rectangle always has four right angles, while a triangle can have different types of angles.
Page 15
Use the dot grid given below to draw several three- angle and four-sided shapes. Circle the shapes that have one or more right angles.
Answer:
What shapes did you make? How many shapes have you made with:
a) 1 right angle
b) 2 right angles
c) 3 right angles
d) all right angles
Answer:
a) 1 Shape with 1 right angle
b) 0 Shape with 2 right angles
c) 0 Shape with 3 right angles
d) 2 Shapes with 4 right angles)
In what ways are rectangle and square different from these shapes?
Answer:
Rectangles and squares have all right angles (4 right angles), while the other shapes have varying angles. Squares additionally have all sides equal.
Page 16
Try to make this 5-sided shape with all sides equal (Pentagon)
1. Are these right angles?
Answer:
No, the angles in the pentagon are not right angles.
2. Does the shape of the pentagon change if we gently push one of its sides?
Answer:
Yes, it changes shape.
3. How does this change the angles?
Answer:
Some angles become bigger (obtuse) and some become smaller (acute).
Can you make a circle using straws?
1. Look at the picture. The lengths of the straws in this picture are…
(Equal/Unequal)
Answer: Equal
2. What will happen if we take straws of unequal lengths?
Answer: The circle will look uneven and will not be a perfect circle.
Page 17
Amazing Circles
1. The length of all the creases are _____.
Answer: Equal
2. These creases are called diameters of the circle.
Answer: Yes, that’s correct.
3. Discuss where the centre is. Do you notice that all the diameters pass through the centre?
Answer: The center is where all diameters intersect. Yes, all diameters pass through the center.
4. Measure the length of the creases from the center to the border of the circle. This is called the radius of the circle.
Answer: The measurement would depend on the size of the circular paper used.
5. Discuss if there is any relationship between the radius and the diameter of a circle.
Answer: The diameter is twice the radius, or the radius is half the diameter.
page 18
Let Us Do
The length of the diameter is _____ (half/double) of the length of radius.
Answer: Double
Look at the carpet design. A beautiful circle, right?
Answer:
Page 19
All wheels look like……….
Answer: Circles
Name the wheel with the
Answer:
1. Longest radius B.
2. Shortest radius D.
3. Longest diameter B.
4. Shortest diameter D.
Puzzling Shapes
Identify the hidden shapes and write their names.
Answer: Square, Rectangle, Triangle, Circle
2. Draw 2 lines to divide the triangle into 1 square and 2 triangles
Answer:
You can draw:
- 1 vertical line to make a square on the left
- 1 diagonal line from the top of the square to the bottom right corner of the triangle
