CBSE Class 3 Mathematics – Where to Look From – CBSE NCERT Study Resources
All Question Types with Solutions – CBSE Exam Pattern
Explore a complete set of CBSE-style questions with detailed solutions, categorized by marks and question types. Ideal for exam preparation, revision and practice.
Very Short Answer (1 Mark) – with Solutions (CBSE Pattern)
These are 1-mark questions requiring direct, concise answers. Ideal for quick recall and concept clarity.
The mirror line is an imaginary line that divides a shape into two identical halves.
Each half is a mirror image of the other.
- A butterfly
- A leaf
A square has 4 lines of symmetry.
These lines pass through its opposite corners and midpoints of opposite sides.
Horizontal symmetry divides an object into top and bottom halves.
Vertical symmetry divides it into left and right halves.
No, a scalene triangle has no lines of symmetry because all sides and angles are unequal.
A circle has an infinite number of lines of symmetry.
Any line passing through its center divides it into equal halves.
The letter 'M' has a vertical line of symmetry down its center.
No, both a rectangle and a rhombus have 2 lines of symmetry.
A human face is nearly symmetrical because its left and right sides are almost mirror images of each other.
Small differences like moles or expressions make it not perfectly symmetrical.
Very Short Answer (2 Marks) – with Solutions (CBSE Pattern)
These 2-mark questions test key concepts in a brief format. Answers are expected to be accurate and slightly descriptive.
A 2D shape is flat and has only length and width, like a square or circle.
A 3D shape has length, width, and height, like a cube or sphere.
A triangle has three sides and three corners.
It is a 2D shape with straight edges.
Two objects that look like a cylinder are:
- A water bottle
- A tin can
A cylinder has two circular faces and one curved surface.
The line where two faces of a 3D shape meet is called an edge.
For example, a cube has 12 edges.
The top view of a book looks like a rectangle.
It shows only the flat surface of the book when viewed from above.
A circle has no corners and no edges.
It is a smooth, round 2D shape with one curved side.
A mirror image is a clear and exact flipped copy of an object, while a water reflection may appear wavy or less clear due to water movement.
Example: A tree in a mirror looks sharp, but in water, it might look blurry.
A square has 4 lines of symmetry.
Explanation: It can be folded into equal halves vertically, horizontally, and along both diagonals.
Two objects with no line of symmetry are:
- A football (irregular shape)
- A hand fan (asymmetrical design)
The mirror image of 'A' looks like this:
Ɐ (a flipped version).
Tip: Hold a mirror beside the letter to see the reflection.
A clock looks different in a mirror because the image is flipped.
Example: If the time is 3:00, the mirror shows 9:00.
Reason: Mirrors reverse left and right.
A heart has one vertical line of symmetry.
Explanation: If you fold it vertically, both halves match perfectly.
Short Answer (3 Marks) – with Solutions (CBSE Pattern)
These 3-mark questions require brief explanations and help assess understanding and application of concepts.
A mirror image is a flipped copy of an object created by a mirror, where left and right sides are reversed.
A water reflection is a less clear, wavy version of the object due to water movement.
Example: Your face in a mirror is sharp (mirror image), but its reflection in a pond may look blurry (water reflection).
The letter 'A' has a vertical line of symmetry down its center.
Reason: If you fold the letter along this line, both halves match perfectly.
Diagram: Imagine a straight line splitting 'A' into two equal mirror halves.
The scalene triangle has no line of symmetry.
Reason: All sides and angles are unequal, so no folding line can make matching halves.
Note: Circle (infinite symmetry lines), Square (4 symmetry lines).
In a mirror, 'MOM' would still look the same (spelled as 'MOM').
Reason: It is a palindrome (reads the same forwards and backwards), so the mirror image matches the original.
Fun fact: Words like 'WOW' or 'DAD' also behave this way!
The mirror will show 9:00.
Logic: A mirror flips objects horizontally. The hour hand at 3 moves to 9 in the reflection.
Tip: For any clock time, subtract it from 12 to find its mirror time (e.g., 12 - 3 = 9).
The mirror image of the letter 'A' looks the same because it is symmetrical.
However, if the letter was 'B', its mirror image would flip the left and right sides.
Symmetry means both sides of an object are identical when divided by a line.
A shape has a line of symmetry if it can be folded into two identical halves.
For example, a square has 4 lines of symmetry because it can be folded vertically, horizontally, and diagonally.
An equilateral triangle has 3 lines of symmetry.
Objects with symmetry (like a circle or square) look the same in a mirror because both halves are identical.
Objects without symmetry (like a hand or the letter 'R') appear flipped because their left and right sides are different.
Symmetrical objects do not change in a mirror.
1. Mirror: It reflects light perfectly, creating a clear image.
2. Still water: It reflects objects but the image may be wavy if the water moves.
Reflection happens when light bounces back from a smooth surface.
The mirror image of B looks like a backward B.
In the mirror, the left side of the original B becomes the right side of the reflected image.
This happens because mirrors flip objects horizontally.
Objects like a ball look the same because they are symmetrical—their left and right sides are identical.
Words or letters are not symmetrical, so their mirror images appear flipped.
For example, MOM looks the same in a mirror, but DOG does not.
A shape has a line of symmetry if it can be folded into two identical halves.
For example, a square has 4 lines of symmetry—fold it vertically, horizontally, or diagonally, and both halves match.
A rectangle has 2 lines of symmetry (vertical and horizontal).
Your reflection raises its left hand.
This happens because mirrors flip images sideways, making the right side appear as the left.
It’s like how the word AMBULANCE is written backward on vehicles so it appears correct in mirrors.
Long Answer (5 Marks) – with Solutions (CBSE Pattern)
These 5-mark questions are descriptive and require detailed, structured answers with proper explanation and examples.
Mirror symmetry is when one half of an object is the exact reflection of the other half, just like how a mirror works. If you draw a line (called the line of symmetry) through the middle of the object, both sides will match perfectly.
Examples from everyday life:
- A butterfly's wings are mirror symmetric.
- The letter A has a vertical line of symmetry.
- A human face (though not perfectly) is roughly symmetric.
How to identify mirror symmetry:
- Imagine or draw a line dividing the object into two parts.
- Check if one side is the mirror image of the other.
- If both sides match exactly, the object has mirror symmetry.
Fun fact: Some objects, like a circle, have many lines of symmetry, while others, like a rectangle, have only two!
The shape Rahul drew is a rectangle because it has 4 sides, and opposite sides are equal and parallel.
Properties of a rectangle:
- It has 4 sides and 4 corners (vertices).
- Opposite sides are equal in length and parallel.
- All four angles are right angles (90 degrees).
Lines of symmetry in a rectangle:
- A rectangle has two lines of symmetry.
- One line is vertical, dividing it into two equal left and right halves.
- The other line is horizontal, dividing it into two equal top and bottom halves.
Note: Unlike a square, a rectangle does not have diagonal lines of symmetry unless it is a square (where all sides are equal).
Mirror symmetry (also called line symmetry) means one half of an object is the exact mirror image of the other half when folded along a line. For example, a butterfly has mirror symmetry because if you draw a line down its center, both sides match perfectly.
Rotational symmetry means an object looks the same after being rotated (turned) by a certain angle. For example, a windmill blade has rotational symmetry because it looks identical after a 90° turn.
Diagrams:
1. Draw a butterfly with a dotted line down the middle to show mirror symmetry.
2. Draw a windmill with arrows showing how it rotates to match itself.
When we look at a cube from different sides, we see different 2D shapes:
1. Top view: We see a square because the top face is flat and square-shaped.
2. Front view: Another square since the front face is identical to the top.
3. Side view: Again a square, but it might look like it’s beside the front face.
This helps us understand that a cube has equal sides and all faces are squares. If we only saw one view, we might think it’s a flat shape, but multiple views show it’s 3D.
Mirror symmetry (also called line symmetry) means one half of an object is the exact mirror image of the other half when folded along a line.
Example: A butterfly's wings or a human face.
Rotational symmetry means an object looks the same after being rotated (turned) by a certain angle.
Example: A windmill blade or a pizza slice when rotated.
Diagram:
1. For mirror symmetry: Draw a butterfly with a dotted line down the middle showing both sides match.
2. For rotational symmetry: Draw a starfish with arrows showing it looks identical when rotated by 72°.
The letter 'A' block looks different from different angles because objects appear to change shape based on the viewing direction.
Top view: Shows a flat rectangle (the base of the block).
Front view: Shows the letter 'A' with its triangular shape.
Side view: Shows a thin rectangle (the thickness of the block).
Diagram:
1. Top view: Draw a simple rectangle.
2. Front view: Draw a capital 'A' with a triangle and crossbar.
3. Side view: Draw a narrow rectangle.
This happens because our eyes see only one side of the 3D object at a time.
When Rahul looks at the book from the top, he sees the flat rectangular surface of the book, like looking down at a table.
From the front, he sees the cover with the title and maybe a picture.
From the side, he sees the thin edge of the pages stacked together.
Observing objects from different sides is important because:
- It helps us understand the complete shape of an object.
- We learn that objects can look different from various angles.
- It improves our spatial awareness and helps in drawing or describing objects accurately.
For example, if we only see a book from the front, we might not realize how thick it is until we look from the side.
Here’s how the views help us understand the toy car:
- Top view: Shows the shape of the car's roof and how wide it is. We can see if it has a sunroof or any designs on top.
- Front view: Reveals the headlights, grille, and windshield. It helps us see how tall the car is.
- Side view: Displays the doors, windows, and wheels. We can count how many doors it has and the size of the wheels.
By combining these views, we get a complete idea of the car's 3D structure. For example, the top view alone doesn’t show the wheels, but the side view does. This is why multiple views are important in understanding objects fully.
When Rahul looks at the toy car from the top, he sees the roof and the overall shape of the car, like a rectangle with circles (wheels) at the bottom.
From the front, he sees the headlights, grille, and windshield, which helps him understand the car's design.
From the side, he observes the doors, windows, and the length of the car, giving a complete idea of its size.
It is important to observe objects from different sides because:
- It helps us understand the complete structure of the object.
- Different angles show different features, like wheels from the side or roof from the top.
- In real life, we need multiple views to recognize objects easily, like identifying a friend from the back or front.
Top view: A rectangle (base of the house) with a triangle attached (roof). No door or window is visible from above.
Front view: A rectangle (wall) with a triangle (roof) on top, a smaller rectangle (door) at the bottom, and a square (window) beside it.
Side view: A rectangle (side wall) with a triangle (roof) and a square (window), but no door.
Each view helps in understanding:
- Top view shows the shape and size of the house and roof.
- Front view reveals the door and window placement for entry and light.
- Side view gives details about the window's position and the roof's slope.
Case-based Questions (4 Marks) – with Solutions (CBSE Pattern)
These 4-mark case-based questions assess analytical skills through real-life scenarios. Answers must be based on the case study provided.
When Riya looks at the toy car from the top, she sees the roof and the outline of the car's shape. This view shows the length and width of the car.
From the front, she sees the headlights, bumper, and windshield, which helps identify the height and width of the car.
From the side, she sees the doors, wheels, and the entire length and height of the car.
Each view is different because the car is a 3D object, and different angles reveal different features.
From above, the book looks like a rectangle, showing its length and width.
From the side, it looks like a thinner rectangle, showing its height and length.
From the front, it looks like a rectangle showing its height and width.
The shapes appear different because each view captures only two dimensions of the 3D object at a time.
From the top, the cube looks like a square because only one face is visible.
From the front, it also looks like a square, showing another face.
From the side, it still looks like a square, showing a third face.
All views look the same because a cube has equal length, width, and height, making all faces identical squares. This is a special property of a cube.
Explain how the shape of the butterfly appears differently from these three views.
When Riya looks at the butterfly from different angles, its shape changes because of perspective.
- Front view: The butterfly appears wide with its wings spread out, showing patterns on both wings.
- Side view: The butterfly looks narrow, with one wing visible and the other hidden behind it.
- Top view: Only the upper part of the wings is visible, making the butterfly look flat.
This happens because objects look different based on the direction we observe them from.
Draw how the dice might look from these two sides and explain why the number of dots changes.
The dice shows different numbers of dots because each face has a unique arrangement.
Side with 3 dots: The dots are arranged in a diagonal line (e.g., top-left, center, bottom-right).
Side with 5 dots: The dots form a cross (one in the center and one on each corner except one).
The change occurs because a dice has 6 faces, and each face shows a different number (1 to 6). When Amit changes his viewing angle, he sees a different face of the dice.
Describe how the book would look if she moves to the front or the top. What does this tell us about observing objects?
When Priya moves to observe the book from different angles:
- Front view: She sees the cover of the book with its title and pictures.
- Top view: She sees the edges of the pages, making the book look like a thin rectangle.
This shows that objects appear differently based on our viewing position. The same object can look completely distinct when seen from various sides, helping us understand its full shape.
When Riya looks at the butterfly from different sides, its shape appears differently due to perspective.
Front View: The butterfly's wings are fully visible, spread out symmetrically.
Side View: Only one wing is visible, and the body appears thinner.
Top View: The butterfly's wings may appear folded or less spread out.
This happens because objects look different based on the angle from which we observe them. Drawing these views helps understand spatial awareness.
A cube looks different from various angles due to its 3D structure.
Front View: A square (one face of the cube).
Side View: Another square, identical to the front view if the cube is perfectly aligned.
Top View: A square again, showing the upper face.
All views are squares because a cube has equal sides. Drawing these helps understand symmetry and dimensions.
The toy house's roof is a triangular prism, so its appearance changes with the viewing angle.
Front View: A triangle (the roof's peak is visible).
Side View: A rectangle (the length of the roof is visible).
This difference occurs because the side view shows the depth, while the front view shows the height. Sketching these views helps learn about shapes in real-life objects.
(a) Which view shows the wheels clearly?
(b) Which view shows the front of the car?
(c) Why do the views look different?
(a) The side view shows the wheels clearly because from the side, we can see the circular shape of the wheels.
(b) The front view shows the front of the car, including details like the headlights and grille.
(c) The views look different because we are observing the car from different angles. Each angle gives us a unique perspective of the object, highlighting different features.
- Front view: 4 dots
- Top view: 1 dot
- Side view: 3 dots
(a) How many dots are on the opposite face of the side showing 3 dots?
(b) Why can't Aarav see all the dots from one side?
(a) The opposite face of the side showing 3 dots would have 4 dots because, in a standard dice, the sum of opposite faces is always 7 (3 + 4 = 7).
(b) Aarav can't see all the dots from one side because a 3D object like a dice has multiple faces, and some faces are hidden depending on the angle of view. This is why we need different views to understand the complete structure.
- From the front, she sees the title.
- From the side, she sees the pages.
- From the top, she sees the cover.
(a) Which view helps her count the number of pages?
(b) What does this tell us about observing objects?
(a) The side view helps Priya count the number of pages because the edges of the pages are visible from this angle.
(b) This tells us that different views of an object reveal different details. To fully understand an object, we need to observe it from multiple angles.