NCERT Class 4 Mathematics • Classic CBSE Track

Chapter 5: The Way The World Looks

Q: Why do the two sides of a railway track or road look wide and far apart near your feet, but appear to meet at a single point in the far distance?

Scientific & Geometric Reason: This phenomenon is called Perspective Convergence. • Objects or distances that are close to our eyes subtend a larger visual angle, so they appear wider and larger. • As objects move farther away, their visual angle shrinks, so they appear smaller and narrower. • Altho

Q: Draw or describe: (a) The top view of a teacup, (b) The side view of a pressure cooker, (c) The top view of a railway track.

Perspective Projections: • (a) Top View of a Teacup: Shows two concentric circles (the inner circle representing the cup rim and the outer circle representing the saucer) with a small oval loop on one side representing the handle. • (b) Side View of a Pressure Cooker: Shows the cylindrical metallic

Q: On a neighbourhood map, Neha starts at the Park facing East. She walks 50 metres straight, turns 90° right, walks 30 metres, and enters the Library. (

Spatial Navigation: 1. Direction after turning: Starting facing East, turning 90° to the right means she is now facing South. She walked 30 metres South. 2. Position of Library relative to Park: The Library is 50 m East and 30 m South of the Park. Therefore, the Library is located to the South-East

Q: A boy looks at a dice. The sum of opposite faces of a standard dice is always 7. If the top face shows 3 and the front face shows 2, what numbers are

Opposite Face Rule (Sum = 7): • (a) Bottom Face: Opposite to the top face (3). Bottom = 7 - 3 = 4. • (b) Back Face: Opposite to the front face (2). Back = 7 - 2 = 5.

Q: A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.(a) What is the shape of a brick?(b) What is the area of its largest face?(c) How ma

Brick Mathematics:• (a) Shape: A standard brick is a cuboid.• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.

Q: During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:(a) H

Step-by-Step Solution:• (a) Total diesel: 4 buses × 50 L = 200 litres.• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.

Q: The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.(a) Express the High Jump record in metres and centimetres.(b)

Calculations:• (a) High Jump: 245 cm = 2 metres 45 centimetres.• (b) Difference: 250 cm - 245 cm = 5 centimetres.

Q: A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.

Date Verification:• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.

Q: Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.(a) How much money does she pay back in t

Loan Repayment:• (a) Total paid: 6 months × ₹51/month = ₹306.• (b) Extra money (interest): ₹306 - ₹300 = ₹6.

Q: A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.(a) How much cough syrup does the child

Dosage Calculations:• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.

Gappu's Balloon Journey, Aerial Maps, Matching Top Views & Perspective Drawing | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Perspective changes with distance: objects look big and wide at the near end, but small and narrow at the distant end.
Gappu's view from a gas balloon: seeing the top of the bed, fan blades, chairs, and park benches.
Matching top view (bird's-eye view) with ground view for bowls, shoes, cars, and railway lines.
Navigating classroom floor maps and finding doors, windows, and blackboards.

All Textbook Exercises & In-Text Tasks (15 Questions)

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Q1 Perspective Illusion Explanation

Why do the two sides of a railway track or road look wide and far apart near your feet, but appear to meet at a single point in the far distance?

[3 Marks]

✅ Step-by-Step Solution & Working

Scientific & Geometric Reason:
This phenomenon is called Perspective Convergence.
• Objects or distances that are close to our eyes subtend a larger visual angle, so they appear wider and larger.
• As objects move farther away, their visual angle shrinks, so they appear smaller and narrower.
• Although the two rails of a train track are strictly parallel and always equal distance apart on the ground, our eye's perspective causes them to appear to converge toward a 'vanishing point' on the horizon.

CBSE Step-by-Step Marking Scheme

Mentions perspective / visual angle effect 1.5 M

Explains parallel lines appearing to converge at horizon 1.5 M

Q2 Perspective Views • Everyday Objects

Draw or describe: (a) The top view of a teacup, (b) The side view of a pressure cooker, (c) The top view of a railway track.

[3 Marks]

✅ Step-by-Step Solution & Working

Perspective Projections:
• (a) Top View of a Teacup: Shows two concentric circles (the inner circle representing the cup rim and the outer circle representing the saucer) with a small oval loop on one side representing the handle.
• (b) Side View of a Pressure Cooker: Shows the cylindrical metallic body, the side handle, the lid clamp, and the safety weight (whistle) sitting on the top vent pipe.
• (c) Top View of a Railway Track: Shows two parallel vertical lines with horizontal wooden or concrete sleepers spaced evenly across them like a ladder.

CBSE Step-by-Step Marking Scheme

Accurate geometric description of teacup top view 1.0 M

Accurate side view of cooker 1.0 M

Accurate top view of railway track 1.0 M

Q3 Grid Map Navigation • Directions

On a neighbourhood map, Neha starts at the Park facing East. She walks 50 metres straight, turns 90° right, walks 30 metres, and enters the Library. (a) In which direction did she walk after turning? (b) In which direction is the Library from the Park?

[3 Marks]

✅ Step-by-Step Solution & Working

Spatial Navigation:
1. Direction after turning:
Starting facing East, turning 90° to the right means she is now facing South. She walked 30 metres South.

2. Position of Library relative to Park:
The Library is 50 m East and 30 m South of the Park. Therefore, the Library is located to the South-East of the Park.

CBSE Step-by-Step Marking Scheme

Right turn from East = South 1.5 M

Combined position = South-East 1.5 M

Q4 Isometric 3D Blocks • Visual Reasoning

A boy looks at a dice. The sum of opposite faces of a standard dice is always 7. If the top face shows 3 and the front face shows 2, what numbers are on: (a) the bottom face, (b) the back face?

[2 Marks]

✅ Step-by-Step Solution & Working

Opposite Face Rule (Sum = 7):
• (a) Bottom Face: Opposite to the top face (3).
Bottom = 7 - 3 = 4.

• (b) Back Face: Opposite to the front face (2).
Back = 7 - 2 = 5.

CBSE Step-by-Step Marking Scheme

Bottom face = 4 1.0 M

Back face = 5 1.0 M

Q5 Building with Bricks • Brick Geometry & Measurement

A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?

[3 Marks]

✅ Step-by-Step Solution & Working

Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.

CBSE Step-by-Step Marking Scheme

Cuboid shape 1 M

Area = 200 cm² 1 M

5 bricks 1 M

Q6 A Trip to Bhopal • Diesel Fuel Budget

During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.

CBSE Step-by-Step Marking Scheme

200 litres 1.5 M

₹14,000 bill 1.5 M

Q7 Long and Short • Height Comparisons

The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?

[2 Marks]

✅ Step-by-Step Solution & Working

Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.

CBSE Step-by-Step Marking Scheme

2 m 45 cm 1 M

5 cm difference 1 M

Q8 Tick-Tick-Tick • Expiry Dates on Food

A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.

[2 Marks]

✅ Step-by-Step Solution & Working

Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.

CBSE Step-by-Step Marking Scheme

Time elapsed is ~90 days 1 M

Safe to consume within 180 days 1 M

Q9 The Junk Seller • Loan and Interest

Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?

[3 Marks]

✅ Step-by-Step Solution & Working

Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.

CBSE Step-by-Step Marking Scheme

Total repayment = ₹306 1.5 M

Interest = ₹6 1.5 M

Q10 Jugs and Mugs • Measuring Medicine Dose

A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?

[3 Marks]

✅ Step-by-Step Solution & Working

Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.

CBSE Step-by-Step Marking Scheme

15 mL daily 1.5 M

Bottle lasts 10 days 1.5 M

Q11 Carts and Wheels • Circle Geometry

A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?

[2 Marks]

✅ Step-by-Step Solution & Working

Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.

CBSE Step-by-Step Marking Scheme

Diameter = 70 cm 1 M

Formula D = 2r stated 1 M

Q12 Halves and Quarters • Fraction Sharing

Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?

[3 Marks]

✅ Step-by-Step Solution & Working

Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.

CBSE Step-by-Step Marking Scheme

Book = ₹50 1 M

Pen = ₹25 1 M

Remaining = ₹25 1 M

Q13 Play with Patterns • Secret Message Cipher

In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?

[2 Marks]

✅ Step-by-Step Solution & Working

Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.

CBSE Step-by-Step Marking Scheme

Correct decoding to spell MATHS 2 M

Q14 Tables and Shares • Division with Remainder

A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over?

[2 Marks]

✅ Step-by-Step Solution & Working

Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.

CBSE Step-by-Step Marking Scheme

9 bouquets 1 M

4 leftover roses 1 M

Q15 Review Questions • True or False

State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.

[3 Marks]

✅ Step-by-Step Solution & Working

Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.

CBSE Step-by-Step Marking Scheme

True, False, True with explanations 3 M

🌟 NEP 2020 Competency-Based Case Study

Classroom Blackboard Location Map

In a classroom top-view plan, the teacher's table is at (3, 5), the entrance door is at (1, 1), and student benches are arranged in 4 columns from X = 2 to 5.

Analytical Task: If a student enters through the door and walks straight North along the left aisle, which direction should she turn to face the teacher's table?

Evaluation & Model Answer:

She should walk North up to Y = 5, and then turn Right (East) to face the teacher's table at (3, 5).

Rubric: 1 Mark for North direction; 1 Mark for Right / East turn.