NCERT Class 4 Mathematics • Classic CBSE Track

Chapter 1: Building with Bricks

Q: Answer the following questions about a brick: (a) How many faces does a brick have? (b) Is any face of a standard brick a square? (c) Draw the smalles

(a) A standard brick has 6 rectangular faces. (b) No, in standard construction bricks, all 6 faces are rectangles of varying dimensions (length × width, length × height, width × height). None of the faces is a square. (c) Smallest face: The side face measuring width × height (approximately 10 cm × 7

Q: Bhajan went to buy bricks. The rate was ₹1,800 for 1,000 old bricks, ₹2,000 for 1,000 new bricks from Brickabad, and ₹1,200 for 1,000 bricks from Itap

Step 1: Cost of 3,000 new bricks from Brickabad: • Cost of 1,000 new bricks = ₹2,000. • Cost of 3,000 new bricks = 3 × ₹2,000 = ₹6,000. Step 2: Cost of 500 old bricks: • Cost of 1,000 old bricks = ₹1,800. • Cost of 500 bricks (half of 1,000) = ₹1,800 ÷ 2 = ₹900. Step 3: Total Payment: • Total = ₹6,0

Q: What is an 'Arch' (कमान) in brick architecture? Where can you see traditional brick jali patterns in historical Indian monuments?

1. Brick Arch (Kaman): An arch is a curved symmetrical structural opening built of wedge-shaped bricks arranged over an entrance or bridge. The bricks support each other by pressing against one another, transferring heavy downward weight safely to the side pillars without needing a horizontal wooden

Q: Bhajan went to buy bricks. The price of new bricks from Brickabad was ₹2,000 for 1,000 bricks. He bought 3,000 bricks. If he also bought 500 old brick

Step-by-Step Calculation: 1. Cost of New Bricks from Brickabad: • Cost of 1,000 bricks = ₹2,000. • Cost of 3,000 bricks = 3 × ₹2,000 = ₹6,000. 2. Cost of Old Bricks: • Cost of 1,000 bricks = ₹1,200. • Cost of 500 bricks (half of 1,000) = ₹1,200 ÷ 2 = ₹600. 3. Total Money Paid: ₹6,000 + ₹600 = ₹6,600

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.

Brick Patterns, Arch Designs (Mehrab, Jharokha), Brick Geometry & Brick Kiln Arithmetic | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Architectural brick patterns from Jagriti School, Murshidabad: floor patterns, circular patterns, and mirror patterns.
Geometric dimensions and faces of a standard brick: 6 rectangular faces, 12 edges, 8 corners.
Traditional Indian architectural arches: Mehrab, circular arches, and decorative Jharokhas.
Large number calculations: Indian brick kilns producing 1,00,000 (one lakh) bricks; calculating the cost of thousands of bricks.

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

100% Complete Ingestion

Q1 Textbook Exercise • Geometric Properties of a Brick

Answer the following questions about a brick: (a) How many faces does a brick have? (b) Is any face of a standard brick a square? (c) Draw the smallest face of a brick. (d) Which of the following shapes can be a face of a brick: Triangle, Square, Rectangle, Circle?

[3 Marks]

✅ Step-by-Step Solution & Working

(a) A standard brick has 6 rectangular faces.
(b) No, in standard construction bricks, all 6 faces are rectangles of varying dimensions (length × width, length × height, width × height). None of the faces is a square.
(c) Smallest face: The side face measuring width × height (approximately 10 cm × 7 cm) is the smallest face.
(d) Face shape: Only a Rectangle can be a face of a standard brick (triangles and circles cannot form brick faces).

CBSE Step-by-Step Marking Scheme

Correct face count (6) and shape verification 1.5 M

Smallest face description and rectangle identification 1.5 M

Q2 Brick Kiln Cost Calculation

Bhajan went to buy bricks. The rate was ₹1,800 for 1,000 old bricks, ₹2,000 for 1,000 new bricks from Brickabad, and ₹1,200 for 1,000 bricks from Itapur. If Bhajan buys 3,000 new bricks from Brickabad and 500 old bricks, how much money will he pay in total?

[3 Marks]

✅ Step-by-Step Solution & Working

Step 1: Cost of 3,000 new bricks from Brickabad:
• Cost of 1,000 new bricks = ₹2,000.
• Cost of 3,000 new bricks = 3 × ₹2,000 = ₹6,000.

Step 2: Cost of 500 old bricks:
• Cost of 1,000 old bricks = ₹1,800.
• Cost of 500 bricks (half of 1,000) = ₹1,800 ÷ 2 = ₹900.

Step 3: Total Payment:
• Total = ₹6,000 + ₹900 = ₹6,900.

CBSE Step-by-Step Marking Scheme

Calculation for 3,000 new bricks (₹6,000) 1.0 M

Calculation for 500 old bricks (₹900) 1.0 M

Total payment ₹6,900 with clear working 1.0 M

Q3 Architectural Patterns • Arches & Jali

What is an 'Arch' (कमान) in brick architecture? Where can you see traditional brick jali patterns in historical Indian monuments?

[3 Marks]

✅ Step-by-Step Solution & Working

1. Brick Arch (Kaman):
An arch is a curved symmetrical structural opening built of wedge-shaped bricks arranged over an entrance or bridge. The bricks support each other by pressing against one another, transferring heavy downward weight safely to the side pillars without needing a horizontal wooden beam.

2. Traditional Brick Jali (Lattice):
Brick jalis are decorative screen walls created by leaving systematic hollow spaces between bricks during masonry. They allow cool breeze and soft geometric light patterns to enter while keeping harsh sun and rain out. Famous examples include the Jaagrithi School in Murshidabad (West Bengal) and historical Mughal monuments.

CBSE Step-by-Step Marking Scheme

Structural principle of brick arch and weight distribution 1.5 M

Jali pattern description and historical monument examples 1.5 M

Q4 Commercial Arithmetic • Cost of Bricks

Bhajan went to buy bricks. The price of new bricks from Brickabad was ₹2,000 for 1,000 bricks. He bought 3,000 bricks. If he also bought 500 old bricks at ₹1,200 for 1,000 bricks, how much total money did he pay?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Calculation:
1. Cost of New Bricks from Brickabad:
• Cost of 1,000 bricks = ₹2,000.
• Cost of 3,000 bricks = 3 × ₹2,000 = ₹6,000.

2. Cost of Old Bricks:
• Cost of 1,000 bricks = ₹1,200.
• Cost of 500 bricks (half of 1,000) = ₹1,200 ÷ 2 = ₹600.

3. Total Money Paid:
₹6,000 + ₹600 = ₹6,600.

CBSE Step-by-Step Marking Scheme

Cost of new bricks (₹6,000) 1.0 M

Cost of old bricks (₹600) 1.0 M

Total sum: ₹6,600 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

Estimating Bricks for a Compound Wall

A mason calculates that 1 metre length of a 1-metre high boundary wall requires 100 bricks. The school desires to construct a 45-metre long and 1-metre high wall.

Analytical Task: How many bricks should the school order? If each truck carries 2,500 bricks, how many truckloads are needed?

Evaluation & Model Answer:

Step 1: Total bricks needed:
45 m × 100 bricks/m = 4,500 bricks.
Step 2: Number of truckloads:
4,500 ÷ 2,500 = 1 full truck (2,500 bricks) with 2,000 bricks remaining.
Therefore, 2 truckloads must be ordered so the project has enough bricks.

Rubric: 1 Mark for 4,500 bricks; 1 Mark for practical answer of 2 truckloads.