Chapter 10 of 14
⬅️ Ch 9: Halves and Quarters Ch 11: Tables and Shares ➡️
NCERT Class 4 Mathematics • Classic CBSE Track

Chapter 10: Play with Patterns

Tiling Patterns, Number Towers, Magic Squares & Secret Message Decryption | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Tiling patterns (tessellations) on floors and historical monuments.
  • Number towers: each box is the sum of the two boxes directly below it.
  • Magic Squares (3×3 grid): where every row, column, and diagonal adds up to the exact same magic sum (e.g., 15 or 45).
  • Secret message decoding using alphabet-number substitutions.
Number Tower & 3×3 Magic Square 50 25 25 10 15 10 Number Tower 8 1 6 3 5 7 4 9 2 Magic Sum = 15

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

100% Complete Ingestion
Q1 Number Tower Solving Rule
In a number tower, the bottom row has the numbers 20, 30, and 50. Fill in the missing numbers for the middle row and the top box. State the rule used.
[3 Marks]
✅ Step-by-Step Solution & Working
Rule of the Number Tower:
The number in each higher box is the sum of the two boxes directly below it.

• Middle row left box: 20 + 30 = 50.
• Middle row right box: 30 + 50 = 80.
• Top box: Sum of middle row = 50 + 80 = 130.

Completed Tower:
    [ 130 ]
  [ 50 ] [ 80 ]
[ 20 ] [ 30 ] [ 50 ]
CBSE Step-by-Step Marking Scheme
States addition rule of number tower 1.0 M
Correct values: middle row 50, 80; top box 130 2.0 M
Q2 Magic Square Construction
Complete a 3×3 magic square using numbers from 1 to 9 so that every row, column, and diagonal adds up to 15.
[3 Marks]
✅ Step-by-Step Solution & Working
The standard 3×3 magic square with sum 15 is:
816
357
492
• Rows: 8+1+6 = 15; 3+5+7 = 15; 4+9+2 = 15.
• Columns: 8+3+4 = 15; 1+5+9 = 15; 6+7+2 = 15.
• Diagonals: 8+5+2 = 15; 6+5+4 = 15. All equal 15!
CBSE Step-by-Step Marking Scheme
Correct 3x3 grid layout with numbers 1 to 9 2.0 M
Verification of rows, columns, and diagonals = 15 1.0 M
Q3 Magic Squares • 3x3 Grid Puzzle
In a 3×3 magic square using numbers 1 to 9, the sum of numbers along every row, column, and diagonal is 15. If the central cell is 5, explain why 5 must be in the centre.
[3 Marks]
✅ Step-by-Step Solution & Working
Magic Square Mathematical Logic:
1. Sum of all numbers 1 to 9:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Dividing by 3 rows gives the magic constant: 45 ÷ 3 = 15.

2. Why 5 must be in the Centre:
The central cell belongs to 4 lines (1 horizontal row, 1 vertical column, and 2 diagonals). Therefore, it must be the exact median (average) of all 9 numbers. Pairing numbers that sum to 10 (1+9=10, 2+8=10, 3+7=10, 4+6=10) with 5 in the centre always yields: 10 + 5 = 15.
CBSE Step-by-Step Marking Scheme
Calculating total sum 45 and magic constant 15 1.5 M
Explaining central cell median alignment with 4 intersecting lines 1.5 M
Q4 Number Pyramids • Addition Rules
In a number tower, the bottom row has numbers 10, 20, 30. The rule is that adding two adjacent lower numbers gives the number above them. Find the top number of the tower.
[2 Marks]
✅ Step-by-Step Solution & Working
Tower Addition Steps:
• Bottom Row (Row 1): [ 10 ]    [ 20 ]    [ 30 ]

• Middle Row (Row 2):
Left box = 10 + 20 = 30.
Right box = 20 + 30 = 50.
Row 2: [ 30 ]    [ 50 ]

• Top Row (Row 3):
Top box = 30 + 50 = 80.

The number in the top box is 80.
CBSE Step-by-Step Marking Scheme
Middle row calculation (30 and 50) 1.0 M
Top number = 80 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

Coded Message for Class Picnic

Teenu writes a secret note using numbers for letters: A=1, B=2, C=3, ... Z=26. Her note reads: '13-5-5-20   13-5   1-20   14-15-15-14'.

Analytical Task: Decrypt Teenu's secret note.
Evaluation & Model Answer:
Decoded Note: 'MEET ME AT NOON'.
• 13=M, 5=E, 5=E, 20=T (MEET)
• 13=M, 5=E (ME)
• 1=A, 20=T (AT)
• 14=N, 15=O, 15=O, 14=N (NOON)
Rubric: 1 Mark for letter substitution method; 1 Mark for 'MEET ME AT NOON'.
⬅️ Ch 9: Halves and Quarters Ch 11: Tables and Shares ➡️