Chapter 10 of 14
⬅️ Ch 9: How Many Times? Ch 11: Jugs and Mugs ➡️
NCERT Class 3 Mathematics • Classic CBSE Track

Chapter 10: Play with Patterns

Repeating Patterns, Growing Patterns, Number Sequences & Secret Coded Messages | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Identifying rules of repeating shape patterns (AB, AAB, ABC).
  • Growing patterns in shapes and numbers (e.g., triangular numbers, square sequences).
  • Even and odd number patterns: ending digits (0, 2, 4, 6, 8 vs 1, 3, 5, 7, 9).
  • Secret messages: decoding messages with letter-to-number replacement rules.
Growing Number Patterns & Secret Decoding 1 3 6 Rule: A=1, B=2, C=3... Code: 13-1-20-8 = MATH Patterns can grow by rules, repeat in cycles, or hide secret words!

All Textbook Exercises & In-Text Tasks (17 Questions)

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Q1 Growing Patterns • Number Rules
Look at the pattern: 1, 3, 6, 10, ___, ___. (a) What are the next two numbers? (b) State the mathematical rule for how the pattern grows.
[3 Marks]
✅ Step-by-Step Solution & Working
Analysis:
• From 1 to 3: +2
• From 3 to 6: +3
• From 6 to 10: +4
• Next step: +5 → 10 + 5 = 15.
• Next step: +6 → 15 + 6 = 21.
• (a) Next two numbers: 15, 21 (Triangular numbers).
• (b) Rule: Each step adds 1 more than was added in the previous step (+2, +3, +4, +5, +6...).
CBSE Step-by-Step Marking Scheme
Correct calculation of 15 and 21 1.5 M
Clear rule formulation explaining growing increments 1.5 M
Q2 Even and Odd Patterns • Properties
Classify the following as Even or Odd: 246, 381, 500, 789. What happens when you add two odd numbers together? Give an example.
[3 Marks]
✅ Step-by-Step Solution & Working
Classification:
• 246: Ends in 6 → EVEN
• 381: Ends in 1 → ODD
• 500: Ends in 0 → EVEN
• 789: Ends in 9 → ODD.

Rule: The sum of any two odd numbers is always an EVEN number.
• Example: 3 (Odd) + 5 (Odd) = 8 (Even); 7 + 9 = 16 (Even).
CBSE Step-by-Step Marking Scheme
Correct even/odd classification for all 4 numbers 1.5 M
Correct rule and supporting example (Odd + Odd = Even) 1.5 M
Q3 Secret Coded Message • Decoding
If each letter is replaced by its alphabetical position (A=1, B=2, C=3... Z=26): (a) Decode the message: '7 - 15 - 15 - 4'. (b) Encode the word 'BOOK' in numbers.
[2 Marks]
✅ Step-by-Step Solution & Working
Solutions:
• (a) Decoding '7 - 15 - 15 - 4':
7 = G, 15 = O, 15 = O, 4 = D → GOOD.
• (b) Encoding 'BOOK':
B = 2, O = 15, O = 15, K = 11 → 2 - 15 - 15 - 11.
CBSE Step-by-Step Marking Scheme
Correct decoding to GOOD 1.0 M
Correct encoding for BOOK (2-15-15-11) 1.0 M
Q4 Number Towers • Pyramid Patterns
In a number tower, the number in each block is the sum of the two blocks directly below it.
The bottom row has blocks: [10], [20], [30].
(a) Find the numbers in the two blocks of the second row.
(b) Find the number in the top block of the tower.
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Number Tower:
• Bottom row: [10], [20], [30].
(a) Second Row:
• First block = 10 + 20 = 30.
• Second block = 20 + 30 = 50.

(b) Top Block:
• Top block = 30 + 50 = 80.

Completed Tower:
[ 80 ]
[ 30 ] [ 50 ]
[ 10 ] [ 20 ] [ 30 ]
CBSE Step-by-Step Marking Scheme
Correct second row blocks (30 and 50) 1.5 M
Correct top block (80) 1.5 M
Q5 Secret Messages • Number-Alphabet Code
Teenu and Jaggu are sending secret messages using the rule: A = 1, B = 2, C = 3 ... Z = 26.
(a) Decode the secret message: '7 - 15 - 15 - 4'
(b) Encode the word 'MATHS' into numbers.
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Cryptography:
(a) Decoding '7 - 15 - 15 - 4':
• 7 = G
• 15 = O
• 15 = O
• 4 = D
• Decoded word: GOOD.

(b) Encoding 'MATHS':
• M = 13
• A = 1
• T = 20
• H = 8
• S = 19
• Secret code: 13 - 1 - 20 - 8 - 19.
CBSE Step-by-Step Marking Scheme
Correct decoding of 'GOOD' 1.5 M
Correct encoding of 'MATHS' (13-1-20-8-19) 1.5 M
Q6 Growing Patterns • Geometric Series
Look at the growing dot patterns:
Figure 1: 1 dot
Figure 2: 3 dots (1 + 2)
Figure 3: 6 dots (1 + 2 + 3)
(a) How many dots will be in Figure 4?
(b) How many dots will be in Figure 5?
(c) What kind of numbers are these called?
[3 Marks]
✅ Step-by-Step Solution & Working
Growing Pattern (Triangular Numbers):
• (a) Figure 4: 1 + 2 + 3 + 4 = 10 dots.
• (b) Figure 5: 1 + 2 + 3 + 4 + 5 = 15 dots.
• (c) Number Type: These are called Triangular Numbers because dots arranged in these quantities form equilateral triangles.
CBSE Step-by-Step Marking Scheme
Correct dots in Figure 4 (10 dots) 1.0 M
Correct dots in Figure 5 (15 dots) 1.0 M
Identification of triangular numbers 1.0 M
Q7 Even and Odd Patterns • Digit Endings
(a) Write all even numbers between 41 and 51.
(b) What digits do all even numbers end with?
(c) Is the sum of two even numbers always even or odd? Give an example.
[3 Marks]
✅ Step-by-Step Solution & Working
Even & Odd Rules:
• (a) Even Numbers: 42, 44, 46, 48, 50.
• (b) Even Endings: All even numbers end in 0, 2, 4, 6, or 8 in the ones place.
• (c) Sum Rule: The sum of two even numbers is always Even.
- Example: 4 + 6 = 10 (Even), 12 + 14 = 26 (Even).
CBSE Step-by-Step Marking Scheme
Correct even numbers listed 1.0 M
Correct ending digits (0, 2, 4, 6, 8) 1.0 M
Correct sum rule with clear example 1.0 M
Q8 Textbook Exercise • Real-Life Math
In Chapter 10 ('Play with Patterns'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120 1 M
Oranges = ₹120 1 M
Total = ₹240 1 M
Q9 In-Text Activity • Hands-on Investigation
In 'Play with Patterns', how do you measure and compare quantities accurately? Explain with an example using standard units.
[3 Marks]
✅ Step-by-Step Solution & Working
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined 1.5 M
Examples for length, weight, liquid 1.5 M
Q10 Practice Time • Two-Step Word Problem
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220 1.5 M
Change = ₹280 1.5 M
Q11 Mental Math • Quick Calculations
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ?
[2 Marks]
✅ Step-by-Step Solution & Working
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct 2 M
Q12 Geometry & Shapes • Edge and Corner Counting
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners.
[3 Marks]
✅ Step-by-Step Solution & Working
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube 1 M
Cylinder 1 M
Sphere 1 M
Q13 Pattern Time • Sequences and Rules
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
[2 Marks]
✅ Step-by-Step Solution & Working
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160 1 M
Rule: multiplying by 2 1 M
Q14 Time & Calendar • Date Calculation
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
[3 Marks]
✅ Step-by-Step Solution & Working
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17 1.5 M
June days = 30; Total = 47 days 1.5 M
Q15 Equal Sharing • Division Problem
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
[2 Marks]
✅ Step-by-Step Solution & Working
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies 2 M
Q16 Data Handling • Reading a Bar Chart
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots?
[3 Marks]
✅ Step-by-Step Solution & Working
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least 1 M
Total = 38 1 M
Difference = 8 1 M
Q17 Money • Making a Change
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
[2 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15 1 M
3 coins of ₹5 1 M
🌟 NEP 2020 Competency-Based Case Study

Tile Border Geometric Pattern

A walkway is paved with a repeating 4-tile sequence: [Circle, Square, Triangle, Hexagon] that repeats continuously along a path of 50 tiles.

Analytical Task: Which shape will be on the 20th tile? Which shape will be on the 47th tile?
Evaluation & Model Answer:
1. Sequence length = 4 shapes.
• 1 = Circle, 2 = Square, 3 = Triangle, 4 = Hexagon.
2. 20th tile: 20 ÷ 4 = 5 with remainder 0 (4th shape) → Hexagon.
3. 47th tile: 47 ÷ 4 = 11 with remainder 3 (3rd shape) → Triangle.
Rubric: 1.5M modulo calculation for 20th tile + 1.5M modulo calculation for 47th tile.
⬅️ Ch 9: How Many Times? Ch 11: Jugs and Mugs ➡️