Chapter 5 of 15
Chapter 5: Patterns
Border Patterns, Tile Shapes, Number Patterns & Secret Messages | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Identifying repeating units in border patterns on dupattas, sarees, and iron grills.
- Tessellation and tiling: shapes that tile a floor without leaving any gaps.
- Number patterns: skip counting by 2s, 3s, 5s, 10s, and finding missing terms.
- Decoding secret messages written with alternating letters and numbers.
All Textbook Exercises & In-Text Tasks (19 Questions)
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Q1
Textbook Exercise • Bindi & Leaf Patterns
Look at the pattern on Bini and Ginni's mother's saree border: Leaf pointing UP, Leaf pointing DOWN, Leaf pointing UP, Leaf pointing DOWN... Draw or describe the next two leaves in this pattern.
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• The pattern alternates direction: UP, DOWN, UP, DOWN...
• The next leaf will point UP.
• The following leaf will point DOWN.
• The pattern alternates direction: UP, DOWN, UP, DOWN...
• The next leaf will point UP.
• The following leaf will point DOWN.
CBSE Step-by-Step Marking Scheme
Next leaf points UP
1 M
Following leaf points DOWN
1 M
Q2
Textbook Exercise • Iron Grill Patterns
Bini and Ginni saw an iron window grill made of curved loop shapes. When they walked in the park, they saw the same grill turned sideways. Can a single pattern unit look different when rotated?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Explanation:
• Yes, rotating a design changes its orientation from vertical to horizontal.
• The basic shape remains the same, but the overall design appears completely transformed when turned 90 degrees.
• Yes, rotating a design changes its orientation from vertical to horizontal.
• The basic shape remains the same, but the overall design appears completely transformed when turned 90 degrees.
CBSE Step-by-Step Marking Scheme
Affirmative answer (Yes)
1 M
Rotation effect on pattern explained
1 M
Q3
Textbook Exercise • Floor Tiling
Why can square and rectangular tiles cover an entire bathroom floor without leaving any empty gaps?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Explanation:
1. Squares and rectangles have straight edges and 90-degree square corners.
2. When placed edge-to-edge, they fit flush against each other, completely covering the flat surface without any gaps or overlaps (this is called tessellation).
1. Squares and rectangles have straight edges and 90-degree square corners.
2. When placed edge-to-edge, they fit flush against each other, completely covering the flat surface without any gaps or overlaps (this is called tessellation).
CBSE Step-by-Step Marking Scheme
Straight edges & corners fitting flush explained
1 M
No gaps or overlaps concept
1 M
Q4
Textbook Exercise • Number Patterns (Skip Counting)
Find the rule and fill in the missing numbers in the following patterns:
(a) 20, 30, 40, ___, ___, 70, 80
(b) 2, 4, 6, 8, ___, ___, 14
[2 Marks]
(a) 20, 30, 40, ___, ___, 70, 80
(b) 2, 4, 6, 8, ___, ___, 14
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
(a) Rule: Adding 10 each time.
Missing numbers: 40 + 10 = 50, 50 + 10 = 60.
(b) Rule: Adding 2 each time.
Missing numbers: 8 + 2 = 10, 10 + 2 = 12.
(a) Rule: Adding 10 each time.
Missing numbers: 40 + 10 = 50, 50 + 10 = 60.
(b) Rule: Adding 2 each time.
Missing numbers: 8 + 2 = 10, 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
(a) 50, 60 with rule +10
1 M
(b) 10, 12 with rule +2
1 M
Q5
Textbook Exercise • Skip by Threes and Fives
Fill in the missing numbers:
(a) 3, 6, 9, 12, ___, ___, 21
(b) 5, 10, 15, 20, ___, ___, 35
[2 Marks]
(a) 3, 6, 9, 12, ___, ___, 21
(b) 5, 10, 15, 20, ___, ___, 35
✅ Step-by-Step Solution & Working
Answers:
(a) Rule: Skip counting by 3s.
12 + 3 = 15, 15 + 3 = 18.
(b) Rule: Skip counting by 5s.
20 + 5 = 25, 25 + 5 = 30.
(a) Rule: Skip counting by 3s.
12 + 3 = 15, 15 + 3 = 18.
(b) Rule: Skip counting by 5s.
20 + 5 = 25, 25 + 5 = 30.
CBSE Step-by-Step Marking Scheme
(a) 15, 18
1 M
(b) 25, 30
1 M
Q6
NCERT Secret Message • Letter Patterns
Shablu wrote a secret message to Jaggu by placing a number before each letter:
1G 2O 3O 4D 5M 6O 7R 8N 9I 10N 11G
Remove the numbers and decode the secret message.
[2 Marks]
1G 2O 3O 4D 5M 6O 7R 8N 9I 10N 11G
Remove the numbers and decode the secret message.
✅ Step-by-Step Solution & Working
Step-by-Step Decoding:
• Numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
• Letters: G - O - O - D - M - O - R - N - I - N - G.
• Secret Message: GOOD MORNING.
• Numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
• Letters: G - O - O - D - M - O - R - N - I - N - G.
• Secret Message: GOOD MORNING.
CBSE Step-by-Step Marking Scheme
Pattern logic identified
1 M
Correct message 'GOOD MORNING'
1 M
Q7
Textbook Creative • Secret Message Challenge
Write the secret message 'I LOVE MATHS' using alternating numbers (1, 2, 3...).
[2 Marks]
✅ Step-by-Step Solution & Working
Solution:
• 1I 2L 3O 4V 5E 6M 7A 8T 9H 10S (or 1I 2L 3O 4V 5E 6M 7A 8T 9H 10S).
• 1I 2L 3O 4V 5E 6M 7A 8T 9H 10S (or 1I 2L 3O 4V 5E 6M 7A 8T 9H 10S).
CBSE Step-by-Step Marking Scheme
Correct application of alternating numbers to message
2 M
Q8
Odd and Even Number Pattern
Look at the pattern of numbers: 95, 96, 97, 98, 99, 100.
(a) Which of these end in 5, 7, or 9 (odd)?
(b) Which of these end in 6, 8, or 0 (even)?
[2 Marks]
(a) Which of these end in 5, 7, or 9 (odd)?
(b) Which of these end in 6, 8, or 0 (even)?
✅ Step-by-Step Solution & Working
Classification:
(a) Odd numbers (ending in 5, 7, 9): 95, 97, 99.
(b) Even numbers (ending in 6, 8, 0): 96, 98, 100.
(a) Odd numbers (ending in 5, 7, 9): 95, 97, 99.
(b) Even numbers (ending in 6, 8, 0): 96, 98, 100.
CBSE Step-by-Step Marking Scheme
Odd numbers identified
1 M
Even numbers identified
1 M
Q9
Geometric Growth Pattern
Look at the growth pattern:
1 circle, then 2 circles, then 3 circles...
How many circles will be in the 5th step of this pattern?
[2 Marks]
1 circle, then 2 circles, then 3 circles...
How many circles will be in the 5th step of this pattern?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• Step 1 = 1 circle
• Step 2 = 2 circles
• Step 3 = 3 circles
• Step 4 = 4 circles
• Step 5 = 5 circles.
• Step 1 = 1 circle
• Step 2 = 2 circles
• Step 3 = 3 circles
• Step 4 = 4 circles
• Step 5 = 5 circles.
CBSE Step-by-Step Marking Scheme
Growth rule identified (+1 circle per step)
1 M
Step 5 = 5 circles correct
1 M
Q10
Alphabet Sequence Pattern
Complete the alphabet pattern:
AA, BB, CC, DD, ___, ___, GG.
[2 Marks]
AA, BB, CC, DD, ___, ___, GG.
✅ Step-by-Step Solution & Working
Solution:
The pattern doubles each successive English alphabet letter:
AA, BB, CC, DD, EE, FF, GG.
The pattern doubles each successive English alphabet letter:
AA, BB, CC, DD, EE, FF, GG.
CBSE Step-by-Step Marking Scheme
Missing pairs EE and FF filled correctly
2 M
Q11
Backward Counting Pattern
Find the rule and fill in the blanks: 40, 38, 36, 34, ___, ___, 28.
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• Rule: Subtracting 2 at each step (counting backward by 2s).
• 34 - 2 = 32
• 32 - 2 = 30
• Complete sequence: 40, 38, 36, 34, 32, 30, 28.
• Rule: Subtracting 2 at each step (counting backward by 2s).
• 34 - 2 = 32
• 32 - 2 = 30
• Complete sequence: 40, 38, 36, 34, 32, 30, 28.
CBSE Step-by-Step Marking Scheme
Subtracting 2 rule stated
1 M
Terms 32 and 30 filled correctly
1 M
Q12
Floor Tile Shape Analysis
Can circular plates be used as floor tiles to cover a kitchen floor without any spaces between them? Explain why or why not.
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Explanation:
• No, circular shapes cannot tile a floor without gaps.
• Reason: Circles have curved rims. When round plates are placed together touching each other, curved empty spaces (gaps) are always left between them.
• No, circular shapes cannot tile a floor without gaps.
• Reason: Circles have curved rims. When round plates are placed together touching each other, curved empty spaces (gaps) are always left between them.
CBSE Step-by-Step Marking Scheme
Negative answer (No)
1 M
Gaps between touching circles explained
1 M
Q13
Day & Night Natural Pattern
Explain how Day and Night form a natural repeating pattern in our life.
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Explanation:
• The Sun rises to give Day, and sets to give Night, followed again by Sunrise and Day.
• This cycle repeats continuously every 24 hours without end, making it one of the most fundamental natural patterns on Earth.
• The Sun rises to give Day, and sets to give Night, followed again by Sunrise and Day.
• This cycle repeats continuously every 24 hours without end, making it one of the most fundamental natural patterns on Earth.
CBSE Step-by-Step Marking Scheme
Day and night cycle described
1 M
Repeating 24-hour nature explained
1 M
Q14
Pattern in Multiples of 10
What is common among the units digits of the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 100?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Answer:
• In every multiple of 10, the digit in the units (ones) place is always 0.
• Only the tens digit increases by 1 each time.
• In every multiple of 10, the digit in the units (ones) place is always 0.
• Only the tens digit increases by 1 each time.
CBSE Step-by-Step Marking Scheme
Identifies 0 in ones place
1 M
Identifies tens digit increasing by 1
1 M
Q15
Colour Sequence Pattern
A string of festival lights flashes in the sequence: Red, Blue, Green, Red, Blue, Green, Red... What colour will the 10th light bulb be?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• Repeating unit = Red (1), Blue (2), Green (3) [Group of 3]
• 1st=Red, 2nd=Blue, 3rd=Green
• 4th=Red, 5th=Blue, 6th=Green
• 7th=Red, 8th=Blue, 9th=Green
• 10th light bulb = Red.
• Repeating unit = Red (1), Blue (2), Green (3) [Group of 3]
• 1st=Red, 2nd=Blue, 3rd=Green
• 4th=Red, 5th=Blue, 6th=Green
• 7th=Red, 8th=Blue, 9th=Green
• 10th light bulb = Red.
CBSE Step-by-Step Marking Scheme
Group of 3 cycle identified
1 M
10th bulb = Red correct
1 M
Q16
Triangle Orientation Pattern
Look at the pattern: ▲, ▼, ▲, ▼, ▲... What will be the 6th and 7th shapes in this pattern?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• Odd positions (1st, 3rd, 5th, 7th) = ▲ (Pointing UP)
• Even positions (2nd, 4th, 6th) = ▼ (Pointing DOWN)
• Therefore, the 6th shape is ▼ (Pointing DOWN), and the 7th shape is ▲ (Pointing UP).
• Odd positions (1st, 3rd, 5th, 7th) = ▲ (Pointing UP)
• Even positions (2nd, 4th, 6th) = ▼ (Pointing DOWN)
• Therefore, the 6th shape is ▼ (Pointing DOWN), and the 7th shape is ▲ (Pointing UP).
CBSE Step-by-Step Marking Scheme
6th shape: ▼
1 M
7th shape: ▲
1 M
Q17
Chapter Summary • Pattern Rules
What is a pattern in mathematics?
[2 Marks]
✅ Step-by-Step Solution & Working
Definition & Summary:
• A pattern is an arrangement of lines, shapes, colours, or numbers that repeats or grows following a definite, predictable rule.
• By finding the rule, we can easily predict what comes next.
• A pattern is an arrangement of lines, shapes, colours, or numbers that repeats or grows following a definite, predictable rule.
• By finding the rule, we can easily predict what comes next.
CBSE Step-by-Step Marking Scheme
Arrangement with definite rule defined
1 M
Predictive nature of pattern explained
1 M
Q18
Quick Quiz Problem
What comes next in the pattern: 10A, 20B, 30C, 40D, _____?
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• Numbers increase by 10: 10, 20, 30, 40 -> 50.
• Letters follow the alphabet: A, B, C, D -> E.
• The next term is 50E.
• Numbers increase by 10: 10, 20, 30, 40 -> 50.
• Letters follow the alphabet: A, B, C, D -> E.
• The next term is 50E.
CBSE Step-by-Step Marking Scheme
Number part 50
1 M
Letter part E (combined: 50E)
1 M
Q19
Textbook Exercise • Window Grill Pattern
Look at the iron grill on the boundary wall. It repeats: Up Arrow, Down Arrow, Up Arrow, Down Arrow. Draw and state the next two arrows in the sequence.
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• The repeating pattern is alternating up and down.
• The next two shapes are: Up Arrow (↑) and Down Arrow (↓).
• The repeating pattern is alternating up and down.
• The next two shapes are: Up Arrow (↑) and Down Arrow (↓).
CBSE Step-by-Step Marking Scheme
Identification of alternating rule
1 M
Next two arrows: ↑, ↓
1 M
🌟 NEP 2020 Competency-Based Case Study
School Cleanliness Day Teams (Tens & Ones)
Students in a school are forming teams of 10 for Clean School Day. Class 1 has 53 students, Class 2 has 42 students, and Class 3 has 35 students.
Analytical Task: How many teams of 10 can be made from Class 2? How many students will be left over? If leftover students from all three classes join together, how many additional teams of 10 can they form?
Evaluation & Model Answer:
1. For Class 2 (42 students): 4 teams of 10 can be formed, and 2 students are left over.
2. Leftovers from all 3 classes: Class 1 leaves 3, Class 2 leaves 2, Class 3 leaves 5. Total leftovers = 3 + 2 + 5 = 10 students.
3. These 10 students form exactly 1 more team of 10 with 0 students remaining.
2. Leftovers from all 3 classes: Class 1 leaves 3, Class 2 leaves 2, Class 3 leaves 5. Total leftovers = 3 + 2 + 5 = 10 students.
3. These 10 students form exactly 1 more team of 10 with 0 students remaining.
Rubric: 1 M for Class 2 teams & leftover + 1 M for total leftovers + 1 M for new team calculation