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CBSE Class 5 Mathematics★ 4-6 marks in Class 5 Mathematics assessments; number patterns and magic squares

Can You See the Pattern

Can You See the Pattern is a current Class 5 CBSE Mathematics chapter from NCERT Math Magic. These notes cover number patterns, magic squares, calendar patterns, coding-decoding, and hexagonal numbers with activities and practice.

⏱ 12 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Find the rule in a number pattern and extend it
2Verify and complete magic squares
3Discover patterns hidden in a calendar
4Code and decode using simple rules
5Recognise special sequences like triangular and hexagonal numbers

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Why this chapter matters

'Can You See the Pattern' develops observation and logical thinking through number patterns, magic squares, calendar patterns, coding, and special sequences. Spotting patterns is a key skill for algebra, puzzles, coding, and reasoning.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 4 Mathematics: Number sequences

Skip counting and simple patterns

Can You See the Pattern — Class 5 Mathematics (CBSE)

Based on the NCERT Math Magic Grade 5 textbook. Find patterns in numbers and shapes, then solve the practice set without looking at the answers.

1. Why this chapter matters

Patterns are the language of mathematics. They help us predict, generalise, and understand how numbers and shapes behave. This chapter develops observation skills by exploring number patterns, magic squares, calendar patterns, coding and decoding, and special sequences like hexagonal numbers. Pattern recognition is a key skill for algebra, puzzles, coding, and logical reasoning.

2. Number patterns

A number pattern is a sequence of numbers that follows a rule.

Pattern 1: Adding a constant

2, 4, 6, 8, 10... (add 2 each time — even numbers) 5, 10, 15, 20, 25... (add 5 each time — multiples of 5)

Pattern 2: Multiplying by a constant

1, 2, 4, 8, 16... (multiply by 2 each time) 1, 3, 9, 27, 81... (multiply by 3 each time)

Pattern 3: Alternating operation

1, 2, 3, 6, 7, 14, 15... (add 1, multiply by 2, add 1, multiply by 2...)

Pattern 4: Difference increases

1, 3, 6, 10, 15... (add 2, then 3, then 4, then 5 — triangular numbers)

Position (n)	1	2	3	4	5	6
Triangular number	1	3	6	10	15	21
Difference	—	+2	+3	+4	+5	+6

3. Magic squares

A magic square is a grid of numbers where each row, each column, and both diagonals add up to the same total (the magic constant).

3 x 3 magic square

2	7	6
9	5	1
4	3	8

Check: Row 1: 2 + 7 + 6 = 15 Row 2: 9 + 5 + 1 = 15 Row 3: 4 + 3 + 8 = 15 Column 1: 2 + 9 + 4 = 15 Column 2: 7 + 5 + 3 = 15 Column 3: 6 + 1 + 8 = 15 Diagonal (top-left to bottom-right): 2 + 5 + 8 = 15 Diagonal (top-right to bottom-left): 6 + 5 + 4 = 15

Magic constant = 15

How to complete a magic square

If some numbers are missing, use the property that all rows, columns, and diagonals add to the same total.

Example: Complete this 3x3 magic square (magic constant = 18):

8	?	4
?	6	?
3	?	7

Solution:

Top row: 8 + ? + 4 = 18, so ? = 6
Left column: 8 + ? + 3 = 18, so ? = 7
Bottom row: 3 + ? + 7 = 18, so ? = 8
Right column: 4 + ? + 7 = 18, so ? = 7
Middle row: 7 + 6 + ? = 18, so ? = 5

Completed square:

8	6	4
7	6	5
3	8	7

4. Calendar patterns

A calendar hides many number patterns.

Pattern 1: Dates in a row

Look at any row of 7 days in a calendar. The numbers increase by 1 each day. The total of any complete row = 7 x (middle number).

Pattern 2: 3x3 block

Pick any 3x3 block of dates. The sum of all 9 numbers = 9 x (middle number).

Example: For the block 5-11 in a month:

5	6	7
12	13	14
19	20	21

Middle number = 13. Sum = 9 x 13 = 117. Check: 5 + 6 + 7 + 12 + 14 + 19 + 20 + 21 + 13 = 117. Yes!

Pattern 3: Sum of opposite corners

In the same 3x3 block, sum of top-left + bottom-right = sum of top-right + bottom-left. 5 + 21 = 26 and 7 + 19 = 26.

5. Coding and decoding

Patterns help us create and break codes.

Simple coding rules

Rule	Input	Output
Add 2 to each digit	3, 7, 1	5, 9, 3
Multiply by 3 then add 1	2, 4, 6	7, 13, 19
Reverse the digits	123	321
Replace each letter with position in alphabet	A=1, B=2...	C A T = 3, 1, 20

Decoding: Find the rule

Sequence: 5, 8, 11, 14, 17, ? Rule: Add 3 each time. Next number = 20.

Sequence: 2, 6, 18, 54, ? Rule: Multiply by 3 each time. Next number = 162.

Sequence: 100, 90, 81, 73, ? Rule: Subtract 10, then 9, then 8... Next subtract 7. Next number = 66.

6. Hexagonal numbers

Hexagonal numbers are numbers that can be arranged as a hexagon pattern.

The sequence of hexagonal numbers: 1, 6, 15, 28, 45...

Position (n)	Hexagonal number	Pattern
1	1	1
2	6	1 + 5
3	15	6 + 9
4	28	15 + 13
5	45	28 + 17

The difference increases by 4 each time: +5, +9, +13, +17...

7. Activity corner

Activity 1: Create your own 3x3 magic square using numbers 1 to 9 (not in order). Verify that all rows, columns, and diagonals add up to 15.

Activity 2: Take a calendar page for any month. Pick four dates that form a 2x2 block. Find the sum. How does each sum relate to the smallest number?

Activity 3: Create a secret code where each letter gets a symbol. Write a short message in your code. Ask a friend to decode it.

Activity 4: Draw hexagonal patterns by arranging dots in hexagon shapes. Verify the first four hexagonal numbers.

8. Common mistakes

Mistake: Assuming a pattern always uses the same operation Fix: Check the differences between consecutive terms. If they change, the rule may involve a variable difference.
Mistake: Forgetting to check both diagonals in a magic square Fix: Always verify all rows, all columns, and both diagonals before declaring a solution.
Mistake: Writing the next term without confirming the rule Fix: State the rule explicitly (e.g., 'add 3 each time'), then apply it to find the next term.

9. Key facts

Number patterns follow a rule. Find the rule, predict the next term.
Magic squares: all rows, columns, and diagonals add to the same total.
Calendars show multiple number patterns — explore a calendar page.
Coding replaces information using a secret rule.
Hexagonal numbers grow by increasing differences.
Pattern spotting is a foundation for algebra and coding.

10. Self-test

Find the next term: 3, 6, 9, 12, ?
Is this a magic square? Check.

4	9	2
3	5	7
8	1	6

If a code adds 3 to each digit, what does 472 become?
What is the 4th hexagonal number?
A 3x3 calendar block has middle number 16. What is the sum of all 9 numbers?

11. Answer key

Find the next term: 3, 6, 9, 12, ? Answer: 15. The rule is 'add 3 each time'. 12 + 3 = 15.
Is this a magic square? Answer: Yes. Row 1: 4+9+2=15. Row 2: 3+5+7=15. Row 3: 8+1+6=15. Column 1: 4+3+8=15. Column 2: 9+5+1=15. Column 3: 2+7+6=15. Diagonals: 4+5+6=15 and 2+5+8=15. Magic constant = 15.
If a code adds 3 to each digit, what does 472 become? Answer: 7, 10, 5. But 10 is two digits, so we write 705 (or 7-10-5 as separate digits).
What is the 4th hexagonal number? Answer: 28. The sequence is 1, 6, 15, 28, 45...
A 3x3 calendar block has middle number 16. What is the sum of all 9 numbers? Answer: 9 x 16 = 144.

12. Quick revision

Find the rule in number patterns by looking at differences.
Magic squares have equal sums in all directions.
Calendar blocks follow predictable sum patterns.
Coding and decoding use reversible rules.
Hexagonal numbers form a special sequence.
Practise by creating your own patterns and magic squares.
Pattern recognition helps in puzzles, tests, and everyday thinking.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Magic square

All rows, columns, and diagonals share the same total (magic constant)

A 3x3 square of 1-9 has magic constant 15.

Calendar 3x3 block

Sum of nine numbers = 9 x middle number

Opposite corners also add to the same total.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Assuming a pattern always uses the same operation

✓ Check the differences between terms; the rule may involve a changing difference.

WATCH OUT

✗ Forgetting to check both diagonals in a magic square

✓ Verify all rows, all columns, and both diagonals before deciding it is magic.

WATCH OUT

✗ Writing the next term without confirming the rule

✓ State the rule clearly first, then apply it to find the next term.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Find the Rule

Extending number patterns and sequences

Questions

Magic Squares and Calendars

Completing magic squares and exploring calendar patterns

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Pattern

Find the next term: 3, 6, 9, 12, ?

▶ Show solution

15, because the rule is to add 3 each time (12 + 3 = 15).

Q2MEDIUM· Magic Square

Is the square (4,9,2 / 3,5,7 / 8,1,6) a magic square?

▶ Show solution

Yes. Every row, column, and diagonal adds up to 15, so the magic constant is 15.

Q3EASY· Sequence

What is the 4th hexagonal number?

▶ Show solution

28 (the sequence is 1, 6, 15, 28, 45).

Q4EASY· Calendar

A 3x3 calendar block has middle number 16. What is the sum of all nine numbers?

▶ Show solution

9 x 16 = 144.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•A number pattern follows a rule; find it to predict the next term.
•Magic squares: all rows, columns, and diagonals add to the same total.
•A 3x3 calendar block sums to 9 times its middle number.
•Coding replaces information using a reversible rule.
•Triangular numbers: 1, 3, 6, 10, 15...
•Hexagonal numbers: 1, 6, 15, 28, 45 (differences grow by 4).
•Pattern spotting supports algebra and logical reasoning.

CBSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 4-6 marks, depending on the school paper

Question type	Marks each	Typical count	What it tests
Number patterns	2-3	1-2	Finding rules and next terms
Magic squares / calendars	2-3	1	Completing squares and calendar patterns

Prep strategy

Look at differences to find the rule
Check all directions in a magic square
Explore calendar blocks for patterns
Learn special sequences like triangular and hexagonal numbers

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Puzzles and games

Pattern skills help solve sudoku, magic squares, and brain teasers.

Coding

Patterns and rules are the basis of computer programming and codes.

Predicting and planning

Recognising patterns helps make predictions in maths and daily life.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Write the rule before extending a pattern
Check every row, column, and diagonal in magic squares
Use the middle-number shortcut for calendar blocks
Memorise common special sequences

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Create your own 3x3 magic square using 1 to 9.
Explore the link between triangular and square numbers.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

CBSE Class 5 School ExamHigh

Maths Olympiad / IMOMedium

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Look at how each term changes to the next. First check whether a constant number is being added or subtracted each time, such as adding 3 in 3, 6, 9, 12. If the differences are not constant, check whether each term is multiplied by a number, like doubling in 2, 4, 8, 16. Sometimes the difference itself changes in a regular way, as in 1, 3, 6, 10 where the differences are 2, 3, 4. Once you can state the rule in words, you can confidently find the next terms.

A magic square is a grid of numbers in which every row, every column, and both main diagonals add up to the same total, called the magic constant. For a 3x3 square using the numbers 1 to 9, that total is 15. To test a square, add up each row, each column, and the two diagonals; only if all of these sums are equal is it a true magic square. To complete a partly filled one, use the known magic constant to work out the missing numbers.

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