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CBSE Class 3 Mathematics★ 4–5 marks · CBSE Class 3 Mathematics (Math-Magic) Chapter 10

Play with Patterns

Number patterns — growing and shrinking. Secret codes and ciphers. Magic squares. Pattern recognition and creation. CBSE Class 3 Mathematics (Math-Magic) Chapter 10.

⏱ 8 min readEasy difficulty✓ Free · NCERT-aligned

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

1Identify the rule in a number pattern (e.g., add 3, subtract 5, double) and extend the sequence
2Complete growing patterns (numbers increasing) and shrinking patterns (numbers decreasing)
3Create simple number patterns with a clear rule
4Understand and create simple secret codes where numbers represent letters (A=1, B=2...)
5Fill in magic squares where all rows, columns, and diagonals sum to the same number

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Why this chapter matters

Pattern recognition is the heart of mathematical thinking. This chapter teaches children to identify rules in number sequences (2, 4, 6, 8... → add 2), complete growing and shrinking patterns, explore secret codes and ciphers, and play with magic squares. Recognizing patterns is not just a math skill — it's the foundation of coding, scientific reasoning, and problem-solving in every field.

Before you start — revise these

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

🔗

Class 3 Mathematics Chapter 2: Fun with Numbers

Must be comfortable with skip counting, which is essentially following a number pattern.

Play with Patterns

What is a Pattern?

A PATTERN is something that REPEATS or FOLLOWS a RULE.

Patterns are EVERYWHERE!

On your CLOTHES (stripes, checks)
In NATURE (honeycomb, flower petals)
In NUMBERS (2, 4, 6, 8...)
In SOUNDS (clap, stomp, clap, stomp)

Number Patterns

Adding Patterns (Growing)

The numbers INCREASE by a fixed amount each time.

Pattern	Rule	Next Number
2, 4, 6, 8	Add 2	10
5, 10, 15, 20	Add 5	25
10, 20, 30, 40	Add 10	50
100, 200, 300	Add 100	400
3, 6, 9, 12	Add 3	15

Subtracting Patterns (Shrinking)

The numbers DECREASE by a fixed amount each time.

Pattern	Rule	Next Number
20, 18, 16, 14	Subtract 2	12
100, 90, 80, 70	Subtract 10	60
50, 45, 40, 35	Subtract 5	30
99, 88, 77, 66	Subtract 11	55

Complex Patterns

Some patterns use MIXED rules.

Pattern	Rule	Next
1, 2, 4, 7, 11	Add 1, add 2, add 3, add 4	16 (add 5)
2, 4, 8, 16	Multiply by 2	32
100, 90, 81, 73	Subtract 10, subtract 9, subtract 8	66 (subtract 7)
1, 1, 2, 3, 5, 8	Add previous two numbers	13

Growing and Shrinking Patterns

Growing Patterns

A growing pattern gets BIGGER by a rule.

Example: 🌱 🌿 🌳

One leaf → Two leaves → A whole tree!
In numbers: 1, 3, 5, 7, 9 (add 2 each time)

Shrinking Patterns

A shrinking pattern gets SMALLER by a rule.

Example: 🍎🍎🍎🍎🍎 → 🍎🍎🍎🍎 → 🍎🍎🍎 → 🍎🍎 → 🍎

5 apples, 4 apples, 3 apples, 2 apples, 1 apple
In numbers: 50, 45, 40, 35, 30 (subtract 5 each time)

Draw the Pattern

Growing: Δ, ΔΔ, ΔΔΔ, ____ (ΔΔΔΔ) Shrinking: ○○○○, ○○○, ○○, ____ (○)

Secret Codes and Ciphers

A CIPHER is a SECRET CODE that changes letters or numbers so only people who know the rule can read it.

Simple Number Code (A=1, B=2, C=3...)

Letter	Code
A	1
B	2
C	3
D	4
E	5
F	6
G	7
H	8
I	9
J	10
K	11
L	12
M	13
N	14
O	15
P	16
Q	17
R	18
S	19
T	20
U	21
V	22
W	23
X	24
Y	25
Z	26

Decode: 13-1-20-8 = M-A-T-H → MATH

Try: Decode 3-1-20 = ? Answer: C-A-T = CAT

Reverse Alphabet Code

A = Z, B = Y, C = X, D = W...

CODE = XLVW

Adding a Number Code

Add 3 to each letter: A → D, B → E, C → F...

HELLO → KHOOR

Magic Squares

A MAGIC SQUARE is a grid where every ROW, COLUMN, and DIAGONAL adds up to the SAME number (called the MAGIC SUM).

A Simple 3×3 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: 2 + 5 + 8 = 15
Diagonal: 6 + 5 + 4 = 15

Magic Sum = 15

Try This Magic Square

Fill in the MISSING numbers:

4	9	?
?	5	?
8	?	6

Answer:

4	9	2
3	5	7
8	1	6

Interesting Fact

The Chinese discovered magic squares thousands of years ago! According to legend, Emperor Yu saw a turtle with a 3×3 magic square on its shell.

Pattern Recognition

Finding the Rule

To find the rule, LOOK at:

How the numbers CHANGE (increase or decrease?)
By HOW MUCH they change each time
Does the change happen EVERY time or every OTHER time?

Practice

Pattern 1: 1, 4, 7, 10, 13, ___

Rule: Add 3 each time
Answer: 16

Pattern 2: 80, 72, 64, 56, ___

Rule: Subtract 8 each time
Answer: 48

Pattern 3: 1, 4, 9, 16, 25, ___

Rule: Multiply the number by itself (1×1, 2×2, 3×3, 4×4, 5×5)
Answer: 36 (6×6)

Pattern 4: A, C, E, G, ___

Rule: Every SECOND letter of the alphabet
Answer: I

Creating Your Own Patterns

Step 1: Choose a Rule

Add 2: ___, ___, ___, ___
Subtract 3: ___, ___, ___, ___
Multiply by 2: ___, ___, ___, ___

Step 2: Write the First Number

Step 3: Apply the Rule

Example Rule: Add 5, starting at 10 Pattern: 10, 15, 20, 25, 30, 35...

Example Rule: Subtract 2, starting at 20 Pattern: 20, 18, 16, 14, 12...

Common Mistakes

'Patterns are only about numbers.' — Patterns are EVERYWHERE! In shapes, colours, sounds, letters, and nature.
'2, 4, 6, 8... next number is 10, then 12, then 13.' — 2, 4, 6, 8, 10, 12, 14 (add 2 each time). 13 does not follow the rule.
'A magic square can have any sum in each row.' — No! In a magic square, EVERY row, column, and diagonal adds to the SAME sum.
'A code and a pattern are different things.' — A code IS a pattern! If A=1, B=2, C=3, that is a pattern.
'3, 6, 9... is the same as 2, 4, 6...' — Both add a constant number, but the rules are DIFFERENT (add 3 vs add 2). The patterns are NOT the same.

Quick Self-Test

Q1: What comes next: 5, 10, 15, 20, ___ A1: 25 (add 5 each time).

Q2: What is the rule: 100, 90, 80, 70, ___ A2: Subtract 10. Next: 60.

Q3: Decode this: 5-1-19-20 if A=1, B=2... A3: F-A-S-T = FAST.

Q4: In a 3×3 magic square, every row, column, and diagonal adds to the same number. What is the magic sum for numbers 1 to 9? A4: 15.

Q5: Fill in: 2, 6, 10, 14, ___, 22 A5: 18 (add 4 each time).

Q6: What comes next: 10, 7, 4, 1, ___ A6: -2 (subtract 3 each time).

Q7: If A=Z, B=Y, C=X, what is BAD? A7: B=Y, A=Z, D=W → YZW.

Q8: Create a pattern starting at 5, adding 3. A8: 5, 8, 11, 14, 17, 20...

Key formulas & results

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

Number patterns by addition (growing)

Identify the 'jump': 2, 4, 6, 8 → +2 each time. Next = 10. 5, 10, 15, 20 → +5 each time. Next = 25. 100, 200, 300 → +100 each time. Next = 400.

The RULE is the 'jump' between numbers. Find the difference between consecutive numbers — that's your rule.

Number patterns by subtraction (shrinking)

100, 90, 80, 70 → −10 each time. Next = 60. 50, 45, 40, 35 → −5 each time. Next = 30. The numbers get smaller by the SAME amount each step.

Shrinking patterns go DOWN. The rule is what you SUBTRACT each time.

Secret codes (number-letter substitution)

A=1, B=2, C=3, D=4 ... Z=26. To encode: replace each letter with its number. To decode: replace each number with its letter. Example: CAT → 3, 1, 20. 8, 1, 20 → HAT.

Secret codes make pattern recognition fun. Children love encoding and decoding messages.

Magic squares

A grid of numbers where EVERY row, column, and diagonal sums to the SAME number (the 'magic constant'). A 3×3 magic square using 1-9 sums to 15 in all directions.

Magic squares have fascinated mathematicians for thousands of years. At Class 3 level, fill in missing numbers in simple magic squares.

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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

✗ Looking only at the first two numbers to guess the pattern

✓ Always check at least 3 pairs: 2→4 (+2), 4→6 (+2), 6→? — if all jumps are +2, the rule is confirmed. The pattern 2, 4, 7 could be +2, +3 — always check multiple steps.

WATCH OUT

✗ In shrinking patterns, adding instead of subtracting (or vice versa)

✓ Check direction: are numbers getting BIGGER (growing → add) or SMALLER (shrinking → subtract)? 100, 90, 80 is clearly going down → subtract.

WATCH OUT

✗ In secret codes, confusing encoding (letters→numbers) with decoding (numbers→letters)

✓ Encoding = hide the message (letters become numbers). Decoding = reveal the message (numbers become letters). Think: EN-close, DE-open.

NCERT exercises (with solutions)

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

Pattern identification and extension

Identify the rule and write next 2-3 numbers; create own patterns; complete given patterns

Questions

Codes and magic squares

Encode and decode messages using A=1, B=2...; fill missing numbers in magic squares

Questions

Practice problems

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

Q1EASY· Growing

What is the rule? 4, 8, 12, 16, ___ . Write the next number.

▶ Show solution

Rule: Add 4 each time. Next number: 20.

Q2EASY· Shrinking

What is the rule? 90, 80, 70, 60, ___ . Write the next number.

▶ Show solution

Rule: Subtract 10 each time. Next number: 50.

Q3EASY· Create

Create a growing pattern that starts at 3 and adds 6 each time. Write the first 5 numbers.

▶ Show solution

3, 9, 15, 21, 27. (3+6=9, 9+6=15, 15+6=21, 21+6=27.)

Q4EASY· Code

Using A=1, B=2, C=3... decode this message: 13, 1, 20, 8.

▶ Show solution

M=13, A=1, T=20, H=8 → MATH.

Q5MEDIUM· Magic Square

In a 3×3 magic square, one row is 2, 7, 6 (sum = 15). Fill the missing numbers: Row 1: 2, 7, 6. Row 2: 9, 5, 1. Row 3: 4, 3, 8. Verify all rows, columns, and diagonals sum to 15.

▶ Show solution

All rows: 2+7+6=15, 9+5+1=15, 4+3+8=15. All columns: 2+9+4=15, 7+5+3=15, 6+1+8=15. Diagonals: 2+5+8=15, 6+5+4=15. Magic constant is 15. ✓

5-minute revision

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

•A pattern follows a RULE — numbers change by the same amount each step
•Growing patterns: numbers get BIGGER (add a fixed number). Shrinking patterns: numbers get SMALLER (subtract a fixed number)
•To find the rule: subtract consecutive numbers (next − current). If always the same, that's the rule
•Secret codes: A=1, B=2 ... Z=26. Encoding = letters → numbers. Decoding = numbers → letters
•Magic square: all rows, columns, and diagonals sum to the same magic constant
•Patterns are everywhere — in math, nature, art, music, and daily life. Spotting them is a superpower

CBSE marks blueprint

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

Typical chapter weightage: 4–5 marks in Class 3 Mathematics assessment

Question type	Marks each	Typical count	What it tests
Fill in the blanks (1 mark)	1	2–3	Writing next 1-2 numbers in a pattern; identifying the rule; simple code decoding
Short answer (2 marks)	2	1	Creating a pattern with given rule; completing a magic square; encoding a short message

Prep strategy

Play 'What's the Rule?': say a sequence (3, 6, 9, 12...) — child guesses the rule (add 3) and says next number
Create secret coded messages to each other — write 'I LOVE YOU' as 9, 12, 15, 22, 5, 25, 15, 21
Look for patterns in daily life: tile designs, rangoli, fabric prints, calendar numbers
Draw a pattern with shapes (circle, square, circle, square...) and ask: 'What comes next? What's the rule?'
Explore the 3×3 magic square (sum 15) — it's a classic that has amazed people for thousands of years

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