Maths

Patterns

Class 4

🎯 Learning Objectives

Students will identify and extend growing and decreasing number patterns.
Students will recognise patterns based on addition, subtraction, and multiplication rules.
Students will find the rule behind a given pattern.
Students will create their own patterns and explore magic squares.

📖 Let Us Begin!

Patterns are everywhere -- in rangoli designs, in the way floor tiles are arranged, and in numbers too! A pattern is a sequence that follows a fixed rule. If you can find the rule, you can predict what comes next.

In Class 4, we will explore number patterns that grow, shrink, or multiply. We will also look at shape patterns and magic squares.

Introduction

In Class 4, we will explore number patterns that grow, shrink, or multiply. We will also look at shape patterns and magic squares.

Growing Number Patterns (Addition Rule)

In a growing pattern, each number is obtained by adding a fixed number to the previous one.

Example

Example 1: Add 6

5, 11, 17, 23, 29, ... (Rule: add 6 each time)

Next two numbers: 29 + 6 = 35, 35 + 6 = 41.

Example

Example 2: Add 15

10, 25, 40, 55, 70, ... (Rule: add 15 each time)

Decreasing Number Patterns (Subtraction Rule)

In a decreasing pattern, each number is obtained by subtracting a fixed number.

Example

Example 3: Subtract 7

100, 93, 86, 79, 72, ... (Rule: subtract 7 each time)

Next two numbers: 72 - 7 = 65, 65 - 7 = 58.

Patterns with Multiplication

Some patterns grow very fast because each number is obtained by multiplying the previous number by a fixed number.

Example

Example 4: Multiply by 3

2, 6, 18, 54, 162, ... (Rule: multiply by 3 each time)

Check: 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54, 54 x 3 = 162.

Example

Example 5: Multiply by 2

5, 10, 20, 40, 80, ... (Rule: multiply by 2 each time)

To find the rule, look at how each number changes to the next. Is it adding, subtracting, or multiplying?

Finding the Rule

Example

Example 6: What is the rule?

Pattern: 4, 12, 36, 108, ...

12 / 4 = 3, 36 / 12 = 3, 108 / 36 = 3. Rule: multiply by 3.

Example

Example 7: What is the rule?

Pattern: 95, 86, 77, 68, ...

95 - 86 = 9, 86 - 77 = 9, 77 - 68 = 9. Rule: subtract 9.

Magic Squares -- Introduction

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

Example

Example 8: A 3x3 Magic Square (Magic Sum = 15)

2	7	6
9	5	1
4	3	8

Check: Row 1: 2+7+6 = 15. Column 1: 2+9+4 = 15. Diagonal: 2+5+8 = 15. It works!

📝 Key Words

Word	Meaning
Pattern	A sequence that follows a fixed rule
Rule	The operation (add, subtract, multiply) used to get the next number
Growing Pattern	A pattern where numbers increase
Decreasing Pattern	A pattern where numbers decrease
Magic Square	A grid where every row, column, and diagonal adds up to the same number

⭐ Key Points to Remember

In a growing pattern (add rule), each term is larger than the one before.
In a decreasing pattern (subtract rule), each term is smaller than the one before.
In a multiplication pattern, numbers grow very quickly.
To find the rule: check the difference or ratio between consecutive numbers.
In a magic square, all rows, columns, and diagonals have the same sum.

✏️ Practice Questions

A. Find the next three numbers in each pattern

1. 8, 15, 22, 29, , , (Rule: )

2. 3, 9, 27, 81, , , (Rule: )

3. 200, 185, 170, 155, , , (Rule: )

4. 4, 8, 16, 32, , , (Rule: )

5. 1000, 900, 800, 700, , , (Rule: )

B. Find the rule for each pattern

1. 7, 14, 28, 56, 112 -- Rule:

2. 50, 43, 36, 29, 22 -- Rule:

3. 6, 18, 54, 162 -- Rule:

C. Multiple Choice Questions

1. What comes next: 5, 10, 20, 40, ?

(a) 50(b) 60(c) 80(d) 100

2. The rule for 100, 91, 82, 73 is:

(a) Add 9(b) Subtract 9(c) Subtract 11(d) Multiply by 9

E. Create Your Own Pattern

1. Create a growing pattern using the rule "add 8". Start from 3.

2. Create a multiplication pattern using the rule "multiply by 2". Start from 7.

🎨 Fun Activity -- Pattern Detective

Look around your home or school. Find 3 patterns (on a saree border, floor tiles, a rangoli, or a number plate). Write or draw each pattern below and describe the rule.

Pattern 1:

Pattern 2:

Pattern 3:

Want to use this as a worksheet? Switch to the A4 printable view.

Learning Objectives

Students will identify and extend growing and decreasing number patterns.
Students will recognise patterns based on addition, subtraction, and multiplication rules.
Students will find the rule behind a given pattern.
Students will create their own patterns and explore magic squares.

Introduction

In Class 4, we will explore number patterns that grow, shrink, or multiply. We will also look at shape patterns and magic squares.

Growing Number Patterns (Addition Rule)

In a growing pattern, each number is obtained by adding a fixed number to the previous one.

Example 1: Add 6

5, 11, 17, 23, 29, ... (Rule: add 6 each time)

Next two numbers: 29 + 6 = 35, 35 + 6 = 41.

Example 2: Add 15

10, 25, 40, 55, 70, ... (Rule: add 15 each time)

Decreasing Number Patterns (Subtraction Rule)

In a decreasing pattern, each number is obtained by subtracting a fixed number.

Example 3: Subtract 7

100, 93, 86, 79, 72, ... (Rule: subtract 7 each time)

Next two numbers: 72 - 7 = 65, 65 - 7 = 58.

Patterns with Multiplication

Some patterns grow very fast because each number is obtained by multiplying the previous number by a fixed number.

Example 4: Multiply by 3

2, 6, 18, 54, 162, ... (Rule: multiply by 3 each time)

Check: 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54, 54 x 3 = 162.

Example 5: Multiply by 2

5, 10, 20, 40, 80, ... (Rule: multiply by 2 each time)

To find the rule, look at how each number changes to the next. Is it adding, subtracting, or multiplying?

Finding the Rule

Example 6: What is the rule?

Pattern: 4, 12, 36, 108, ...

12 / 4 = 3, 36 / 12 = 3, 108 / 36 = 3. Rule: multiply by 3.

Example 7: What is the rule?

Pattern: 95, 86, 77, 68, ...

95 - 86 = 9, 86 - 77 = 9, 77 - 68 = 9. Rule: subtract 9.

Key Words and Meanings

Word	Meaning
Pattern	A sequence that follows a fixed rule
Rule	The operation (add, subtract, multiply) used to get the next number
Growing Pattern	A pattern where numbers increase
Decreasing Pattern	A pattern where numbers decrease
Magic Square	A grid where every row, column, and diagonal adds up to the same number

Magic Squares -- Introduction

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

Example 8: A 3x3 Magic Square (Magic Sum = 15)

2	7	6
9	5	1
4	3	8

Check: Row 1: 2+7+6 = 15. Column 1: 2+9+4 = 15. Diagonal: 2+5+8 = 15. It works!

Key Points to Remember

In a growing pattern (add rule), each term is larger than the one before.
In a decreasing pattern (subtract rule), each term is smaller than the one before.
In a multiplication pattern, numbers grow very quickly.
To find the rule: check the difference or ratio between consecutive numbers.
In a magic square, all rows, columns, and diagonals have the same sum.

Practice Questions

A. Find the next three numbers in each pattern

8, 15, 22, 29, , , (Rule: )
3, 9, 27, 81, , , (Rule: )
200, 185, 170, 155, , , (Rule: )
4, 8, 16, 32, , , (Rule: )
1000, 900, 800, 700, , , (Rule: )

B. Find the rule for each pattern

7, 14, 28, 56, 112 -- Rule:
50, 43, 36, 29, 22 -- Rule:
6, 18, 54, 162 -- Rule:

C. Multiple Choice Questions

What comes next: 5, 10, 20, 40, ?
(a) 50(b) 60(c) 80(d) 100
The rule for 100, 91, 82, 73 is:
(a) Add 9(b) Subtract 9(c) Subtract 11(d) Multiply by 9

D. Complete the Magic Square (Magic Sum = 15)

8		4
	5
	9

E. Create Your Own Pattern

Create a growing pattern using the rule "add 8". Start from 3.
Create a multiplication pattern using the rule "multiply by 2". Start from 7.

Fun Activity -- Pattern Detective

Look around your home or school. Find 3 patterns (on a saree border, floor tiles, a rangoli, or a number plate). Write or draw each pattern below and describe the rule.

Pattern 1:

Pattern 2:

Pattern 3:

Patterns

🎯 Learning Objectives

📖 Let Us Begin!

Introduction

Growing Number Patterns (Addition Rule)

Decreasing Number Patterns (Subtraction Rule)

Patterns with Multiplication

Finding the Rule

Magic Squares -- Introduction

📝 Key Words

✏️ Practice Questions

Mathematics -- Class 4

Mathematics -- Class 4 (continued)