Mathematics -- Class 4

Topic: Patterns
Name: ____________________________Class: 4Date: ________________
Learning Objectives
Introduction

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.

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
WordMeaning
PatternA sequence that follows a fixed rule
RuleThe operation (add, subtract, multiply) used to get the next number
Growing PatternA pattern where numbers increase
Decreasing PatternA pattern where numbers decrease
Magic SquareA grid where every row, column, and diagonal adds up to the same number

Mathematics -- Class 4 (continued)

Topic: Patterns -- Magic Squares and Practice
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)
276
951
438

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

Key Points to Remember
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

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

84
5
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: