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
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.
[Image: Three visual patterns — one with shapes (circle, square, triangle repeating), one with numbers (2, 4, 6, 8...), one with growing dot patterns (1, 3, 6, 10 dots arranged in triangles). Title: "Number and Shape Patterns"]
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.
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)
Check: Row 1: 2+7+6 = 15. Column 1: 2+9+4 = 15. Diagonal: 2+5+8 = 15. It works!
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 |
⭐ 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
D. Complete the Magic Square (Magic Sum = 15)
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: