🔍 Finding Patterns and Writing Rules
In this post, we will see how algebra helps us understand patterns.
Instead of checking again and again, we write one rule that works every time.
This idea is used again and again in maths .
🔢 What is a Pattern?
A pattern means:
Something repeats
Something increases or decreases in a fixed way
Examples:
2, 4, 6, 8, 10
Shapes made with matchsticks
Designs on a saree border
Dates in a calendar
Algebra helps us write a general rule for these.
🧵 Pattern Example: Repeating Designs
Suppose a design repeats like this:
A B C A B C A B C …
Positions:
Design A → 1, 4, 7, 10 …
Design B → 2, 5, 8, 11 …
Design C → 3, 6, 9, 12 …
Let:
n = number of times the design appears
Then:
Design A appears at → 3n − 2
Design B appears at → 3n − 1
Design C appears at → 3n
This helps us find any position, even very big numbers.
📅 Pattern in a Calendar (Very Interesting)
Look at any 2 × 2 box in a calendar.
Example:
Diagonal sums:
12 + 20 = 32
13 + 19 = 32
👉 Both are equal.
Instead of checking many boxes, we prove it once using algebra.
Let:
Top left number = a
Then the box becomes:
Diagonal sums:
a + (a + 8) = 2a + 8
(a + 1) + (a + 7) = 2a + 8
Same result → pattern is always true.
🔥 Matchstick Pattern (Favourite Question)
Look at this pattern:
Step | Matchsticks
1 → 3
2 → 5
3 → 7
4 → 9
Each step adds 2 matchsticks.
Let:
y = step number
Formula:
2y + 1
Now you can find matchsticks for:
Step 10
Step 50
Step 100
No drawing needed 😄
🧠 Why Algebra is Powerful
Without algebra:
We only check few cases
With algebra:
We prove it works for all cases
That is why algebra is used in:
Maths
Science
Computers
Daily life problems
📝 Final Learning from Post 3
✔ Patterns can be written using expressions
✔ Letters help us generalise rules
✔ One formula works for many values
✔ Algebra explains why a pattern works
📌 Chapter 4 Big Picture
Post 1 → What are expressions
Post 2 → Simplifying expressions
Post 3 → Patterns and rules
Together, they build a strong algebra foundation.