How to Use Patterns to Solve Math Problems Faster
You’ve probably heard someone say, “I’m just not a math person.” But the truth is, being good at math isn’t about memorizing formulas—it’s about seeing patterns. Once you start recognizing those patterns, even complex problems begin to feel… easy.
At Matiks, we design our mental math challenges around this idea: math is full of shortcuts hiding in plain sight. And if you can spot them, you can solve faster—with less effort and more confidence.
Here’s how to unlock that skill.
1. Look for Multiplication Shortcuts
Some multiplication problems follow built-in patterns. For example:
Multiplying by 5
If the number is even: just take half, then add a zero.
6 × 5 = (6 ÷ 2) = 3 → 30
If the number is odd: subtract one, halve it, then add 5.
7 × 5 = (7 - 1) ÷ 2 = 3 + 5 = 35
Multiplying by 11 (for 2-digit numbers)
11 × 23 = 2(2 + 3)3 = 253
Works like this: put the sum of the digits in the middle.
These aren’t just tricks—they’re patterns that reveal the logic behind the numbers.
2. Watch What Happens When You Add or Multiply in Series
Squares of consecutive numbers
Notice this?
1² = 1 2² = 4 3² = 9 4² = 16 5² = 25
The difference between squares is an odd number:
4 - 1 = 3 9 - 4 = 5 16 - 9 = 7 25 - 16 = 9
Recognizing this helps you estimate or predict without calculating from scratch.
3. Break Apart Numbers Using Patterns
Sometimes, numbers look harder than they are—until you break them into friendlier parts.
Example:
36 × 25
→ 36 × 100 ÷ 4 = 3600 ÷ 4 = 900
You just rewrote the problem using a known pattern:
Multiplying by 25 = divide by 4 after multiplying by 100
4. Use Doubling and Halving
This works especially well when one number is even.
Example:
16 × 35
→ Double one number, halve the other:
8 × 70 = 560 — Same result. Often faster.
Why it works: You’re keeping the product the same by balancing the change.
5. Recognize Common Ending Patterns
Last digits can give away answers
- Any number ending in 5 × another ending in 5 = ends in 25 or 75
- Squaring a number ending in 5 always ends in 25
Examples:
15² = 225
25² = 625
35² = 1225
Knowing this helps you guess or check your answer faster when solving mentally.
6. Add with Visual Grouping
Even addition has patterns.
Example:
47 + 58
→ Think: 47 + 3 = 50 → now add 55
50 + 55 = 105
You simplified the problem by “completing the ten” first. That pattern of rounding up and balancing is key to mental agility.
Why Patterns Matter
Using patterns doesn't mean you're skipping the hard stuff.
You're just solving it smarter. You’re freeing up brainpower to focus on strategy, not stress.
In school, in exams, in everyday decisions—pattern recognition makes mental math faster, smoother, and more intuitive.
Final Thought
Once you start noticing math patterns, they’re hard to unsee.
And that’s a good thing.
They turn big numbers into small steps.
They make you feel in control.
At Matiks, we turn these patterns into daily practice—so they go from “cool trick” to second nature.
Start spotting. Start solving.