Most schools stop formally teaching times tables at 12×12. That makes sense as a starting point, but it leaves students stranded the moment a multiplication problem involves 13, 14, 15 or larger numbers. The response for most students is to fall back on long multiplication — which is slow, error-prone under pressure, and unusable in a 10-second battle timer.
Here's the thing: you don't need to memorise every fact beyond 12. You need to understand the patterns that let you calculate those facts instantly. The times table isn't a random list. It's a structured grid built on relationships, and once you see those relationships, numbers up to 20×20 stop being scary and start being fast.
- The Symmetry Secret — You Already Know Half
- Mastering the 13 Times Table
- The 14 and 16 Tables — Splitting Strategy
- The 15 Times Table — Two Steps to Any Answer
- The 19 and 18 Tables — Near-20 Method
- Squaring Numbers from 11 to 20
- Pattern Drills — Build Speed Through Recognition
- Which Method to Use When
THE SYMMETRY SECRET — YOU ALREADY KNOW HALF THE TABLE
Before going further, internalise one fact that cuts your memorisation workload in half: multiplication is commutative. That means 13×7 and 7×13 give the same answer. So does 14×8 and 8×14, 17×6 and 6×17.
What this means in practice: if you know your 1–12 times table well, you already know every multiplication where one of the numbers is 12 or under — regardless of the order they appear. The "new" territory when moving beyond 12 is only the combinations where both numbers are 13 or higher. That's a much smaller set than it first appears.
To master the 13–20 range, you only need to learn calculations where both numbers are in that range — things like 13×14, 15×17, 18×19. Everything else (13×7, 15×9, 17×4, etc.) is already covered by your existing 1–12 knowledge, just presented in a different order.
MASTERING THE 13 TIMES TABLE
13 = 10 + 3 — Always Split It
The fastest way to multiply by 13 is to split it: 13 × N = (10 × N) + (3 × N). Find the ×10 (easy — just add a zero) and the ×3, then add them together.
Notice the pattern in the 13 table: the units digit of 13×N is always the same as the units digit of 3×N. So 13×7 ends in 1 (because 3×7=21), 13×8 ends in 4 (because 3×8=24), 13×9 ends in 7 (because 3×9=27). This is a quick sanity-check while you calculate.
THE 14 AND 16 TABLES — SPLITTING STRATEGY
Any "Teen" Number Splits Cleanly into 10 + Remainder
The same split technique works for every number from 13–19. 14 = 10+4. 16 = 10+6. 17 = 10+7. You always get two easy multiplications and one addition.
The key habit to build is automatically seeing any teen number as (10 + something). Once that decomposition is your first instinct when you see 14, 16, 17 or 18, these calculations become two-step operations rather than one scary problem.
THE 15 TIMES TABLE — TWO STEPS TO ANY ANSWER
Multiply by 15 Using the ×10 and ×5 Shortcut
15 = 10 + 5, and 5 is always half of 10. So to multiply by 15: find ×10, halve it to get ×5, then add both together. This two-step calculation is extremely fast once practised.
The 15 times table has an elegant pattern worth noticing: the answers alternate between ending in 0 and ending in 5. 15×1=15, 15×2=30, 15×3=45, 15×4=60, 15×5=75... This is a reliable sanity check — if your answer doesn't follow this alternating pattern, something went wrong.
THE 19 AND 18 TABLES — NEAR-20 METHOD
Multiply by 20, Then Subtract One or Two Lots
19 is very close to 20, and multiplying by 20 is easy (double the number, then multiply by 10). So for ×19: multiply by 20, then subtract the original number once. For ×18: multiply by 20, then subtract the original number twice.
The near-20 method works for any number close to a multiple of 10. 29×N? Multiply by 30, subtract N. 49×N? Multiply by 50, subtract N. 99×N? Multiply by 100, subtract N. Spotting that a number is "one away from a round number" and using that to simplify is a core mental math instinct that pays off across all four operations.
SQUARING NUMBERS FROM 11 TO 20
Squaring teen numbers (finding N×N for N between 11 and 20) comes up surprisingly often in competitive maths, and there's a beautiful pattern hiding in these results that makes them all calculable in seconds.
The Teen Squaring Formula
For any teen number (let's call it 10+d, where d is the units digit): the answer is always 100 + 20d + d². In plain English: start at 100, add twenty times the units digit, then add the units digit squared.
Once you've used this formula a few times, you'll notice you can go even faster. For 14²: you know 100 + 80 + 16 = 196. For 12²: 100 + 40 + 4 = 144. The formula becomes a quick mental calculation rather than a multi-step algorithm.
The Visual Pattern in Teen Squares
Look at the sequence of squares from 10 to 20 and notice the differences between consecutive values:
The differences between consecutive squares are always consecutive odd numbers (21, 23, 25, 27...). This means if you know one square, you can calculate the next one by adding the next odd number. Knowing 15² = 225, you immediately know 16² = 225 + 31 = 256.
PATTERN DRILLS — BUILD SPEED THROUGH RECOGNITION
Knowing these patterns intellectually is different from being able to apply them in under 3 seconds under battle pressure. The gap between understanding and speed is closed only through deliberate repetition. Here's how to drill these specific patterns efficiently:
The 5-Minute Pattern Sprint
Pick one pattern per session — say, the 13 times table. Set a 5-minute timer. Write down (or mentally calculate) 13×1 through 13×20 as fast as possible. Check your answers. Note which ones slowed you down. Repeat the slow ones three more times. Move to the next pattern in the next session.
Recognition Over Recall
The goal isn't to memorise individual facts — it's to recognise which method to apply the moment you see a number. When you see 18, your brain should automatically trigger "near-20 method." When you see 15, it should trigger "10+5 split." When you see any teen number squared, the formula should activate instantly.
Build this recognition through exposure. Look at multiplication problems and before calculating, say (or think) the method name out loud: "14×9 — that's the 10+4 split." This meta-cognitive step accelerates the pattern-matching process significantly.
Solve all ten using the pattern that fits. Aim for under 5 seconds each:
- 13 × 9 = ?
- 15 × 7 = ?
- 19 × 8 = ?
- 14 × 11 = ?
- 16 × 7 = ?
- 18 × 6 = ?
- 13² = ?
- 17 × 9 = ?
- 15 × 16 = ?
- 19 × 14 = ?
Answers: 117 · 105 · 152 · 154 · 112 · 108 · 169 · 153 · 240 · 266
WHICH METHOD TO USE WHEN
The real skill is not just knowing the methods — it's instantly selecting the right one. Here's the decision pattern experienced mental mathematicians follow when they see a multiplication with a teen number:
- Is one number 19 or 18? → Use the near-20 method (×20 then subtract)
- Is one number 15? → Use the 10+5 split (add ×10 and ×5)
- Is one number 13, 14, 16, or 17? → Use the 10+remainder split
- Are both numbers teen numbers? → Split the larger one, multiply each part separately, add
- Is it a perfect square (N×N)? → Use the teen squaring formula if N is 11–20
THE DEEPER SKILL THESE PATTERNS DEVELOP
Here is something more important than any individual technique in this article: learning to see numbers as flexible, decomposable structures rather than fixed, scary facts. The student who sees 17 and automatically thinks "10+7" has a fundamentally different relationship with numbers than the student who sees 17 and thinks "I need to memorise this."
Every pattern in this article is an expression of the same underlying truth: multiplication distributes over addition. That principle — formally called the distributive property — is the foundation of algebra, of polynomial expansion, of matrix multiplication, of calculus. Students who build their times-table fluency by understanding why the shortcut works are building a bridge to every more advanced topic they'll ever study.
So don't think of this as learning tricks. Think of it as developing a deep structural understanding of how numbers work — starting with something as concrete as 13×8.