Introduction
Multiplication tables are the backbone of arithmetic, and mastering the tables from 11 to 20 opens the door to faster mental calculations, stronger problem‑solving skills, and greater confidence in higher‑level mathematics. While most students become comfortable with the 1‑10 tables early on, the next ten rows often feel intimidating because the patterns are less obvious and the numbers grow larger. This article demystifies the 11‑20 multiplication tables, explains the underlying patterns, provides practical learning strategies, and answers common questions so that learners of any age can master them with ease.
Why the 11‑20 Tables Matter
- Foundation for algebra – equations, factorisation, and polynomial expansion all rely on quick recall of products up to 20.
- Real‑world relevance – budgeting, cooking, and engineering calculations frequently involve numbers beyond 10.
- Boosts mental agility – practising larger tables trains the brain to recognise numerical relationships, improving overall numeracy.
Understanding these tables is not just about memorisation; it’s about recognising systematic relationships that make the numbers intuitive.
Patterns and Tricks for Each Table
11‑Table
The 11‑table is the simplest of the higher tables because of a clear digit‑addition pattern:
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Single‑digit multiplicands (1‑9): Write the multiplicand, then repeat it Easy to understand, harder to ignore. Nothing fancy..
- 1 × 11 = 11
- 2 × 11 = 22
- …
- 9 × 11 = 99
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Two‑digit multiplicands (10‑20): Add the two digits of the multiplicand and place the sum between them. If the sum exceeds 9, carry over.
- 10 × 11 = 110 (1 + 0 = 1 → 1|1|0)
- 12 × 11 = 132 (1 + 2 = 3 → 1|3|2)
- 15 × 11 = 165 (1 + 5 = 6 → 1|6|5)
12‑Table
The 12‑table is closely tied to the dozen system and shows a regular increase of 12:
- 1 × 12 = 12
- 2 × 12 = 24
- 3 × 12 = 36
- …
- 10 × 12 = 120
A handy shortcut: Add 12 to the previous product. Here's one way to look at it: after knowing 7 × 12 = 84, simply add 12 to get 8 × 12 = 96 Not complicated — just consistent..
13‑Table
The 13‑table can be broken down using the “10 + 3” method:
- Multiply the number by 10, then add three times the original number.
- 6 × 13 = (6 × 10) + (6 × 3) = 60 + 18 = 78
This technique works for any multiplier and reinforces the distributive property Took long enough..
14‑Table
Since 14 = 7 × 2, you can double the 7‑table results:
- 4 × 14 = 2 × (4 × 7) = 2 × 28 = 56
Alternatively, use the “10 + 4” method: add four times the number to ten times the number.
15‑Table
Fifteen is half of thirty, so multiply by 30 and halve the result:
- 5 × 15 = (5 × 30) ÷ 2 = 150 ÷ 2 = 75
Another shortcut: add 5 to the product of the number and 10 (because 15 = 10 + 5).
16‑Table
Sixteen is a power of two (2⁴). Doubling the 8‑table works well:
- 3 × 16 = 2 × (3 × 8) = 2 × 24 = 48
If you already know the 4‑table, simply double twice: 3 × 4 = 12 → double → 24 → double → 48 Nothing fancy..
17‑Table
Use the “20 − 3” approach:
- Multiply by 20, then subtract three times the original number.
- 7 × 17 = (7 × 20) − (7 × 3) = 140 − 21 = 119
18‑Table
Eighteen is three times six, so triple the 6‑table:
- 9 × 18 = 3 × (9 × 6) = 3 × 54 = 162
You can also use the “10 + 8” method: add eight times the number to ten times the number.
19‑Table
Treat 19 as “20 − 1”:
- Multiply by 20, then subtract the original number.
- 4 × 19 = (4 × 20) − 4 = 80 − 4 = 76
20‑Table
The 20‑table is essentially doubling the 10‑table:
- 6 × 20 = 2 × (6 × 10) = 2 × 60 = 120
A quick visual: just add a zero to the number and double it.
Step‑by‑Step Learning Plan
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Familiarise with Patterns
- Spend 5 minutes each day reviewing the shortcuts listed above.
- Write the pattern in your own words; teaching it to a peer reinforces memory.
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Chunk the Tables
- Break the ten tables into groups of two (11‑12, 13‑14, etc.).
- Master one group before moving to the next, using flashcards or a digital quiz app.
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Use Real‑World Context
- Shopping: Calculate total price for 13 items priced at $7 each.
- Cooking: Scale a recipe that requires 4 × 15 g of sugar.
- Sports: Determine the total distance run if a runner completes 17 laps of a 400‑m track.
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Daily Speed Drills
- Set a timer for 60 seconds. Recite as many products from a chosen table as possible.
- Record your score and aim to improve by at least one correct answer each session.
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Visualization Techniques
- Create a grid chart (11‑20 on both axes). Fill in the products; the symmetry helps you see that 13 × 17 = 17 × 13.
- Highlight diagonal entries (e.g., 14 × 14 = 196) to notice perfect squares.
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Periodic Review
- Every weekend, revisit the previous weeks’ tables.
- Mix them with the 1‑10 tables to maintain overall fluency.
Scientific Explanation: How the Brain Stores Multiplication Facts
Neuroscientific research shows that multiplication facts are stored in the left angular gyrus, a region associated with verbal‑numeric processing. On top of that, repetition strengthens synaptic connections, converting conscious calculation into automatic retrieval. In real terms, the strategies above (e. Practically speaking, g. , “20 − 3”) engage the prefrontal cortex, encouraging procedural understanding rather than rote memorisation. This dual‑coding—semantic (meaningful patterns) plus procedural (stepwise methods)—creates more dependable memory traces, making recall faster and less error‑prone.
Frequently Asked Questions
Q1: Do I need to memorise every product from 11 to 20?
A: Full memorisation is ideal for speed, but understanding the shortcuts reduces the load. Knowing the pattern for each table lets you reconstruct any product quickly.
Q2: What if I forget a specific product during a test?
A: Use the nearest‑known fact and adjust. To give you an idea, if you forget 14 × 9, recall that 14 × 10 = 140, then subtract 14 → 126 And that's really what it comes down to..
Q3: Are there digital tools that help without giving away answers?
A: Yes, many apps offer spaced‑repetition flashcards that present a product, ask you to type the answer, and only reveal the solution after you attempt it Simple, but easy to overlook..
Q4: How long does it typically take to become fluent?
A: With 10‑15 minutes of focused practice daily, most learners achieve 90 % accuracy within 3‑4 weeks. Consistency outweighs session length.
Q5: Can these tables help with division?
A: Absolutely. Knowing that 18 × 7 = 126 instantly tells you that 126 ÷ 7 = 18, reinforcing reciprocal understanding of multiplication and division And that's really what it comes down to..
Common Mistakes and How to Avoid Them
| Mistake | Why It Happens | Fix |
|---|---|---|
| Adding instead of multiplying (e.g., 12 + 12 = 24, then thinking 12 × 12 = 24) | Confusing addition with multiplication for larger numbers. Day to day, | Emphasise the repeated addition concept: 12 × 12 means adding 12 twelve times, not twice. In real terms, |
| Skipping the carry‑over step in two‑digit products | Over‑reliance on mental shortcuts without checking place value. | Write out the multiplication on paper for the first few rows; practice the carry‑over explicitly. |
| Assuming all tables increase by a constant amount | Only the 12‑table has a constant +12 increase; others follow different patterns. | Memorise each table’s unique rule; use the “10 + x” or “20 − x” frameworks as guides. |
Creative Ways to Reinforce Learning
- Multiplication Rap: Turn the 11‑20 tables into a short rap or chant. Rhythm aids memory.
- Board Games: Design a simple board where each square requires solving a product from the 15‑table to advance.
- Art Integration: Draw a multiplication mandala where each ring represents a table; fill in the numbers with colourful markers.
- Peer Teaching: Pair up and quiz each other. Teaching a concept solidifies your own understanding.
Conclusion
Mastering the multiplication tables from 11 to 20 is a realistic goal that dramatically enhances mathematical fluency. By recognising patterns, applying strategic shortcuts, and practising with purposeful drills, learners can transition from hesitant calculation to confident, instant recall. The brain’s ability to store these facts improves with meaningful repetition and conceptual insight, turning what once felt like a mountain of numbers into a set of intuitive tools. Embrace the step‑by‑step plan, experiment with the creative reinforcement ideas, and watch the speed and accuracy of your arithmetic soar—opening the door to smoother algebra, geometry, and everyday problem solving Still holds up..
