Times Tables

Part of Mathematics

The complete multiplication facts from 1×1 to 12×12, with patterns, tricks, and a systematic learning progression.

Why This Matters

Times tables are the arithmetic equivalent of the alphabet — they are not the goal, but you cannot do serious work without them. Every multiplication, every long division, every area calculation and trade estimate relies on quick recall of small multiplication facts. A person who must calculate 7×8 by counting up by sevens will be slow, error-prone, and unable to handle more complex calculations in their head.

In a rebuilding community, memorized multiplication facts are a force multiplier for practical work. The builder who instantly knows that 7 rows × 12 tiles = 84 tiles can plan without reaching for a counting aid. The miller who knows that 9 sacks × 25 kg = 225 kg can give a total instantly. The teacher who can demonstrate multiplication with fluency will teach it effectively.

This article covers the complete 1–12 times tables, organized by difficulty, with patterns and mnemonics that reduce the memorization load. It also addresses the teaching sequence — not all tables are equally important, and learning them in the right order builds on patterns and reduces the number of truly unique facts to memorize.

The Complete 12×12 Table

×	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	96	108	120	132	144

Symmetry Reduces the Load

The table is symmetric: 3×7 = 7×3 = 21. This means you only need to memorize the upper triangle (or lower triangle) — essentially half the facts.

For a 12×12 table, there are 144 cells. But:

• 12 diagonal entries (n×n): separate memorization
• Remaining 132 entries: only 66 unique facts (each appears twice)
• Total unique facts: 12 + 66 = 78

With patterns and tricks below, many of these fall out automatically. The genuinely “hard” facts that require rote memorization number perhaps 20–30.

Table-by-Table Patterns

1× Table

Every number × 1 = itself. No memorization needed.

2× Table

Every number × 2 = double it. Even numbers all end in 0, 2, 4, 6, or 8.

• Learning aid: count by 2s — 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

5× Table

Every answer ends in 0 or 5. Even numbers × 5 end in 0; odd numbers × 5 end in 5.

• Learning aid: clock face — 1×5=5 (one minute mark), 2×5=10 (two minute marks), etc.

10× Table

Append a zero: 7×10=70. No memorization beyond this rule.

3× Table

Digits of every multiple of 3 sum to a multiple of 3 (divisibility rule).

• 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
• Pattern: add 3 each time; last digit cycles 3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 3, 6

4× Table

Double the 2× table.

• 4×7 = 2×7 doubled = 14 doubled = 28
• 4×9 = 2×9 doubled = 18 doubled = 36

9× Table

Two tricks:

1. Finger trick: Hold up all 10 fingers. For 9×N, fold down the Nth finger. Fingers to the left = tens digit; fingers to the right = ones digit.

   • 9×3: fold 3rd finger. 2 fingers left, 7 right → 27 ✓
   • 9×7: fold 7th finger. 6 fingers left, 3 right → 63 ✓

2. Digit sum rule: Every product of 9 (from 9×1 to 9×10) has digits that sum to 9.

   • 9×4=36, 3+6=9 ✓; 9×8=72, 7+2=9 ✓

11× Table (1–9)

Write the digit twice: 11×3=33, 11×7=77.

For 11×10–12:

• 11×10 = 110
• 11×11 = 121
• 11×12 = 132

12× Table

Add the 10× and 2× results:

• 12×7 = 70 + 14 = 84
• 12×9 = 90 + 18 = 108
• 12×11 = 110 + 22 = 132

The Hard Facts: 6×7 to 8×9

Once you know 1, 2, 3, 4, 5, 9, 10, 11, and 12 tables through patterns, the genuinely hard-to-derive facts are in the 6–8 range. These 9 products should be memorized by rote:

Fact	Answer	Mnemonic
6×6	36	Square of six
6×7	42	”Six and seven went to heaven — forty-two”
6×8	48	6×8=48, both even, close together
7×7	49	Square of seven
7×8	56	”Five-six-seven-eight: 56 = 7×8”
7×9	63	Digit sum 9, tens digit 6 → 63
8×8	64	Square of eight
8×9	72	Digit sum 9, tens digit 7 → 72
9×9	81	Square of nine

7×8 mnemonic: 5-6-7-8 — five six equals seven eight (56 = 7×8). This is the most commonly forgotten fact; the sequence mnemonic is highly effective.

Teaching Sequence

For fastest acquisition, teach in this order:

1. 1× and 10× — immediate pattern rules, no memorization
2. 2× — counting by twos, everyone knows this
3. 5× — clock face / ends in 0 or 5
4. 9× — finger trick
5. 11× — write digit twice (for 1–9)
6. Square numbers — 2×2, 3×3… 9×9 (9 facts, high recall value)
7. 3× and 4× — patterns and doubling
8. 6× and 7× — from known facts: 6×7 = (5×7) + 7 = 35+7 = 42
9. 8× and 12× — doubling from known tables
10. Hard facts drill — the 9 facts in the table above

With this sequence, students are always building on known patterns, which reduces the cognitive load and builds confidence.

Practice Methods

Chanting: Say table sequences aloud rhythmically: “seven ones are seven, seven twos are fourteen…” Rhythm aids memorization.

Flashcards: Write facts on cards (question side: “7×8?”, answer side: “56”). Shuffle daily. Set aside cards you know; focus drill on those you do not.

Random quiz: Call out random pairs from the hard facts list. Speed matters — the goal is instant recall, not working it out.

Skip-counting: Count by 7s to 84 (7, 14, 21… 84). Count by 8s to 96. Count by 6s to 72. This builds fluency and also reveals patterns.

Real-world application: Use facts in actual calculations every day. The student who calculates the number of bricks needed for a wall is practicing multiplication in context — and retention from application is far higher than from drill alone.

A community that prioritizes times table fluency — and teaches it systematically using these patterns — will produce arithmetic-competent adults in 2–3 years of consistent schooling.