Learning Objectives
- Use skip counting to build the rhythm of each times table
- Apply the commutative property to cut the learning load in half
- Exploit the nines trick, doubling method, and 11s pattern
- Identify which 15 facts account for the majority of student errors
- Design a spaced-repetition practice routine that actually sticks
Prerequisites
You should understand what multiplication means — that 4 × 3 means "four groups of three" = 12. Basic addition up to 20 is also essential. No prior table memorisation needed — that is what this lesson is for.
The Lesson
Step 1 — The commutative shortcut (halve your work immediately)
Multiplication is commutative: a × b = b × a. This means 3×7 and 7×3 are the same fact. In a 12×12 grid there are 144 cells, but thanks to commutativity only 78 unique facts need learning (including the trivial ×1 and ×10 families). That is a huge head start.
Step 2 — Start with the easy families (×0, ×1, ×2, ×5, ×10)
×1: Anything × 1 = itself. 7×1=7.
×2: Just double the number. 2×8 = 8+8 = 16.
×5: The answer always ends in 0 or 5. 5×6=30, 5×7=35. Skip-count: 5,10,15,20,25,30…
×10: Add a zero. 10×7=70. Done.
Mastering these five families eliminates roughly 40% of the table instantly.
Step 3 — The Nines Trick
For any 9 × n (where n is 1–10), the tens digit of the answer equals n − 1 and the two digits of the answer always sum to 9.
9 × 8: tens digit = 8−1 = 7; units digit = 9−7 = 2 → answer is 72
Finger trick: Hold up 10 fingers. For 9×4, fold down finger 4. You see 3 fingers left + 6 fingers right = 36.
Step 4 — Doubling for the ×4 and ×8 families
×4 = double twice. ×8 = double three times. Use ×2 (which you already know) as the foundation.
8 × 6: double 6 → 12, double → 24, double again → 48
Step 5 — The 11s pattern
Two-digit × 11 (e.g. 11×35): outer digits stay (3 _ 5), middle = 3+5 = 8 → 385.
Step 6 — Handle the "hard" 15 facts with skip counting + stories
After using commutativity and the tricks above, the remaining "difficult" facts include 3×6, 3×7, 3×8, 4×6, 4×7, 4×8, 6×6, 6×7, 6×8, 7×7, 7×8, 8×8, and a few others. For these, use a two-step approach:
- Skip count aloud until the fact clicks: "6, 12, 18, 24, 30, 36, 42" → 6×7=42.
- Create a story or rhyme: "5, 6, 7, 8 — 56 is 7 times 8." The rhyme "5,6,7,8" encodes 7×8=56.
Step 7 — Spaced repetition practice plan
Research on memory (Hermann Ebbinghaus's forgetting curve) shows that reviewing a fact right before you forget it creates the strongest retention. Practically:
- Day 1: Learn a new family (e.g. ×6). Practice 10 min.
- Day 2: Quick review of ×6, then add ×7.
- Day 4: Mixed drill on all learned families. 15 min.
- Day 7: Timed challenge sheet — beat your previous time.
Practice Problems
- Q: Use the nines trick: what is 9 × 7?
Solution: tens digit = 7−1=6; units = 9−6=3 → 63 - Q: Use doubling: what is 8 × 9?
Solution: 9×2=18, ×2=36, ×2=72 - Q: What is 11 × 8?
Solution: Repeat the digit: 88 - Q: Skip-count to find 6 × 8.
Solution: 6,12,18,24,30,36,42,48 (8 steps) = 48 - Q: How many unique multiplication facts exist in a 1–12 table (using commutativity)?
Solution: (12×13)/2 = 78 unique facts
Common Mistakes
Further Practice Resources
Frequently Asked Questions
Combining pattern recognition (nines trick, doubling), skip counting, and spaced-repetition flashcards produces the fastest long-term retention.
With 10–15 minutes of focused daily practice, most students solidify all tables through 12×12 within 4–6 weeks.
For 9 × n, the tens digit = n−1 and the two digits sum to 9. Example: 9×7=63 (6=7−1, 6+3=9).
Skip counting means counting by a fixed number: by 3s (3,6,9,12…), by 6s (6,12,18…). It builds the rhythm of each times table.
Yes! For 11 × any single-digit number, repeat the digit: 11×7=77. For two-digit numbers, the middle digit is the sum of the outer digits.