Tangyuan MathLesson 6 · 15 min Stage 2 · Rules that shrink the work
The nines secret
Nines look like the scary row of the table. They're actually the friendliest — 9 is just 10 wearing a disguise.
In this lesson your child will turn any ×9 into ×10 minus one group, check nines answers with the digit pattern, and meet the famous finger trick as a backup.
Talk it through
"The nines row looks hard. Here's the secret: 9 is just 10 in disguise — it's 10, minus one. Watch."
Open the demo below on 3. See the three rows of ten — and how each row is missing exactly one dot at the end. "3 × 10 would be 30. But every row lost one dot. Three rows, three dots lost. 30 − 3 = 27. So 3 × 9 = 27."
"The recipe works for every nines fact: take the ten, give one back per group. 6 × 9? Six tens are 60, give back six: 54. 8 × 9? Eighty minus eight: 72."
"Want to check a nines answer? Two giveaways: the two digits always add up to 9 (27 → 2 + 7 = 9), and the tens digit is always one less than your number (3 × 9 → starts with 2)."
Ten fingers up in a row. For 7 × 9, fold the 7th finger from the left. Fingers still up on the left of it: 6 — that's the tens. On the right: 3 — the ones. 63. Try it for 4 × 9 and 9 × 9.
Try it together
Tap each number and say the sentence together: "n tens, minus n, is …". Check the digits add to nine. Your child is reading the whole nines row in one minute.
Quick check
Common mix-ups
Subtracting 1 instead of n. 3 × 9 = 30 − 3, not 30 − 1 = 29. Every group loses one, and there are n groups.- Trusting the digit check alone. Digits adding to 9 is true for 54 and 63. Add the second check — tens digit is one less than n — and wrong answers have nowhere to hide.
- Mixing 8 × 9 and 9 × 9. Both start with the ×10 idea (80 − 8 vs 90 − 9). Slow down on eights-vs-nines for a few days — they sort themselves out with practice.
Play it now
A round locked to the nines: one number roams 1–10, the other is always 9. Let your child pick a tool — the ×10 recipe or the fingers — and use it openly. Speed is not today's goal.