Tangyuan MathLesson 8 · 15 min Stage 3 · Power strategies
You already know most of it
The times table looks like 100 facts. Today you and your child cross out everything owned — and count what's really left.
In this lesson your child will watch 100 shrink to 10 before their eyes, meet one bonus rule (×4 is double twice), and walk away with a named, finishable list: the final ten.
Talk it through
"The whole times table, 1 to 10, is 100 facts. Sounds like a mountain. Let's cross out everything you already own — you press the buttons, you say the rule, we count together."
"One rule we haven't named: ×4 is double, then double again. 4 × 6? Double 6 is 12, double again is 24. Now you own the fours too."
Press the rules one at a time, in any order. After each press, your child says the rule out loud before you look at the count: ×1 is itself… ×10 is tens… swap makes twins free… Watch the number fall: 100… 55… fewer… ten.
"Ten. The entire times table is ten facts, and even those you can break apart when your memory hiccups. That's not a mountain. That's a pebble."
Name the final ten together — write them on paper: 3×3, 3×6, 3×7, 3×8, 6×6, 6×7, 6×8, 7×7, 7×8, 8×8. These are everyone's hard facts. Nobody finds them easy. That's why they're the famous ten.
Try it together
Press a rule, say the rule. Toggle rules off and on to test: "turn off the nines — what comes back?" Notice the swap button grays the mirror half of the table — those are the free twins from Lesson 4.
Quick check
Common mix-ups
"So I never have to learn anything?" Rules are bridges, not destinations. Deriving 6 × 8 is great; knowing it instantly is better. The plan: figure it out now, own it through practice.- Expecting the ×3 row to vanish. It doesn't — 3×6, 3×7, 3×8 survive in the final ten. Only whole rows with rules disappear completely.
- Being discouraged that ten remain. Flip it: those ten are hard for every child on Earth, and there are only ten, and there's a strategy for each. Finishable.
Play it now
Straight into the final ten's neighborhood: both numbers 6–9. Small round, five questions, full attention on figuring — the famous ten get their reps here.