Fact Families

Some numbers belong together like a family. 3, 4 and 12 are one: 3 fours make 12. Draw them as a triangle — the whole (12) at the top, the two parts (3 and 4) at the bottom. This one little triangle is about to give you FOUR facts for free.

From the 3 · 4 · 12 triangle you can write FOUR true facts: 3 × 4 = 12 and 4 × 3 = 12 (the parts build the whole), plus 12 ÷ 3 = 4 and 12 ÷ 4 = 3 (the whole splits into parts). Learn one fact, own all four. That's why fact families are the fastest way to master tables AND division together.

The triangle solves missing-number puzzles. ▢ × 5 = 30: put your finger over the mystery corner. What's left? 30 and 5 — and whole with a part means DIVIDE: 30 ÷ 5 = 6. The hidden number is 6. Cover-up works every time: hide what you don't know, and the two visible numbers tell you what to do.

Every table fact you've learned is secretly a whole family. 2 · 6 · 12, 3 · 5 · 15, 4 · 8 · 32, 5 · 10 · 50… each triangle holds four facts. If you know twenty multiplication facts, you actually own EIGHTY facts. Fact families are how a little learning becomes a lot of power.

Real questions become easy when you think in families. '24 wheels, 4 per car' — that's the 4 · 6 · 24 family: 6 cars. '▢ ÷ 3 = 8' — the mystery is the whole, so multiply the parts: 3 × 8 = 24. Whenever ×, ÷ or a missing number shows up, sketch the triangle in your head and let the family do the work.