✖️ Multiplication 📚 Grade 3-4 ⏱ 7 min
Multi-Digit Multiplication: How to Teach Step by Step
The problem 23×14 looks scary before the distributive property. After it — just two multiplications and one addition.
The distributive property — the key
23×14 = 23×10 + 23×4. A big problem splits into two small ones by breaking the second factor by place value. The idea opens up through an area rectangle.
💡 Prerequisites: fluent times tables, multiplying by 10, adding three-digit numbers. Gaps here turn the distributive property into chaos.
The rectangle model
A 23-by-14 rectangle splits with a vertical line into two: 23×10 and 23×4. Their areas add up: 230+92=322. The child sees both partial products before writing a column.
The column algorithm
Three steps
Example 23×14:
Step 1: multiply by 4 → 23×4=92
Step 2: multiply by 10 → 23×10=230 (shift row left)
Step 3: add → 92+230=322
Practice chain:
21×12=252 · 13×21=273
32×14=448 · 25×13=325
45×23=1035 · 34×31=1054
21×12=252 · 13×21=273
32×14=448 · 25×13=325
45×23=1035 · 34×31=1054
Common mistakes
- Forgotten row shift — the rectangle reminds: the second product is tens
- Addition errors on large numbers — use column addition
- Multiplying by 1 instead of 10 — say it aloud before writing
✖️ The times table is the foundation!
Every algorithm step rests on the times table. Our Pro game drives it to automatic.
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