The area model
The area model breaks multiplication into smaller, friendlier pieces.
Example: 23 × 14
Split each number by place value and multiply each pair. Then add all four parts: 200 + 80 + 30 + 12 = 322
This works because 23 × 14 = (20 + 3) × (10 + 4) — the distributive property!
The standard algorithm
Once you’re comfortable with the area model, the standard algorithm is faster:
2 3
× 1 4
-----
9 2 ← 23 × 4
2 3 0 ← 23 × 10
-----
3 2 2Steps:
- Multiply 23 by the ones digit (4): 23 × 4 = 92
- Multiply 23 by the tens digit (10): 23 × 10 = 230
- Add the partial products: 92 + 230 = 322
Step 1: Ones
Step 2: Tens
Step 3: Add
The standard algorithm is just the area model written vertically. Each row is a partial product.
Tips for carrying
When a column product is 10 or more, carry the tens digit:
Example: 47 × 6
- 6 × 7 = 42 → write 2, carry 4
- 6 × 4 = 24, plus carried 4 = 28
- Answer: 282
Practice
Use any method: 36 × 12 = ?
Area model: (30×10) + (30×2) + (6×10) + (6×2) = 300 + 60 + 60 + 12 = 432.
Calculate 54 × 23.
54 × 3 = 162. 54 × 20 = 1,080. Total: 162 + 1,080 = 1,242.
Which area-model partial product is missing? 45 × 27: (40×20) + (40×7) + (5×20) + ?
The four parts are: (40×20), (40×7), (5×20), and (5×7). The missing piece is 5 × 7 = 35.
A cinema has 28 rows with 32 seats in each row. How many seats total?
28 × 32 = (28 × 30) + (28 × 2) = 840 + 56 = 896 seats.
When multiplying 63 × 8, you get 6 × 8 = 48 in the tens column. What do you carry?
48 tens = 4 hundreds and 8 tens. Write 8 in the tens place and carry 4 to the hundreds.
Challenge
Quick-Fire Round