Multiplication Area Model | STrofin - Free Printable

You’ve uploaded a worksheet titled “Multiplication Area Model”. This method breaks down multiplication into smaller, easier-to-calculate parts using the distributive property and visual area rectangles.

Each problem uses a 2x2 grid to represent multiplying two 2-digit numbers. The top row and left column are split into tens and ones (place value decomposition), and each box in the grid represents the product of those parts. Then you add all four partial products to get the final answer.

Let’s solve each problem step by step.

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🔹 Problem 1: 34 × 23

Decompose:
- 34 = 30 + 4
- 23 = 20 + 3

Fill the grid:

| | 20 | 3 |
|-----------|--------|--------|
| 30 | 30×20=600 | 30×3=90 |
| 4 | 4×20=80 | 4×3=12 |

Add the four parts:
→ 600 + 90 + 80 + 12 = 782

✔ Final Answer: 782

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🔹 Problem 2: 40 × 32

Decompose:
- 40 = 40 + 0 (or just 40)
- 32 = 30 + 2

Grid:

| | 30 | 2 |
|-----------|--------|--------|
| 40 | 40×30=1200 | 40×2=80 |
| 0 | 0×30=0 | 0×2=0 |

Add: 1200 + 80 + 0 + 0 = 1280

✔ Final Answer: 1280

*(Note: Since one number is a multiple of 10, it simplifies — but we still follow the model.)*

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🔹 Problem 3: 58 × 27

Decompose:
- 58 = 50 + 8
- 27 = 20 + 7

Grid:

| | 20 | 7 |
|-----------|--------|--------|
| 50 | 50×20=1000 | 50×7=350 |
| 8 | 8×20=160 | 8×7=56 |

Add: 1000 + 350 + 160 + 56 =
→ 1000 + 350 = 1350
→ 1350 + 160 = 1510
→ 1510 + 56 = 1566

✔ Final Answer: 1566

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🔹 Problem 4: 83 × 19

Decompose:
- 83 = 80 + 3
- 19 = 10 + 9

Grid:

| | 10 | 9 |
|-----------|--------|--------|
| 80 | 80×10=800 | 80×9=720 |
| 3 | 3×10=30 | 3×9=27 |

Add: 800 + 720 + 30 + 27 =
→ 800 + 720 = 1520
→ 1520 + 30 = 1550
→ 1550 + 27 = 1577

✔ Final Answer: 1577

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🔹 Problem 5: 34 × 44

Decompose:
- 34 = 30 + 4
- 44 = 40 + 4

Grid:

| | 40 | 4 |
|-----------|--------|--------|
| 30 | 30×40=1200 | 30×4=120 |
| 4 | 4×40=160 | 4×4=16 |

Add: 1200 + 120 + 160 + 16 =
→ 1200 + 120 = 1320
→ 1320 + 160 = 1480
→ 1480 + 16 = 1496

✔ Final Answer: 1496

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🔹 Problem 6: 62 × 15

Decompose:
- 62 = 60 + 2
- 15 = 10 + 5

Grid:

| | 10 | 5 |
|-----------|--------|--------|
| 60 | 60×10=600 | 60×5=300 |
| 2 | 2×10=20 | 2×5=10 |

Add: 600 + 300 + 20 + 10 =
→ 600 + 300 = 900
→ 900 + 20 = 920
→ 920 + 10 = 930

✔ Final Answer: 930

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## ✔ Summary of Answers:

| Problem | Answer |
|---------------|--------|
| 34 × 23 | 782 |
| 40 × 32 | 1280 |
| 58 × 27 | 1566 |
| 83 × 19 | 1577 |
| 34 × 44 | 1496 |
| 62 × 15 | 930 |

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## 📌 How to Fill the Worksheet:

For each problem, draw or imagine a 2x2 grid. Label the top with the tens and ones of the first number, and the side with the tens and ones of the second number.

Then fill each box with the product of its row and column headers.

Finally, write each partial product next to the “+” signs on the right, then add them all for the total.

This method reinforces place value understanding and makes large multiplication more intuitive!

Let me know if you want printable versions or diagrams for each!