4 Digit by 1 Digit Area Model Multiplication Worksheets - ExperTuition - Free Printable

You’ve uploaded a math worksheet focused on 4-digit by 1-digit multiplication using the area model, aligned with Common Core standard 4.NBT.B.5. The worksheet is split into two sets:

- Set A1 (Multiple Choice) — Left side
- Set B2 (Open-ended) — Right side

I’ll solve all problems from both sets, explain the area model method, and give you the correct answers.

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## ✔ What is the Area Model?

The area model breaks down multiplication by decomposing the 4-digit number into its place values (thousands, hundreds, tens, ones), then multiplying each part by the 1-digit number, and finally adding the partial products.

Example:
4,324 × 3
Break 4,324 into:
→ 4,000 + 300 + 20 + 4
Multiply each by 3:
→ 4,000×3 = 12,000
→ 300×3 = 900
→ 20×3 = 60
→ 4×3 = 12
Add them: 12,000 + 900 + 60 + 12 = 12,972

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# 📘 SET A1 — Multiple Choice (Solved with Explanation)

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1. 4,324 × 3 = ?

Breakdown:
- 4,000 × 3 = 12,000
- 300 × 3 = 900
- 20 × 3 = 60
- 4 × 3 = 12
→ Total = 12,000 + 900 + 60 + 12 = 12,972

✔ Correct Answer: C. 12,972

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2. 5,423 × 2 = ?

Breakdown:
- 5,000 × 2 = 10,000
- 400 × 2 = 800
- 20 × 2 = 40
- 3 × 2 = 6
→ Total = 10,000 + 800 + 40 + 6 = 10,846

✔ Correct Answer: A. 10,846

*(Note: Worksheet shows only “10,000” filled in — you’d fill in 800, 40, 6 in the other boxes)*

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3. 3,241 × 4 = ?

Breakdown:
- 3,000 × 4 = 12,000
- 200 × 4 = 800
- 40 × 4 = 160
- 1 × 4 = 4
→ Total = 12,000 + 800 + 160 + 4 = 12,964

✔ Correct Answer: D. 12,964

*(Worksheet shows “3,000 + 200 + 40 + 1” → multiply each by 4)*

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4. 2,513 × 5 = ?

Breakdown:
- 2,000 × 5 = 10,000
- 500 × 5 = 2,500
- 10 × 5 = 50
- 3 × 5 = 15
→ Total = 10,000 + 2,500 + 50 + 15 = 12,565

✔ Correct Answer: C. 12,565

*(Worksheet shows “2,000 + ...” — complete: 500, 10, 3 → times 5)*

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# 📗 SET B2 — Open-ended (Solved Step-by-Step)

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1. 4,276 × 6 = ?

Breakdown:
- 4,000 × 6 = 24,000
- 200 × 6 = 1,200
- 70 × 6 = 420
- 6 × 6 = 36
→ Total = 24,000 + 1,200 + 420 + 36 = 25,656

✔ Answer: 25,656

*(Worksheet already has 24,000, 1,200, 420 — add 36)*

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2. 3,645 × 8 = ?

Breakdown:
- 3,000 × 8 = 24,000
- 600 × 8 = 4,800
- 40 × 8 = 320
- 5 × 8 = 40
→ Total = 24,000 + 4,800 + 320 + 40 = 29,160

✔ Answer: 29,160

*(Worksheet has 24,000 — fill in: 4,800, 320, 40)*

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3. 5,364 × 7 = ?

Breakdown:
- 5,000 × 7 = 35,000
- 300 × 7 = 2,100
- 60 × 7 = 420
- 4 × 7 = 28
→ Total = 35,000 + 2,100 + 420 + 28 = 37,548

✔ Answer: 37,548

*(Worksheet shows 5,000 + 300 + 60 + 4 — multiply each by 7)*

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4. 6,253 × 9 = ?

Breakdown:
- 6,000 × 9 = 54,000
- 200 × 9 = 1,800
- 50 × 9 = 450
- 3 × 9 = 27
→ Total = 54,000 + 1,800 + 450 + 27 = 56,277

✔ Answer: 56,277

*(Worksheet shows 6,000 + ... — fill in: 200, 50, 3 → ×9)*

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5. 1,572 × 7 = ?

Breakdown:
- 1,000 × 7 = 7,000
- 500 × 7 = 3,500
- 70 × 7 = 490
- 2 × 7 = 14
→ Total = 7,000 + 3,500 + 490 + 14 = 11,004

✔ Answer: 11,004

*(Fill in boxes: 7,000 | 3,500 | 490 | 14)*

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6. 8,153 × 6 = ?

Breakdown:
- 8,000 × 6 = 48,000
- 100 × 6 = 600
- 50 × 6 = 300
- 3 × 6 = 18
→ Total = 48,000 + 600 + 300 + 18 = 48,918

✔ Answer: 48,918

*(Fill in boxes: 48,000 | 600 | 300 | 18)*

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7. 2,714 × 9 = ?

Breakdown:
- 2,000 × 9 = 18,000
- 700 × 9 = 6,300
- 10 × 9 = 90
- 4 × 9 = 36
→ Total = 18,000 + 6,300 + 90 + 36 = 24,426

✔ Answer: 24,426

*(Fill in boxes: 18,000 | 6,300 | 90 | 36)*

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8. 8,271 × 8 = ?

Breakdown:
- 8,000 × 8 = 64,000
- 200 × 8 = 1,600
- 70 × 8 = 560
- 1 × 8 = 8
→ Total = 64,000 + 1,600 + 560 + 8 = 66,168

✔ Answer: 66,168

*(Fill in boxes: 64,000 | 1,600 | 560 | 8)*

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## ✔ Final Answers Summary

Set A1 (Multiple Choice)

1. C. 12,972
2. A. 10,846
3. D. 12,964
4. C. 12,565

Set B2 (Open-ended)

1. 25,656
2. 29,160
3. 37,548
4. 56,277
5. 11,004
6. 48,918
7. 24,426
8. 66,168

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## 🧠 Teaching Tip:

This worksheet reinforces place value understanding and distributive property (a × (b + c) = a×b + a×c). Students should practice breaking numbers apart, multiplying each part, then summing — this builds strong mental math and prepares them for multi-digit multiplication algorithms.

Let me know if you want printable answer keys or step-by-step visuals!