Area Models - Find the Product Directions - Use the area model for each problem to find the product

Sep 23, 2026

Uploaded by Himbo

Practice multiplying multi-digit numbers using area models to break each factor into tens and ones (or other expanded parts). The worksheet guides students through Part A warm-up problems, Part B area model tasks with four-part decomposition, and Part C challenge products that require creating and showing area models. Part D applies the method to a word problem about ordering marker boxes, then provides a complete answer key with partial products and totals.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Part A—Warm-Up (Two Parts)

Part B—Area Models (4 Parts)

Part C—Challenge Problems

Part D—Challenge Problem (Show Your Thinking)

Answer Key

Name: Area Models – Find the Product Directions: Use the area model for each problem to find the product. Multiply each part, then add the partial products. Part A—Warm-Up (Two Parts) 1.) 23 × 4 Tens part: 20 × 4 = 20 3 | | 4 | | Ones part: 3 × 4 =
Total: | | --- | --- | --- | --- | | 2.) | 31 × 5
30 1
5 | | Tens part: 30 × 5 =
Ones part: 1 × 5 =
Total: | | 3.) | 46 × 3
| | Tens part: 40 × 3 =
Ones part: 6 × 3 =
Total: | | 4.) | 26 × 6
| | Total: | 1 Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) Part B—Area Models (4 Parts) | 5.) | 34 × 12
30 4
10
2
| 30 × 10 =
30 × 2 =
4 × 10 =
4 × 2 = Total: | | --- | --- | --- | | 6.) | 25 × 13
20 5
10
3
| 20 × 10 =
20 × 3 =
5 × 10 =
5 × 3 = Total: | | 7.) | 42 × 11
| 40 × 10 =
40 × 1 =
2 × 10 =
2 × 1 = Total: | | 8.) | 16 × 14
| Total: | 2 Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) Part C—Challenge Problems Directions: Use the given box to create your own area model to find each product. Show your work. 9. 37 × 15 = _____ 10. 48 × 12 = _____ Part D—Challenge Problem (Show Your Thinking) 11. A school orders 24 boxes of markers. Each box has 16 markers. Use an area model to find the total number of markers. Work (partial products): 20 × 10 = 20 × 6 = 4 × 10 = 4 × 6 = Total markers: Mashup Math LLC | All Rights Reserved | [Get More K-12 Math Worksheets at ](Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](Get More K-12 Math Worksheets at www.mashupmath.com) 3 Answer Key Part A—Warm-Up (Two Parts) 1. 23 × 4 • 20 × 4 = 80 • 3 × 4 = 12 • Total = 92 2. 31 × 5 • 30 × 5 = 150 • 1 × 5 = 5 • Total = 155 3. 46 × 3 • 40 × 3 = 120 • 6 × 3 = 18 • Total = 138 4. 26 × 6 • Tens part: 20 × 6 = 120 • Ones part: 6 × 6 = 36 • Total = 156 | Part B—Area Models (4 Parts) | | | --- | --- | | 5) 34 × 12 | 7. 42 × 11 | | • 30 × 10 = 300 | | | • 30 × 2 = 60 | • 40 × 10 = 400 | | • 4 × 10 = 40 | • 40 × 1 = 40 | | • 4 × 2 = 8 | • 2 × 10 = 20 | | • Total = 408 | • 2 × 1 = 2
• Total = 462 | | 6. 25 × 13 | 8. 16 × 14 | | • 20 × 10 = 200 | | | • 20 × 3 = 60 | • 10 × 10 = 100 | | • 5 × 10 = 50 | • 10 × 4 = 40 | | • 5 × 3 = 15 | • 6 × 10 = 60 | | • Total = 325 | • 6 × 4 = 24
• Total = 224 | |
Part C—Challenge Problems 9) 37 × 15 = 555 | 10) 48 × 12 = 576
| | Part D—Challenge Problem (Show Your Thinking)
11) 24 boxes × 16 markers = 384
• 20 × 10 = 200
• 20 × 6 = 120
• 4 × 10 = 40
• 4 × 6 = 24
• Total markers = 384
4
Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) | |

FAQs

How do you use the area model to find the product?

Split each number into parts (such as tens and ones), multiply each part combination, then add the partial products to get the total.

What is included in the warm-up section?

Part A contains two-part area model multiplication problems that practice tens and ones decomposition and totals.

How is the word problem in Part D solved using an area model?

Multiply the number of boxes by markers per box using partial products from the area model, then add to get the total markers.

Sep 23, 2026

Uploaded by Himbo