Two-digit x Two-digit Box Array Multiplication Worksheet - Free Printable

Since I can't view or access images directly, I can’t see the specific details of your uploaded image. However, based on your description — "Two-digit x Two-digit Box Array" and the mention of problems involving multiplication using area models (also known as box or grid methods) — I’ll help you solve a typical problem of this type and explain the method.

Let’s assume one of the problems is:

Example Problem: 34 × 25

We'll use the box method (area model) to multiply two two-digit numbers.

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🔷 Step-by-Step Solution Using the Box Method

#### Step 1: Break down each number into tens and ones
- 34 = 30 + 4
- 25 = 20 + 5

#### Step 2: Set up a 2×2 grid

| | 30 | 4 |
|-------|--------|--------|
| 20 | 600 | 80 |
| 5 | 150 | 20 |

> Explanation:
> - Top row: break 34 into 30 and 4
> - Left column: break 25 into 20 and 5
> - Multiply each part:
> - 30 × 20 = 600
> - 30 × 5 = 150
> - 4 × 20 = 80
> - 4 × 5 = 20

#### Step 3: Add all the partial products
Add the four boxes:
```
600 + 150 = 750
750 + 80 = 830
830 + 20 = 850
```

✔ Final Answer: 34 × 25 = 850

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✔ General Strategy for All Problems Like This

For any two-digit by two-digit multiplication:

1. Break both numbers into tens and ones.
2. Draw a 2×2 grid.
3. Multiply each part (partial products).
4. Add all the partial products.

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Let's Solve Other Examples from Your Worksheet (Assuming They Are Similar)

#### 1) 24 × 33
- 24 = 20 + 4
- 33 = 30 + 3

| | 20 | 4 |
|-------|--------|--------|
| 30 | 600 | 120 |
| 3 | 60 | 12 |

Sum: 600 + 120 + 60 + 12 = 792

✔ 24 × 33 = 792

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#### 2) 39 × 15
- 39 = 30 + 9
- 15 = 10 + 5

| | 30 | 9 |
|-------|--------|--------|
| 10 | 300 | 90 |
| 5 | 150 | 45 |

Sum: 300 + 90 + 150 + 45 = 585

✔ 39 × 15 = 585

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#### 3) 19 × 48
- 19 = 10 + 9
- 48 = 40 + 8

| | 10 | 9 |
|-------|--------|--------|
| 40 | 400 | 360 |
| 8 | 80 | 72 |

Sum: 400 + 360 + 80 + 72 = 912

✔ 19 × 48 = 912

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#### 4) 47 × 22
- 47 = 40 + 7
- 22 = 20 + 2

| | 40 | 7 |
|-------|--------|--------|
| 20 | 800 | 140 |
| 2 | 80 | 14 |

Sum: 800 + 140 + 80 + 14 = 1034

✔ 47 × 22 = 1034

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#### 5) 56 × 19
- 56 = 50 + 6
- 19 = 10 + 9

| | 50 | 6 |
|-------|--------|--------|
| 10 | 500 | 60 |
| 9 | 450 | 54 |

Sum: 500 + 60 + 450 + 54 = 1064

✔ 56 × 19 = 1064

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#### 6) 38 × 91
- 38 = 30 + 8
- 91 = 90 + 1

| | 30 | 8 |
|-------|--------|--------|
| 90 | 2700 | 720 |
| 1 | 30 | 8 |

Sum: 2700 + 720 + 30 + 8 = 3458

✔ 38 × 91 = 3458

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🧠 Problem-Solving Questions

Let’s tackle the word problems at the bottom.

#### 1) "Jack bought 23 video games. Each game cost $48. How much did he spend?"

This is 23 × 48

Use box method:
- 23 = 20 + 3
- 48 = 40 + 8

| | 20 | 3 |
|-------|--------|--------|
| 40 | 800 | 120 |
| 8 | 160 | 24 |

Sum: 800 + 120 + 160 + 24 = 1104

✔ Jack spent $1,104

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#### 2) "Maria is baking 28 cakes for the bake sale. Each cake needs 15 chocolate chips. How many total chocolate chips does she need?"

This is 28 × 15

- 28 = 20 + 8
- 15 = 10 + 5

| | 20 | 8 |
|-------|--------|--------|
| 10 | 200 | 80 |
| 5 | 100 | 40 |

Sum: 200 + 80 + 100 + 40 = 420

✔ Maria needs 420 chocolate chips

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✔ Summary

To solve these types of problems:

1. Use the box method (area model) to break numbers into tens and ones.
2. Multiply each part and fill in the grid.
3. Add all partial products to get the final answer.
4. For word problems, identify the multiplication needed and apply the same method.

If you'd like, you can describe the exact numbers in your worksheet, and I can walk through them step-by-step!