Area Model Division Worksheets for Teaching Division Strategies

Problem Description:

The task involves solving division problems using the Area Model Division method. The area model is a visual representation that helps break down division into smaller, more manageable steps. The goal is to solve the given division problems step by step, filling in the area model grid as instructed.

Steps to Solve Using the Area Model Division:

#### Step 1: Understand the Area Model
The area model for division works similarly to how we use it for multiplication. Here, the total area represents the dividend, one side represents the divisor, and the other side represents the quotient. We break the division problem into smaller parts to make it easier to solve.

#### Step 2: Break Down the Problem
We will solve each division problem step by step using the area model. Let's go through the examples provided in the image.

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Example 1: \( 309 \div 36 \)

#### Step 1: Set Up the Problem
- Dividend: \( 309 \)
- Divisor: \( 36 \)

#### Step 2: Estimate the Quotient
We estimate how many times \( 36 \) can fit into \( 309 \). A good starting point is to consider multiples of \( 36 \):
- \( 36 \times 8 = 288 \) (close but not exceeding 309)
- \( 36 \times 9 = 324 \) (exceeds 309)

So, the first estimate for the quotient is \( 8 \).

#### Step 3: Fill in the Area Model
We set up the area model with:
- One side as the divisor (\( 36 \))
- The other side as the partial quotient (\( 8 \))

| | \( 36 \) |
|---|----------|
| \( 8 \) | \( 288 \) |

#### Step 4: Subtract to Find the Remainder
Subtract the product from the dividend:
\[ 309 - 288 = 21 \]

#### Step 5: Check for Further Division
Since \( 21 \) is less than \( 36 \), we cannot divide further. The remainder is \( 21 \).

#### Final Answer:
\[ 309 \div 36 = 8 \text{ R } 21 \]

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Example 2: \( 230 \div 79 \)

#### Step 1: Set Up the Problem
- Dividend: \( 230 \)
- Divisor: \( 79 \)

#### Step 2: Estimate the Quotient
We estimate how many times \( 79 \) can fit into \( 230 \):
- \( 79 \times 2 = 158 \) (close but not exceeding 230)
- \( 79 \times 3 = 237 \) (exceeds 230)

So, the first estimate for the quotient is \( 2 \).

#### Step 3: Fill in the Area Model
We set up the area model with:
- One side as the divisor (\( 79 \))
- The other side as the partial quotient (\( 2 \))

| | \( 79 \) |
|---|----------|
| \( 2 \) | \( 158 \) |

#### Step 4: Subtract to Find the Remainder
Subtract the product from the dividend:
\[ 230 - 158 = 72 \]

#### Step 5: Check for Further Division
Since \( 72 \) is less than \( 79 \), we cannot divide further. The remainder is \( 72 \).

#### Final Answer:
\[ 230 \div 79 = 2 \text{ R } 72 \]

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Example 3: \( 241 \div 28 \)

#### Step 1: Set Up the Problem
- Dividend: \( 241 \)
- Divisor: \( 28 \)

#### Step 2: Estimate the Quotient
We estimate how many times \( 28 \) can fit into \( 241 \):
- \( 28 \times 8 = 224 \) (close but not exceeding 241)
- \( 28 \times 9 = 252 \) (exceeds 241)

So, the first estimate for the quotient is \( 8 \).

#### Step 3: Fill in the Area Model
We set up the area model with:
- One side as the divisor (\( 28 \))
- The other side as the partial quotient (\( 8 \))

| | \( 28 \) |
|---|----------|
| \( 8 \) | \( 224 \) |

#### Step 4: Subtract to Find the Remainder
Subtract the product from the dividend:
\[ 241 - 224 = 17 \]

#### Step 5: Check for Further Division
Since \( 17 \) is less than \( 28 \), we cannot divide further. The remainder is \( 17 \).

#### Final Answer:
\[ 241 \div 28 = 8 \text{ R } 17 \]

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Example 4: \( 356 \div 37 \)

#### Step 1: Set Up the Problem
- Dividend: \( 356 \)
- Divisor: \( 37 \)

#### Step 2: Estimate the Quotient
We estimate how many times \( 37 \) can fit into \( 356 \):
- \( 37 \times 9 = 333 \) (close but not exceeding 356)
- \( 37 \times 10 = 370 \) (exceeds 356)

So, the first estimate for the quotient is \( 9 \).

#### Step 3: Fill in the Area Model
We set up the area model with:
- One side as the divisor (\( 37 \))
- The other side as the partial quotient (\( 9 \))

| | \( 37 \) |
|---|----------|
| \( 9 \) | \( 333 \) |

#### Step 4: Subtract to Find the Remainder
Subtract the product from the dividend:
\[ 356 - 333 = 23 \]

#### Step 5: Check for Further Division
Since \( 23 \) is less than \( 37 \), we cannot divide further. The remainder is \( 23 \).

#### Final Answer:
\[ 356 \div 37 = 9 \text{ R } 23 \]

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Final Answers:

1. \( 309 \div 36 = 8 \text{ R } 21 \)
2. \( 230 \div 79 = 2 \text{ R } 72 \)
3. \( 241 \div 28 = 8 \text{ R } 17 \)
4. \( 356 \div 37 = 9 \text{ R } 23 \)

\[
\boxed{8 \text{ R } 21, 2 \text{ R } 72, 8 \text{ R } 17, 9 \text{ R } 23}
\]