Area Models & Distributive Property

Name:

Date:

Rectangle divided into sections showing area model

📐 Part 1: Area Models & Expressions

1. A rectangle has length (x + 3) and width 4. Write two different expressions for the total area:

Expression 1: _____________________

Expression 2: _____________________

2. Look at this area model: A rectangle is divided into two parts. The left part has area 5x and the right part has area 20. What is the length and width of the original rectangle?

Length: ___________

Width: ___________

3. Which expression represents the area of a rectangle with length (x + 6) and width 3?

3x + 6

x + 18

3x + 18

3(x + 6)

4. Draw an area model for the expression 2(x + 5). Label each section with its area.

🧮 Part 2: Distributive Property & Mental Math

5. Use the distributive property to rewrite each expression:

a) 4(x + 7) = _____________________

b) 6(x + 2 + 3) = _____________________

c) 3(x + 9) = _____________________

6. Use mental math and the distributive property to calculate:

a) 5 × 23 = 5 × (20 + 3) = ___________

b) 7 × 34 = 7 × (_____ + _____) = ___________

7. Which property allows us to write 3(x + 4) = 3x + 12?

Commutative Property

Associative Property

Distributive Property

Identity Property

✏️ Part 3: Problem Solving

8. A gardener has a rectangular plot with length (x + 8) feet and width 6 feet. Write an expression for the total area and explain how you could use an area model to show this.

9. Explain in your own words how breaking a rectangle into smaller parts helps us understand the distributive property.

10. Create your own problem: Design a rectangle with one side length that includes a variable and addition. Write the area expression two different ways.