Lesson 3

Lots of Rectangles

• Let’s express the areas of some rectangles.

3.1: Math Talk: Many Ways to Area

A rectangle is partitioned into smaller rectangles. Explain why each of these expressions represents the area of the entire rectangle.

$$7(7+7+4+4)$$

$$7(2 \boldcdot 7 + 2 \boldcdot 4)$$

$$7^2+7^2+4 \boldcdot 7+4 \boldcdot 7$$

$$2(7^2) + 2 (4 \boldcdot 7)$$

3.2: Representing Areas

Match each figure with one or more expressions for its area. Every shape that looks like a square is a square.

• $$2 \boldcdot 3^2$$
• $$6n^2$$
• $$n^2+1^2$$
• $$3^2$$
• $$(n+1)(n+1)$$
• $$(2n)(3n)$$
• $$(n+1)^2$$
• $$3(3+3)$$
• $$n^2$$
• $$(n+n)(n+n+n)$$
• $$3^2+3^2$$

3.3: Areas of Rectangles

Complete the table with the length, width, and area of each rectangle.

rectangle length (units) width (units) area (square units)
A $$a+4$$
B 2
C
D
E