Lesson 12 Decompose Area

- Let’s decompose rectangles to find their area.

Warm-up Number Talk: Partial Products

Find the value of each expression mentally.

$3 \times 20$
$3 \times 24$
$5 \times 2$
$5 \times 2 \frac{1}{2}$

Activity 1 Which Garden Is Larger?

Noah’s garden is 5 yards by $6 \frac{1}{4}$ yards. Draw a diagram of Noah’s garden on the grid.
Priya’s garden is 6 yards by $5 \frac{1}{4}$ yards. Draw a diagram of Priya’s garden on the grid.
Whose garden covers a larger area? Be prepared to explain your reasoning.

Activity 2 Different Ways to Find the Area

Each problem shows the first step a student used to find the area of the shaded region. Explain how each student could finish their work to find the area and show your thinking on the diagram.
Share your response with your partner. What is the same? What is different?

Partner A

Area diagram. Horizontal side, 4. Vertical side, 5 and 1 half.

Jada: $4 \times 5$

Priya: $4 \times \frac{1}{2}$

Tyler: $6 \times 4$

Partner B

Area diagram. Length, 4. Width, 11 halves.

Clare: $\frac{10}{2} \times 4$

Diego: $4 \times 6$

Elena: $4 \times 11$

Practice Problem

Problem 1

Find the area of the shaded region. Explain or show your reasoning.

Area diagram. Length, 3 feet. Width, 4 and 1 fourth feet.