Lesson objective: Understand that area is additive, meaning the area of a figure is the same as the sum of the area of non-overlapping regions of the figure.

Students bring prior knowledge of finding the area of a rectangle from 4.MD.A.3. This prior knowledge is extended to figures composed of rectangles as students learn how to decompose figures. A conceptual challenge students may encounter is recognizing the need for non-overlapping regions and complete coverage of the figure.

The concept is developed through work with models of rectangles and graph paper, which helps students see the overlapping areas.

This work helps students deepen their understanding of operations and equivalence because students will see that the area of regions can be added to find the area of an entire figure.

Students engage in Mathematical Practice 4 (Model with mathematics) as they view, manipulate, and create models to represent decomposing the figures.

**Key vocabulary:**

**Special materials needed:**

- Graph paper will be helpful for many students.