FIGURE 2-6 Relationships among rectangles.

FIGURE 2-6 Relationships among rectangles.

composed of rows and columns of squares, as illustrated in Figure 2-6, is key to understanding areas of rectangles.

Likewise, composing and decomposing 3-D shapes is an important foundation for understanding volume in later grades. In particular, viewing rectangular prisms as composed of layers of rows and columns of cubes is key to understanding volumes of rectangular prisms (see Figure 2-7). Also, reasoning about fractions often takes place in a context of reasoning about decomposing shapes into pieces.

Composition and decomposition is discussed in greater detail in the section on mathematical connections across content areas and to later mathematics.

Motion, Relative Location, and Spatial Structuring

Part of the study of geometry is the analysis of both 2-D and 3-D space. A flat tabletop or piece of paper (imagined to extend infinitely in all



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