Where the Geometry Progression is HeadingComposition and decomposition of shapes is used throughout geometry from Grade 6 to high school and beyond. Compositions and decompositions of regions continues to be important for solving a wide variety of area problems, including justiﬁcations of formulas and solving real world problems that involve complex shapes. Decompositions are often indicated in geometric diagrams by an auxiliary line, and using the strategy of drawing an auxiliary line to solve a problem are part of looking for and making use of structure
(MP7). Recognizing the signiﬁcance of an existing line in a ﬁgure is also part of looking for and making use of structure. This may involve identifying the length of an associated line segment, which in turn may rely on students’ abilities to identify relationships of line segments and angles in the ﬁgure. These abilities become more sophisticated as students gain more experience in geometry. In Grade 7, this experience includes making scale drawings of geometric ﬁgures and solving problems involving angle measure, surface area,
and volume (which builds on understandings described in the Geometric Measurement Progression as well as the ability to compose and decompose ﬁgures) 6/23/2012, comment at commoncoretools.wordpress.com.
Just for those teachers who sometimes ask, "Why do I need to teach this?" These papers answer the question.