Geometry helps people describe the world around them through the study of geometric shapes, structures, and their characteristics and relationships. Through the study of geometry, students will learn about shapes and dimensions around them and how to analyze spatial relationships in everyday life. Spatial visualization—building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives—is an important aspect of geometric thinking. An understanding of the attributes and relationships of geometric objects can be applied to diverse contexts.
In the first grade, children continue to build and draw 2- and 3-dimensional shapes. Composing and decomposing plane or solid figures (e.g., putting two triangles together to make a quadrilateral) helps to build an understanding of part-whole relationships, as well as the properties of the original and composite shapes. As students combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different. These activities help students develop the background for measurement and for initial understandings of properties, such as congruence and symmetry. Through the decomposition of shapes, students also begin to develop an understanding of fractions and equal shares.