Main Idea

This lesson bundles student expectations that address creating, sorting, and classifying three-dimensional figures, as well as composing and decomposing geometric figures based on geometric attributes. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

During this unit, students analyze attributes of three-dimensional solids in order to develop generalizations about their properties. Using formal geometric language, students classify and sort polygons with 12 or fewer sides by identifying the number of sides and number of vertices. Students use attributes based on formal geometric language to classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prism (including cubes as special rectangular prisms), and triangular prisms. Students develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes. Spatial visualization is also reinforced as students compose three-dimensional solids with given properties or attributes.

In the primary grades, the instruction of geometry concepts relies heavily on hands-on manipulation of concrete objects. While early experiences with naming shapes is critical to geometry, research by the National Research Council (2001) concludes that rather than limiting geometrical investigations to simply identifying shapes, students who are "encouraged to reflect on and articulate their developing knowledge...subsequently [demonstrate] levels of reasoning well beyond their earlier performance, both in their precision of language and in their use of arguments based on the properties of shapes" (p. 285). Van de Walle (2005) explains that the teaching of geometry involves the gradual attainment of concept levels based on the accurate application of formal geometric vocabulary focused more on properties of figures than on simple identification. The advent of virtual three-dimensional manipulation using technology has increased the need for a well-developed spatial sense and understanding of geometric attributes and properties in order for students to be prepared for the future.