Thus, using manipulative materials to develop geometric concepts and spatial sense remains important at these grade levels. Exploring concepts in a number of different contexts helps students to generalize. Students are extending their understanding of cause and effect and their ability to make conjectures. Connections among geometry, spatial sense, other areas of mathematics, and other subject areas provide many opportunities for students to see how mathematics fits into their lives. With respect to spatial relationships , students in these grade levels continue to examine direction, orientation, and perspectives of objects in space.
Students also expand their understanding of congruence, similarity, and symmetry.
They can identify congruent shapes, draw and identify a line of symmetry, and describe the symmetries found in nature. Students are extending their understanding of properties of geometric figures . Now they are ready to discuss these more carefully and to begin relating different figures to each other. By experimenting with concrete materials, drawings, and computers, they are able to discover properties of shapes and to make generalizations like all squares have four equal sides. They use the language of properties to describe shapes and to explain solutions for geometric problems, but they are not yet able to deduce new properties from old ones or consider which properties are necessary and sufficient for defining a shape.