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. They recognize the concepts of point, line, line segment, ray, plane, intersecting lines, radius, diameter, inside, outside, and on a figure. They extend the shapes they can identify to include ellipses, pentagons, octagons, cubes, cylinders, cones, prisms, pyramids, and spheres.
Students continue to explore geometric transformations .
Using concrete materials, pictures, and computer graphics, they explore the effects of transformations on shapes. Using coordinate geometry students create and interpret maps, sometimes making use of information found in tables and charts. Some grids use only numbers at these grade levels, while others use a combination of letters and numbers. The geometry of measurement begins to take on more significance in grades 3 and 4, as students focusmore on the concepts of perimeter and area. Geometric modeling allows students to approach topics visually.