# GM4-5: Identify classes of two- and three-dimensional shapes by their geometric properties.

Elaboration on this Achievement Objective

This means students will use geometric properties to identify classes of shapes. Classes are categories of two or three-dimensional shapes. Shapes are sorted into classes according to defined geometric properties, such as number and relationship of sides (for example equal and parallel); number and nature of angles (for example four right angles); symmetry, number, nature, and shape of faces and surfaces (for 3-dimensional shapes). Classes can be included within other classes, can intersect or be disjoint, for example all squares are rectangles or no triangles are pentagons. At Level Four students should be familiar with:

- classes of polygons defined by the number of sides; triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides)...octagons (8 sides)...
- classes of 3-dimensional shapes defined by the nature of faces and surfaces; prisms (constant cross-section) and cylinders, pyramids and cones, regular polyhedral (identical faces)
- classes of 2-dimensional closed curves and their 3-dimensional equivalents by rotation; circles and spheres, ellipses and ellipsoids
- sub-classes that are included within classes: squares within rectangles, rectangles within parallelograms, parallelograms within quadrilaterals, circles within ellipses, cubes within rectangular prisms
- classes that are disjoint, scalene and isosceles triangles, prisms and pyramids.