Sorting and Classifying Solids
areas of more complex shapes, cubic units model,varying the unit, triangle shape and area, lines of symmetry, more symmetry
In this lesson, we expand our concepts about symmetry to include three-dimensional solids, and in the process, explore characteristics of various prisms and their catagories. The introduction to the lesson includes definitions of axis of symmetry,and plane of symmetry.
Prisms are three-dimensional shapes with two parallel, congruent polygon bases. The lateral sides are all parallelograms. If the lateral sides are rectangular parallelograms, the prisms are called right prisms.
Triangular right prisms can have right triangle bases, scalene triangle bases, isoceles triangle bases, equilateral triangle bases, and right isoceles triangle bases
Rectangular right prisms are also called rectangular parallelipipeds.
The angles formed by the intersecting faces of a three-dimensional solid are called dihedral angles.
Cubic rectangular prisms have six square faces. The length of each edge of the cube is the cube root of the volume of the cube.
If the volume of the cube is 8u3, the length of the edge, orthe cube root, is 2u (2x2x2 = 8). If the volume is 1/8u3, then
the length of the edge is 1/2u (1/2x1/2x1/2 = 1/8).
In-class explorations center on the relationships of dimension, surface area and volume of solid geometric shapes, especially of rectangular prisms. Volume formulas are explored as they relate to the distribution of cubic units in the prism.
