Analyzing 3-D Shapes and 2-D Representations
Students can analyze 3-D objects better with actual physical models and by also drawing 2-D representations of them.
By Donna Iadipaolo
Analyzing geometric solids, such as prisms, pyramids, cylinders, cones, and spheres, is an engaging way to get students to begin thinking about geometry. Teachers can begin a lesson on geometric solids by bringing in everyday objects, such as cereal boxes, oatmeal cylinders, ice cream cones, and different kinds of sports balls for students to begin to think about and analyze the shapes. If your school has not supplied them, teachers might want to invest in a set of 3-dimensional plastic shapes for students to pass around and examine when imagining cross-sections, for instance. If the budget does not allow for this, you might ask students to construct or collect 3-D shapes and then have them measure and calculate their surface areas and volumes. Toothpicks and mini marshmallows provide a great hands-on approach to constructing many of the rigid three dimensional shapes, such as prisms and pyramids, and may be further utilized to develop a prototype for a building or bridge. Students might also be challenged to actually create “nets,” which are 2-dimensional patterns for 3-dimensional shapes that they can then fold up into a particular shape.
Students should explore this concept using as many different kinds of 2-dimensional representations of 3-dimensional shapes as possible. For instance, orthogonal representations, which show the top, front, and side view of an object, is yet another way students can study common 3-dimensional objects. Isometric drawings (using isometric dot paper) are another way figures may be represented. Students should begin with simple 2-D drawings of a cube, for example, with orthogonal and isometric renderings, and then develop representations of more complex figures. If possible, students could then construct the figures as 3-D models as well.
Since isometric drawings relate to perspective drawings, math teachers may also find it valuable to work with the art teacher in a broader study of perspective drawings, stressing its relationship to proportional thinking. Similarly, math teachers can introduce various optical illusions, constructed by 2-dimensional representation, which give a 3-dimensional appearance. You can challenge students to even create their own optical illusion designs. There are a variety of topics teachers can discuss, including symmetry, both line symmetry and rotational symmetry. Here are some 3-D and 2-D shape lesson plans.
Analyzing 3-D Shapes and 2-D Representations:
Students create isometric drawings, orthogonal views, and a model of a castle. Students also describe the reflection of rotational symmetry of an object.
Students use isometric dot paper or graph paper to draw various 2-dimensional representations of 3-D figures. Students study vertices, bases, and faces of objects, and create nets.
Using Cubes and Isometric Drawings
Students use isometric drawings to determine when two representations create the same shape. Student use an “isometric drawing tool” to build figures.
Students create a 2-dimensional representation of their city, and create a 3-dimensional model of it. Students calculate the surface areas of 3-dimensional figures.
Students create art that gives the impression of three dimensions using perspective and mathematical concepts.