Triangle Constructions

Who can grasp solid geometry? Make 3-dimensional shapes to manipulate into polyhedra using Color Explosion™ paper.

• 1.

  When most people study the geometry of three-dimensional space, it is helpful to be able to see, feel, and build the structures. A polyhedron is a 3-D solid that made up of polygons (2-D figures made up of line segments, edges that are connected two at a time at their endpoints) or more simply, flat faces usually joined at their edges.

• 2.

  For this exercise, try using a triangle (although other shapes such as squares will work). First, make a template to trace several triangles. Using a ruler, draw an equilateral triangle (3 equal sides, 3 equal angles) on cardboard with Crayola Erasable Colored Pencils. This will be the flat surface building block for your polyhedra.

• 3.

  On each side of the triangle, extend the edge equally to make three tabs around the triangle as shown in the picture. (When you are constructing shapes, these tabs will align with tabs of other triangles.) Cut out your template with Crayola Scissors.

• 4.

  Trace the template on white Crayola Color Explosion™ Paper. To get as many triangles per sheet as possible, draw triangles next to each other so they share edges. Start out with at least 12 triangles. Cut out the triangles with scissors. Using Color Explosion™ Markers, decorate each triangle with a unique design.

• 5.

  Place a ruler along each tab of the cutout triangles. Bend up tab edges.

• 6.

  Line up the tabs of two triangles and join them together with a rubber band. Keep adding triangles until you have constructed a simple polyhedron. Count the number of faces, vertices, and edges to determine what shape you constructed.

• 7.

  After making regular polyhedra (shapes with equal edge lengths), see if you can create irregular ones, where the sides and angles are not equal.

Benefits

• Students understand and apply basic and advanced properties of the concepts of solid geometry.
• Students practice accurate measuring to devise a template to create shapes that fit together.
• Students manipulate two-dimensional shapes to create three-dimensional solids.

Adaptations

• Use the Polyhedral Formula to check on your shapes. The number of faces plus the number of vertices minus the number of edges should equal 2.
• Go deeper into the subject by finding out about the different types of Polyhedra, such as Platonic solids, prisms, and pyramids.
• Go on a Polyhedra Scavenger Hunt to locate three-dimensional shapes in your everyday life.
• Assessment: Did students make triangles of equal measurement? Can students define polygon and polyhedron? Did students manipulate the triangles to create a three-dimensional shape from a two-dimensional drawing? Do students feel comfortable experimenting with triangles to create shapes with their imagination?