3-Dimensional Shapes

To know a geometric shape, learners need to play with it—hold it, see it from all angles, even create it. These resources offer activities on making actual models that students can hold, but also virtual activities in which they can view, move, and rotate figures too complex to make in the classroom. Not every shape is here—only polyhedra, the objects most encountered in school mathematics. But there’s a wide range of materials here, arranged in order from activities for the youngest of the middle grades through materials more appropriate for high school students. We hope your students enjoy getting to know 3-D shapes.

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2D to 3D Morphing http://pbskids.org/cyberchase/games/23dgeometry/index.html

As students follow the directions on the printable pages, they construct a pyramid, a cube, and an octahedron. They can see the flat two-dimensional polygons rise up to form three-dimensional polyhedra. Each page is decorated with colorful images of the Cyberchase team so that one image appears on each face of the constructed three-dimensional objects. MSP full record

Scaling the Pyramids http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html

These several activities engage students through their fascination with the sheer size of the Great Pyramid. In one hands-on activity, students use a template to construct a scale model of the Great Pyramid. In another, students are given the actual dimensions for two other pyramids and challenged to create their own models. MSP full record

Geometric Solids and Their Properties http://illuminations.nctm.org/LessonDetail.aspx?id=U122

A five-part lesson plan has students investigate several polyhedra through an applet. Students can revolve each shape, color each face, and mark each edge or vertex. They can even see the figure without the faces colored in—a skeletal view of the "bones" forming the shape. The lesson leads to Euler’s formula connecting the number of edges, vertices, and faces, and ends with creating nets to form polyhedra. An excellent introduction to three-dimensional figures!

Platonic Solids (Grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_128_g_3_t_3.html?open=instructions

Students examine in detail the five Platonic solids—their shapes, vertices, edges, and regular polygonal faces. With the virtual manipulative, they can rotate each solid, viewing it from every angle, change its size, then use the transparent mode to see only the skeletal structure of the polyhedron. The site is part of the National Library of Virtual Manipulatives. MSP full record

Studying Polyhedra http://mathforum.org/alejandre/applet.polyhedra.html

What is a polyhedron? This lesson defines the word. Students explore online the five regular polyhedra, called the Platonic solids, to find how many faces and vertices each has, and what polygons make up the faces. An excellent applet! From this page, click on Polyhedra in the Classroom. Here you have middle school classroom activities to pursue with a computer. Developed by a teacher; the lessons use interactive applets and other activities to investigate polyhedra. Activities extend to paper nets to print out and fold, studies of buckyballs and crystals, and cube-coloring problems.

Slicing Solids (Grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_126_g_3_t_3.html?open=instructions

So what happens when a plane intersects a Platonic solid? This virtual manipulative opens two windows on the same screen: one showing exactly where the intersection occurred and the other showing the cross-section of the solid created in the collision. Students decide which solid to view, and where the plane will slice it. The site is part of the National Library of Virtual Manipulatives. MSP full record

Polyhedral Solids http://mathforum.org/library/view/2371.html

The site opens with: "The study of polyhedra is one of those special areas of Mathematics which allow the amateur and expert to work with an equal delight." Each page here gives a crisp, succinct definition of a type of polyhedra: Platonic, Archimedean, stellated, prisms and antiprisms—and even more! Each set is carefully illustrated with a view to clear instruction. MSP full record

Virtual Polyhedra: Encyclopedia of Polyhedra http://www.georgehart.com/virtual-polyhedra/vp.html

The ultimate site for those who want to play with every kind of polyhedron! You may simply let your class view and manipulate the virtual objects, or study the polyhedra more in depth through the background explanations and the exercises offered. An incredible collection of material!

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Copyright September 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.