Transforming The Net of A Cube Into The Net of A PyramidStudent View (Opens in new window)
Students use scissors to transform a net for a unit cube into a net for a square pyramid. They then investigate how changing a figure from a cube to a square pyramid affects the number of faces, edges, and vertices and how it changes the surface area and volume.
A square pyramid is a 3-D figure with a square base and four triangular faces.
In this lesson, the net for a cube is transformed into a net for a square pyramid. This requires cutting off one square completely and changing four others into isosceles triangles.
It is easy to see that the surface area of the pyramid is less than the surface area of the cube, because part of the cube's surface is cut off to create the pyramid. Specifically, the surface area of the pyramid is 3 square units, and the surface area of the cube is 6 square units. Students will be able to see visually that the volume of the pyramid is less than that of the cube.
Students consider the number of faces, vertices, and edges of the two figures. A face is a flat side of a figure. An edge is a segment where 2 faces meet. A vertex is the point where three or more faces meet. A cube has 6 faces, 8 vertices, and 12 edges. A square pyramid has 5 faces, 5 vertices, and 8 edges.
Goals and Learning Objectives
- Change the net of a cube into the net of a pyramid.
- Find the surface area of the pyramid.