Building a Box

This lesson presents the students with a real-world situation to help develop their spatial visualization skills using nets of a cube. The students are to design all the different nets possible that can be folded into a cube. This lesson presents the students with a real-world situation to help develop their spatial visualization skills using nets of a cube. The students are to design all the different nets possible that can be folded into a cube.

 

Weblink address (URL): 
Building a Box

Standards & Objectives

Learning objectives: 

Students will:

  • Create, compare and describe different two-dimensional nets that can be folded into a three-dimensional cube.
  • Examine the properties of the nets and resulting cubes, including surface area.
  • Use rotations and flips to compare various nets.

Lesson Variations

Blooms taxonomy level: 
Applying
Extension suggestions: 
  • Have students determine the net for a typical cereal box. Draw a sketch, and then cut it out and fold it. See if they can design nets for other boxes they have seen. Also, you might have them use the Patch Tool to create nets for other three‎ dimensional objects using triangles, hexagons, and rhombi.
  • Give students the following challenge problem:
  • The ACME box company wants to make these jewelry boxes as efficiently as possible. They can save money by fitting as many nets as possible on one piece of cardboard. If the company use a piece of cardboard that measures 20 cm × 20 cm, how many nets (of any type) can you arrange to fit on one piece of cardboard? You may use any of the working net designs you created and you may arrange them in any way on your piece of cardboard.
  • As an alternative, allow students to use the drawing area of the Patch Tool to represent the cardboard, and see how many different nets they can fit into this region.
  • Draw a net on a single sheet of 8½" × 11" piece of paper that will result in the largest cube possible. Which net will you use? What is its volume?
     

Helpful Hints

Materials:

  • Computers with Internet connection
  • Building a Box Activity Sheet 
  • Square Polydron or Geofix pieces, or centimeter grid paper to cut and fold

References

Contributors: 
Angela Collins
Originator: 
Ayers Institute for Learning & Innovation