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Building a Box

This lesson uses a real-world situation to help develop students' spatial visualization skills and geometric understanding. Emma, a new employee at a box factory, is supposed to make cube?shaped jewelry boxes. Students help Emma determine how many different nets are possible and then analyze the resulting cubes. This activity is a good way for students to visualize surface area.

Weblink address (URL): 
Building a Box

Standards & Objectives

Learning 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.
Essential and guiding questions: 

Questions for Students:

  • What properties are common to all nets that will form a cube?
  • What type of nets will not work? Why not?
  • Without folding, is there a quick way to determine whether or not a net will fold into a cube?
  • How can you determine if two nets are identical?
  • What sort of properties does your final cube have? How do these compare to the properties of the nets?

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • 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:

  • Computer with internet connection
  • Building a Bod Activity Sheet
  • Square Polydron or Geofix pieces, or centimeter grid paper to cut and fold

References

Contributors: 
Roxann Johnson
Originator: 
Ayers Institute for Learning & Innovation