New Boxes from Old

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Learners determine the surface area and volume of two identical boxes, and then figure out the dimensions of a cubical box with the same volume. Then they construct a new, cube-shaped box from one of the original boxes, discovering the new box has less surface area than the original box. This activity requires learners to have previous knowledge of calculating surface area and volume. Activity time can be divided over multiple meetings.

Quick Guide

Preparation Time:
Under 5 minutes

Learning Time:
2 to 4 hours

Estimated Materials Cost:
1 cent - $1 per student

Age Range:
Ages 11 - 14

Resource Types:
Activity, Lesson/Lesson Plan


Materials List (per student)

  • two identical boxes
  • ruler (metric)
  • calculator
  • scissors
  • tape (masking and transparent)
  • large envelope or zipper-style plastic bag
  • large paper clip


  • Engineering and Technology
    • Engineering
      • Manufacturing Engineering
  • Mathematics
    • Algebra
      • Equations and Inequalities
    • Geometry
      • Plane Geometry
      • Solid Geometry
    • Measurement
      • Units of Measurement
      • Size and Scale
  • The Nature of Technology
    • The Design Process


To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • Involves hands-on or lab activities


Components that are part of this resource:

Includes alignment to state and/or national standards:

This resource is part of:

Access Rights:

  • Free access


  • Hebrank, Mary R.

Source Collection

  • TeachEngineering


  • All rights reserved, Regents of the University of Colorado, 2004