Designing 3D products: candy cartons

This is a problem solving lesson, designed to help you assess how well students are able to:

• Select appropriate mathematical methods to use for an unstructured problem
• Interpret a problem situation, identifying constraints and variables and specify assumptions.
• Work with 2- and 3-dimensional shapes to solve a problem involving capacity and surface area
• Communicate their reasoning clearly

The problem is set in the context of a candy company wanting students to design a carton that will contain 18 candies. Students are given the following constraints:

• The size of the candies
• The carton must be made from a single sheet of letter-sized card
• The design should require as little cutting as possible
• The sides of the carton will be fixed together using glue flaps

Students work collaboratively to design the packaging. They then discuss the merits of different designs, taking practical considerations into account.

This is a problem solving lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.