Designing 3D Products: Candy Cartons

Mathematical goals

This lesson unit is intended 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.


This activity will take two lessons. The lessons are structured in the following way:

  • Before the first lesson, students tackle the problem individually. You review their work and write questions to help students improve their solutions.
  • At the beginning of the first lesson, students respond to your questions. They then work collaboratively in pairs to produce a better solution, using their designs to construct a carton.
  • To launch the second lesson there is a whole-class discussion. Then in small groups students evaluate and comment on sample solutions, followed by a whole-class discussion about the work.
  • Finally, in a follow-up lesson students review and evaluate their work on the problem.

Materials required

  • Each student will need a mini-whiteboard, a pen, an eraser, a copy of the task sheet, Design a Candy Carton, and a copy of the Design Review questionnaire.
  • Each small group of students will need a large sheet of paper for making a poster, a sheet of light, letter-sized cardboard, scissors, a glue stick, highlighter pens, and a copy of each of the Sample Responses to Discuss.
  • Provide calculators, rules, protractors, pencils, grid and plain papers, compasses, and cylindrical counters (such as checkers pieces) for students who wish to use them.
  • You may also want to bring a couple of cartons to the class.
  • There is a projector resource to support whole-class discussions.

Time needed

20 minutes before the lesson, two one-hour lessons, and 15 minutes in a follow-up lesson. Timings are approximate; exact timings will depend on the needs of your students.