Using Space Efficiently: Packing a Truck

Mathematical goals

This lesson unit is intended to help students to:

  • Reason precisely and defend their conclusions.
  • Use mathematics to model a scenario concerning volume.


The lesson unit is structured in the following way:

  • Before the lesson, students attempt the Packing It In task individually. You review their responses and formulate questions that will help them improve their work.
  • At the start of the lesson, students read your comments and consider ways to improve their work.
  • In pairs or threes, students work together to develop a better solution, producing a poster to show their conclusions and their reasoning.
  • Then, in the same small groups, students look at some sample student work showing different approaches to the problem. They evaluate the strategies used and seek to improve the arguments given.
  • In a whole-class discussion, students compare different solution methods.
  • Finally, students reflect individually on their learning.

Materials required

  • Each student will need a copy of Packing it In and How Did You Work? and some blank paper to work on. Provide calculators for students who wish to use them.
  • Each pair of students will need the three Sample Responses to Discuss, a piece of poster paper, a marker and some glue.
  • Have graph paper and if possible, unifix cubes or small cardboard boxes available.
  • There is a projector resource to support whole-class discussions.

Time needed