The purpose of this multiple-level activity is to engage students in applying their knowledge of three dimensional solids to solve a package and packing problem.

This background knowledge and skills that need to be established before and/or during this task are outlined in the diagram below:

This task may be 'scaffolded' with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently. The approach should be chosen in sympathy with their skills and depth of understanding.

Task: A chocolate manufacture produces bars shaped in a triangular prism of length 12 cm. The cross section of the bars is an equilateral triangle of side length 4 cm.

- Design a net for the packaging of the individual bars.
- The packaged bars are to be put into boxes that are 40 x 40 x 40 cm
^{3}. Find the maximum number of bars that can be packed into each box.

### The procedural approach (show more)

- The student is able to produce a net that meets the specifications given. The student can follow instructions to solve a packing problem involving volumes that need to be calculated.

### The conceptual approach (show more)

- The student is able to produce a net that meets the specifications given. The student can solve a packing problem involving volumes that need to be calculated.