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.
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.
Prompts from the teacher could be:
- Draw a diagram of the package for the chocolate. Show all the measurements for the dimensions of the package.
- Design a net to produce the package. Take care to add flaps that will be needed to stick edges together.
- To fit the packages in the box, think about layers. How many packages would cover the base of the box? Being triangular prisms, some packages could go upside down to fit neatly on the packages that are covering the base. All of these make up one layer. How many packages in one layer?
- Work out the height of a layer. How many layers fit in the box?
- Is there any spare space for more packages to fit in? Consider the layers and the spare space and calculate the total number of packages that can fit in a 40 x 40 x 40 cm3 box.
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.