Optimizing Storage Box Design
Understand the MYP Criterion D box optimisation investigation in Extended Geometry Year 5. Volume, surface area, algebraic modelling, and real-life evaluation strategies.
What This Task Is About
Optimizing Storage Box Design is a Criterion D investigation context in which students apply geometric knowledge — specifically volume and surface area — to a real-life design problem. The task asks students to find the dimensions of a box that maximise volume or minimise surface area under given constraints, then evaluate and justify their solution.
The Mathematics Behind the Task
Students model the box using algebraic expressions for volume and surface area. For a rectangular box with a fixed volume, the surface area depends on the dimensions chosen. Students use algebraic manipulation to express one variable in terms of others, reducing the problem to a function of fewer variables.
Key Techniques Used
- Expressing surface area or volume as a formula with constraints substituted in
- Using a table of values or graphical approach to identify the optimal dimensions
- Interpreting the minimum or maximum in context — dimensions must be positive and physically reasonable
- Considering whether the optimal solution changes if the box has a lid or no lid
How Criterion D Is Assessed Here
Criterion D asks students to identify a genuine real-life problem, select appropriate mathematical strategies, apply them to reach a solution, and critically evaluate both the solution and the process. For this task, a strong response:
- Clearly defines the constraints (fixed volume or fixed material area)
- Shows the algebraic setup with all variables defined
- Tests multiple configurations and justifies why the optimal one is selected
- Reflects on limitations — for example, whether a cube is practical to store, or whether manufacturing constraints affect the solution
Common Weaknesses in Student Responses
- Finding a numerical answer without evaluating whether it is truly optimal or just one option tested
- Failing to define variables or constraints before calculating
- Not addressing real-world validity — a box with one dimension of 0.1 cm is not practical
- Presenting the solution without reflecting on what assumptions were made
Practice Approach
Before attempting the full task, practise setting up volume and surface area expressions for boxes with different constraints. Understand how changing one dimension while holding volume constant affects surface area. The GradePerfect Extended volume page has relevant calculation practice to build this foundation.