Mathematical Modelling: Packaging Designer


This unit Packaging Designer is one of 5 units making up the Special Topic “Mathematical Modelling”.

Students assume the role of consultants to a packaging company that produces packs for a range of different cylindrical objects such as candles, drinks bottles, and perfumes. Comparison is made between the design cycle and the modelling cycle, and students reflect upon how design work might be informed by an understanding of mathematical modelling processes. 

As an additional task, students are given some practice scenarios so they can develop their skills in interpreting and critiquing mathematical models. 

For classes who have not recently done Unit 1 Introduction to Modelling, a single ‘quick start’ lesson is provided.

Read the Teachers’ Guide (included in the download package) before using this resource.


Lesson 1: The Design Task

Students think their way into the role of being a designer by considering the factors that would be important in designing packaging. They consider the priorities of the manufacturer (e.g. easily manufactured and transported), the retailer (e.g. easy to display on shelves) and the perspectives of customers (e.g. attractive). They begin to design a container to hold five essentially cylindrical products, that will come in various sizes.

Lesson 2: Designing the Packaging

Students develop their packaging design. They consider how mathematics is useful in this task, and see the role of mathematical modelling in designing. They begin to prepare a report in which they communicate their work clearly.

Lesson 3: Critiquing Reports

Students are given three pre-prepared student reports on the packaging problem to critique. They work with a partner to understand, complete and correct a report, and identify the mathematical modelling involved. Then they explain their report to another pair. This task provides an opportunity to consider alternative approaches students might take to develop their own work further, and it enables them to see characteristics of a good report.

Lesson 4: Modelling and Designing

As many pairs as possible present the important features of their design (very briefly) orally or as posters, while other students evaluate the work against a set of criteria. Finally, students think again about how mathematical modelling contributes to design work.

Lesson 5: Back to Reality

Students undertake three short activities that highlight the interpreting and evaluating phases of modelling. Writing a commentary for a race using only a distance time graph, focusses on interpretation. Predicting running world records focusses on evaluating a model. Predicting future numbers of teachers focusses on selecting a model that uses the best available data, and appreciating which data influences the outcome most.


Last updated November 9 2018.