Real world maths – a pet ownership puzzle

Each year, the International Mathematical Modeling Challenge (IM2C) gives students an opportunity to team up on a complex task that connects their mathematical learning with a real-world situation. Previous tasks have included determining the most effective way to board and disembark planes, identifying which items were likely to be the most popular during a sale event, and declaring who the ‘GOAT’ of women’s tennis is.

This year 2 Australian teams, from Northern Beaches Secondary College (NBSC) Manly Campus and Brisbane Boys’ College (BBC), were among 6 entrants to be named in the coveted Meritorious category. Teacher spoke to ‘Team Radar’ from Brisbane Boys’ College and BBC Head of Mathematics Jeremy Hunter about how they faced up to the challenge.

Millions of households worldwide have a pet of some kind. However, in addition to the love and companionship these pets bring, there are also plenty of challenges.

Whether it be financial costs, behavioural issues, or just finding a pet sitter for when you’re away, owning a pet is a big responsibility. As a result, every year many pets are returned, left at shelters, or simply abandoned as owners struggle to care for them.

So, how can you determine if a household is ready to take on a pet? And how do you decide if they’re better off with a cat or a dog (or perhaps just a goldfish)?

These were some of the questions Team Radar from Brisbane Boys’ College had to consider for this year’s International Mathematical Modeling Challenge (IM2C), which tasked teams with developing models that could determine household readiness for pet ownership, as well as factors like future pet demographics, rates of ownership and retention.

To start, can we get a little background about BBC’s experience with the IM2C?

Jeremy Hunter: BBC has had a successful engagement with the IM2C for many years. Two BBC teams achieved Meritorious at the State level in 2021, 2 teams were National finalists (one Meritorious) in 2019, and one team was an Honourable Mention in 2018. One of our teams also travelled to Hong Kong in 2019.

This current team – Team Radar, [students Llewellyn Hosking, Junpeng Huang, Hemish Dubey, Joshua Liew, and team advisor Ms Heather Meinecke] – won the National title last year and achieved an Honourable Mention in International Judging.

We are excited to enter 2 teams next year as we have a very strong years 9 and 10 group. Team Radar has agreed to coach the next group coming through later this year, which is very exciting.

Engagement with the IMMC was initiated by our long-standing Mathematics leader, Mr Chicri Maksoud, who passed away at the beginning of 2022. As the Head of Mathematics and the Coordinator of Gifted and Talented, I am attempting to carry on his legacy by continuing our efforts to establish BBC as one of the top mathematical schools in the country.

I felt a bit overwhelmed just reading this year’s challenge… how did the team approach it?

Team Radar: Thankfully, we've had experience with handling intimidating problems such as these, including when we competed in the IM2C last year.

It was important to not dive straight into writing, but rather brainstorm how we would tackle the task through defining variables, finding context and making assumptions. Creating a structure of how we would order our report really helped us to go one step at a time. We didn't start writing anything until Day 2 in order to fully understand what the task required us to do.

Can you talk us through your model?

TR: The task required us to decide whether any given household would be suitable to own a pet. This could have been done many different ways, but due to the mathematical nature of this task, we decided on creating a score rating for household suitability to simplify the problem.

This was done by considering the different factors that would influence household suitability and creating an overall rating based on how well each household conformed to a pet's need for each of these factors. These factors were then scaled into a radar chart, and a final score was calculated.

The task also required us to use our model as a gauge of how many households are suitable for any pet in any given area over a period of time. This was modelled through differential equations, allowing the rate of change over time to considered.

Of course, in a mathematical model, not all values can be considered, as in real life, there are realistically an infinite amount of very specific variables that can be looked at. However, as long as a generalisable and sensitive model was created, we had completed the main aim of the task.

This was the first year AI was permitted. How did you use AI? What role do you see AI having in the future?

TR: We used AI to create code for radar chart models and for random generation of households to create a fair spread of examples to show the generalisability of our model. Of course, AI has flaws, and code and household generation was reviewed by us, but was very helpful as these tasks can be really time consuming.

JH: BBC has embraced AI as an emerging technology that will only become more prominent in classrooms and beyond. We are developing policies around its appropriate use and are familiarising our staff and students with how it can be used to enhance teaching and learning without circumnavigating crucial educational processes.

What value is there in entering challenges such as the IM2C?

JH: Students learn to collaborate, to problem solve, and to place themselves in situations that replicate real life, where the answers aren’t provided on the whiteboard or in the back of a textbook.

These competitions act as an opportunity to broaden skills, challenge their skill base, and establish networks beyond the classroom.

[The team] demonstrate an impressive skill set and method of approach, showcasing resilience and perseverance as they apply different strategies to reach the correct answer, pivoting when necessary to a different, more fruitful method.

Any advice for schools looking ahead to next year?

JH: Jump in! Encourage your students to have a go and to test themselves. It’s complex, though, so they should be ready for that. Pick a team with members who complement each other’s strengths.

If any schools would like to engage our services to mentor and support their involvement, please reach out.

IM2C is a global team competition open to secondary school teams of up to 4 students, enrolled in the same school, and a nominated team advisor (usually a teacher). The competition takes place during a fixed period each year, during which teams have 5 consecutive days (of their choosing) to complete the challenge.

Judging is first held on a national level, with the best Australian reports progressing to international judging. In 2024, 73 Australian teams from 21 schools entered. The national judges selected 13 finalists, with the top 2 finalists progressing to international judging.

The Australian challenge is managed by the Australian Council for Educational Research (ACER), and you can find more information here.

Editor's note: This article was updated on 24 July 2024 to clarify that the top 2 finalists progressed to international judging.