Mathematical investigations serve as an excellent avenue for senior students to engage with mathematics in a meaningful and intellectually stimulating way. These inquiries highlight the relevance of mathematics to real-world contexts, promoting not only academic growth but also the development of critical thinking, analytical reasoning, and if undertaken as a group or class – collaborative problem-solving skills.
At this level, students are encouraged to delve deeper into complex problems, formulate hypotheses, and present logical, well-structured arguments supported by evidence. Investigations provide a platform to explore mathematical concepts beyond the standard curriculum, allowing students to take ownership of their learning and demonstrate originality in their approach.
Participation in such projects also offers the potential for significant recognition. A well-executed investigation can enhance a student’s academic portfolio, bring prestige to their school, and may result in monetary awards. More importantly, it develops a deeper appreciation for the discipline and cultivates skills that are essential for success in higher education and future careers.
Engaging in mathematical investigations is not merely an academic exercise—it is an opportunity to experience the power and elegance of mathematics in action.
Information on Undertaking the Competition
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In March 2025 a video conference was convened with teachers, parents, and guardians of secondary-level students who expressed interest in supporting their children’s involvement in the 2025 South Australian Investigating with Mathematics Competition.
The meeting was structured around a comprehensive PowerPoint presentation, which outlined the key discussion points and systematically guided participants through the competition framework. Additionally, the presentation provided valuable recommendations and strategies designed to support the successful planning and execution of the students’ mathematical investigations.
>> Download PowerPoint presentation (pptx)
Project Information: This A3 poster guideline sets out the terms of the competition.
- What is the competition?
- Who can enter?
- What is the purpose of the competition?
- What are the important dates to know?
Guidelines for Completing the Investigation: This A3 poster puts the four key steps in developing and then seeing through an investigation:
- See
- Plan
- Do
- Check
Guidelines for Presenting the Investigation: This A3 poster sets out the nine recommended steps to lead the entrant to present a well constructed investigation.
100 Inspirational Titles is a list of possibilities that can spark each entrant’s imagination in their pursuit of an investigation.
The marking rubric will provide teachers and guardians of secondary school level competitors with an understanding of how the entrants’ markers will be assessing the submissions. Two rubrics are provided; (1.) Years 3 to 12, and (2.) Reception to Year 2.Â
Examples from 2024
Year 8 Investigation
The aim of this investigation was to uncover the cost of owning a smoothie stall at the Mount Gambier Farmers Market. This included starting up the business, and operating for 12 weeks (or 12 market days). The purpose of this was to see if having a market stall can be profitable and worthwhile. Also, is 12 weeks enough time to make a profit? If so, how much profit can be made in 12 weeks?
Year 9 Investigation
Ensuring the safety of student crossing the West Terrace Intersection is a significant concern, as there are flaws towards the trafficking system. Pedestrian safety is influenced by various factors, including traffic volume, pedestrian behaviour, and traffic control measures such as crossing lights.
Within this investigation the fundamental aim was to analyse and determine the optimal green light time for pedestrian crossings to maximize the number of students who can cross safely and efficiently.
Year 11 Investigation
While base ten is the most widely used number system—likely due to the anatomical influence of having ten fingers—it is not necessarily the most efficient for all applications. Alternative bases, such as base six and base two, present distinct advantages depending on context. Some offer greater divisibility, others enhance computational efficiency or data compression. Different bases are suited to different tasks. By examining finger counting systems and comparing various bases, this investigation explores their respective benefits and limitations from a balanced perspective.
Year 12 Investigation
The goal of this investigation was to find the value within a series of functions that produced the curve for which the triangle formed by the tangents’ x- and y-intercepts and the origin has the smallest possible area.
Ready to submit your Investigation? – Send to MASA
Please send your investigation to MASA at admin@masanet.com.au. Your Year level, and whether the Investigation was undertaken by; an individual, a group, or a class are to be identified by completing and submitting an entry cover sheet:
>> Years 7 to 10 entries (.docx)
>> Years 11 and 12 entries (.docx)
Due date for 2025 Competition: Entries closed – thank you to all applicants!
Due date for Semester 2 submissions: 3 December 2025
Parents, students and teachers reflect on their experiences in the 2024 Competition.
Sponsor of Senior Competition Years 7 to 10 : S.A. Department for Education
The S.A. Investigating with Mathematics Competition’s Years 7 to 10 sections are proudly supported by the South Australian Depatment for Education.
Public education is for every child and young person in every community across our state.
Educators and staff work in partnership with families and communities to nurture, develop and empower all South Australian children and young people with the knowledge, skills and capabilities they need to become fulfilled individuals, active, compassionate citizens and lifelong learners.
Our preschools and schools are the heart of local communities. They are safe, inclusive, and collaborative – a place where every child and young person is encouraged to contribute, develops positive relationships, has a say in their learning, and where their needs, interests and cultures are recognised and supported.
We are relentless in our ambition for all children and young people to enter the world beyond the classroom ready to learn and to create opportunities to live a satisfying and fulfilling life of their choosing.
When our children and young people thrive so does South Australia.
Sponsor of Senior Competition Years 11 and 12 : The Mathematical Association of South Australia
The S.A. Investigating with Mathematics Competition’s Years 11 and 12 sections are proudly supported by The Mathematical Association of South Australia.
The Mathematical Association of South Australia Inc. (MASA) is the South Australian affiliate of the Australian Association of Mathematics Teachers Inc. (AAMT).
MASA’s membership spans all educational levels, from reception through to tertiary institutions.
The Association is committed to encouraging interest in mathematics and advocating for continuous improvement in its teaching and application. It serves as a vital platform for support and communication among educators, students, and schools. MASA also actively promotes the importance of mathematics as a significant field of study and encourages the development of mathematical learning at all levels.