Suggested activities for masterclasses for Victorian High-Ability Program students in the Secondary Mathematics course.
Guest speakers and documentaries
Inviting a guest speaker who uses networks in their daily work would allow students to be exposed to some real-life applications of the maths they have explored in the Victorian High-Ability Program (VHAP). High ability practice leaders can use their networks and resources to arrange for an expert guest speaker to address the students. Professional teaching associations such as the Mathematical Association of Victoria, as well as universities, may be able to provide this service to schools.
See 10 Best Documentaries for Teaching Mathematics for suggested videos. High ability practice leaders can use the ideas addressed in any of these documentaries to structure a discussion or lead into an activity.
For a virtual option, a guest speaker could run an online lecture followed by a question-and-answer session using Webex.
Other masterclass activities
Any of the activities below could be adapted to a virtual classroom. Students could use Padlet or other software to collaborate with one another to solve problems.
Sequence this!
This masterclass links closely with the content from week 5 of the Secondary Mathematics course. High ability practice leaders create a day in which students come together to recognise patterns in sequences and create their own sequence challenges. This masterclass is an excellent way to extend students’ ability to demonstrate that their solutions are correct BAD (‘beyond all doubt’). Depending on the size of your group and the amount of time available, this day can be set up in a variety of ways.
Ideas for activity sessions:
- Students are placed in different teams and move around a room to complete different sequence challenges.
- In groups of 2-4, students create challenging sequences for each other to find the patterns.
Resources for this masterclass include:
Does your network work?
This masterclass links closely with the content from weeks 3-4 of the Secondary Mathematics course. High ability practice leaders create a day in which students graph networks and solve shortest route problems.
This masterclass is an excellent way to extend students’ ability to demonstrate that their solutions are correct BAD (‘beyond all doubt’). Depending on the size of your group and the amount of time available, this day can be set up in a variety of ways.
Ideas for activity sessions:
- Students graph network puzzles.
- Students work in groups to solve shortest route puzzles such as the Travelling Salesman, and create their own shortest route puzzles.
- Students collaborate to explore critical path analysis.
Resources for this masterclass include:
Are we there yet?
This masterclass links closely with the content from weeks 7-8 of the Secondary Mathematics course. High ability practice leaders create a day in which students solve problems related to infinity and paradoxes.
This masterclass is an excellent way to extend students’ understanding of the paradoxical nature of infinity and will allow students to continue ‘breaking their brains in a good way’. Depending on the size of your group and the amount of time available, this day can be set up in a variety of ways.
Ideas for activity sessions:
- Students explore the ‘route to infinity’ problem.
- Students examine graphs that extend to infinity (asymptotes).
- Students collaborate to find and create paradoxical problems.
Resources for this masterclass include:
Acknowledgement, resources and references
The activities, resources and ideas for masterclasses were adapted and developed by the Victorian High-Ability Program teaching staff at .
Additional sample activities and suggestions for masterclasses for Secondary mathematics may be obtained by contacting Virtual School Victoria at
vhap-support@vsv.vic.edu.au.
‘Approaching Asymptotes’,
NRICH, Faculty of Mathematics, University of Cambridge.
'Decision Maths', Nuffield Mathematics, Level 3 - Advanced Resources, STEM Learning, United Kingdom.
‘Decision Resources’,
NRICH, Faculty of Mathematics, University of Cambridge.
Eisele, R (2023) ‘Codingame solution: The Travelling Salesman Problem’,
Computer Science and Machine Learning.
‘Hamiltonian Cube’,
NRICH, Faculty of Mathematics, University of Cambridge.
‘Infinity’,
Wild Maths, University of Cambridge.
Joyce H, ‘Mathematical mysteries: The Barber’s Paradox’,
Plus Bringing Mathematics to Life, University of Cambridge.
‘Maximum Flow’,
NRICH, Faculty of Mathematics, University of Cambridge.
NRICH (2023) Faculty of Mathematics, University of Cambridge.
‘Patterns and sequences: short problems’ (2023)
NRICH, Faculty of Mathematics, University of Cambridge.
‘Patterns and sequences: Stage 3 (11-14)’ (2023)
NRICH, Faculty of Mathematics, University of Cambridge.
‘Route to Infinity’ (2023)
NRICH, Faculty of Mathematics, University of Cambridge.
‘Sequence challenge answers’ (Harder sequence challenges) (Fall 1984)
The Virginia Mathematics Teacher.
Special Sequences (zipfile), GCSE Maths 9-1, New content resources.
youcubed®, Stanford Graduate School of Education, California.