What is “Exploring Mathematics”?

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Exploring Mathematics is an elective semester course offered to Stage 5 (Year 9-10) students at Cherrybrook Technology High School.

To understand what this course is, you must first understand what it is not:

  • This course is not about acceleration (learning content from years 11-12 in advance so that you will be more familiar with it when you encounter it in the future). In fact, topics in the Stage 6 mathematics subjects have been intentionally avoided so that they can be given their proper introduction in the Preliminary and HSC courses.
  • This course is not like your regular mathematics class in its classroom activities or its assessments. In fact, there is a very conscious emphasis on branches of mathematics that are not understood through repetitive exercises, nor assessed in traditional examination formats.

By contrast, the goals of this course are:

  • To expose you to different areas in mathematics that you would not otherwise experience
  • To cultivate your ability to think in mathematically abstract terms
  • To assist you in seeing and appreciating the mathematics that surrounds you everyday

In other words, the purpose of this course is to explore mathematics in a cognitively intensive and engaging environment.


Below is a list of the proposed topics to be covered in Exploring Mathematics. The flexible nature of this course provides us the opportunity to investigate topics that are not on this list (based on student interest), or conversely to eschew some topics in favour of covering others in more depth. The order of these topics is likewise adaptable.

  • Matrices: The Workhorses of Mathematics
  • Set Theory: The Families of Mathematics
  • Fractals: The Mathematics of Self-Similarity
  • Cryptography: The Mathematics of Secrecy
  • Paradoxes: When Mathematics Doesn’t Make Sense
  • Play: The Mathematics Behind Games
  • Beauty: Symmetry, Magical Numbers & Music
  • Math Error: What It Means To Be Undefined
  • Number Systems: The Language of Mathematics
  • History: The Battleground of Mathematics



This course is designed to form and assess mathematical understanding in a variety of ways. This includes, but is not limited to:

  • Two-dimensional artwork
  • Three-dimensional construction project
  • Video composition
  • Short-response quiz
  • Photography
  • Class participation and discussion (both physical & electronic)

This text is taken from the official course outline for Exploring Mathematics.


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