Thinking Mathematically

Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying, proving... are all at the heart of mathematical thinking. 

These collections of activities are designed to develop your capacity to work as a mathematician.

To give you a taste of how mathematicians work you may like to watch this film telling the story of the British mathematician Andrew Wiles and his bid to find a proof for Fermat's last theorem.

Stage: 3

Exploring and Noticing Structure - Lower Secondary

What mathematical structures do you notice as you explore these problems?

Stage: 3

Working Systematically - Lower Secondary

Work on these problems to improve your ability to work systematically.

Stage: 3

Thinking Strategically - Lower Secondary

Work on these problems to improve your strategic thinking.

Stage: 3

Posing Questions and Making Conjectures - Lower Secondary

Work on these problems to improve your questioning skills.

Stage: 3

Visualising - Lower Secondary

Work on these problems to improve your visualisation skills.

Stage: 3

Mathematical Modelling - Lower Secondary

Work on these problems to improve your mathematical modelling skills.

Stage: 3

Representing - Lower Secondary

Consider how alternative representations can help us to understand the underlying mathematical concepts.

Stage: 3

Reasoning, Justifying, Convincing and Proof - Lower Secondary

Work on these problems to improve your reasoning skills.