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.

In this film the mathematician Andrew Wiles talks about his personal experience of seeking a proof of Fermat's Last Theorem.  He describes what it is like to do mathematics, to be creative, to have difficulties, to make mistakes, to persevere, to make progress, to have a dream and love what you are doing so much that you are willing to devote yourself to it for a long time.  Of course, each mathematician's experience is different, and most mathematicians do not work alone for such prolonged periods without discussing their work with others, but much of Andrew Wiles' experience is shared amongst mathematicians, and reminds us of the rewards of perseverance in the face of difficulty.


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.

Developing Mathematical Habits of Mind

We learn better when we are curious, thoughtful, determined and collaborative.

Here are some collections of mathematical activities designed to help you develop these characteristics.

Stage: 3 Challenge Level: Challenge Level:1

Being Curious

Here are some problems that we hope will appeal to curious and inquisitive students. Take a look, we think you'll get hooked on them!

Stage: 3 Challenge Level: Challenge Level:1

Being Thoughtful

Here are some problems that require careful consideration. Immerse yourself in them - we think they are worth the effort!

Stage: 3 Challenge Level: Challenge Level:1

Being Collaborative

Here are some problems that are ideal for working on with others. Find a friend, share ideas, and see if two heads really are better than one!

Stage: 3 Challenge Level: Challenge Level:1

Being Determined

Here are some problems that require you to be determined and persistent. We hope you'll stick with them and feel a sense of achievement at the end!