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.
Age 11 to 14

Exploring and Noticing Structure

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

Age 11 to 14

Working Systematically

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

Age 11 to 14

Thinking Strategically

Work on these problems to improve your strategic thinking.

Age 11 to 14

Posing Questions and Making Conjectures

Work on these problems to improve your questioning skills.

Age 11 to 14

Visualising

Work on these problems to improve your visualisation skills.

Age 11 to 14

Mathematical Modelling

Work on these problems to improve your mathematical modelling skills.

Age 11 to 14

Representing

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

Age 11 to 14

Reasoning, Justifying, Convincing and Proof

Work on these problems to improve your reasoning skills.

Developing Mathematical Habits of Mind

We learn better when we are curious, resourceful, resilient and collaborative.

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

Age 11 to 14 Challenge Level:

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!

Age 11 to 14 Challenge Level:

Being Resourceful

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

Age 11 to 14 Challenge Level:

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!

Age 11 to 14 Challenge Level:

Being Resilient

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

In this film (available here if you live outside the UK) 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.


Recommended Books
We have compiled a list of books for young people who are interested in mathematics.