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# Thinking Mathematically

### Working Systematically

### Conjecturing and Generalising

### Visualising and Representing

### Reasoning, Convincing and Proving

### Thinking Mathematically - Short Problems

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Successful mathematicians understand and use mathematical ideas and methods, solve problems, explain and justify their thinking, and have a positive attitude towards learning mathematics.

Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, convincing, proving... are all at the heart of mathematical thinking. The activities below are designed to give you the opportunity to think and work as a mathematician.

*For problems arranged by mathematical topics, see our Topics in Secondary Mathematics page.
For problems arranged by mathematical mindsets, see our Mathematical Mindsets page.*

Age 11 to 16

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

Age 11 to 16

Work on these problems to improve your conjecturing and generalising skills.

Age 11 to 16

Work on these problems to improve your visualising and representing skills.

Age 11 to 16

Work on these problems to improve your reasoning skills.

Age 11 to 16

A collection of short problems which require students to think mathematically.

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.

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