Successful mathematicians understand curriculum concepts, are fluent in mathematical procedures, can 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 learners the opportunity to think and work as mathematicians.

*For problems arranged by curriculum topic, see our **Primary Curriculum** page**For problems arranged by mathematical mindsets, see our **Mathematical Mindsets** page*

### Exploring and noticing - Primary teachers

Age: 5 to 11

These problems offer learners an opportunity to explore by trying something out, and reflect on what they notice.

Working Systematically

### Working Systematically - Primary teachers

Age: 5 to 11

These problems will offer your learners opportunities to appreciate the value of working systematically in a variety of contexts.

### Conjecturing and generalising - Primary teachers

Age: 5 to 11

These problems will offer opportunities for your learners to use specific examples as a springboard to generalising.

### Visualising and Representing - Primary teachers

Age: 5 to 11

These lower primary tasks all specifically draw on the use of visualising.

### Reasoning and Convincing at KS1 - Primary teachers

Age: 5 to 7

The tasks in this collection can be used to encourage children to convince others of their reasoning, using 'because' statements.

### Reasoning and Convincing at KS2 - Primary teachers

Age: 7 to 11

The tasks in this collection can be used to encourage children to convince others of their reasoning, by first convincing themselves, then a friend, then a 'sceptic'.