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 Primary Mathematics** page**For problems arranged by mathematical mindsets, see our **Mathematical Mindsets** page*

### Exploring and noticing - Primary students

Age: 5 to 11

What do you notice as you explore these problems?

### Working Systematically - Primary Students

Age: 5 to 11

Mathematicians try to work systematically so they can see how they worked something out, and see patterns which messy work might not reveal. Here's a selection of tasks where having good ways to sort and organise can be very helpful.

### Conjecturing and generalising - Primary students

Age: 5 to 11

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

### Visualising and Representing – Primary students

Age: 5 to 11

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

### Convince me! - Lower Primary Students

Age: 5 to 7

Here are some challenges that you can work on and then see if you can convince someone that your solutions are right! Have a go!

### Convince me! - Upper Primary Students

Age: 7 to 11

Here are some challenges that you can work on and then see if you can convince someone that your solutions are right! Have a go!

### Practice makes perfect - Lower Primary Students

Age: 5 to 7

These activities make use of things you probably already know and help you to understand them even better for solving problems!

### Practice makes perfect - Upper Primary Students

Age: 7 to 11

These activities make use of things you probably already know and help you to understand them even better for solving problems!