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
![Working Systematically - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9807-icon.jpg?itok=U0xk927P)
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Working Systematically - Primary Students
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.
![Saying what you see - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9126-icon.png?itok=Llg0TpYG)
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Saying what you see - Lower Primary Students
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.
![What can you find out? - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9127-icon.png?itok=r47rN4h6)
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What can you find out? - Lower Primary
Have a go at exploring as you look at these challenges, maybe with others. Talk about how it is going and if a slip-up occurs, then find a way out!
![What if ... ? - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9128-icon.png?itok=VmUaTdEh)
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What if ... ? - Lower Primary Students
Here are some exciting activities for you - have a go at them and then see what happens if you change one of the little questions. You may be able to change it more than just once!
![Convince me! - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9129-icon.png?itok=j77YhVMO)
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Convince me! - Lower Primary Students
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!
![What's your plan? - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9130-icon.png?itok=z3V2lJwe)
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What's your plan? - Lower Primary
Sometimes it's not easy to know how to start a problem. Try talking to a friend about how to start, and what sort of plan you'll have to carry on.
![Practice makes perfect - Lower Primary](/sites/default/files/styles/medium/public/thumbnails/content-id-9131-icon.png?itok=Yve867xt)
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Practice makes perfect - Lower Primary Students
These activities make use of things you probably already know and help you to understand them even better for solving problems!