A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Which of these games would you play to give yourself the best possible chance of winning a prize?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Is it really greener to go on the bus, or to buy local?

Can you make sense of these three proofs of Pythagoras' Theorem?

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

Harry sent us a very clear algebraic solution to this problem, and we also received lots of ideas on how to solve it numerically.

This fascinating article delves into the world of talk in the classroom and explains how an understanding of talking can really improve the learning of mathematics.

This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.