If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Morgan, Sara, Billie and Lucy discovered some rules for predicting what will happen when you join the numbers round the circle in different step-sizes.

Written for teachers, this article discusses mathematical representations and takes, in the second part of the article, examples of reception children's own representations.

Vicki Pike was one of four NRICH Teacher Fellows who worked on embedding NRICH materials into their teaching. In this article, she writes about her experiences of working with students at Key Stage two.