How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

How many generations would link an evolutionist to a very distant ancestor?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

What is the same and what is different about these circle questions? What connections can you make?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

The nice things about the solutions we received to this problem are that they revealed different insights and different levels of generalisation.

Peter Hall was one of four NRICH Teacher Fellows who worked on embedding NRICH materials into their teaching. In this article, he writes about his experiences of working with students at Key Stage Three.

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.