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...
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Articles about mathematics which can help to invigorate your classroom
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Working systematically and introducing some algebra led to some excellent solutions to this problem.
Go to last month's problems to see more solutions.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
An article describing what LTHC tasks are, and why we think they're a good idea.
Maths is everywhere in the world! Take a look at these images. What mathematics can you see?