Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Can you use the information to find out which cards I have used?

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?

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

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?

Articles about mathematics which can help to invigorate your classroom

We were overwhelmed with excellent solutions to this challenge. You gave very clear explanations to each different part of the problem.

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

This article explores what LTHC tasks are and why they are a firm favourite here at NRICH. We recommend that you start by reading the article to understand what makes a task LTHC and then delve into some of the activities we have selected.

In this article Liz Woodham reflects on just how much we really listen to learners’ own questions to determine the mathematical path of lessons.