In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

Suryasnato, Bradley, Alex and Rhiannon all had a very logical way to solve this problem, each one slightly different to the others.

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

Some questions and prompts to encourage discussion about what experiences you want to give your pupils to help them reach their full potential in mathematics.