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?

Have you seen this way of doing multiplication ?

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

How good are you at finding the formula for a number pattern ?

This article gives a proof of the uncountability of the Cantor set.

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.