Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
A game in which players take it in turns to choose a number. Can you block your opponent?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
