Follow this recipe for sieving numbers and see what interesting patterns emerge.

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either. . . .

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

A game in which players take it in turns to choose a number. Can you block your opponent?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

An introduction to proof by contradiction, a powerful method of mathematical proof.